From dc0a42bc61ec533aa1d3257c7d8b094cfcfbb4f4 Mon Sep 17 00:00:00 2001
From: Mike Lodder <mike.lodder@coinbase.com>
Date: Thu, 2 Dec 2021 07:23:45 -0800
Subject: [PATCH] Initial commit

---
 .gitignore                                    |   19 +
 .spdx.yml                                     |   37 +
 CHANGELOG.md                                  |   49 +
 CONTRIBUTING.md                               |   95 +
 LICENSE                                       |  201 +
 Makefile                                      |  105 +
 NOTICE                                        |    5 +
 README.md                                     |   43 +
 SECURITY.md                                   |    9 +
 api/README.md                                 |    0
 cmd/benchcomp/README.md                       |   31 +
 cmd/benchcomp/main.go                         |  134 +
 cmd/benchcomp/main_test.go                    |   44 +
 cmd/spdx/.gitignore                           |    3 +
 cmd/spdx/Cargo.toml                           |   13 +
 cmd/spdx/rust-toolchain                       |    1 +
 cmd/spdx/src/commands.rs                      |   21 +
 cmd/spdx/src/config.rs                        |   47 +
 cmd/spdx/src/main.rs                          |  175 +
 docs/Coinbase_Pseudocode.pdf                  |  Bin 0 -> 333536 bytes
 docs/Coinbase_Pseudocode_v5.pdf               |  Bin 0 -> 384564 bytes
 docs/FROST_pseudocode_for_Coinbase_v2.pdf     |  Bin 0 -> 142235 bytes
 docs/GennaroDkg.pdf                           |  Bin 0 -> 190577 bytes
 docs/README.md                                |    0
 docs/pull_request_template.md                 |    4 +
 docs/rsa-membership.pdf                       |  Bin 0 -> 142474 bytes
 examples/README.md                            |    0
 go.mod                                        |   23 +
 go.sum                                        |  131 +
 internal/README.md                            |  161 +
 internal/err.go                               |   22 +
 internal/hash.go                              |   93 +
 internal/hash_test.go                         |   62 +
 internal/point.go                             |   44 +
 internal/testutils.go                         |   93 +
 pkg/accumulator/README.md                     |  454 ++
 pkg/accumulator/accumulator.go                |  165 +
 pkg/accumulator/accumulator_test.go           |  176 +
 pkg/accumulator/key.go                        |  239 +
 pkg/accumulator/key_test.go                   |   86 +
 pkg/accumulator/lib.go                        |  203 +
 pkg/accumulator/lib_test.go                   |  403 ++
 pkg/accumulator/proof.go                      |  499 ++
 pkg/accumulator/proof_test.go                 |  178 +
 pkg/accumulator/witness.go                    |  363 ++
 pkg/accumulator/witness_test.go               |  227 +
 pkg/core/README.md                            |  274 +
 pkg/core/commit.go                            |  115 +
 pkg/core/commit_test.go                       |  374 ++
 pkg/core/curves/README.md                     | 5329 +++++++++++++++++
 pkg/core/curves/bls12377_curve.go             | 1216 ++++
 pkg/core/curves/bls12377_curve_test.go        |  516 ++
 pkg/core/curves/bls12381_curve.go             | 1227 ++++
 pkg/core/curves/bls12381_curve_test.go        |  510 ++
 pkg/core/curves/curve.go                      |  892 +++
 pkg/core/curves/ec_point.go                   |  255 +
 pkg/core/curves/ec_point_test.go              |  371 ++
 pkg/core/curves/ec_scalar.go                  |  357 ++
 pkg/core/curves/ecdsa.go                      |   38 +
 pkg/core/curves/ed25519_curve.go              |  784 +++
 pkg/core/curves/ed25519_curve_test.go         |  401 ++
 pkg/core/curves/field.go                      |  280 +
 pkg/core/curves/field_test.go                 |  295 +
 pkg/core/curves/k256_curve.go                 |  636 ++
 pkg/core/curves/k256_curve_test.go            |  398 ++
 pkg/core/curves/native/bls12-381/LICENSE      |  202 +
 pkg/core/curves/native/bls12-381/README.md    |  828 +++
 .../native/bls12-381/arithmetic_decl.go       |   72 +
 .../native/bls12-381/arithmetic_fallback.go   |  565 ++
 .../bls12-381/arithmetic_fallback_test.go     |  230 +
 .../curves/native/bls12-381/arithmetic_x86.s  | 2151 +++++++
 pkg/core/curves/native/bls12-381/bls12_381.go |  255 +
 .../curves/native/bls12-381/bls12_381_test.go |   77 +
 .../curves/native/bls12-381/field_element.go  |  394 ++
 .../native/bls12-381/field_element_test.go    |  258 +
 pkg/core/curves/native/bls12-381/fp.go        |  131 +
 pkg/core/curves/native/bls12-381/fp12.go      |  270 +
 pkg/core/curves/native/bls12-381/fp2.go       |  251 +
 pkg/core/curves/native/bls12-381/fp6.go       |  348 ++
 pkg/core/curves/native/bls12-381/fp_test.go   | 1411 +++++
 pkg/core/curves/native/bls12-381/g1.go        |  634 ++
 pkg/core/curves/native/bls12-381/g1_test.go   |  537 ++
 pkg/core/curves/native/bls12-381/g2.go        |  684 +++
 pkg/core/curves/native/bls12-381/g2_test.go   |  669 +++
 pkg/core/curves/native/bls12-381/gt.go        |  112 +
 .../curves/native/bls12-381/hash_to_field.go  |   82 +
 pkg/core/curves/native/bls12-381/isogeny.go   |  217 +
 pkg/core/curves/native/bls12-381/pairing.go   |  303 +
 .../curves/native/bls12-381/pairing_test.go   |  280 +
 pkg/core/curves/native/bls12-381/swu.go       |  148 +
 .../curves/native/bls12-381/tests/README.md   |    1 +
 .../g1_compressed_valid_test_vectors.dat      |  Bin 0 -> 48000 bytes
 .../g1_uncompressed_valid_test_vectors.dat    |  Bin 0 -> 96000 bytes
 .../g2_compressed_valid_test_vectors.dat      |  Bin 0 -> 96000 bytes
 .../g2_uncompressed_valid_test_vectors.dat    |  Bin 0 -> 192000 bytes
 pkg/core/curves/native/bls12-381/utils.go     |   22 +
 pkg/core/curves/native/bls12-381/wnaf.go      |   41 +
 pkg/core/curves/native/pasta/README.md        |   15 +
 pkg/core/curves/native/pasta/fp/README.md     |  301 +
 pkg/core/curves/native/pasta/fp/fp.go         |  367 ++
 pkg/core/curves/native/pasta/fp/fp_test.go    |  248 +
 pkg/core/curves/native/pasta/fp/pasta_fp.go   | 1432 +++++
 pkg/core/curves/native/pasta/fq/README.md     |  306 +
 pkg/core/curves/native/pasta/fq/fq.go         |  361 ++
 pkg/core/curves/native/pasta/fq/fq_test.go    |  248 +
 pkg/core/curves/native/pasta/fq/pasta_fq.go   | 1432 +++++
 pkg/core/curves/native/pasta/pallas.go        |    7 +
 pkg/core/curves/p256_curve.go                 |  604 ++
 pkg/core/curves/p256_curve_test.go            |  364 ++
 pkg/core/curves/pallas_curve.go               | 1163 ++++
 pkg/core/curves/pallas_curve_test.go          |  136 +
 pkg/core/hash.go                              |  272 +
 pkg/core/hash_test.go                         |  132 +
 pkg/core/mod.go                               |  175 +
 pkg/core/mod_test.go                          |  564 ++
 pkg/core/primes.go                            |   42 +
 pkg/dkg/README.md                             |  230 +
 pkg/dkg/benchmarks.txt                        |  111 +
 pkg/dkg/frost/README.md                       |   88 +
 pkg/dkg/frost/dkg_round1.go                   |  118 +
 pkg/dkg/frost/dkg_round2.go                   |  157 +
 pkg/dkg/frost/dkg_rounds_test.go              |  167 +
 pkg/dkg/frost/participant.go                  |   64 +
 pkg/dkg/gennaro/README.md                     |  117 +
 pkg/dkg/gennaro/participant.go                |   96 +
 pkg/dkg/gennaro/participant_test.go           |   47 +
 pkg/dkg/gennaro/round1.go                     |   80 +
 pkg/dkg/gennaro/round2.go                     |   91 +
 pkg/dkg/gennaro/round3.go                     |   89 +
 pkg/dkg/gennaro/round4.go                     |   76 +
 pkg/dkg/gennaro/rounds_test.go                |  381 ++
 pkg/dkg/gennaro2p/README.md                   |   96 +
 pkg/dkg/gennaro2p/genarro2p.go                |  148 +
 pkg/dkg/gennaro2p/genarro2p_test.go           |  181 +
 pkg/paillier/README.md                        |  403 ++
 pkg/paillier/paillier.go                      |  374 ++
 pkg/paillier/paillier_test.go                 | 1067 ++++
 pkg/paillier/psf.go                           |  222 +
 pkg/paillier/psf_test.go                      |  285 +
 pkg/sharing/README.md                         |  248 +
 pkg/sharing/ed25519_feldman_test.go           |  131 +
 pkg/sharing/feldman.go                        |  107 +
 pkg/sharing/pedersen.go                       |  147 +
 pkg/sharing/polynomial.go                     |   34 +
 pkg/sharing/polynomial_test.go                |   31 +
 pkg/sharing/shamir.go                         |  200 +
 pkg/sharing/shamir_test.go                    |  182 +
 pkg/sharing/v1/README.md                      |  477 ++
 pkg/sharing/v1/bls12381g1_feldman_test.go     |  140 +
 pkg/sharing/v1/bls12381g1curve.go             |  143 +
 pkg/sharing/v1/bls12381g2_feldman_test.go     |  131 +
 pkg/sharing/v1/bls12381g2curve.go             |  143 +
 pkg/sharing/v1/common.go                      |   14 +
 pkg/sharing/v1/ed25519_feldman_test.go        |  131 +
 pkg/sharing/v1/ed25519_pedersen_test.go       |  153 +
 pkg/sharing/v1/ed25519curve.go                |  140 +
 pkg/sharing/v1/ed25519curve_test.go           |   26 +
 pkg/sharing/v1/feldman.go                     |  106 +
 pkg/sharing/v1/k256_feldman_test.go           |  132 +
 pkg/sharing/v1/k256_pedersen_test.go          |  155 +
 pkg/sharing/v1/p256_feldman_test.go           |  132 +
 pkg/sharing/v1/pedersen.go                    |  175 +
 pkg/sharing/v1/polynomial.go                  |   49 +
 pkg/sharing/v1/polynomial_test.go             |   29 +
 pkg/sharing/v1/shamir.go                      |  211 +
 pkg/sharing/v1/shamir_test.go                 |  205 +
 pkg/signatures/bbs/README.md                  |  386 ++
 pkg/signatures/bbs/blind_signature.go         |   73 +
 pkg/signatures/bbs/blind_signature_context.go |  253 +
 .../bbs/blind_signature_context_test.go       |   94 +
 pkg/signatures/bbs/doc.go                     |    7 +
 pkg/signatures/bbs/message_generators.go      |   67 +
 pkg/signatures/bbs/pok_signature.go           |  157 +
 pkg/signatures/bbs/pok_signature_proof.go     |  200 +
 .../bbs/pok_signature_proof_test.go           |  163 +
 pkg/signatures/bbs/public_key.go              |   67 +
 pkg/signatures/bbs/secret_key.go              |  170 +
 pkg/signatures/bbs/signature.go               |   60 +
 pkg/signatures/bbs/signature_test.go          |   76 +
 pkg/signatures/bls/CHANGELOG                  |    8 +
 pkg/signatures/bls/README.md                  |  112 +
 pkg/signatures/bls/bls_sig/lib.go             |  187 +
 pkg/signatures/bls/bls_sig/lib_test.go        |  239 +
 pkg/signatures/bls/bls_sig/tiny_bls.go        |  432 ++
 pkg/signatures/bls/bls_sig/tiny_bls_sig.go    |  484 ++
 .../bls/bls_sig/tiny_bls_sig_aug_test.go      |  378 ++
 .../bls/bls_sig/tiny_bls_sig_basic_test.go    |  373 ++
 .../bls/bls_sig/tiny_bls_sig_pop_test.go      |  841 +++
 pkg/signatures/bls/bls_sig/usual_bls.go       |  440 ++
 pkg/signatures/bls/bls_sig/usual_bls_sig.go   |  483 ++
 .../bls/bls_sig/usual_bls_sig_aug_test.go     |  406 ++
 .../bls/bls_sig/usual_bls_sig_basic_test.go   |  406 ++
 .../bls/bls_sig/usual_bls_sig_pop_test.go     |  862 +++
 .../bls/docs/audit-kudeski-coinbase-bls.pdf   |  Bin 0 -> 516551 bytes
 .../bls/docs/pull_request_template.md         |    4 +
 pkg/signatures/bls/finitefield/finitefield.go |  188 +
 .../bls/finitefield/finitefield_test.go       |  254 +
 pkg/signatures/bls/rust/Cargo.toml            |   17 +
 pkg/signatures/bls/rust/src/main.rs           |  392 ++
 pkg/signatures/bls/shamir/shamir.go           |  269 +
 pkg/signatures/bls/shamir/shamir_test.go      |  237 +
 pkg/signatures/bls/tests/bls/main.go          |  230 +
 pkg/signatures/bls/tmp.json                   |    1 +
 pkg/signatures/common/README.md               |  259 +
 pkg/signatures/common/challenge.go            |   14 +
 pkg/signatures/common/commitment.go           |   15 +
 pkg/signatures/common/hmacdrbg.go             |   99 +
 pkg/signatures/common/nonce.go                |   15 +
 .../common/proof_committed_builder.go         |   85 +
 pkg/signatures/common/proof_message.go        |   78 +
 pkg/signatures/common/signature_blinding.go   |   14 +
 pkg/tecdsa/dkls/README.md                     |  448 ++
 pkg/tecdsa/dkls/conn.go                       |   33 +
 pkg/tecdsa/dkls/dkg.go                        |   98 +
 pkg/tecdsa/dkls/dkg_test.go                   |   73 +
 pkg/tecdsa/dkls/doc.go                        |   13 +
 pkg/tecdsa/dkls/multiply.go                   |  172 +
 pkg/tecdsa/dkls/multiply_test.go              |   66 +
 pkg/tecdsa/dkls/ot.go                         |  534 ++
 pkg/tecdsa/dkls/ot_test.go                    |  112 +
 pkg/tecdsa/dkls/params.go                     |   48 +
 pkg/tecdsa/dkls/proto.go                      |  305 +
 pkg/tecdsa/dkls/proto_test.go                 |  269 +
 pkg/tecdsa/dkls/schnorr.go                    |  112 +
 pkg/tecdsa/dkls/sign.go                       |  285 +
 pkg/tecdsa/dkls/sign_test.go                  |   65 +
 pkg/tecdsa/dkls/testdata/alice-dkls-dkg.bin   |  Bin 0 -> 13107 bytes
 pkg/tecdsa/dkls/testdata/bob-dkls-dkg.bin     |  Bin 0 -> 25884 bytes
 pkg/tecdsa/gg20/README.md                     |  694 +++
 pkg/tecdsa/gg20/dealer/README.md              |  252 +
 pkg/tecdsa/gg20/dealer/dealer.go              |  297 +
 pkg/tecdsa/gg20/dealer/dealer_test.go         |  298 +
 pkg/tecdsa/gg20/dealer/keygentype.go          |   48 +
 pkg/tecdsa/gg20/participant/README.md         |  379 ++
 pkg/tecdsa/gg20/participant/benches_test.go   |  595 ++
 pkg/tecdsa/gg20/participant/dkg_round1.go     |  188 +
 pkg/tecdsa/gg20/participant/dkg_round2.go     |  122 +
 pkg/tecdsa/gg20/participant/dkg_round3.go     |  183 +
 pkg/tecdsa/gg20/participant/dkg_round4.go     |   91 +
 .../gg20/participant/dkg_rounds_test.go       | 1044 ++++
 pkg/tecdsa/gg20/participant/participant.go    |  342 ++
 .../gg20/participant/participant_test.go      |  450 ++
 pkg/tecdsa/gg20/participant/round1.go         |  132 +
 pkg/tecdsa/gg20/participant/round2.go         |  131 +
 pkg/tecdsa/gg20/participant/round3.go         |  141 +
 pkg/tecdsa/gg20/participant/round4.go         |   60 +
 pkg/tecdsa/gg20/participant/round5.go         |  151 +
 pkg/tecdsa/gg20/participant/round6.go         |  244 +
 pkg/tecdsa/gg20/participant/rounds_test.go    |  996 +++
 pkg/tecdsa/gg20/proof/README.md               |  349 ++
 pkg/tecdsa/gg20/proof/cdl.go                  |  167 +
 pkg/tecdsa/gg20/proof/cdl_test.go             |  356 ++
 pkg/tecdsa/gg20/proof/mta.go                  |  905 +++
 pkg/tecdsa/gg20/proof/mta_test.go             | 1217 ++++
 pkg/tecdsa/gg20/proof/pdl.go                  |  317 +
 pkg/tecdsa/gg20/proof/pdl_test.go             |  393 ++
 pkg/tecdsa/gg20/proof/util.go                 |   64 +
 pkg/ted25519/frost/README.md                  |  116 +
 pkg/ted25519/frost/challenge_derive.go        |   26 +
 pkg/ted25519/frost/participant.go             |   81 +
 pkg/ted25519/frost/round1.go                  |   53 +
 pkg/ted25519/frost/round2.go                  |  156 +
 pkg/ted25519/frost/round3.go                  |  124 +
 pkg/ted25519/frost/rounds_test.go             |  403 ++
 pkg/ted25519/ted25519/README.md               |  382 ++
 pkg/ted25519/ted25519/ed25519.go              |  291 +
 pkg/ted25519/ted25519/ed25519_test.go         |  241 +
 pkg/ted25519/ted25519/ext.go                  |  122 +
 pkg/ted25519/ted25519/ext_test.go             |  110 +
 pkg/ted25519/ted25519/keygen.go               |  239 +
 pkg/ted25519/ted25519/keygen_test.go          |  126 +
 pkg/ted25519/ted25519/noncegen.go             |  121 +
 pkg/ted25519/ted25519/noncegen_test.go        |  105 +
 pkg/ted25519/ted25519/partialsig.go           |   55 +
 pkg/ted25519/ted25519/partialsig_test.go      |   55 +
 pkg/ted25519/ted25519/sigagg.go               |   61 +
 pkg/ted25519/ted25519/sigagg_test.go          |   93 +
 pkg/ted25519/ted25519/twobytwo_test.go        |   53 +
 pkg/verenc/camshoup/README.md                 |  361 ++
 pkg/verenc/camshoup/ciphertext.go             |   53 +
 pkg/verenc/camshoup/ciphertext_test.go        |   39 +
 pkg/verenc/camshoup/decryption_key.go         |  151 +
 pkg/verenc/camshoup/decryption_key_test.go    |   69 +
 pkg/verenc/camshoup/doc.go                    |   55 +
 pkg/verenc/camshoup/encryption_key.go         |  167 +
 pkg/verenc/camshoup/encryption_key_test.go    |  119 +
 pkg/verenc/camshoup/paillier_group.go         |  191 +
 pkg/verenc/camshoup/paillier_group_test.go    |  184 +
 pkg/verenc/camshoup/proof_enc.go              |  266 +
 pkg/verenc/camshoup/proof_enc_test.go         |  111 +
 pkg/verenc/elgamal/README.md                  |  269 +
 pkg/verenc/elgamal/ciphertext.go              |  143 +
 pkg/verenc/elgamal/ciphertext_test.go         |   40 +
 pkg/verenc/elgamal/decryption_key.go          |  163 +
 pkg/verenc/elgamal/decryption_key_test.go     |   57 +
 pkg/verenc/elgamal/encryption_key.go          |  154 +
 pkg/verenc/elgamal/encryption_key_test.go     |   88 +
 pkg/verenc/elgamal/proof_enc.go               |  210 +
 pkg/verenc/elgamal/proof_enc_test.go          |  222 +
 scripts/perf-comp-local                       |   20 +
 test/accumulator/ecc/README.md                |   15 +
 test/accumulator/ecc/main.go                  |  156 +
 test/data/sign.input.gz                       |  Bin 0 -> 50330 bytes
 test/dkg/2p/README.md                         |   15 +
 test/dkg/2p/main.go                           |  139 +
 test/dkg/2p/server.go                         |   85 +
 test/dkg/bls/README.md                        |   26 +
 test/dkg/bls/main.go                          |  205 +
 test/dkg/ed25519/README.md                    |   26 +
 test/dkg/ed25519/main.go                      |  237 +
 test/dkg/k256/README.md                       |   26 +
 test/dkg/k256/main.go                         |  197 +
 test/frost_dkg/bls/README.md                  |   30 +
 test/frost_dkg/bls/main.go                    |  177 +
 test/frost_dkg/ed25519/README.md              |   30 +
 test/frost_dkg/ed25519/main.go                |  246 +
 test/frost_dkg/frost/README.md                |   30 +
 test/frost_dkg/frost/main.go                  |  217 +
 test/frost_dkg/k256/README.md                 |   30 +
 test/frost_dkg/k256/main.go                   |  168 +
 test/verenc/elgamal/README.md                 |   15 +
 test/verenc/elgamal/main.go                   |  106 +
 322 files changed, 77883 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 .spdx.yml
 create mode 100644 CHANGELOG.md
 create mode 100644 CONTRIBUTING.md
 create mode 100644 LICENSE
 create mode 100644 Makefile
 create mode 100644 NOTICE
 create mode 100644 README.md
 create mode 100644 SECURITY.md
 create mode 100644 api/README.md
 create mode 100755 cmd/benchcomp/README.md
 create mode 100644 cmd/benchcomp/main.go
 create mode 100644 cmd/benchcomp/main_test.go
 create mode 100644 cmd/spdx/.gitignore
 create mode 100644 cmd/spdx/Cargo.toml
 create mode 100644 cmd/spdx/rust-toolchain
 create mode 100644 cmd/spdx/src/commands.rs
 create mode 100644 cmd/spdx/src/config.rs
 create mode 100644 cmd/spdx/src/main.rs
 create mode 100644 docs/Coinbase_Pseudocode.pdf
 create mode 100644 docs/Coinbase_Pseudocode_v5.pdf
 create mode 100644 docs/FROST_pseudocode_for_Coinbase_v2.pdf
 create mode 100644 docs/GennaroDkg.pdf
 create mode 100644 docs/README.md
 create mode 100644 docs/pull_request_template.md
 create mode 100644 docs/rsa-membership.pdf
 create mode 100644 examples/README.md
 create mode 100644 go.mod
 create mode 100644 go.sum
 create mode 100755 internal/README.md
 create mode 100644 internal/err.go
 create mode 100644 internal/hash.go
 create mode 100644 internal/hash_test.go
 create mode 100644 internal/point.go
 create mode 100644 internal/testutils.go
 create mode 100755 pkg/accumulator/README.md
 create mode 100644 pkg/accumulator/accumulator.go
 create mode 100644 pkg/accumulator/accumulator_test.go
 create mode 100644 pkg/accumulator/key.go
 create mode 100644 pkg/accumulator/key_test.go
 create mode 100644 pkg/accumulator/lib.go
 create mode 100644 pkg/accumulator/lib_test.go
 create mode 100644 pkg/accumulator/proof.go
 create mode 100644 pkg/accumulator/proof_test.go
 create mode 100644 pkg/accumulator/witness.go
 create mode 100644 pkg/accumulator/witness_test.go
 create mode 100644 pkg/core/README.md
 create mode 100644 pkg/core/commit.go
 create mode 100644 pkg/core/commit_test.go
 create mode 100755 pkg/core/curves/README.md
 create mode 100644 pkg/core/curves/bls12377_curve.go
 create mode 100644 pkg/core/curves/bls12377_curve_test.go
 create mode 100644 pkg/core/curves/bls12381_curve.go
 create mode 100644 pkg/core/curves/bls12381_curve_test.go
 create mode 100644 pkg/core/curves/curve.go
 create mode 100644 pkg/core/curves/ec_point.go
 create mode 100644 pkg/core/curves/ec_point_test.go
 create mode 100644 pkg/core/curves/ec_scalar.go
 create mode 100644 pkg/core/curves/ecdsa.go
 create mode 100644 pkg/core/curves/ed25519_curve.go
 create mode 100644 pkg/core/curves/ed25519_curve_test.go
 create mode 100644 pkg/core/curves/field.go
 create mode 100644 pkg/core/curves/field_test.go
 create mode 100644 pkg/core/curves/k256_curve.go
 create mode 100644 pkg/core/curves/k256_curve_test.go
 create mode 100644 pkg/core/curves/native/bls12-381/LICENSE
 create mode 100644 pkg/core/curves/native/bls12-381/README.md
 create mode 100644 pkg/core/curves/native/bls12-381/arithmetic_decl.go
 create mode 100644 pkg/core/curves/native/bls12-381/arithmetic_fallback.go
 create mode 100644 pkg/core/curves/native/bls12-381/arithmetic_fallback_test.go
 create mode 100644 pkg/core/curves/native/bls12-381/arithmetic_x86.s
 create mode 100644 pkg/core/curves/native/bls12-381/bls12_381.go
 create mode 100644 pkg/core/curves/native/bls12-381/bls12_381_test.go
 create mode 100644 pkg/core/curves/native/bls12-381/field_element.go
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diff --git a/.gitignore b/.gitignore
new file mode 100644
index 00000000..58f313f2
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,19 @@
+# Binaries for programs and plugins
+*.exe
+*.exe~
+*.dll
+*.so
+*.dylib
+
+# Test binary, built with `go test -c`
+*.test
+
+# Output of the go coverage tool, specifically when used with LiteIDE
+*.out
+
+# Dependency directories (remove the comment below to include it)
+# vendor/
+.idea/
+
+.DS_Store
+vendor/
diff --git a/.spdx.yml b/.spdx.yml
new file mode 100644
index 00000000..89589a00
--- /dev/null
+++ b/.spdx.yml
@@ -0,0 +1,37 @@
+#
+# Copyright Coinbase, Inc. All Rights Reserved.
+#
+# SPDX-License-Identifier: Apache-2.0
+#
+copyright: Copyright Coinbase, Inc. All Rights Reserved.
+license: Apache-2.0
+comments:
+  gitignore: '#'
+  dockerignore: '#'
+  sh: '#'
+  py: '#'
+  pl: '#'
+  rb: '#'
+  yml: '#'
+  yaml: '#'
+  go: '//'
+  rs: '//'
+ignore:
+  - 'testdata/'
+  - 'test/data'
+  - 'Cargo\.lock$'
+  - 'Cargo\.toml$'
+  - 'target'
+  - 'go\.mod$'
+  - 'go\.sum$'
+  - '\.gitignore$'
+  - '\.dockerignore$'
+  - '\.git$'
+  - '\.idea$'
+  - '\.vscode$'
+  - '\bLICENSE$'
+  - '\w+\.md$'
+  - '\w+\.pdf$'
+  - 'Makefile$'
+  - .DS_Store
+  - '\w+\.dat$'
\ No newline at end of file
diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
index 00000000..6dda0553
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,49 @@
+# Changelog
+
+All notable changes to this repo will be documented in this file.
+
+The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/)
+and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
+
+## v1.5.0
+- Add BLS12-381 curve
+- Add BLS signatures
+
+## v1.4.1
+- Update accumulator implementation to use alias-ing instead of one field structs
+- Update accumulator implementation marshaling implementation
+
+## v1.4.0
+- Update verifiable encryption API
+
+## v1.3.0
+- Add Accumulator
+- Update for new curve abstraction
+- Update verifiable encryption API 
+
+## v1.2.0
+
+- Add Verifiable Encryption
+- Add FROST DKG
+- Add DKLS threshold signing 
+- Add curve abstraction
+- Pasta Curves: Pallas and Vesta
+- BBS+ signatures
+
+## v1.1.0
+
+- Add recovery id to output of tECDSA signatures in Round 6
+- Add Neg and Bytes to EcScalar
+- Add SubFieldOrder to Field struct
+
+## v1.0.0
+### Added
+
+- This document and other meta-information
+- tECDSA dealered and distributed key generations
+- tECDSA based on [GG20](https://eprint.iacr.org/2020/540.pdf) signing
+- Gennaro [DKG07](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.134.6445&rep=rep1&type=pdf) usable for Ed25519 and BLS keys.
+- Shamir Secret Sharing
+- Feldman Verifiable Secret Sharing
+- Pedersen Verifiable Secret Sharing
+- Paillier Encryption Scheme
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
new file mode 100644
index 00000000..7e1ae64c
--- /dev/null
+++ b/CONTRIBUTING.md
@@ -0,0 +1,95 @@
+# Contributing to Kryptology
+
+Kryptology is Apache 2.0 licensed and accepts contributions via
+GitHub pull requests.
+
+# Ways to contribute to Kryptology
+
+- Bugs or issues: Report problems or defects as github issues
+- Features and enhancements: Provide expanded capabilities or optimizations
+- Documentation: Improve existing documentation or create new information
+- Tests for events and results:
+    - Functional
+    - Performance
+    - Usability
+    - Security
+    - Localization
+    - Recovery 
+    - Deployability
+
+# The Commit Process
+
+When contributing code, please follow these guidelines:
+
+- Fork the repository and make your changes in a feature branch
+- Include unit and integration tests for any new features and updates to existing tests
+- Ensure that the unit and integration tests run successfully.
+- Check that the lint tests pass
+
+## Important
+Use `git rebase origin/master` to limit creating merge commits.
+Kryptology accepts single commits. If you have more than one, they will be
+squashed when merged.
+
+## Commit Email Address
+Your commit email address must match your GitHub or GitLab email address. For more information, see https://help.github.com/articles/setting-your-commit-email-address-in-git/.
+
+## Commit messages
+
+Each commit message consists of a header, a body, and a footer.
+
+The header includes a type, a scope and a subject:
+
+```markdown
+<type>(<scope>): <subject>
+<BLANK LINE>
+<body>
+<BLANK LINE>
+<footer>
+```
+
+`<subject>` *required*, must not be longer than 100 characters.
+
+`<type` *required*, must be lower case and have one of the following values:
+
+- `build:` changes that affect the build system or external dependencies. Kryptology uses buildkite.
+- `chore:` some minor change that doesn't fall in any of the other types
+- `ci:` changes to the continuous integration configuration files
+- `docs:` documentation only change
+- `feat:` new feature
+- `fix:` a bug fix
+
+`<scope>` *optional*, must be lower case and have a tag about which primitive it affects like 'tecdsa/dkls', 'paillier', 'verenc'.  
+
+`<subject>` *optional*, must be lower case and not end in a period describing changes in the imperative-mood.
+
+`<body>` *optional*, characters no more 100 wide, must have a blank line above it describing changes in the imperative-mood.
+
+`<footer>` *optional*, must not be longer than 100 characters.
+
+For more information see [here](https://gist.github.com/joshbuchea/6f47e86d2510bce28f8e7f42ae84c716)
+
+**Kryptology requires that all commits are signed by a PGP key.** 
+
+## Issues and Bugs
+
+If you find a bug in the source code, help us by submitting an issue to the repository. Even better, submit a Pull Request with a fix.
+
+Before submitting an issue search the archive, maybe your question is already answered.
+
+If the issue is a bug, and hasn't been reported, open a new issue. Help us to maximize the effort we can spend fixing issues and adding new features, by not reporting duplicate issues.
+
+For security bugs see the security [policy](SECURITY.md).
+
+In general, providing the following information will increase the chances of the issue being handled quickly:
+
+**Expected Behavior** - Is there documentation or an example that represents the discrepancy?
+
+**Actual Behavior** - Be sure to explain why this is a bug for you.
+
+**Steps to Reproduce the Problem** - Code snippets and screen shots are always helpful.
+
+**Environment** - What hardware, OS, and versions are you using?
+
+**Suggest a Fix** - if you can't fix the bug yourself, perhaps you can point to what might cause the problem (line of code or commit)
+
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 00000000..261eeb9e
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
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+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
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+      to the Licensor or its representatives, including but not limited to
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+      designated in writing by the copyright owner as "Not a Contribution."
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+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
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+      Work and such Derivative Works in Source or Object form.
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+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
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+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
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+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
+      identification within third-party archives.
+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/Makefile b/Makefile
new file mode 100644
index 00000000..d12411ce
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,105 @@
+.PHONY: all build bench clean cover deflake fmt lint test test-clean test-long
+
+GOENV=GO111MODULE=on
+GO=${GOENV} go
+
+COVERAGE_OUT=/tmp/coverage.out
+PACKAGE=./...
+
+TEST_CLAUSE= $(if ${TEST}, -run ${TEST})
+
+DOCTOOLS=docker run --rm  -v "$$(pwd)":"$$(pwd)" -w "$$(pwd)" doctools:latest
+
+.PHONY: all
+all: githooks test build lint fmt deps docs
+
+.PHONY: build
+build:
+	${GO} build ./...
+
+.PHONY: bench
+bench:
+	${GO} test -short -bench=. -test.timeout=0 -run=^noTests ./...
+
+.PHONY: clean
+clean:
+	${GO} clean -cache -modcache -i -r
+
+.PHONY: cover
+cover: ## compute and display test coverage report
+	${GO} test -short -coverprofile=${COVERAGE_OUT} ${PACKAGE}
+	${GO} tool cover -html=${COVERAGE_OUT}
+
+.PHONY: deps
+deps: ## Build dockerized autodoc tools
+	@docker build -t doctools:latest .
+
+.PHONY: docs
+docs: ## Apply copyright headers and re-build package-level documents
+	@${DOCTOOLS} spdx
+	@${DOCTOOLS} gomarkdoc --output '{{.Dir}}/README.md' ./...
+
+.PHONY: deflake
+deflake: ## Runs tests many times to detect flakes
+	${GO} test -count=1000 -short -timeout 0 ${TEST_CLAUSE} ./...
+
+.PHONY: fmt
+fmt:
+	${GO} fmt ./...
+
+.PHONY: githooks
+githooks:
+	git config core.hooksPath .githooks
+
+.PHONY: lint
+lint:
+	${GO} vet ./...
+	golangci-lint run
+
+.PHONY: test
+test:
+	${GO} test -short ${TEST_CLAUSE} ./...
+
+.PHONY: test-clean
+test-clean: ## Clear test cache and force all tests to be rerun
+	${GO} clean -testcache && ${GO} test -count=1 -short ${TEST_CLAUSE} ./...
+
+.PHONY: test-long
+test-long: ## Runs all tests, including long-running tests
+	${GO} test ${TEST_CLAUSE} ./...
+
+.PHONY: run-dkg-bls
+run-dkg-bls: ## Runs test of gennaro dkg w/ BLS signature
+	${GO} run test/dkg/bls/main.go
+
+.PHONY: run-dkg-ed25519
+run-dkg-ed25519: ## Runs test of gennaro dkg w/ ed25519 signature
+	${GO} run test/dkg/ed25519/main.go
+
+.PHONY: run-frost-dkg-bls
+run-frost-dkg-bls: ## Runs test of frost dkg w/ BLS signature
+	${GO} run test/frost_dkg/bls/main.go
+
+.PHONY: run-frost-dkg-ed25519
+run-frost-dkg-ed25519: ## Runs test of frost dkg w/ ed25519 signature
+	${GO} run test/frost_dkg/ed25519/main.go
+
+.PHONY: run-frost-dkg-ecdsa
+run-frost-dkg-ecdsa: ## Runs test of frost dkg w/ ecdsa signature
+	${GO} run test/frost_dkg/k256/main.go
+
+.PHONY: run-frost-full
+run-frost-full: ## Runs test of frost dkg w/ frost signature
+	${GO} run test/frost_dkg/frost/main.go
+
+.PHONY: run-verenc-elgamal
+run-verenc-elgamal: ## Runs test of el-gamal verifiable encryption
+	${GO} run test/verenc/elgamal/main.go
+
+.PHONY: run-accumulator-ecc
+run-accumulator-ecc: ## Runs test of cryptographic accumulator
+	${GO} run test/accumulator/ecc/main.go
+
+.PHONY: compare-bench
+compare-bench: ## Runs bench on master and the current branch and compares the result
+	bash scripts/perf-comp-local
diff --git a/NOTICE b/NOTICE
new file mode 100644
index 00000000..62abaec2
--- /dev/null
+++ b/NOTICE
@@ -0,0 +1,5 @@
+Coinbase Kryptology
+Copyright [2021] contributors to Coinbase Kryptology
+
+This product includes software developed at
+Coinbase (http://www.coinbase.com/).
diff --git a/README.md b/README.md
new file mode 100644
index 00000000..91a6aec9
--- /dev/null
+++ b/README.md
@@ -0,0 +1,43 @@
+# Kryptology
+Coinbase's advanced cryptography library
+
+## Quickstart
+Use the latest version of this library:
+```$xslt
+go get github.com/coinbase/kryptology
+```
+
+Pin a specific release of this library:
+```$xslt
+go get github.com/coinbase/kryptology@v1.0.0
+```
+
+## Components
+- [Shamir's secret sharing scheme](pkg/sharing)
+- Threshold ECDSA
+    - [GG20](pkg/tecdsa/gg20)
+    - [DKLs18](pkg/tecdsa/dkls)
+- [Distributed key generation](pkg/dkg/gennaro) 
+    - [BLS DKG](test/dkg/bls)
+    - [ed25119 DKG](test/dkg/ed25519)
+- [Verifiable encryption](pkg/verenc)
+    
+## Developer Setup
+**Prerequisites**: `golang 1.16`, `make`
+
+```$xslt
+git clone git@github.com:coinbase/kryptology.git && make 
+``` 
+
+## Contributing
+- [Versioning](https://blog.golang.org/publishing-go-modules): `vMajor.Minor.Patch`
+    - Major revision indicates breaking API change or significant new features
+    - Minor revision indicates no API breaking changes and may include significant new features or documentation
+    - Patch indicates no API breaking changes and may include only fixes
+ 
+ 
+## [References](docs/)
+- [[GG20] _One Round Threshold ECDSA with Identifiable Abort._](https://eprint.iacr.org/2020/540.pdf)
+- [[specV5] _One Round Threshold ECDSA for Coinbase._](docs/Coinbase_Pseudocode_v5.pdf)
+- [[EL20] _Eliding RSA Group Membership Checks._](docs/rsa-membership.pdf) [src](https://www.overleaf.com/project/5f9c3b0624a9a600012037a3)
+- [[P99] _Public-Key Cryptosystems Based on Composite Degree Residuosity Classes._](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf)
diff --git a/SECURITY.md b/SECURITY.md
new file mode 100644
index 00000000..a2d77e49
--- /dev/null
+++ b/SECURITY.md
@@ -0,0 +1,9 @@
+# Coinbase Security Policy
+
+## Reporting a Security Bug
+
+If you think you have discovered a security issue in any of the code, please let us know. We take all security bugs seriously and if confirmed upon investigation will patch it within a reasonable amount of time and release a public security bulletin discussing the impact and credit the discoverer.
+
+There are two ways to report a security bug. The easiest is to submit a report to [Hackerone](https://hackerone.com/coinbase) that includes a description of the flaw and any related information (e.g. reproduction steps, version).
+
+The other way is to file a confidential security bug in [Github](https://github.com/coinbase/kryptology/security/advisories).
\ No newline at end of file
diff --git a/api/README.md b/api/README.md
new file mode 100644
index 00000000..e69de29b
diff --git a/cmd/benchcomp/README.md b/cmd/benchcomp/README.md
new file mode 100755
index 00000000..c6570481
--- /dev/null
+++ b/cmd/benchcomp/README.md
@@ -0,0 +1,31 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# benchcomp
+
+```go
+import "github.com/coinbase/kryptology/cmd/benchcomp"
+```
+
+## Index
+
+- [Constants](<#constants>)
+- [func Compare(currBench, newBench io.Reader) error](<#func-compare>)
+
+
+## Constants
+
+```go
+const THRESHOLD = 1.1
+```
+
+## func [Compare](<https://github.com/coinbase/kryptology/blob/master/cmd/benchcomp/main.go#L51>)
+
+```go
+func Compare(currBench, newBench io.Reader) error
+```
+
+Compare expects two readers which contain the output of two runs of \`go test \-bench\` command and throws an error if the performance has degraded by more than \`THRESHOLD\` amount\.
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/cmd/benchcomp/main.go b/cmd/benchcomp/main.go
new file mode 100644
index 00000000..b931dfa4
--- /dev/null
+++ b/cmd/benchcomp/main.go
@@ -0,0 +1,134 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"bytes"
+	"flag"
+	"fmt"
+	"io"
+	"io/ioutil"
+
+	"github.com/pkg/errors"
+	"golang.org/x/tools/benchmark/parse"
+)
+
+const THRESHOLD = 1.1
+
+func main() {
+	cReader, nReader, err := parseCmdArgs()
+	if err != nil {
+		panic(err)
+	}
+
+	if err := Compare(cReader, nReader); err != nil {
+		panic(err)
+	}
+}
+
+func parseCmdArgs() (io.Reader, io.Reader, error) {
+	cFlag := flag.String("current", "current-bench.log", "The patch to the log file containing the output of the current benchmark result.")
+	nFlag := flag.String("new", "new-bench.log", "The patch to the log file containing the output of the new benchmark result.")
+	flag.Parse()
+	cBytes, err := ioutil.ReadFile(*cFlag)
+	if err != nil {
+		return nil, nil, fmt.Errorf("reading current log file %v", err)
+	}
+	nBytes, err := ioutil.ReadFile(*nFlag)
+	if err != nil {
+		return nil, nil, fmt.Errorf("reading new log file %v", err)
+	}
+
+	return bytes.NewBuffer(cBytes), bytes.NewBuffer(nBytes), nil
+}
+
+// Compare expects two readers which contain the output of two runs of `go test -bench` command and throws an error if
+// the performance has degraded by more than `THRESHOLD` amount.
+func Compare(currBench, newBench io.Reader) error {
+	c, n, err := parseBenchmarks(currBench, newBench)
+	if err != nil {
+		return errors.Wrap(err, "parsing benchmark outputs")
+	}
+
+	perfDeviations := make([]string, 0)
+	for bench := range c {
+		if _, ok := n[bench]; !ok {
+			// New benchmark, skipping
+			continue
+		} else {
+			currB := c[bench]
+			newB := n[bench]
+			err = compareBenches(currB, newB)
+			if err != nil {
+				perfDeviations = append(perfDeviations, fmt.Sprintf("%v", err))
+			}
+		}
+	}
+
+	if len(perfDeviations) != 0 {
+		return fmt.Errorf("%#v", perfDeviations)
+	}
+	return nil
+}
+
+func parseBenchmarks(currBench, newBench io.Reader) (parse.Set, parse.Set, error) {
+	c, err := parse.ParseSet(currBench)
+	if err != nil {
+		return nil, nil, errors.Wrap(err, "parsing current benchmark output")
+	}
+	n, err := parse.ParseSet(newBench)
+	if err != nil {
+		return nil, nil, errors.Wrap(err, "parsing new benchmark output")
+	}
+
+	return c, n, nil
+}
+
+func compareBenches(currB, newB []*parse.Benchmark) error {
+	currMap := make(map[string]*parse.Benchmark)
+	newMap := make(map[string]*parse.Benchmark)
+	for _, b := range currB {
+		// TODO: double check what is in Name
+		currMap[b.Name] = b
+	}
+	for _, b := range newB {
+		// TODO: double check what is in Name
+		newMap[b.Name] = b
+	}
+	for name := range currMap {
+		if _, ok := newMap[name]; ok {
+			compare := []struct {
+				current float64
+				new     float64
+			}{
+				{
+					current: float64(currMap[name].AllocedBytesPerOp),
+					new:     float64(newMap[name].AllocedBytesPerOp),
+				},
+				{
+					current: float64(currMap[name].AllocsPerOp),
+					new:     float64(newMap[name].AllocsPerOp),
+				},
+				{
+					current: currMap[name].NsPerOp,
+					new:     newMap[name].NsPerOp,
+				},
+				{
+					current: currMap[name].MBPerS,
+					new:     newMap[name].MBPerS,
+				},
+			}
+			for _, t := range compare {
+				if t.new > t.current*THRESHOLD {
+					percent := (t.new - t.current) * 100 / t.current
+					return fmt.Errorf("benchmark %s exceeded previous benchmark by %0.2f percent. Current: %0.2f, New: %0.2f", name, percent, t.current, t.new)
+				}
+			}
+		}
+	}
+	return nil
+}
diff --git a/cmd/benchcomp/main_test.go b/cmd/benchcomp/main_test.go
new file mode 100644
index 00000000..329dd117
--- /dev/null
+++ b/cmd/benchcomp/main_test.go
@@ -0,0 +1,44 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"strings"
+	"testing"
+)
+
+func TestPerformanceDeviation(t *testing.T) {
+	goodComputationBench := "Benchmark_ABC             842688              1396 ns/op"
+	badComputationBench := "Benchmark_ABC             842688              13960 ns/op"
+	if err := Compare(strings.NewReader(goodComputationBench), strings.NewReader(badComputationBench)); err == nil {
+		t.Errorf("Expected performance deviation: [%v], but did not detect any!", err)
+	}
+}
+
+func TestParsing(t *testing.T) {
+	// TODO: the current parser ignores the 3rd and 4th column of data (e.g., the custom benchmarks)
+	output := `
+garbage data
+BenchmarkSigning/Secp256k1_-_5_of_9-16                         1        5794642205 ns/op
+BenchmarkSign2p-16                                             2         685590314 ns/op             29319 bytes/sign           16.00 msgs/sign
+garbage data
+`
+	o, _, err := parseBenchmarks(strings.NewReader(output), strings.NewReader(output))
+	if err != nil {
+		t.Errorf("Failed to parse test input %v", err)
+	}
+
+	if len(o) != 2 {
+		t.Errorf("Incorrect output length. Expected 2, got %#v", o)
+	}
+	if _, ok := o["BenchmarkSigning/Secp256k1_-_5_of_9-16"]; !ok {
+		t.Errorf("Did not find BenchmarkSigning/Secp256k1_-_5_of_9-16 in the parsed output")
+	}
+	if _, ok := o["BenchmarkSign2p-16"]; !ok {
+		t.Errorf("Did not find BenchmarkSign2p-16 in the parsed output")
+	}
+}
diff --git a/cmd/spdx/.gitignore b/cmd/spdx/.gitignore
new file mode 100644
index 00000000..ac671d8d
--- /dev/null
+++ b/cmd/spdx/.gitignore
@@ -0,0 +1,3 @@
+Cargo.lock
+target/
+.idea/
diff --git a/cmd/spdx/Cargo.toml b/cmd/spdx/Cargo.toml
new file mode 100644
index 00000000..b731a39f
--- /dev/null
+++ b/cmd/spdx/Cargo.toml
@@ -0,0 +1,13 @@
+[package]
+authors = ["Coinbase Core Cryptography Developers"]
+description = "Checks and adds the specified files for the SPDX-License-Identifier and Copyright headers"
+edition = "2018"
+name = "spdx"
+readme = "README.md"
+version = "1.0.0"
+
+[dependencies]
+regex = "1.5"
+serde = { version = "1.0", features = ["serde_derive"] }
+serde_yaml = "0.8"
+structopt = "0.3"
diff --git a/cmd/spdx/rust-toolchain b/cmd/spdx/rust-toolchain
new file mode 100644
index 00000000..3f483015
--- /dev/null
+++ b/cmd/spdx/rust-toolchain
@@ -0,0 +1 @@
+1.53.0
diff --git a/cmd/spdx/src/commands.rs b/cmd/spdx/src/commands.rs
new file mode 100644
index 00000000..48dabc7a
--- /dev/null
+++ b/cmd/spdx/src/commands.rs
@@ -0,0 +1,21 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+use std::path::PathBuf;
+use structopt::StructOpt;
+
+#[derive(Debug, StructOpt)]
+pub struct Commands {
+    #[structopt(short, long, parse(from_os_str), default_value = ".spdx.yml")]
+    pub config_file: PathBuf,
+    #[structopt(long)]
+    pub copyright: Option<String>,
+    #[structopt(short, long)]
+    pub ignore: Option<Vec<String>>,
+    #[structopt(long)]
+    pub license: Option<String>,
+    #[structopt(name = "DIR", parse(from_os_str), default_value = ".")]
+    pub starting_directory: PathBuf,
+}
diff --git a/cmd/spdx/src/config.rs b/cmd/spdx/src/config.rs
new file mode 100644
index 00000000..28e3a573
--- /dev/null
+++ b/cmd/spdx/src/config.rs
@@ -0,0 +1,47 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+use serde::{Deserialize, Serialize};
+use std::collections::{HashMap, HashSet};
+
+#[derive(Clone, Debug, Deserialize, Serialize)]
+pub struct Config {
+    /// The name of the copyright owner
+    pub copyright: String,
+    /// The chosen license
+    pub license: String,
+    /// File extensions to comments to use
+    /// For example
+    /// yml: #
+    /// python: #
+    /// sh: #
+    /// go: //
+    /// rs: ///
+    pub comments: HashMap<String, String>,
+    /// Ignore files that match these patterns as regex's
+    pub ignore: HashSet<String>,
+}
+
+impl Default for Config {
+    fn default() -> Self {
+        let mut comments = HashMap::new();
+        comments.insert("gitignore".to_string(), "#".to_string());
+        comments.insert("dockerignore".to_string(), "#".to_string());
+        comments.insert("sh".to_string(), "#".to_string());
+        comments.insert("py".to_string(), "#".to_string());
+        comments.insert("pl".to_string(), "#".to_string());
+        comments.insert("rb".to_string(), "#".to_string());
+        comments.insert("yml".to_string(), "#".to_string());
+        comments.insert("yaml".to_string(), "#".to_string());
+        comments.insert("go".to_string(), "//".to_string());
+        comments.insert("rs".to_string(), "///".to_string());
+        Config {
+            copyright: "Copyright Coinbase, Inc. All Rights Reserved.".to_string(),
+            license: "Apache-2.0".to_string(),
+            comments,
+            ignore: HashSet::new(),
+        }
+    }
+}
diff --git a/cmd/spdx/src/main.rs b/cmd/spdx/src/main.rs
new file mode 100644
index 00000000..328240ee
--- /dev/null
+++ b/cmd/spdx/src/main.rs
@@ -0,0 +1,175 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+#![deny(warnings)]
+mod commands;
+mod config;
+
+use commands::*;
+use config::*;
+use regex::{Regex, RegexSet};
+use std::{
+    collections::{HashSet, VecDeque},
+    env,
+    ffi::OsStr,
+    fs::{self, File, OpenOptions},
+    io::{Read, Seek, SeekFrom, Write},
+    path::{Path, PathBuf},
+    process::exit,
+};
+use structopt::StructOpt;
+
+fn main() -> Result<(), String> {
+    let mut cmd: Commands = Commands::from_args();
+    let config = read_config(&cmd)?;
+    if cmd.starting_directory.ends_with(".") && cmd.starting_directory.starts_with(".") {
+        cmd.starting_directory = get_proj_root();
+    }
+
+    let ignore_patterns = RegexSet::new(config.ignore.iter()).unwrap();
+
+    let mut examine = VecDeque::new();
+    examine.push_back(cmd.starting_directory);
+    while !examine.is_empty() {
+        let curdir = examine.pop_front().unwrap();
+        if curdir.is_dir() {
+            match curdir.to_str() {
+                None => {
+                    eprintln!("Unable to determine directory name: {:?}", curdir);
+                    continue;
+                }
+                Some(s) => {
+                    if ignore_patterns.is_match(s) {
+                        println!("Ignoring {}", s);
+                        continue;
+                    }
+                    println!("Scanning {}", s);
+                }
+            }
+            // Traverse the current directory and subdirectories
+            let readdir = fs::read_dir(curdir).map_err(|e| e.to_string())?;
+            for path in readdir {
+                examine.push_back(path.map_err(|e| e.to_string())?.path());
+            }
+        } else if curdir.is_file() {
+            match curdir.to_str() {
+                None => eprintln!("Can't handle file '{:?}'", curdir),
+                Some(s) => {
+                    if ignore_patterns.is_match(s) {
+                        println!("Ignoring {}", s);
+                        continue;
+                    }
+                    process_file(s, &config)?;
+                }
+            }
+        }
+    }
+    Ok(())
+}
+
+fn process_file(file_name: &str, config: &Config) -> Result<(), String> {
+    println!("Processing {}", file_name);
+    let mut f = OpenOptions::new()
+        .read(true)
+        .write(true)
+        .open(PathBuf::from(file_name.to_string()))
+        .map_err(|e| e.to_string())?;
+    let length = f.metadata().map_err(|e| e.to_string())?.len() as usize;
+    let mut buffer = String::new();
+    let size = f.read_to_string(&mut buffer).map_err(|e| e.to_string())?;
+    if size != length {
+        return Err("Unable to read entire file contents".to_string());
+    }
+    let suffix = Path::new(file_name).extension().and_then(OsStr::to_str);
+    let sfx = match suffix {
+        Some(s) => s,
+        None => Path::new(file_name)
+            .file_name()
+            .and_then(OsStr::to_str)
+            .unwrap(),
+    };
+    match config.comments.get(sfx) {
+        None => {}
+        Some(comment) => {
+            // Found, check for header
+            let rx_header = Regex::new(
+                format!(
+                    r#"{}\s+{}\s+{}\s+{}\s+{}\s+SPDX-License-Identifier:\s+{}\s+{}\s+"#,
+                    comment, comment, config.copyright, comment, comment, config.license, comment
+                )
+                .as_str(),
+            )
+            .unwrap();
+            if rx_header.is_match(&buffer) {
+                return Ok(());
+            }
+            let header = format!(
+                r#"{}
+{} {}
+{}
+{} SPDX-License-Identifier: {}
+{}
+
+"#,
+                comment, comment, config.copyright, comment, comment, config.license, comment
+            );
+            f.seek(SeekFrom::Start(0)).map_err(|e| e.to_string())?;
+            f.write_all(header.as_bytes()).map_err(|e| e.to_string())?;
+            f.write_all(buffer.as_bytes()).map_err(|e| e.to_string())?;
+        }
+    }
+    Ok(())
+}
+
+fn get_proj_root() -> PathBuf {
+    match env::current_dir() {
+        Err(e) => {
+            eprintln!("{}", e);
+            exit(5);
+        }
+        Ok(p) => p,
+    }
+}
+
+fn read_config(cmd: &Commands) -> Result<Config, String> {
+    let mut config = Config::default();
+    match cmd.ignore.as_ref() {
+        None => {}
+        Some(patterns) => {
+            config.ignore = patterns.iter().cloned().collect::<HashSet<_>>();
+        }
+    }
+    match cmd.license.as_ref() {
+        None => {}
+        Some(s) => config.license = s.clone(),
+    }
+    match cmd.copyright.as_ref() {
+        None => {}
+        Some(s) => config.copyright = s.clone(),
+    }
+    if !cmd.config_file.exists() {
+        return Ok(config);
+    }
+
+    let mut f = File::open(&cmd.config_file).map_err(|e| e.to_string())?;
+    let len = f.metadata().map_err(|e| e.to_string())?.len() as usize;
+    let mut bytes = Vec::with_capacity(len);
+    let s = f.read_to_end(&mut bytes).map_err(|e| e.to_string())?;
+    if s != len {
+        return Err("Unable to read entire file contents".to_string());
+    }
+    let cfg = serde_yaml::from_slice::<Config>(bytes.as_slice()).map_err(|e| e.to_string())?;
+    if !cfg.copyright.is_empty() {
+        config.copyright = cfg.copyright.clone();
+    }
+    if !cfg.license.is_empty() {
+        config.license = cfg.license.clone();
+    }
+    if !cfg.ignore.is_empty() {
+        config.ignore = cfg.ignore.clone();
+    }
+    config.comments = cfg.comments;
+    Ok(config)
+}
diff --git a/docs/Coinbase_Pseudocode.pdf b/docs/Coinbase_Pseudocode.pdf
new file mode 100644
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diff --git a/docs/README.md b/docs/README.md
new file mode 100644
index 00000000..e69de29b
diff --git a/docs/pull_request_template.md b/docs/pull_request_template.md
new file mode 100644
index 00000000..517b4646
--- /dev/null
+++ b/docs/pull_request_template.md
@@ -0,0 +1,4 @@
+
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diff --git a/docs/rsa-membership.pdf b/docs/rsa-membership.pdf
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zGMg;UA=*Wf7_{!xnvE+15&};W`9&R3+h5_4*7aG7uJtbq%L^KmFTq|B!eZCr@*rj~
zzpU&7Dc|se4G+l!m9n2X1rcLDulKIqAV>XBc3bKNisDxMdm$5;erd4#UM#5f1KBq`
zZk1mO9doB&s(_lZt?JI~eDW-PHJ8B_cIO%|^z#UgPtrhGtqiQ76P9?1vAw3%oKpJ@
z^o9t5#w)Rr>u$sz+?YCCa-pZ|Udl}zR65um+u{X?B>3xzWKDVN*AOz0$`{*7cN*6g
z9ZrwCoMwEN@Jea1a6wWx1O?UYxSZqlCKb3^;8az|F=jN4xP&CFpVzvadBeHL04PxT
z-;;b?@6?fh2qS`m05)+ah>?q>y`6-S3k1L*!T(MZVF!WO!5knE9|yZO<A0v8cLFec
zfoQ&O73@v__p{1hBsGCjt~NHtMs{|Pe`G8yodNH+gQ?lOI14}>;^h2p4ZsNmfk9k+
z9Nb*296)YX5D?4`<NyJ5|1koPw{(O2gEe8-Wdv9|7`a$DLyQ1!|0&50<OFiO`=RV)
zZ|Z9DkBxun{x2Qxuf8}LIXFN}0c=u6HqQSYslxr=KKx(I6-^b0*?%=Y133BKMJ#Px
z-j%XR*}Mlt0%Brs`c7u~*ZPiev2_OgpP<>>xZ2t|1GxTi;~o2A;_@D!cixMzFn~?t
zo&N#?aK1n9<QG*-F9?7Kz$POB&=CZ2bDMy`#vB}`#>Sl7#>O1HynM!H>^vNtd`6t6
zATD7+US2bZsWH0=n2Q_2Va(0R&T9fP<^l6@81sR6*ttxF_5MdP)x;PInog?!CnsSl
zAtB*A9W0D7&h(1|R23vUsL!7R3hHw?T++Y)e!%~7Av?PmIk|W^LClajK-|c*w313v
G$o~Ppbn77i

literal 0
HcmV?d00001

diff --git a/examples/README.md b/examples/README.md
new file mode 100644
index 00000000..e69de29b
diff --git a/go.mod b/go.mod
new file mode 100644
index 00000000..e085d790
--- /dev/null
+++ b/go.mod
@@ -0,0 +1,23 @@
+module github.com/coinbase/kryptology
+
+go 1.15
+
+require (
+	filippo.io/edwards25519 v1.0.0-rc.1
+	git.sr.ht/~sircmpwn/go-bare v0.0.0-20210406120253-ab86bc2846d9
+	github.com/btcsuite/btcd v0.21.0-beta.0.20201114000516-e9c7a5ac6401
+	github.com/btcsuite/btcutil v1.0.2
+	github.com/bwesterb/go-ristretto v1.2.0
+	github.com/consensys/gnark-crypto v0.5.3
+	github.com/dropbox/godropbox v0.0.0-20200228041828-52ad444d3502
+	github.com/gtank/merlin v0.1.1
+	github.com/kr/text v0.2.0 // indirect
+	github.com/nixberg/chacha-rng-go v0.1.0
+	github.com/pkg/errors v0.9.1
+	github.com/stretchr/testify v1.7.0
+	golang.org/x/crypto v0.0.0-20210711020723-a769d52b0f97
+	golang.org/x/sys v0.0.0-20210630005230-0f9fa26af87c
+	golang.org/x/tools v0.1.5
+	gopkg.in/check.v1 v1.0.0-20201130134442-10cb98267c6c // indirect
+	gopkg.in/yaml.v3 v3.0.0-20210107192922-496545a6307b // indirect
+)
diff --git a/go.sum b/go.sum
new file mode 100644
index 00000000..edebf4c8
--- /dev/null
+++ b/go.sum
@@ -0,0 +1,131 @@
+filippo.io/edwards25519 v1.0.0-rc.1 h1:m0VOOB23frXZvAOK44usCgLWvtsxIoMCTBGJZlpmGfU=
+filippo.io/edwards25519 v1.0.0-rc.1/go.mod h1:N1IkdkCkiLB6tki+MYJoSx2JTY9NUlxZE7eHn5EwJns=
+git.sr.ht/~sircmpwn/getopt v0.0.0-20191230200459-23622cc906b3/go.mod h1:wMEGFFFNuPos7vHmWXfszqImLppbc0wEhh6JBfJIUgw=
+git.sr.ht/~sircmpwn/go-bare v0.0.0-20210406120253-ab86bc2846d9 h1:Ahny8Ud1LjVMMAlt8utUFKhhxJtwBAualvsbc/Sk7cE=
+git.sr.ht/~sircmpwn/go-bare v0.0.0-20210406120253-ab86bc2846d9/go.mod h1:BVJwbDfVjCjoFiKrhkei6NdGcZYpkDkdyCdg1ukytRA=
+github.com/coinbase/bls12-381 v0.0.0-20210114210818-577bfdc5cb9c h1:H6qPVjeq1XbGuaFaFD9aIXh7ZBmFziVAQCNRhBw8XnU=
+github.com/coinbase/bls12-381 v0.0.0-20210114210818-577bfdc5cb9c/go.mod h1:GKWeplG/c6sSm2WEWBVzld/RnaaMxB/4U0hk5lbKWqc=
+github.com/coinbase/bls_sig v0.0.0-20210205213533-31fa0b155b9a h1:V/oa+MQmcgH3U5ZJZnGVWgAgIMIBicO3UGmgIU1THp4=
+github.com/coinbase/bls_sig v0.0.0-20210205213533-31fa0b155b9a/go.mod h1:P+Pl33i6GlTrysuyUB6sI3TUmV3TRpQT5rocN1iD8E8=
+github.com/aead/siphash v1.0.1/go.mod h1:Nywa3cDsYNNK3gaciGTWPwHt0wlpNV15vwmswBAUSII=
+github.com/btcsuite/btcd v0.20.1-beta/go.mod h1:wVuoA8VJLEcwgqHBwHmzLRazpKxTv13Px/pDuV7OomQ=
+github.com/btcsuite/btcd v0.21.0-beta.0.20201114000516-e9c7a5ac6401 h1:0tjUthKCaF8zwF9Qg7lfnep0xdo4n8WiFUfQPaMHX6g=
+github.com/btcsuite/btcd v0.21.0-beta.0.20201114000516-e9c7a5ac6401/go.mod h1:Sv4JPQ3/M+teHz9Bo5jBpkNcP0x6r7rdihlNL/7tTAs=
+github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f/go.mod h1:TdznJufoqS23FtqVCzL0ZqgP5MqXbb4fg/WgDys70nA=
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+github.com/btcsuite/goleveldb v0.0.0-20160330041536-7834afc9e8cd/go.mod h1:F+uVaaLLH7j4eDXPRvw78tMflu7Ie2bzYOH4Y8rRKBY=
+github.com/btcsuite/goleveldb v1.0.0/go.mod h1:QiK9vBlgftBg6rWQIj6wFzbPfRjiykIEhBH4obrXJ/I=
+github.com/btcsuite/snappy-go v0.0.0-20151229074030-0bdef8d06723/go.mod h1:8woku9dyThutzjeg+3xrA5iCpBRH8XEEg3lh6TiUghc=
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+github.com/btcsuite/websocket v0.0.0-20150119174127-31079b680792/go.mod h1:ghJtEyQwv5/p4Mg4C0fgbePVuGr935/5ddU9Z3TmDRY=
+github.com/btcsuite/winsvc v1.0.0/go.mod h1:jsenWakMcC0zFBFurPLEAyrnc/teJEM1O46fmI40EZs=
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+github.com/fsnotify/fsnotify v1.4.7/go.mod h1:jwhsz4b93w/PPRr/qN1Yymfu8t87LnFCMoQvtojpjFo=
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diff --git a/internal/README.md b/internal/README.md
new file mode 100755
index 00000000..615e2deb
--- /dev/null
+++ b/internal/README.md
@@ -0,0 +1,161 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# internal
+
+```go
+import "github.com/coinbase/kryptology/internal"
+```
+
+## Index
+
+- [Variables](<#variables>)
+- [func AssertBigIntEq(t *testing.T, a, b *big.Int)](<#func-assertbiginteq>)
+- [func AssertBigIntNe(t *testing.T, a, b *big.Int)](<#func-assertbigintne>)
+- [func AssertError(t *testing.T, err error, msg string)](<#func-asserterror>)
+- [func AssertNil(t *testing.T, values ...*big.Int)](<#func-assertnil>)
+- [func AssertNoError(t *testing.T, err error)](<#func-assertnoerror>)
+- [func AssertNotNil(t *testing.T, values ...*big.Int)](<#func-assertnotnil>)
+- [func AssertSomeError(t *testing.T, err error)](<#func-assertsomeerror>)
+- [func B10(s string) *big.Int](<#func-b10>)
+- [func BigInt2Ed25519Point(y *big.Int) (*edwards25519.Point, error)](<#func-bigint2ed25519point>)
+- [func BigInt2Ed25519Scalar(x *big.Int) (*edwards25519.Scalar, error)](<#func-bigint2ed25519scalar>)
+- [func ByteSub(b []byte)](<#func-bytesub>)
+- [func CalcFieldSize(curve elliptic.Curve) int](<#func-calcfieldsize>)
+- [func Hash(info []byte, values ...[]byte) ([]byte, error)](<#func-hash>)
+- [func ReverseScalarBytes(inBytes []byte) []byte](<#func-reversescalarbytes>)
+
+
+## Variables
+
+```go
+var (
+    ErrNotOnCurve           = fmt.Errorf("point not on the curve")
+    ErrPointsDistinctCurves = fmt.Errorf("points must be from the same curve")
+    ErrZmMembership         = fmt.Errorf("x ∉ Z_m")
+    ErrResidueOne           = fmt.Errorf("value must be 1 (mod N)")
+    ErrNCannotBeZero        = fmt.Errorf("N cannot be 0")
+    ErrNilArguments         = fmt.Errorf("arguments cannot be nil")
+    ErrZeroValue            = fmt.Errorf("arguments cannot be 0")
+    ErrInvalidRound         = fmt.Errorf("invalid round method called")
+    ErrIncorrectCount       = fmt.Errorf("incorrect number of inputs")
+    ErrInvalidJson          = fmt.Errorf("json format does not contain the necessary data")
+)
+```
+
+## func [AssertBigIntEq](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L42>)
+
+```go
+func AssertBigIntEq(t *testing.T, a, b *big.Int)
+```
+
+AssertBigIntEq fails the test if a and b are not equal
+
+## func [AssertBigIntNe](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L55>)
+
+```go
+func AssertBigIntNe(t *testing.T, a, b *big.Int)
+```
+
+AssertBigIntNe fails the test if two big\.Ints are the same value
+
+## func [AssertError](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L30>)
+
+```go
+func AssertError(t *testing.T, err error, msg string)
+```
+
+AssertError fails the test if err == nil or the message does not equal msg
+
+## func [AssertNil](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L77>)
+
+```go
+func AssertNil(t *testing.T, values ...*big.Int)
+```
+
+AssertNil fails the test if any of values are nil
+
+## func [AssertNoError](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L15>)
+
+```go
+func AssertNoError(t *testing.T, err error)
+```
+
+AssertNoError FailsNow\(\) the test if err \!= nil
+
+## func [AssertNotNil](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L68>)
+
+```go
+func AssertNotNil(t *testing.T, values ...*big.Int)
+```
+
+AssertNotNil fails if any values are nil
+
+## func [AssertSomeError](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L23>)
+
+```go
+func AssertSomeError(t *testing.T, err error)
+```
+
+AssertSomeError fails the test if err == nil
+
+## func [B10](<https://github.com/coinbase/kryptology/blob/master/internal/testutils.go#L87>)
+
+```go
+func B10(s string) *big.Int
+```
+
+B10 creating a big\.Int from a base 10 string\. panics on failure to to ensure zero\-values aren't used in place of malformed strings\.
+
+## func [BigInt2Ed25519Point](<https://github.com/coinbase/kryptology/blob/master/internal/point.go#L31>)
+
+```go
+func BigInt2Ed25519Point(y *big.Int) (*edwards25519.Point, error)
+```
+
+## func [BigInt2Ed25519Scalar](<https://github.com/coinbase/kryptology/blob/master/internal/point.go#L38>)
+
+```go
+func BigInt2Ed25519Scalar(x *big.Int) (*edwards25519.Scalar, error)
+```
+
+## func [ByteSub](<https://github.com/coinbase/kryptology/blob/master/internal/hash.go#L74>)
+
+```go
+func ByteSub(b []byte)
+```
+
+ByteSub is a constant time algorithm for subtracting 1 from the array as if it were a big number\. 0 is considered a wrap which resets to 0xFF
+
+## func [CalcFieldSize](<https://github.com/coinbase/kryptology/blob/master/internal/point.go#L16>)
+
+```go
+func CalcFieldSize(curve elliptic.Curve) int
+```
+
+## func [Hash](<https://github.com/coinbase/kryptology/blob/master/internal/hash.go#L36>)
+
+```go
+func Hash(info []byte, values ...[]byte) ([]byte, error)
+```
+
+### Hash computes the HKDF over many values
+iteratively such that each value is hashed separately
+and based on preceding values
+
+The first value is computed as okm\_0 = KDF\(f || value\) where
+f is a byte slice of 32 0xFF
+salt is zero\-filled byte slice with length equal to the hash output length
+info is the protocol name
+okm is the 32 byte output
+
+The each subsequent iteration is computed by as okm\_i = KDF\(f\_i || value || okm\_\{i\-1\}\) where f\_i = 2^b \- 1 \- i such that there are 0xFF bytes prior to the value\. f\_1 changes the first byte to 0xFE\, f\_2 to 0xFD\. The previous okm is appended to the value to provide cryptographic domain separation See https://signal.org/docs/specifications/x3dh/#cryptographic-notation and https://signal.org/docs/specifications/xeddsa/#hash-functions for more details\. This uses the KDF function similar to X3DH for each \`value\` But changes the key just like XEdDSA where the prefix bytes change by a single bit
+
+## func [ReverseScalarBytes](<https://github.com/coinbase/kryptology/blob/master/internal/point.go#L21>)
+
+```go
+func ReverseScalarBytes(inBytes []byte) []byte
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/internal/err.go b/internal/err.go
new file mode 100644
index 00000000..2ea5082c
--- /dev/null
+++ b/internal/err.go
@@ -0,0 +1,22 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package internal
+
+import "fmt"
+
+var (
+	ErrNotOnCurve           = fmt.Errorf("point not on the curve")
+	ErrPointsDistinctCurves = fmt.Errorf("points must be from the same curve")
+	ErrZmMembership         = fmt.Errorf("x ∉ Z_m")
+	ErrResidueOne           = fmt.Errorf("value must be 1 (mod N)")
+	ErrNCannotBeZero        = fmt.Errorf("N cannot be 0")
+	ErrNilArguments         = fmt.Errorf("arguments cannot be nil")
+	ErrZeroValue            = fmt.Errorf("arguments cannot be 0")
+	ErrInvalidRound         = fmt.Errorf("invalid round method called")
+	ErrIncorrectCount       = fmt.Errorf("incorrect number of inputs")
+	ErrInvalidJson          = fmt.Errorf("json format does not contain the necessary data")
+)
diff --git a/internal/hash.go b/internal/hash.go
new file mode 100644
index 00000000..bb39e81f
--- /dev/null
+++ b/internal/hash.go
@@ -0,0 +1,93 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package internal
+
+import (
+	"bytes"
+	"crypto/sha256"
+	"fmt"
+
+	"golang.org/x/crypto/hkdf"
+)
+
+// Hash computes the HKDF over many values
+// iteratively such that each value is hashed separately
+// and based on preceding values
+//
+// The first value is computed as okm_0 = KDF(f || value) where
+// f is a byte slice of 32 0xFF
+// salt is zero-filled byte slice with length equal to the hash output length
+// info is the protocol name
+// okm is the 32 byte output
+//
+// The each subsequent iteration is computed by as okm_i = KDF(f_i || value || okm_{i-1})
+// where f_i = 2^b - 1 - i such that there are 0xFF bytes prior to the value.
+// f_1 changes the first byte to 0xFE, f_2 to 0xFD. The previous okm is appended to the value
+// to provide cryptographic domain separation
+// See https://signal.org/docs/specifications/x3dh/#cryptographic-notation
+// and https://signal.org/docs/specifications/xeddsa/#hash-functions
+// for more details.
+// This uses the KDF function similar to X3DH for each `value`
+// But changes the key just like XEdDSA where the prefix bytes change by a single bit
+func Hash(info []byte, values ...[]byte) ([]byte, error) {
+	// Don't accept any nil arguments
+	if anyNil(values...) {
+		return nil, ErrNilArguments
+	}
+
+	salt := make([]byte, 32)
+	okm := make([]byte, 32)
+	f := bytes.Repeat([]byte{0xFF}, 32)
+
+	for _, b := range values {
+		ikm := append(f, b...)
+		ikm = append(ikm, okm...)
+		kdf := hkdf.New(sha256.New, ikm, salt, info)
+		n, err := kdf.Read(okm)
+		if err != nil {
+			return nil, err
+		}
+		if n != len(okm) {
+			return nil, fmt.Errorf("unable to read expected number of bytes want=%v got=%v", len(okm), n)
+		}
+		ByteSub(f)
+	}
+	return okm, nil
+}
+
+func anyNil(values ...[]byte) bool {
+	for _, x := range values {
+		if x == nil {
+			return true
+		}
+	}
+	return false
+}
+
+// ByteSub is a constant time algorithm for subtracting
+// 1 from the array as if it were a big number.
+// 0 is considered a wrap which resets to 0xFF
+func ByteSub(b []byte) {
+	m := byte(1)
+	for i := 0; i < len(b); i++ {
+		b[i] -= m
+
+		// If b[i] > 0, s == 0
+		// If b[i] == 0, s == 1
+		// Computing IsNonZero(b[i])
+		s1 := int8(b[i]) >> 7
+		s2 := -int8(b[i]) >> 7
+		s := byte((s1 | s2) + 1)
+
+		// If s == 0, don't subtract anymore
+		// s == 1, continue subtracting
+		m = s & m
+		// If s == 0 this does nothing
+		// If s == 1 reset this value to 0xFF
+		b[i] |= -s
+	}
+}
diff --git a/internal/hash_test.go b/internal/hash_test.go
new file mode 100644
index 00000000..03bf7904
--- /dev/null
+++ b/internal/hash_test.go
@@ -0,0 +1,62 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package internal
+
+import (
+	"bytes"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestByteSub(t *testing.T) {
+	f := bytes.Repeat([]byte{0xFF}, 32)
+	ByteSub(f)
+	assert.Equal(t, f[0], byte(0xFE))
+	for i := 1; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+	ByteSub(f)
+	assert.Equal(t, f[0], byte(0xFD))
+	for i := 1; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+	f[0] = 0x2
+	ByteSub(f)
+	for i := 1; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+	ByteSub(f)
+	assert.Equal(t, f[0], byte(0xFF))
+	assert.Equal(t, f[1], byte(0xFE))
+	for i := 2; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+	ByteSub(f)
+	assert.Equal(t, f[0], byte(0xFE))
+	assert.Equal(t, f[1], byte(0xFE))
+	for i := 2; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+	f[0] = 1
+	f[1] = 1
+	ByteSub(f)
+	assert.Equal(t, f[0], byte(0xFF))
+	assert.Equal(t, f[1], byte(0xFF))
+	assert.Equal(t, f[2], byte(0xFE))
+	for i := 3; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+}
+
+func TestByteSubAll1(t *testing.T) {
+	f := bytes.Repeat([]byte{0x1}, 32)
+	ByteSub(f)
+	for i := 0; i < len(f); i++ {
+		assert.Equal(t, f[i], byte(0xFF))
+	}
+}
diff --git a/internal/point.go b/internal/point.go
new file mode 100644
index 00000000..6393e803
--- /dev/null
+++ b/internal/point.go
@@ -0,0 +1,44 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package internal
+
+import (
+	"crypto/elliptic"
+	"math/big"
+
+	"filippo.io/edwards25519"
+)
+
+func CalcFieldSize(curve elliptic.Curve) int {
+	bits := curve.Params().BitSize
+	return (bits + 7) / 8
+}
+
+func ReverseScalarBytes(inBytes []byte) []byte {
+	outBytes := make([]byte, len(inBytes))
+
+	for i, j := 0, len(inBytes)-1; j >= 0; i, j = i+1, j-1 {
+		outBytes[i] = inBytes[j]
+	}
+
+	return outBytes
+}
+
+func BigInt2Ed25519Point(y *big.Int) (*edwards25519.Point, error) {
+	b := y.Bytes()
+	var arr [32]byte
+	copy(arr[32-len(b):], b)
+	return edwards25519.NewIdentityPoint().SetBytes(arr[:])
+}
+
+func BigInt2Ed25519Scalar(x *big.Int) (*edwards25519.Scalar, error) {
+	// big.Int is big endian; ed25519 assumes little endian encoding
+	kBytes := ReverseScalarBytes(x.Bytes())
+	var arr [32]byte
+	copy(arr[:], kBytes)
+	return edwards25519.NewScalar().SetCanonicalBytes(arr[:])
+}
diff --git a/internal/testutils.go b/internal/testutils.go
new file mode 100644
index 00000000..8c9202c4
--- /dev/null
+++ b/internal/testutils.go
@@ -0,0 +1,93 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package internal
+
+import (
+	"math/big"
+	"testing"
+)
+
+// AssertNoError FailsNow() the test if err != nil
+func AssertNoError(t *testing.T, err error) {
+	if err != nil {
+		t.Errorf("expected no error, but received: %v", err)
+		t.FailNow()
+	}
+}
+
+// AssertSomeError fails the test if err == nil
+func AssertSomeError(t *testing.T, err error) {
+	if err == nil {
+		t.Errorf("expected an error, but received none")
+	}
+}
+
+// AssertError fails the test if err == nil or the message does not equal msg
+func AssertError(t *testing.T, err error, msg string) {
+	if err == nil {
+		t.Errorf("expected an error, but received none")
+		return
+	}
+
+	if err.Error() != msg {
+		t.Errorf("expected error with messge: \"%s\", got: \"%s\"", msg, err.Error())
+	}
+}
+
+// AssertBigIntEq fails the test if a and b are not equal
+func AssertBigIntEq(t *testing.T, a, b *big.Int) {
+	// Bail out on nil values to avoid panic
+	if a == nil || b == nil {
+		t.Errorf("cannot compare nil values")
+		return
+	}
+
+	if a.Cmp(b) != 0 {
+		t.Errorf("%v != %v", a, b)
+	}
+}
+
+// AssertBigIntNe fails the test if two big.Ints are the same value
+func AssertBigIntNe(t *testing.T, a, b *big.Int) {
+	// Bail out on nil values to avoid panic
+	if a == nil || b == nil {
+		t.Errorf("cannot compare nil values")
+		return
+	}
+
+	if a.Cmp(b) == 0 {
+		t.Errorf("%v == %v", a, b)
+	}
+}
+
+// AssertNotNil fails if any values are nil
+func AssertNotNil(t *testing.T, values ...*big.Int) {
+	for _, x := range values {
+		if x == nil {
+			t.Errorf("result should not be nil")
+		}
+	}
+}
+
+// AssertNil fails the test if any of values are nil
+func AssertNil(t *testing.T, values ...*big.Int) {
+	for _, x := range values {
+		if x != nil {
+			t.Errorf("result should be nil")
+		}
+	}
+}
+
+// B10 creating a big.Int from a base 10 string. panics on failure to
+// to ensure zero-values aren't used in place of malformed strings.
+func B10(s string) *big.Int {
+	x, ok := new(big.Int).SetString(s, 10)
+	if !ok {
+		panic("Couldn't derive big.Int from string")
+	}
+	return x
+}
diff --git a/pkg/accumulator/README.md b/pkg/accumulator/README.md
new file mode 100755
index 00000000..84f0c4dc
--- /dev/null
+++ b/pkg/accumulator/README.md
@@ -0,0 +1,454 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# accumulator
+
+```go
+import "github.com/coinbase/kryptology/pkg/accumulator"
+```
+
+## Index
+
+- [type Accumulator](<#type-accumulator>)
+  - [func (acc *Accumulator) Add(key *SecretKey, e Element) (*Accumulator, error)](<#func-accumulator-add>)
+  - [func (acc *Accumulator) AddElements(key *SecretKey, m []Element) (*Accumulator, error)](<#func-accumulator-addelements>)
+  - [func (acc Accumulator) MarshalBinary() ([]byte, error)](<#func-accumulator-marshalbinary>)
+  - [func (acc *Accumulator) New(curve *curves.PairingCurve) (*Accumulator, error)](<#func-accumulator-new>)
+  - [func (acc *Accumulator) Remove(key *SecretKey, e Element) (*Accumulator, error)](<#func-accumulator-remove>)
+  - [func (acc *Accumulator) UnmarshalBinary(data []byte) error](<#func-accumulator-unmarshalbinary>)
+  - [func (acc *Accumulator) Update(key *SecretKey, additions []Element, deletions []Element) (*Accumulator, []Coefficient, error)](<#func-accumulator-update>)
+  - [func (acc *Accumulator) WithElements(curve *curves.PairingCurve, key *SecretKey, m []Element) (*Accumulator, error)](<#func-accumulator-withelements>)
+- [type Coefficient](<#type-coefficient>)
+- [type Delta](<#type-delta>)
+  - [func (d *Delta) MarshalBinary() ([]byte, error)](<#func-delta-marshalbinary>)
+  - [func (d *Delta) UnmarshalBinary(data []byte) error](<#func-delta-unmarshalbinary>)
+- [type Element](<#type-element>)
+- [type MembershipProof](<#type-membershipproof>)
+  - [func (mp *MembershipProof) Finalize(acc *Accumulator, pp *ProofParams, pk *PublicKey, challenge curves.Scalar) *MembershipProofFinal](<#func-membershipproof-finalize>)
+  - [func (mp MembershipProof) MarshalBinary() ([]byte, error)](<#func-membershipproof-marshalbinary>)
+  - [func (mp *MembershipProof) UnmarshalBinary(data []byte) error](<#func-membershipproof-unmarshalbinary>)
+- [type MembershipProofCommitting](<#type-membershipproofcommitting>)
+  - [func (mpc *MembershipProofCommitting) GenProof(c curves.Scalar) *MembershipProof](<#func-membershipproofcommitting-genproof>)
+  - [func (mpc MembershipProofCommitting) GetChallengeBytes() []byte](<#func-membershipproofcommitting-getchallengebytes>)
+  - [func (mpc *MembershipProofCommitting) New(witness *MembershipWitness, acc *Accumulator, pp *ProofParams, pk *PublicKey) (*MembershipProofCommitting, error)](<#func-membershipproofcommitting-new>)
+- [type MembershipProofFinal](<#type-membershipprooffinal>)
+  - [func (m MembershipProofFinal) GetChallenge(curve *curves.PairingCurve) curves.Scalar](<#func-membershipprooffinal-getchallenge>)
+- [type MembershipWitness](<#type-membershipwitness>)
+  - [func (mw *MembershipWitness) ApplyDelta(delta *Delta) (*MembershipWitness, error)](<#func-membershipwitness-applydelta>)
+  - [func (mw *MembershipWitness) BatchUpdate(additions []Element, deletions []Element, coefficients []Coefficient) (*MembershipWitness, error)](<#func-membershipwitness-batchupdate>)
+  - [func (mw MembershipWitness) MarshalBinary() ([]byte, error)](<#func-membershipwitness-marshalbinary>)
+  - [func (mw *MembershipWitness) MultiBatchUpdate(A [][]Element, D [][]Element, C [][]Coefficient) (*MembershipWitness, error)](<#func-membershipwitness-multibatchupdate>)
+  - [func (mw *MembershipWitness) New(y Element, acc *Accumulator, sk *SecretKey) (*MembershipWitness, error)](<#func-membershipwitness-new>)
+  - [func (mw *MembershipWitness) UnmarshalBinary(data []byte) error](<#func-membershipwitness-unmarshalbinary>)
+  - [func (mw MembershipWitness) Verify(pk *PublicKey, acc *Accumulator) error](<#func-membershipwitness-verify>)
+- [type ProofParams](<#type-proofparams>)
+  - [func (p *ProofParams) MarshalBinary() ([]byte, error)](<#func-proofparams-marshalbinary>)
+  - [func (p *ProofParams) New(curve *curves.PairingCurve, pk *PublicKey, entropy []byte) (*ProofParams, error)](<#func-proofparams-new>)
+  - [func (p *ProofParams) UnmarshalBinary(data []byte) error](<#func-proofparams-unmarshalbinary>)
+- [type PublicKey](<#type-publickey>)
+  - [func (pk PublicKey) MarshalBinary() ([]byte, error)](<#func-publickey-marshalbinary>)
+  - [func (pk *PublicKey) UnmarshalBinary(data []byte) error](<#func-publickey-unmarshalbinary>)
+- [type SecretKey](<#type-secretkey>)
+  - [func (sk SecretKey) BatchAdditions(additions []Element) (Element, error)](<#func-secretkey-batchadditions>)
+  - [func (sk SecretKey) BatchDeletions(deletions []Element) (Element, error)](<#func-secretkey-batchdeletions>)
+  - [func (sk SecretKey) CreateCoefficients(additions []Element, deletions []Element) ([]Element, error)](<#func-secretkey-createcoefficients>)
+  - [func (sk SecretKey) GetPublicKey(curve *curves.PairingCurve) (*PublicKey, error)](<#func-secretkey-getpublickey>)
+  - [func (sk SecretKey) MarshalBinary() ([]byte, error)](<#func-secretkey-marshalbinary>)
+  - [func (sk *SecretKey) New(curve *curves.PairingCurve, seed []byte) (*SecretKey, error)](<#func-secretkey-new>)
+  - [func (sk *SecretKey) UnmarshalBinary(data []byte) error](<#func-secretkey-unmarshalbinary>)
+
+
+## type [Accumulator](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L26-L28>)
+
+Accumulator is a point
+
+```go
+type Accumulator struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*Accumulator\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L73>)
+
+```go
+func (acc *Accumulator) Add(key *SecretKey, e Element) (*Accumulator, error)
+```
+
+Add accumulates a single element into the accumulator V' = \(y \+ alpha\) \* V
+
+### func \(\*Accumulator\) [AddElements](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L59>)
+
+```go
+func (acc *Accumulator) AddElements(key *SecretKey, m []Element) (*Accumulator, error)
+```
+
+AddElements accumulates a set of elements into the accumulator\.
+
+### func \(Accumulator\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L135>)
+
+```go
+func (acc Accumulator) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts Accumulator to bytes
+
+### func \(\*Accumulator\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L31>)
+
+```go
+func (acc *Accumulator) New(curve *curves.PairingCurve) (*Accumulator, error)
+```
+
+New creates a new accumulator\.
+
+### func \(\*Accumulator\) [Remove](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L84>)
+
+```go
+func (acc *Accumulator) Remove(key *SecretKey, e Element) (*Accumulator, error)
+```
+
+Remove removes a single element from accumulator if it exists V' = 1/\(y\+alpha\) \*  V
+
+### func \(\*Accumulator\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L147>)
+
+```go
+func (acc *Accumulator) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary sets Accumulator from bytes
+
+### func \(\*Accumulator\) [Update](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L99>)
+
+```go
+func (acc *Accumulator) Update(key *SecretKey, additions []Element, deletions []Element) (*Accumulator, []Coefficient, error)
+```
+
+Update performs a batch addition and deletion as described on page 7\, section 3 in https://eprint.iacr.org/2020/777.pdf
+
+### func \(\*Accumulator\) [WithElements](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L45>)
+
+```go
+func (acc *Accumulator) WithElements(curve *curves.PairingCurve, key *SecretKey, m []Element) (*Accumulator, error)
+```
+
+WithElements initializes a new accumulator prefilled with entries Each member is assumed to be hashed V = prod\(y \+ α\) \* V0\, for all y∈ Y\_V
+
+## type [Coefficient](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L23>)
+
+Coefficient is a point
+
+```go
+type Coefficient curves.Point
+```
+
+## type [Delta](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L164-L167>)
+
+Delta contains values d and p\, where d should be the division dA\(y\)/dD\(y\) on some value y p should be equal to 1/dD \* \<Gamma\_y\, Omega\>
+
+```go
+type Delta struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*Delta\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L170>)
+
+```go
+func (d *Delta) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts Delta into bytes
+
+### func \(\*Delta\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L185>)
+
+```go
+func (d *Delta) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary converts data into Delta
+
+## type [Element](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/accumulator.go#L20>)
+
+```go
+type Element curves.Scalar
+```
+
+## type [MembershipProof](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L307-L316>)
+
+MembershipProof contains values in the proof to be verified
+
+```go
+type MembershipProof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*MembershipProof\) [Finalize](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L319>)
+
+```go
+func (mp *MembershipProof) Finalize(acc *Accumulator, pp *ProofParams, pk *PublicKey, challenge curves.Scalar) *MembershipProofFinal
+```
+
+Finalize computes values in the proof to be verified\.
+
+### func \(MembershipProof\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L399>)
+
+```go
+func (mp MembershipProof) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts MembershipProof to bytes
+
+### func \(\*MembershipProof\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L415>)
+
+```go
+func (mp *MembershipProof) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary converts bytes to MembershipProof
+
+## type [MembershipProofCommitting](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L102-L125>)
+
+MembershipProofCommitting contains value computed in Proof of knowledge and Blinding phases as described in section 7 of https://eprint.iacr.org/2020/777.pdf
+
+```go
+type MembershipProofCommitting struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*MembershipProofCommitting\) [GenProof](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L263>)
+
+```go
+func (mpc *MembershipProofCommitting) GenProof(c curves.Scalar) *MembershipProof
+```
+
+GenProof computes the s values for Fiat\-Shamir and return the actual proof to be sent to the verifier given the challenge c\.
+
+### func \(MembershipProofCommitting\) [GetChallengeBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L248>)
+
+```go
+func (mpc MembershipProofCommitting) GetChallengeBytes() []byte
+```
+
+GetChallenge returns bytes that need to be hashed for generating challenge\. V || Ec || T\_sigma || T\_rho || R\_E || R\_sigma || R\_rho || R\_delta\_sigma || R\_delta\_rho
+
+### func \(\*MembershipProofCommitting\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L128-L133>)
+
+```go
+func (mpc *MembershipProofCommitting) New(witness *MembershipWitness, acc *Accumulator, pp *ProofParams, pk *PublicKey) (*MembershipProofCommitting, error)
+```
+
+New initiates values of MembershipProofCommitting
+
+## type [MembershipProofFinal](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L474-L484>)
+
+MembershipProofFinal contains values that are input to Fiat\-Shamir Heuristic
+
+```go
+type MembershipProofFinal struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(MembershipProofFinal\) [GetChallenge](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L487>)
+
+```go
+func (m MembershipProofFinal) GetChallenge(curve *curves.PairingCurve) curves.Scalar
+```
+
+GetChallenge computes Fiat\-Shamir Heuristic taking input values of MembershipProofFinal
+
+## type [MembershipWitness](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L16-L19>)
+
+MembershipWitness contains the witness c and the value y respect to the accumulator state\.
+
+```go
+type MembershipWitness struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*MembershipWitness\) [ApplyDelta](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L78>)
+
+```go
+func (mw *MembershipWitness) ApplyDelta(delta *Delta) (*MembershipWitness, error)
+```
+
+ApplyDelta returns C' = dA\(y\)/dD\(y\)\*C \+ 1/dD\(y\) \* \<Gamma\_y\, Omega\> according to the witness update protocol described in section 4 of https://eprint.iacr.org/2020/777.pdf
+
+### func \(\*MembershipWitness\) [BatchUpdate](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L89>)
+
+```go
+func (mw *MembershipWitness) BatchUpdate(additions []Element, deletions []Element, coefficients []Coefficient) (*MembershipWitness, error)
+```
+
+BatchUpdate performs batch update as described in section 4
+
+### func \(MembershipWitness\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L115>)
+
+```go
+func (mw MembershipWitness) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts a membership witness to bytes
+
+### func \(\*MembershipWitness\) [MultiBatchUpdate](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L102>)
+
+```go
+func (mw *MembershipWitness) MultiBatchUpdate(A [][]Element, D [][]Element, C [][]Coefficient) (*MembershipWitness, error)
+```
+
+MultiBatchUpdate performs multi\-batch update using epoch as described in section 4\.2
+
+### func \(\*MembershipWitness\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L22>)
+
+```go
+func (mw *MembershipWitness) New(y Element, acc *Accumulator, sk *SecretKey) (*MembershipWitness, error)
+```
+
+New creates a new membership witness
+
+### func \(\*MembershipWitness\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L129>)
+
+```go
+func (mw *MembershipWitness) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary converts bytes into MembershipWitness
+
+### func \(MembershipWitness\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/witness.go#L44>)
+
+```go
+func (mw MembershipWitness) Verify(pk *PublicKey, acc *Accumulator) error
+```
+
+Verify the MembershipWitness mw is a valid witness as per section 4 in \<https://eprint.iacr.org/2020/777\>
+
+## type [ProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L30-L32>)
+
+ProofParams contains four distinct public generators of G1 \- X\, Y\, Z
+
+```go
+type ProofParams struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ProofParams\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L55>)
+
+```go
+func (p *ProofParams) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts ProofParams to bytes
+
+### func \(\*ProofParams\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L35>)
+
+```go
+func (p *ProofParams) New(curve *curves.PairingCurve, pk *PublicKey, entropy []byte) (*ProofParams, error)
+```
+
+New samples X\, Y\, Z\, K
+
+### func \(\*ProofParams\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/proof.go#L69>)
+
+```go
+func (p *ProofParams) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary converts bytes to ProofParams
+
+## type [PublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L204-L206>)
+
+PublicKey is the public key of accumulator\, it should be sk \* generator of G2
+
+```go
+type PublicKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(PublicKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L209>)
+
+```go
+func (pk PublicKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts PublicKey to bytes
+
+### func \(\*PublicKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L221>)
+
+```go
+func (pk *PublicKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary sets PublicKey from bytes
+
+## type [SecretKey](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L16-L18>)
+
+SecretKey is the secret alpha only held by the accumulator manager\.
+
+```go
+type SecretKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(SecretKey\) [BatchAdditions](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L69>)
+
+```go
+func (sk SecretKey) BatchAdditions(additions []Element) (Element, error)
+```
+
+BatchAdditions computes product\(y \+ sk\) for y in additions and output the product
+
+### func \(SecretKey\) [BatchDeletions](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L87>)
+
+```go
+func (sk SecretKey) BatchDeletions(deletions []Element) (Element, error)
+```
+
+BatchDeletions computes 1/product\(y \+ sk\) for y in deletions and output it
+
+### func \(SecretKey\) [CreateCoefficients](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L101>)
+
+```go
+func (sk SecretKey) CreateCoefficients(additions []Element, deletions []Element) ([]Element, error)
+```
+
+CreateCoefficients creates the Batch Polynomial coefficients See page 7 of https://eprint.iacr.org/2020/777.pdf
+
+### func \(SecretKey\) [GetPublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L27>)
+
+```go
+func (sk SecretKey) GetPublicKey(curve *curves.PairingCurve) (*PublicKey, error)
+```
+
+GetPublicKey creates a public key from SecretKey sk
+
+### func \(SecretKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L36>)
+
+```go
+func (sk SecretKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary converts SecretKey to bytes
+
+### func \(\*SecretKey\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L21>)
+
+```go
+func (sk *SecretKey) New(curve *curves.PairingCurve, seed []byte) (*SecretKey, error)
+```
+
+New creates a new secret key from the seed\.
+
+### func \(\*SecretKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/accumulator/key.go#L48>)
+
+```go
+func (sk *SecretKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary sets SecretKey from bytes
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/accumulator/accumulator.go b/pkg/accumulator/accumulator.go
new file mode 100644
index 00000000..0c6466e0
--- /dev/null
+++ b/pkg/accumulator/accumulator.go
@@ -0,0 +1,165 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+type structMarshal struct {
+	Value []byte `bare:"value"`
+	Curve string `bare:"curve"`
+}
+
+type Element curves.Scalar
+
+// Coefficient is a point
+type Coefficient curves.Point
+
+// Accumulator is a point
+type Accumulator struct {
+	value curves.Point
+}
+
+// New creates a new accumulator.
+func (acc *Accumulator) New(curve *curves.PairingCurve) (*Accumulator, error) {
+	// If we need to support non-membership witness, we need to implement Accumulator Initialization
+	// as described in section 6 of <https://eprint.iacr.org/2020/777.pdf>
+	// for now we don't need non-membership witness
+
+	// i.e., it computes V0 = prod(y + α) * P, y ∈ Y_V0, P is a generator of G1. Since we do not use non-membership witness
+	// we just set the initial accumulator a G1 generator.
+	acc.value = curve.Scalar.Point().Generator()
+	return acc, nil
+}
+
+// WithElements initializes a new accumulator prefilled with entries
+// Each member is assumed to be hashed
+// V = prod(y + α) * V0, for all y∈ Y_V
+func (acc *Accumulator) WithElements(curve *curves.PairingCurve, key *SecretKey, m []Element) (*Accumulator, error) {
+	_, err := acc.New(curve)
+	if err != nil {
+		return nil, err
+	}
+	y, err := key.BatchAdditions(m)
+	if err != nil {
+		return nil, err
+	}
+	acc.value = acc.value.Mul(y)
+	return acc, nil
+}
+
+// AddElements accumulates a set of elements into the accumulator.
+func (acc *Accumulator) AddElements(key *SecretKey, m []Element) (*Accumulator, error) {
+	if acc.value == nil || key.value == nil {
+		return nil, fmt.Errorf("accumulator and secret key should not be nil")
+	}
+	y, err := key.BatchAdditions(m)
+	if err != nil {
+		return nil, err
+	}
+	acc.value = acc.value.Mul(y)
+	return acc, nil
+}
+
+// Add accumulates a single element into the accumulator
+// V' = (y + alpha) * V
+func (acc *Accumulator) Add(key *SecretKey, e Element) (*Accumulator, error) {
+	if acc.value == nil || acc.value.IsIdentity() || key.value == nil || e == nil {
+		return nil, fmt.Errorf("accumulator, secret key and element should not be nil")
+	}
+	y := e.Add(key.value) // y + alpha
+	acc.value = acc.value.Mul(y)
+	return acc, nil
+}
+
+// Remove removes a single element from accumulator if it exists
+// V' = 1/(y+alpha) *  V
+func (acc *Accumulator) Remove(key *SecretKey, e Element) (*Accumulator, error) {
+	if acc.value == nil || acc.value.IsIdentity() || key.value == nil || e == nil {
+		return nil, fmt.Errorf("accumulator, secret key and element should not be nil")
+	}
+	y := e.Add(key.value) // y + alpha
+	y, err := y.Invert()  // 1/(y+alpha)
+	if err != nil {
+		return nil, err
+	}
+	acc.value = acc.value.Mul(y)
+	return acc, nil
+}
+
+// Update performs a batch addition and deletion as described on page 7, section 3 in
+// https://eprint.iacr.org/2020/777.pdf
+func (acc *Accumulator) Update(key *SecretKey, additions []Element, deletions []Element) (*Accumulator, []Coefficient, error) {
+	if acc.value == nil || acc.value.IsIdentity() || key.value == nil {
+		return nil, nil, fmt.Errorf("accumulator and secret key should not be nil")
+	}
+
+	// Compute dA(-alpha) = prod(y + alpha), y in the set of A ⊆ ACC-Y_V
+	a, err := key.BatchAdditions(additions)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Compute dD(-alpha) = 1/prod(y + alpha), y in the set of D ⊆ Y_V
+	d, err := key.BatchDeletions(deletions)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// dA(-alpha)/dD(-alpha)
+	div := a.Mul(d)
+	newAcc := acc.value.Mul(div)
+
+	// build an array of coefficients
+	elements, err := key.CreateCoefficients(additions, deletions)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	coefficients := make([]Coefficient, len(elements))
+	for i := 0; i < len(elements); i++ {
+		coefficients[i] = acc.value.Mul(elements[i])
+	}
+	acc.value = newAcc
+	return acc, coefficients, nil
+}
+
+// MarshalBinary converts Accumulator to bytes
+func (acc Accumulator) MarshalBinary() ([]byte, error) {
+	if acc.value == nil {
+		return nil, fmt.Errorf("accumulator cannot be nil")
+	}
+	tv := &structMarshal{
+		Value: acc.value.ToAffineCompressed(),
+		Curve: acc.value.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary sets Accumulator from bytes
+func (acc *Accumulator) UnmarshalBinary(data []byte) error {
+	tv := new(structMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+
+	value, err := curve.NewIdentityPoint().FromAffineCompressed(tv.Value)
+
+	if err != nil {
+		return err
+	}
+	acc.value = value
+	return nil
+}
diff --git a/pkg/accumulator/accumulator_test.go b/pkg/accumulator/accumulator_test.go
new file mode 100644
index 00000000..1b07afae
--- /dev/null
+++ b/pkg/accumulator/accumulator_test.go
@@ -0,0 +1,176 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestNewAccumulator100(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc, err := new(Accumulator).New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestNewAccumulator10K(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc, err := new(Accumulator).New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestNewAccumulator10M(t *testing.T) {
+	// Initiating 10M values takes time
+	if testing.Short() {
+		t.Skip("skipping test in short mode.")
+	}
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc, err := new(Accumulator).New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestWithElements(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, _ := new(SecretKey).New(curve, seed[:])
+	element1 := curve.Scalar.Hash([]byte("value1"))
+	element2 := curve.Scalar.Hash([]byte("value2"))
+	elements := []Element{element1, element2}
+	newAcc, err := new(Accumulator).WithElements(curve, key, elements)
+	require.NoError(t, err)
+	require.NotNil(t, newAcc)
+	require.NotEqual(t, newAcc.value.ToAffineCompressed(), curve.PointG1.Identity().ToAffineCompressed())
+	require.NotEqual(t, newAcc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	_, _ = newAcc.Remove(key, element1)
+	_, _ = newAcc.Remove(key, element2)
+	require.Equal(t, newAcc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestAdd(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc := &Accumulator{curve.PointG1.Generator()}
+	_, _ = acc.New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+
+	element := curve.Scalar.Hash([]byte("value1"))
+	require.NoError(t, err)
+	require.NotNil(t, element)
+	_, _ = acc.Add(key, element)
+	require.NotEqual(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestRemove(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc, err := new(Accumulator).New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	element := curve.Scalar.Hash([]byte("value1"))
+	require.NoError(t, err)
+	require.NotNil(t, element)
+
+	// add element
+	_, _ = acc.Add(key, element)
+	require.NotEqual(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	// remove element
+	acc, err = acc.Remove(key, element)
+	require.NoError(t, err)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestAddElements(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc := &Accumulator{curve.PointG1.Generator()}
+	_, _ = acc.New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	element1 := curve.Scalar.Hash([]byte("value1"))
+	element2 := curve.Scalar.Hash([]byte("value2"))
+	element3 := curve.Scalar.Hash([]byte("value3"))
+	elements := []Element{element1, element2, element3}
+
+	acc, err = acc.AddElements(key, elements)
+	require.NoError(t, err)
+	require.NotEqual(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
+
+func TestAccumulatorMarshal(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	point := curve.PointG1.Generator().Mul(curve.Scalar.New(2))
+	data, err := Accumulator{point}.MarshalBinary()
+	require.NoError(t, err)
+	require.NotNil(t, data)
+	// element cannot be empty
+	_, err = Accumulator{}.MarshalBinary()
+	require.Error(t, err)
+
+	e := &Accumulator{curve.PointG1.Generator()}
+	_ = e.UnmarshalBinary(data)
+	require.Equal(t, e.value, point)
+}
+
+func TestUpdate(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, err := new(SecretKey).New(curve, seed[:])
+	require.NoError(t, err)
+	require.NotNil(t, key)
+	acc, err := new(Accumulator).New(curve)
+	require.NoError(t, err)
+	require.NotNil(t, acc)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	element1 := curve.Scalar.Hash([]byte("value1"))
+	element2 := curve.Scalar.Hash([]byte("value2"))
+	element3 := curve.Scalar.Hash([]byte("value3"))
+	elements := []Element{element1, element2, element3}
+
+	acc, _, err = acc.Update(key, elements, nil)
+	require.NoError(t, err)
+	require.NotEqual(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+
+	acc, _, err = acc.Update(key, nil, elements)
+	require.NoError(t, err)
+	require.Equal(t, acc.value.ToAffineCompressed(), curve.PointG1.Generator().ToAffineCompressed())
+}
diff --git a/pkg/accumulator/key.go b/pkg/accumulator/key.go
new file mode 100644
index 00000000..05ad0076
--- /dev/null
+++ b/pkg/accumulator/key.go
@@ -0,0 +1,239 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// SecretKey is the secret alpha only held by the accumulator manager.
+type SecretKey struct {
+	value curves.Scalar
+}
+
+// New creates a new secret key from the seed.
+func (sk *SecretKey) New(curve *curves.PairingCurve, seed []byte) (*SecretKey, error) {
+	sk.value = curve.Scalar.Hash(seed)
+	return sk, nil
+}
+
+// GetPublicKey creates a public key from SecretKey sk
+func (sk SecretKey) GetPublicKey(curve *curves.PairingCurve) (*PublicKey, error) {
+	if sk.value == nil || curve == nil {
+		return nil, fmt.Errorf("curve and sk value cannot be nil")
+	}
+	value := curve.Scalar.Point().(curves.PairingPoint).OtherGroup().Generator().Mul(sk.value)
+	return &PublicKey{value.(curves.PairingPoint)}, nil
+}
+
+// MarshalBinary converts SecretKey to bytes
+func (sk SecretKey) MarshalBinary() ([]byte, error) {
+	if sk.value == nil {
+		return nil, fmt.Errorf("sk cannot be empty")
+	}
+	tv := &structMarshal{
+		Value: sk.value.Bytes(),
+		Curve: sk.value.Point().CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary sets SecretKey from bytes
+func (sk *SecretKey) UnmarshalBinary(data []byte) error {
+	tv := new(structMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+
+	value, err := curve.NewScalar().SetBytes(tv.Value)
+
+	if err != nil {
+		return err
+	}
+	sk.value = value
+	return nil
+}
+
+// BatchAdditions computes product(y + sk) for y in additions and output the product
+func (sk SecretKey) BatchAdditions(additions []Element) (Element, error) {
+	if sk.value == nil {
+		return nil, fmt.Errorf("secret key cannot be empty")
+	}
+	mul := sk.value.One()
+	for i := 0; i < len(additions); i++ {
+		if additions[i] == nil {
+			return nil, fmt.Errorf("some element in additions is nil")
+		}
+		// y + alpha
+		temp := additions[i].Add(sk.value)
+		// prod(y + alpha)
+		mul = mul.Mul(temp)
+	}
+	return mul, nil
+}
+
+// BatchDeletions computes 1/product(y + sk) for y in deletions and output it
+func (sk SecretKey) BatchDeletions(deletions []Element) (Element, error) {
+	v, err := sk.BatchAdditions(deletions)
+	if err != nil {
+		return nil, err
+	}
+	y, err := v.Invert()
+	if err != nil {
+		return nil, err
+	}
+	return y, nil
+}
+
+// CreateCoefficients creates the Batch Polynomial coefficients
+// See page 7 of https://eprint.iacr.org/2020/777.pdf
+func (sk SecretKey) CreateCoefficients(additions []Element, deletions []Element) ([]Element, error) {
+	if sk.value == nil {
+		return nil, fmt.Errorf("secret key should not be nil")
+	}
+
+	// vD(x) = ∑^{m}_{s=1}{ ∏ 1..s {yD_i + alpha}^-1 ∏ 1 ..s-1 {yD_j - x}
+	one := sk.value.One()
+	m1 := one.Neg() // m1 is -1
+	vD := make(polynomial, 0, len(deletions))
+	for s := 0; s < len(deletions); s++ {
+		// ∏ 1..s (yD_i + alpha)^-1
+		c, err := sk.BatchDeletions(deletions[0 : s+1])
+		if err != nil {
+			return nil, fmt.Errorf("error in sk batchDeletions")
+		}
+		poly := make(polynomial, 1, s+2)
+		poly[0] = one
+
+		// ∏ 1..(s-1) (yD_j - x)
+		for j := 0; j < s; j++ {
+			t := make(polynomial, 2)
+			// yD_j
+			t[0] = deletions[j]
+			// -x
+			t[1] = m1
+
+			// polynomial multiplication (yD_1-x) * (yD_2 - x) ...
+			poly, err = poly.Mul(t)
+			if err != nil {
+				return nil, err
+			}
+		}
+		poly, err = poly.MulScalar(c)
+		if err != nil {
+			return nil, err
+		}
+		vD, err = vD.Add(poly)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	//vD(x) * ∏ 1..n (yA_i + alpha)
+	bAdd, err := sk.BatchAdditions(additions)
+	if err != nil {
+		return nil, fmt.Errorf("error in sk batchAdditions")
+	}
+	vD, err = vD.MulScalar(bAdd)
+	if err != nil {
+		return nil, err
+	}
+
+	// vA(x) = ∑^n_{s=1}{ ∏ 1..s-1 {yA_i + alpha} ∏ s+1..n {yA_j - x} }
+	vA := make(polynomial, 0, len(additions))
+	for s := 0; s < len(additions); s++ {
+		// ∏ 1..s-1 {yA_i + alpha}
+		var c Element
+		if s == 0 {
+			c = one
+		} else {
+			c, err = sk.BatchAdditions(additions[0:s])
+			if err != nil {
+				return nil, err
+			}
+		}
+		poly := make(polynomial, 1, s+2)
+		poly[0] = one
+
+		// ∏ s+1..n {yA_j - x}
+		for j := s + 1; j < len(additions); j++ {
+			t := make(polynomial, 2)
+			t[0] = additions[j]
+			t[1] = m1
+
+			// polynomial multiplication (yA_1-x) * (yA_2 - x) ...
+			poly, err = poly.Mul(t)
+			if err != nil {
+				return nil, err
+			}
+		}
+		poly, err = poly.MulScalar(c)
+		if err != nil {
+			return nil, err
+		}
+		vA, err = vA.Add(poly)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	// vA - vD
+	vA, err = vA.Sub(vD)
+	if err != nil {
+		return nil, err
+	}
+	result := make([]Element, len(vA))
+	for i := 0; i < len(vA); i++ {
+		result[i] = vA[i]
+	}
+	return result, nil
+}
+
+// PublicKey is the public key of accumulator, it should be sk * generator of G2
+type PublicKey struct {
+	value curves.PairingPoint
+}
+
+// MarshalBinary converts PublicKey to bytes
+func (pk PublicKey) MarshalBinary() ([]byte, error) {
+	if pk.value == nil {
+		return nil, fmt.Errorf("public key cannot be nil")
+	}
+	tv := &structMarshal{
+		Value: pk.value.ToAffineCompressed(),
+		Curve: pk.value.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary sets PublicKey from bytes
+func (pk *PublicKey) UnmarshalBinary(data []byte) error {
+	tv := new(structMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetPairingCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+
+	value, err := curve.NewScalar().Point().FromAffineCompressed(tv.Value)
+
+	if err != nil {
+		return err
+	}
+	pk.value = value.(curves.PairingPoint)
+	return nil
+}
diff --git a/pkg/accumulator/key_test.go b/pkg/accumulator/key_test.go
new file mode 100644
index 00000000..7373721b
--- /dev/null
+++ b/pkg/accumulator/key_test.go
@@ -0,0 +1,86 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestSecretKeyMarshal(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	data, err := SecretKey{curve.Scalar.One()}.MarshalBinary()
+	require.NoError(t, err)
+	require.NotNil(t, data)
+	e := &SecretKey{curve.Scalar.New(2)}
+	err = e.UnmarshalBinary(data)
+	require.NoError(t, err)
+	require.Equal(t, e.value.Bytes(), curve.Scalar.One().Bytes())
+
+	// element cannot be empty
+	_, err = SecretKey{}.MarshalBinary()
+	require.Error(t, err)
+}
+
+func TestPublicKeyMarshal(t *testing.T) {
+	// Actually test both toBytes() and from()
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk := &SecretKey{curve.Scalar.New(3)}
+	pk, _ := sk.GetPublicKey(curve)
+	pkBytes, err := pk.MarshalBinary()
+	require.NoError(t, err)
+	require.NotNil(t, pkBytes)
+
+	pk2 := &PublicKey{}
+	err = pk2.UnmarshalBinary(pkBytes)
+	require.NoError(t, err)
+	require.Equal(t, pk.value, pk2.value)
+}
+
+func TestBatch(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	sk, _ := new(SecretKey).New(curve, seed[:])
+	element1 := curve.Scalar.Hash([]byte("value1"))
+	element2 := curve.Scalar.Hash([]byte("value2"))
+	elements := []Element{element1, element2}
+
+	add, err := sk.BatchAdditions(elements)
+	require.NoError(t, err)
+	require.NotNil(t, add)
+
+	del, err := sk.BatchDeletions(elements)
+	require.NoError(t, err)
+	require.NotNil(t, del)
+
+	result := add.Mul(del)
+	require.Equal(t, result, curve.Scalar.One())
+
+	g1 := curve.PointG1.Generator()
+	acc := g1.Mul(add)
+	require.NotEqual(t, acc, g1)
+	acc = acc.Mul(del)
+	require.Equal(t, acc.ToAffineCompressed(), g1.ToAffineCompressed())
+
+	acc2 := g1.Mul(result)
+	require.Equal(t, acc2, g1)
+}
+
+func TestCoefficient(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	element1 := curve.Scalar.Hash([]byte("value1"))
+	element2 := curve.Scalar.Hash([]byte("value2"))
+	element3 := curve.Scalar.Hash([]byte("value3"))
+	element4 := curve.Scalar.Hash([]byte("value4"))
+	element5 := curve.Scalar.Hash([]byte("value5"))
+	elements := []Element{element1, element2, element3, element4, element5}
+	coefficients, err := sk.CreateCoefficients(elements[0:2], elements[2:5])
+	require.NoError(t, err)
+	require.Equal(t, len(coefficients), 3)
+}
diff --git a/pkg/accumulator/lib.go b/pkg/accumulator/lib.go
new file mode 100644
index 00000000..7ee54133
--- /dev/null
+++ b/pkg/accumulator/lib.go
@@ -0,0 +1,203 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math"
+)
+
+// dad constructs two polynomials - dA(x) and dD(x)
+// dA(y) = prod(y_A,t - y), t = 1...n
+// dD(y) = prod(y_D,t - y), t = 1...n
+func dad(values []Element, y Element) (Element, error) {
+	if values == nil || y == nil {
+		return nil, fmt.Errorf("curve, values or y should not be nil")
+	}
+
+	for _, value := range values {
+		if value == nil {
+			return nil, fmt.Errorf("some element is nil")
+		}
+	}
+
+	result := y.One()
+	if len(values) == 1 {
+		a := values[0]
+		result = a.Sub(y)
+	} else {
+		for i := 0; i < len(values); i++ {
+			temp := values[i].Sub(y)
+			result = result.Mul(temp)
+		}
+	}
+	return result, nil
+}
+
+type polynomialPoint []curves.Point
+
+// evaluate evaluates a PolynomialG1 on input x.
+func (p polynomialPoint) evaluate(x curves.Scalar) (curves.Point, error) {
+	if p == nil {
+		return nil, fmt.Errorf("p cannot be empty")
+	}
+	for i := 0; i < len(p); i++ {
+		if p[i] == nil {
+			return nil, fmt.Errorf("some coefficient in p is nil")
+		}
+	}
+
+	pp := x
+	res := p[0]
+	for i := 1; i < len(p); i++ {
+		r := p[i].Mul(pp)
+		res = res.Add(r)
+		pp = pp.Mul(x)
+	}
+	return res, nil
+}
+
+// Add adds two PolynomialG1
+func (p polynomialPoint) Add(rhs polynomialPoint) (polynomialPoint, error) {
+	maxLen := int(math.Max(float64(len(p)), float64(len(rhs))))
+
+	result := make(polynomialPoint, maxLen)
+
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		result[i] = c.Add(c.Identity())
+	}
+
+	for i, c := range rhs {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		if result[i] == nil {
+			result[i] = c.Add(c.Identity())
+		} else {
+			result[i] = result[i].Add(c)
+		}
+	}
+	return result, nil
+}
+
+// Mul for PolynomialG1 computes rhs * p, p is a polynomial, rhs is a value
+func (p polynomialPoint) Mul(rhs curves.Scalar) (polynomialPoint, error) {
+	result := make(polynomialPoint, len(p))
+
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		result[i] = c.Mul(rhs)
+	}
+
+	return result, nil
+}
+
+type polynomial []curves.Scalar
+
+// Add adds two polynomials
+func (p polynomial) Add(rhs polynomial) (polynomial, error) {
+	maxLen := int(math.Max(float64(len(p)), float64(len(rhs))))
+	result := make([]curves.Scalar, maxLen)
+
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		result[i] = c.Clone()
+	}
+
+	for i, c := range rhs {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		if result[i] == nil {
+			result[i] = c.Clone()
+		} else {
+			result[i] = result[i].Add(c)
+		}
+	}
+
+	return result, nil
+}
+
+// Sub computes p-rhs and returns
+func (p polynomial) Sub(rhs polynomial) (polynomial, error) {
+	maxLen := int(math.Max(float64(len(p)), float64(len(rhs))))
+	result := make([]curves.Scalar, maxLen)
+
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		result[i] = c.Clone()
+	}
+
+	for i, c := range rhs {
+		if c == nil {
+			return nil, fmt.Errorf("invalid coefficient at %d", i)
+		}
+		if result[i] == nil {
+			result[i] = c.Neg()
+		} else {
+			result[i] = result[i].Sub(c)
+		}
+	}
+
+	return result, nil
+}
+
+// Mul multiplies two polynomials - p * rhs
+func (p polynomial) Mul(rhs polynomial) (polynomial, error) {
+	// Check for each coefficient that should not be nil
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("coefficient in p at %d is nil", i)
+		}
+	}
+
+	for i, c := range rhs {
+		if c == nil {
+			return nil, fmt.Errorf("coefficient in rhs at %d is nil", i)
+		}
+	}
+
+	m := len(p)
+	n := len(rhs)
+
+	// Initialize the product polynomial
+	prod := make(polynomial, m+n-1)
+	for i := 0; i < len(prod); i++ {
+		prod[i] = p[0].Zero()
+	}
+
+	// Multiply two polynomials term by term
+	for i, cp := range p {
+		for j, cr := range rhs {
+			temp := cp.Mul(cr)
+			prod[i+j] = prod[i+j].Add(temp)
+		}
+	}
+	return prod, nil
+}
+
+// MulScalar computes p * rhs, where rhs is a scalar value
+func (p polynomial) MulScalar(rhs curves.Scalar) (polynomial, error) {
+	result := make(polynomial, len(p))
+	for i, c := range p {
+		if c == nil {
+			return nil, fmt.Errorf("coefficient at %d is nil", i)
+		}
+		result[i] = c.Mul(rhs)
+	}
+	return result, nil
+}
diff --git a/pkg/accumulator/lib_test.go b/pkg/accumulator/lib_test.go
new file mode 100644
index 00000000..3bf8eb91
--- /dev/null
+++ b/pkg/accumulator/lib_test.go
@@ -0,0 +1,403 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestEvaluatePolyG1(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	output1, err := poly.evaluate(curve.Scalar.New(1))
+	require.NoError(t, err)
+	require.NotNil(t, output1)
+	result1 := curve.PointG1.Generator().Mul(curve.Scalar.New(6))
+	require.Equal(t, output1.ToAffineCompressed(), result1.ToAffineCompressed())
+
+	output2, err := poly.evaluate(curve.Scalar.New(2))
+	require.NoError(t, err)
+	require.NotNil(t, output2)
+	result2 := curve.PointG1.Generator().Mul(curve.Scalar.New(11))
+	require.Equal(t, output2.ToAffineCompressed(), result2.ToAffineCompressed())
+}
+
+func TestEvaluatePolyG1Error(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomialPoint{
+		nil,
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	_, err := poly.evaluate(curve.Scalar.New(1))
+	require.Error(t, err)
+}
+
+func TestAddAssignPolyG1(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	// Test polynomial with equal length
+	poly1 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	poly2 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+	}
+
+	output, err := poly1.Add(poly2)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	result := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(4)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(4)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(4)),
+	}
+	for i := 0; i < len(output); i++ {
+		require.Equal(t, output[i].ToAffineCompressed(), result[i].ToAffineCompressed())
+	}
+
+	// Test polynomials with unequal length
+	poly3 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+	}
+	output2, err := poly1.Add(poly3)
+	require.NoError(t, err)
+	require.NotNil(t, output2)
+	result2 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(4)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(4)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	require.Equal(t, len(output2), len(result2))
+	for i := 0; i < len(output2); i++ {
+		require.Equal(t, output2[i].ToAffineCompressed(), result2[i].ToAffineCompressed())
+	}
+
+	// Test polynomial with Capacity
+	poly4 := make(polynomialPoint, 0, 3)
+	poly5, err := poly4.Add(poly1)
+	require.NoError(t, err)
+	require.Equal(t, len(poly5), len(poly1))
+	for i := 0; i < len(poly5); i++ {
+		require.Equal(t, poly5[i].ToAffineCompressed(), poly1[i].ToAffineCompressed())
+	}
+
+}
+
+func TestAddAssignPolyG1Error(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly1 := polynomialPoint{
+		nil,
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	poly2 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+	}
+	output, err := poly1.Add(poly2)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
+
+func TestMulAssignPolyG1(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	rhs := curve.Scalar.New(3)
+	output, err := poly.Mul(rhs)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	poly2 := polynomialPoint{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(9)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(6)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(3)),
+	}
+	for i := 0; i < len(poly2); i++ {
+		require.Equal(t, output[i].ToAffineCompressed(), poly2[i].ToAffineCompressed())
+	}
+}
+
+func TestMulAssignPolyG1Error(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomialPoint{
+		nil,
+		curve.PointG1.Generator().Mul(curve.Scalar.New(2)),
+		curve.PointG1.Generator().Mul(curve.Scalar.New(1)),
+	}
+	rhs := curve.Scalar.New(3)
+	output, err := poly.Mul(rhs)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
+
+func TestPushPoly(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomial{
+		curve.Scalar.New(3),
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	scalar := curve.Scalar.New(4)
+	result := append(poly, scalar)
+	require.Equal(t, result[3], scalar)
+
+	// Push one more
+	scalar2 := curve.Scalar.New(5)
+	result2 := append(result, scalar2)
+	require.Equal(t, result2[4], scalar2)
+
+	// Push to a new polynomial
+	newPoly := polynomial{}
+	newPoly = append(newPoly, scalar)
+	require.Equal(t, newPoly[0], scalar)
+	newPoly = append(newPoly, scalar2)
+	require.Equal(t, newPoly[1], scalar2)
+}
+
+func TestAddAssignPoly(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	// Test polynomial with equal length
+	poly1 := polynomial{
+		curve.Scalar.New(3),
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+
+	output, err := poly1.Add(poly2)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	result := []curves.Scalar{
+		curve.Scalar.New(4),
+		curve.Scalar.New(4),
+		curve.Scalar.New(4),
+	}
+	for i := 0; i < len(output); i++ {
+		require.Equal(t, output[i], result[i])
+	}
+
+	// Test polynomials with unequal length
+	poly3 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+	}
+	output2, err := poly1.Add(poly3)
+	require.NoError(t, err)
+	require.NotNil(t, output2)
+	result2 := []curves.Scalar{
+		curve.Scalar.New(4),
+		curve.Scalar.New(4),
+		curve.Scalar.New(1),
+	}
+	require.Equal(t, len(output2), len(result2))
+	for i := 0; i < len(output2); i++ {
+		require.Equal(t, output2[i], result2[i])
+	}
+}
+
+func TestAddAssignPolyError(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	// Test polynomial with equal length
+	poly1 := polynomial{
+		nil,
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+
+	output, err := poly1.Add(poly2)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
+
+func TestSubAssignPoly(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	// Test polynomial with equal length
+	poly1 := polynomial{
+		curve.Scalar.New(3),
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+
+	output, err := poly1.Sub(poly2)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	result := []curves.Scalar{
+		curve.Scalar.New(2),
+		curve.Scalar.New(0),
+		curve.Scalar.New(-2),
+	}
+	for i := 0; i < len(output); i++ {
+		require.Equal(t, output[i].Bytes(), result[i].Bytes())
+	}
+
+	// Test polynomials with unequal length
+	poly3 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+	}
+	output2, err := poly1.Sub(poly3)
+	require.NoError(t, err)
+	require.NotNil(t, output2)
+	result2 := []curves.Scalar{
+		curve.Scalar.New(2),
+		curve.Scalar.New(0),
+		curve.Scalar.New(-2),
+		curve.Scalar.New(-4),
+	}
+	require.Equal(t, len(output2), len(result2))
+	for i := 0; i < len(output2); i++ {
+		require.Equal(t, output2[i].Bytes(), result2[i].Bytes())
+	}
+}
+
+func TestSubAssignPolyError(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly1 := polynomial{
+		nil,
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+
+	output, err := poly1.Sub(poly2)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
+
+func TestMulAssignPoly(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	// Test polynomial with equal length
+	poly1 := polynomial{
+		curve.Scalar.New(3),
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+
+	output, err := poly1.Mul(poly2)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	result := []curves.Scalar{
+		curve.Scalar.New(3),
+		curve.Scalar.New(8),
+		curve.Scalar.New(14),
+		curve.Scalar.New(8),
+		curve.Scalar.New(3),
+	}
+	for i := 0; i < len(result); i++ {
+		require.Equal(t, output[i].Bytes(), result[i].Bytes())
+	}
+
+	// Test polynomials with unequal length
+	poly3 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+	}
+	output2, err := poly1.Mul(poly3)
+	require.NoError(t, err)
+	require.NotNil(t, output2)
+	result2 := []curves.Scalar{
+		curve.Scalar.New(3),
+		curve.Scalar.New(8),
+		curve.Scalar.New(5),
+		curve.Scalar.New(2),
+	}
+	require.Equal(t, len(output2), 4)
+	for i := 0; i < len(output2); i++ {
+		require.Equal(t, output2[i].Bytes(), result2[i].Bytes())
+	}
+}
+
+func TestMulAssignPolyError(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly1 := polynomial{
+		nil,
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	poly2 := polynomial{
+		curve.Scalar.New(1),
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+	}
+	output, err := poly1.Mul(poly2)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
+
+func TestMulValueAssignPoly(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomial{
+		curve.Scalar.New(3),
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	rhs := curve.Scalar.New(3)
+	output, err := poly.MulScalar(rhs)
+	require.NoError(t, err)
+	require.NotNil(t, output)
+	coefficients2 := []curves.Scalar{
+		curve.Scalar.New(9),
+		curve.Scalar.New(6),
+		curve.Scalar.New(3),
+	}
+	for i := 0; i < len(coefficients2); i++ {
+		require.Equal(t, output[i].Bytes(), coefficients2[i].Bytes())
+	}
+}
+
+func TestMulValueAssignPolyError(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	poly := polynomial{
+		nil,
+		curve.Scalar.New(2),
+		curve.Scalar.New(1),
+	}
+	rhs := curve.Scalar.New(3)
+	output, err := poly.MulScalar(rhs)
+	require.Error(t, err)
+	require.Nil(t, output)
+}
diff --git a/pkg/accumulator/proof.go b/pkg/accumulator/proof.go
new file mode 100644
index 00000000..d81f7890
--- /dev/null
+++ b/pkg/accumulator/proof.go
@@ -0,0 +1,499 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"bytes"
+	crand "crypto/rand"
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// This file implements the zero knowledge proof of knowledge protocol
+// described in section 7 of https://eprint.iacr.org/2020/777.pdf
+// Note: the paper only describes for non-membership witness case, but we don't
+// use non-membership witness. We only implement the membership witness case.
+
+type proofParamsMarshal struct {
+	X     []byte `bare:"x"`
+	Y     []byte `bare:"y"`
+	Z     []byte `bare:"z"`
+	Curve string `bare:"curve"`
+}
+
+// ProofParams contains four distinct public generators of G1 - X, Y, Z
+type ProofParams struct {
+	x, y, z curves.Point
+}
+
+// New samples X, Y, Z, K
+func (p *ProofParams) New(curve *curves.PairingCurve, pk *PublicKey, entropy []byte) (*ProofParams, error) {
+	pkBytes, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	prefix := bytes.Repeat([]byte{0xFF}, 32)
+	data := append(prefix, entropy...)
+	data = append(data, pkBytes...)
+	p.z = curve.Scalar.Point().Hash(data)
+
+	data[0] = 0xFE
+	p.y = curve.Scalar.Point().Hash(data)
+
+	data[0] = 0xFD
+	p.x = curve.Scalar.Point().Hash(data)
+
+	return p, nil
+}
+
+// MarshalBinary converts ProofParams to bytes
+func (p *ProofParams) MarshalBinary() ([]byte, error) {
+	if p.x == nil || p.y == nil || p.z == nil {
+		return nil, fmt.Errorf("some value x, y, or z is nil")
+	}
+	tv := &proofParamsMarshal{
+		X:     p.x.ToAffineCompressed(),
+		Y:     p.y.ToAffineCompressed(),
+		Z:     p.z.ToAffineCompressed(),
+		Curve: p.x.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary converts bytes to ProofParams
+func (p *ProofParams) UnmarshalBinary(data []byte) error {
+	if data == nil {
+		return fmt.Errorf("expected non-zero byte sequence")
+	}
+	tv := new(proofParamsMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+	x, err := curve.NewIdentityPoint().FromAffineCompressed(tv.X)
+	if err != nil {
+		return err
+	}
+	y, err := curve.NewIdentityPoint().FromAffineCompressed(tv.Y)
+	if err != nil {
+		return err
+	}
+	z, err := curve.NewIdentityPoint().FromAffineCompressed(tv.Z)
+	if err != nil {
+		return err
+	}
+	p.x = x
+	p.y = y
+	p.z = z
+	return nil
+}
+
+// MembershipProofCommitting contains value computed in Proof of knowledge and
+// Blinding phases as described in section 7 of https://eprint.iacr.org/2020/777.pdf
+type MembershipProofCommitting struct {
+	eC             curves.Point
+	tSigma         curves.Point
+	tRho           curves.Point
+	deltaSigma     curves.Scalar
+	deltaRho       curves.Scalar
+	blindingFactor curves.Scalar
+	rSigma         curves.Scalar
+	rRho           curves.Scalar
+	rDeltaSigma    curves.Scalar
+	rDeltaRho      curves.Scalar
+	sigma          curves.Scalar
+	rho            curves.Scalar
+	capRSigma      curves.Point
+	capRRho        curves.Point
+	capRDeltaSigma curves.Point
+	capRDeltaRho   curves.Point
+	capRE          curves.Scalar
+	accumulator    curves.Point
+	witnessValue   curves.Scalar
+	xG1            curves.Point
+	yG1            curves.Point
+	zG1            curves.Point
+}
+
+// New initiates values of MembershipProofCommitting
+func (mpc *MembershipProofCommitting) New(
+	witness *MembershipWitness,
+	acc *Accumulator,
+	pp *ProofParams,
+	pk *PublicKey,
+) (*MembershipProofCommitting, error) {
+	// Randomly select σ, ρ
+	sigma := witness.y.Random(crand.Reader)
+	rho := witness.y.Random(crand.Reader)
+
+	// E_C = C + (σ + ρ)Z
+	t := sigma
+	t = t.Add(rho)
+	eC := pp.z
+	eC = eC.Mul(t)
+	eC = eC.Add(witness.c)
+
+	// T_σ = σX
+	tSigma := pp.x
+	tSigma = tSigma.Mul(sigma)
+
+	// T_ρ = ρY
+	tRho := pp.y
+	tRho = tRho.Mul(rho)
+
+	// δ_σ = yσ
+	deltaSigma := witness.y
+	deltaSigma = deltaSigma.Mul(sigma)
+
+	// δ_ρ = yρ
+	deltaRho := witness.y
+	deltaRho = deltaRho.Mul(rho)
+
+	// Randomly pick r_σ,r_ρ,r_δσ,r_δρ
+	rY := witness.y.Random(crand.Reader)
+	rSigma := witness.y.Random(crand.Reader)
+	rRho := witness.y.Random(crand.Reader)
+	rDeltaSigma := witness.y.Random(crand.Reader)
+	rDeltaRho := witness.y.Random(crand.Reader)
+
+	// R_σ = r_σ X
+	capRSigma := pp.x
+	capRSigma = capRSigma.Mul(rSigma)
+
+	// R_ρ = ρY
+	capRRho := pp.y
+	capRRho = capRRho.Mul(rRho)
+
+	// R_δσ = r_y T_σ - r_δσ X
+	negX := pp.x
+	negX = negX.Neg()
+	capRDeltaSigma := tSigma.Mul(rY)
+	capRDeltaSigma = capRDeltaSigma.Add(negX.Mul(rDeltaSigma))
+
+	// R_δρ = r_y T_ρ - r_δρ Y
+	negY := pp.y
+	negY = negY.Neg()
+	capRDeltaRho := tRho.Mul(rY)
+	capRDeltaRho = capRDeltaRho.Add(negY.Mul(rDeltaRho))
+
+	// P~
+	g2 := pk.value.Generator()
+
+	// -r_δσ - r_δρ
+	exp := rDeltaSigma
+	exp = exp.Add(rDeltaRho)
+	exp = exp.Neg()
+
+	// -r_σ - r_ρ
+	exp2 := rSigma
+	exp2 = exp2.Add(rRho)
+	exp2 = exp2.Neg()
+
+	// rY * eC
+	rYeC := eC.Mul(rY)
+
+	// (-r_δσ - r_δρ)*Z
+	expZ := pp.z.Mul(exp)
+
+	// (-r_σ - r_ρ)*Z
+	exp2Z := pp.z.Mul(exp2)
+
+	// Prepare
+	rYeCPrep := rYeC.(curves.PairingPoint)
+	g2Prep := g2.(curves.PairingPoint)
+	expZPrep := expZ.(curves.PairingPoint)
+	exp2ZPrep := exp2Z.(curves.PairingPoint)
+	pkPrep := pk.value
+
+	// Pairing
+	capRE := g2Prep.MultiPairing(rYeCPrep, g2Prep, expZPrep, g2Prep, exp2ZPrep, pkPrep)
+
+	return &MembershipProofCommitting{
+		eC,
+		tSigma,
+		tRho,
+		deltaSigma,
+		deltaRho,
+		rY,
+		rSigma,
+		rRho,
+		rDeltaSigma,
+		rDeltaRho,
+		sigma,
+		rho,
+		capRSigma,
+		capRRho,
+		capRDeltaSigma,
+		capRDeltaRho,
+		capRE,
+		acc.value,
+		witness.y,
+		pp.x,
+		pp.y,
+		pp.z,
+	}, nil
+}
+
+// GetChallenge returns bytes that need to be hashed for generating challenge.
+// V || Ec || T_sigma || T_rho || R_E || R_sigma || R_rho || R_delta_sigma || R_delta_rho
+func (mpc MembershipProofCommitting) GetChallengeBytes() []byte {
+	res := mpc.accumulator.ToAffineCompressed()
+	res = append(res, mpc.eC.ToAffineCompressed()...)
+	res = append(res, mpc.tSigma.ToAffineCompressed()...)
+	res = append(res, mpc.tRho.ToAffineCompressed()...)
+	res = append(res, mpc.capRE.Bytes()...)
+	res = append(res, mpc.capRSigma.ToAffineCompressed()...)
+	res = append(res, mpc.capRRho.ToAffineCompressed()...)
+	res = append(res, mpc.capRDeltaSigma.ToAffineCompressed()...)
+	res = append(res, mpc.capRDeltaRho.ToAffineCompressed()...)
+	return res
+}
+
+// GenProof computes the s values for Fiat-Shamir and return the actual
+// proof to be sent to the verifier given the challenge c.
+func (mpc *MembershipProofCommitting) GenProof(c curves.Scalar) *MembershipProof {
+	// s_y = r_y + c*y
+	sY := schnorr(mpc.blindingFactor, mpc.witnessValue, c)
+	// s_σ = r_σ + c*σ
+	sSigma := schnorr(mpc.rSigma, mpc.sigma, c)
+	// s_ρ = r_ρ + c*ρ
+	sRho := schnorr(mpc.rRho, mpc.rho, c)
+	// s_δσ = rδσ + c*δ_σ
+	sDeltaSigma := schnorr(mpc.rDeltaSigma, mpc.deltaSigma, c)
+	// s_δρ = rδρ + c*δ_ρ
+	sDeltaRho := schnorr(mpc.rDeltaRho, mpc.deltaRho, c)
+
+	return &MembershipProof{
+		mpc.eC,
+		mpc.tSigma,
+		mpc.tRho,
+		sSigma,
+		sRho,
+		sDeltaSigma,
+		sDeltaRho,
+		sY,
+	}
+}
+
+func schnorr(r, v, challenge curves.Scalar) curves.Scalar {
+	res := v
+	res = res.Mul(challenge)
+	res = res.Add(r)
+	return res
+}
+
+type membershipProofMarshal struct {
+	EC          []byte `bare:"e_c"`
+	TSigma      []byte `bare:"t_sigma"`
+	TRho        []byte `bare:"t_rho"`
+	SSigma      []byte `bare:"s_sigma"`
+	SRho        []byte `bare:"s_rho"`
+	SDeltaSigma []byte `bare:"s_delta_sigma"`
+	SDeltaRho   []byte `bare:"s_delta_rho"`
+	SY          []byte `bare:"s_y"`
+	Curve       string `bare:"curve"`
+}
+
+// MembershipProof contains values in the proof to be verified
+type MembershipProof struct {
+	eC          curves.Point
+	tSigma      curves.Point
+	tRho        curves.Point
+	sSigma      curves.Scalar
+	sRho        curves.Scalar
+	sDeltaSigma curves.Scalar
+	sDeltaRho   curves.Scalar
+	sY          curves.Scalar
+}
+
+// Finalize computes values in the proof to be verified.
+func (mp *MembershipProof) Finalize(acc *Accumulator, pp *ProofParams, pk *PublicKey, challenge curves.Scalar) *MembershipProofFinal {
+	// R_σ = s_δ X + c T_σ
+	negTSigma := mp.tSigma
+	negTSigma = negTSigma.Neg()
+	capRSigma := pp.x.Mul(mp.sSigma)
+	capRSigma = capRSigma.Add(negTSigma.Mul(challenge))
+
+	// R_ρ = s_ρ Y + c T_ρ
+	negTRho := mp.tRho
+	negTRho = negTRho.Neg()
+	capRRho := pp.y.Mul(mp.sRho)
+	capRRho = capRRho.Add(negTRho.Mul(challenge))
+
+	// R_δσ =  s_y T_σ - s_δσ X
+	negX := pp.x
+	negX = negX.Neg()
+	capRDeltaSigma := mp.tSigma.Mul(mp.sY)
+	capRDeltaSigma = capRDeltaSigma.Add(negX.Mul(mp.sDeltaSigma))
+
+	// R_δρ =  s_y T_ρ - s_δρ Y
+	negY := pp.y
+	negY = negY.Neg()
+	capRDeltaRho := mp.tRho.Mul(mp.sY)
+	capRDeltaRho = capRDeltaRho.Add(negY.Mul(mp.sDeltaRho))
+
+	// tildeP
+	g2 := pk.value.Generator()
+
+	// Compute capRE, the pairing
+	// E_c * s_y
+	eCsY := mp.eC.Mul(mp.sY)
+
+	// (-s_delta_sigma - s_delta_rho) * Z
+	exp := mp.sDeltaSigma
+	exp = exp.Add(mp.sDeltaRho)
+	exp = exp.Neg()
+	expZ := pp.z.Mul(exp)
+
+	// (-c) * V
+	exp = challenge.Neg()
+	expV := acc.value.Mul(exp)
+
+	// E_c * s_y + (-s_delta_sigma - s_delta_rho) * Z + (-c) * V
+	lhs := eCsY.Add(expZ).Add(expV)
+
+	// (-s_sigma - s_rho) * Z
+	exp = mp.sSigma
+	exp = exp.Add(mp.sRho)
+	exp = exp.Neg()
+	expZ2 := pp.z.Mul(exp)
+
+	// E_c * c
+	cEc := mp.eC.Mul(challenge)
+
+	// (-s_sigma - s_rho) * Z + E_c * c
+	rhs := cEc.Add(expZ2)
+
+	// Prepare
+	lhsPrep := lhs.(curves.PairingPoint)
+	g2Prep := g2.(curves.PairingPoint)
+	rhsPrep := rhs.(curves.PairingPoint)
+	pkPrep := pk.value
+
+	// capRE
+	capRE := g2Prep.MultiPairing(lhsPrep, g2Prep, rhsPrep, pkPrep)
+
+	return &MembershipProofFinal{
+		acc.value,
+		mp.eC,
+		mp.tSigma,
+		mp.tRho,
+		capRE,
+		capRSigma,
+		capRRho,
+		capRDeltaSigma,
+		capRDeltaRho,
+	}
+}
+
+// MarshalBinary converts MembershipProof to bytes
+func (mp MembershipProof) MarshalBinary() ([]byte, error) {
+	tv := &membershipProofMarshal{
+		EC:          mp.eC.ToAffineCompressed(),
+		TSigma:      mp.tSigma.ToAffineCompressed(),
+		TRho:        mp.tRho.ToAffineCompressed(),
+		SSigma:      mp.sSigma.Bytes(),
+		SRho:        mp.sRho.Bytes(),
+		SDeltaSigma: mp.sDeltaSigma.Bytes(),
+		SDeltaRho:   mp.sDeltaRho.Bytes(),
+		SY:          mp.sY.Bytes(),
+		Curve:       mp.eC.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary converts bytes to MembershipProof
+func (mp *MembershipProof) UnmarshalBinary(data []byte) error {
+	if data == nil {
+		return fmt.Errorf("expected non-zero byte sequence")
+	}
+	tv := new(membershipProofMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+	eC, err := curve.NewIdentityPoint().FromAffineCompressed(tv.EC)
+	if err != nil {
+		return err
+	}
+	tSigma, err := curve.NewIdentityPoint().FromAffineCompressed(tv.TSigma)
+	if err != nil {
+		return err
+	}
+	tRho, err := curve.NewIdentityPoint().FromAffineCompressed(tv.TRho)
+	if err != nil {
+		return err
+	}
+	sSigma, err := curve.NewScalar().SetBytes(tv.SSigma)
+	if err != nil {
+		return err
+	}
+	sRho, err := curve.NewScalar().SetBytes(tv.SRho)
+	if err != nil {
+		return err
+	}
+	sDeltaSigma, err := curve.NewScalar().SetBytes(tv.SDeltaSigma)
+	if err != nil {
+		return err
+	}
+	sDeltaRho, err := curve.NewScalar().SetBytes(tv.SDeltaRho)
+	if err != nil {
+		return err
+	}
+	sY, err := curve.NewScalar().SetBytes(tv.SY)
+	if err != nil {
+		return err
+	}
+
+	mp.eC = eC
+	mp.tSigma = tSigma
+	mp.tRho = tRho
+	mp.sSigma = sSigma
+	mp.sRho = sRho
+	mp.sDeltaSigma = sDeltaSigma
+	mp.sDeltaRho = sDeltaRho
+	mp.sY = sY
+
+	return nil
+}
+
+// MembershipProofFinal contains values that are input to Fiat-Shamir Heuristic
+type MembershipProofFinal struct {
+	accumulator    curves.Point
+	eC             curves.Point
+	tSigma         curves.Point
+	tRho           curves.Point
+	capRE          curves.Scalar
+	capRSigma      curves.Point
+	capRRho        curves.Point
+	capRDeltaSigma curves.Point
+	capRDeltaRho   curves.Point
+}
+
+// GetChallenge computes Fiat-Shamir Heuristic taking input values of MembershipProofFinal
+func (m MembershipProofFinal) GetChallenge(curve *curves.PairingCurve) curves.Scalar {
+	res := m.accumulator.ToAffineCompressed()
+	res = append(res, m.eC.ToAffineCompressed()...)
+	res = append(res, m.tSigma.ToAffineCompressed()...)
+	res = append(res, m.tRho.ToAffineCompressed()...)
+	res = append(res, m.capRE.Bytes()...)
+	res = append(res, m.capRSigma.ToAffineCompressed()...)
+	res = append(res, m.capRRho.ToAffineCompressed()...)
+	res = append(res, m.capRDeltaSigma.ToAffineCompressed()...)
+	res = append(res, m.capRDeltaRho.ToAffineCompressed()...)
+	challenge := curve.Scalar.Hash(res)
+	return challenge
+}
diff --git a/pkg/accumulator/proof_test.go b/pkg/accumulator/proof_test.go
new file mode 100644
index 00000000..8b252eb2
--- /dev/null
+++ b/pkg/accumulator/proof_test.go
@@ -0,0 +1,178 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestProofParamsMarshal(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+
+	params, err := new(ProofParams).New(curve, pk, []byte("entropy"))
+	require.NoError(t, err)
+	require.NotNil(t, params.x)
+	require.NotNil(t, params.y)
+	require.NotNil(t, params.z)
+
+	bytes, err := params.MarshalBinary()
+	require.NoError(t, err)
+	require.NotNil(t, bytes)
+
+	params2 := &ProofParams{
+		curve.PointG1.Generator(),
+		curve.PointG1.Generator(),
+		curve.PointG1.Generator(),
+	}
+	err = params2.UnmarshalBinary(bytes)
+	require.NoError(t, err)
+	require.Equal(t, params.x, params2.x)
+	require.Equal(t, params.y, params2.y)
+	require.Equal(t, params.z, params2.z)
+}
+
+func TestMembershipProof(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+
+	element1 := curve.Scalar.Hash([]byte("3"))
+	element2 := curve.Scalar.Hash([]byte("4"))
+	element3 := curve.Scalar.Hash([]byte("5"))
+	element4 := curve.Scalar.Hash([]byte("6"))
+	element5 := curve.Scalar.Hash([]byte("7"))
+	element6 := curve.Scalar.Hash([]byte("8"))
+	element7 := curve.Scalar.Hash([]byte("9"))
+	elements := []Element{element1, element2, element3, element4, element5, element6, element7}
+
+	// Initiate a new accumulator
+	acc, err := new(Accumulator).WithElements(curve, sk, elements)
+	require.NoError(t, err)
+	require.NotNil(t, acc.value)
+
+	// Initiate a new membership witness for value elements[3]
+	wit, err := new(MembershipWitness).New(elements[3], acc, sk)
+	require.NoError(t, err)
+	require.Equal(t, wit.y, elements[3])
+
+	// Create proof parameters, which contains randomly sampled G1 points X, Y, Z, K
+	params, err := new(ProofParams).New(curve, pk, []byte("entropy"))
+	require.NoError(t, err)
+	require.NotNil(t, params.x)
+	require.NotNil(t, params.y)
+	require.NotNil(t, params.z)
+
+	mpc, err := new(MembershipProofCommitting).New(wit, acc, params, pk)
+	require.NoError(t, err)
+	testMPC(t, mpc)
+
+	challenge := curve.Scalar.Hash(mpc.GetChallengeBytes())
+	require.NotNil(t, challenge)
+
+	proof := mpc.GenProof(challenge)
+	require.NotNil(t, proof)
+	testProof(t, proof)
+
+	finalProof := proof.Finalize(acc, params, pk, challenge)
+	require.NotNil(t, finalProof)
+	testFinalProof(t, finalProof)
+
+	challenge2 := finalProof.GetChallenge(curve)
+	require.Equal(t, challenge, challenge2)
+
+	// Check we can still have a valid proof even if accumulator and witness are updated
+	data1 := curve.Scalar.Hash([]byte("1"))
+	data2 := curve.Scalar.Hash([]byte("2"))
+	data3 := curve.Scalar.Hash([]byte("3"))
+	data4 := curve.Scalar.Hash([]byte("4"))
+	data5 := curve.Scalar.Hash([]byte("5"))
+	data := []Element{data1, data2, data3, data4, data5}
+	additions := data[0:2]
+	deletions := data[2:5]
+	_, coefficients, err := acc.Update(sk, additions, deletions)
+	require.NoError(t, err)
+	require.NotNil(t, coefficients)
+
+	_, err = wit.BatchUpdate(additions, deletions, coefficients)
+	require.NoError(t, err)
+
+	newParams, err := new(ProofParams).New(curve, pk, []byte("entropy"))
+	require.NoError(t, err)
+	require.NotNil(t, newParams.x)
+	require.NotNil(t, newParams.y)
+	require.NotNil(t, newParams.z)
+
+	newMPC, err := new(MembershipProofCommitting).New(wit, acc, newParams, pk)
+	require.NoError(t, err)
+	testMPC(t, newMPC)
+
+	challenge3 := curve.Scalar.Hash(newMPC.GetChallengeBytes())
+	require.NotNil(t, challenge3)
+
+	newProof := newMPC.GenProof(challenge3)
+	require.NotNil(t, newProof)
+	testProof(t, newProof)
+
+	newFinalProof := newProof.Finalize(acc, newParams, pk, challenge3)
+	require.NotNil(t, newFinalProof)
+	testFinalProof(t, newFinalProof)
+
+	challenge4 := newFinalProof.GetChallenge(curve)
+	require.Equal(t, challenge3, challenge4)
+}
+
+func testMPC(t *testing.T, mpc *MembershipProofCommitting) {
+	require.NotNil(t, mpc.eC)
+	require.NotNil(t, mpc.tSigma)
+	require.NotNil(t, mpc.tRho)
+	require.NotNil(t, mpc.deltaSigma)
+	require.NotNil(t, mpc.deltaRho)
+	require.NotNil(t, mpc.blindingFactor)
+	require.NotNil(t, mpc.rSigma)
+	require.NotNil(t, mpc.rRho)
+	require.NotNil(t, mpc.rDeltaSigma)
+	require.NotNil(t, mpc.rDeltaRho)
+	require.NotNil(t, mpc.sigma)
+	require.NotNil(t, mpc.rho)
+	require.NotNil(t, mpc.capRSigma)
+	require.NotNil(t, mpc.capRRho)
+	require.NotNil(t, mpc.capRDeltaSigma)
+	require.NotNil(t, mpc.capRDeltaRho)
+	require.NotNil(t, mpc.capRE)
+	require.NotNil(t, mpc.accumulator)
+	require.NotNil(t, mpc.witnessValue)
+	require.NotNil(t, mpc.xG1)
+	require.NotNil(t, mpc.yG1)
+	require.NotNil(t, mpc.zG1)
+}
+
+func testProof(t *testing.T, proof *MembershipProof) {
+	require.NotNil(t, proof.eC)
+	require.NotNil(t, proof.tSigma)
+	require.NotNil(t, proof.tRho)
+	require.NotNil(t, proof.sSigma)
+	require.NotNil(t, proof.sRho)
+	require.NotNil(t, proof.sDeltaSigma)
+	require.NotNil(t, proof.sDeltaRho)
+	require.NotNil(t, proof.sY)
+}
+
+func testFinalProof(t *testing.T, finalProof *MembershipProofFinal) {
+	require.NotNil(t, finalProof.accumulator)
+	require.NotNil(t, finalProof.eC)
+	require.NotNil(t, finalProof.tSigma)
+	require.NotNil(t, finalProof.tRho)
+	require.NotNil(t, finalProof.capRE)
+	require.NotNil(t, finalProof.capRSigma)
+	require.NotNil(t, finalProof.capRRho)
+	require.NotNil(t, finalProof.capRDeltaSigma)
+	require.NotNil(t, finalProof.capRDeltaRho)
+}
diff --git a/pkg/accumulator/witness.go b/pkg/accumulator/witness.go
new file mode 100644
index 00000000..2b881bf5
--- /dev/null
+++ b/pkg/accumulator/witness.go
@@ -0,0 +1,363 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// MembershipWitness contains the witness c and the value y respect to the accumulator state.
+type MembershipWitness struct {
+	c curves.Point
+	y curves.Scalar
+}
+
+// New creates a new membership witness
+func (mw *MembershipWitness) New(y Element, acc *Accumulator, sk *SecretKey) (*MembershipWitness, error) {
+	if acc.value == nil || acc.value.IsIdentity() {
+		return nil, fmt.Errorf("value of accumulator should not be nil")
+	}
+	if sk.value == nil || sk.value.IsZero() {
+		return nil, fmt.Errorf("secret key should not be nil")
+	}
+	if y == nil || y.IsZero() {
+		return nil, fmt.Errorf("y should not be nil")
+	}
+	newAcc := &Accumulator{acc.value}
+	_, err := newAcc.Remove(sk, y)
+	if err != nil {
+		return nil, err
+	}
+	mw.c = newAcc.value
+	mw.y = y.Add(y.Zero())
+	return mw, nil
+}
+
+// Verify the MembershipWitness mw is a valid witness as per section 4 in
+// <https://eprint.iacr.org/2020/777>
+func (mw MembershipWitness) Verify(pk *PublicKey, acc *Accumulator) error {
+	if mw.c == nil || mw.y == nil || mw.c.IsIdentity() || mw.y.IsZero() {
+		return fmt.Errorf("c and y should not be nil")
+	}
+
+	if pk.value == nil || pk.value.IsIdentity() {
+		return fmt.Errorf("invalid public key")
+	}
+	if acc.value == nil || acc.value.IsIdentity() {
+		return fmt.Errorf("accumulator value should not be nil")
+	}
+
+	// Set -tildeP
+	g2 := pk.value.Generator().(curves.PairingPoint)
+
+	// y*tildeP + tildeQ, tildeP is a G2 generator.
+	p := g2.Mul(mw.y).Add(pk.value).(curves.PairingPoint)
+
+	// Prepare
+	witness := mw.c.(curves.PairingPoint)
+	v := acc.value.Neg().(curves.PairingPoint)
+
+	// Check e(witness, y*tildeP + tildeQ) * e(-acc, tildeP) == Identity
+	result := p.MultiPairing(witness, p, v, g2)
+	if !result.IsOne() {
+		return fmt.Errorf("invalid result")
+	}
+
+	return nil
+}
+
+// ApplyDelta returns C' = dA(y)/dD(y)*C + 1/dD(y) * <Gamma_y, Omega>
+// according to the witness update protocol described in section 4 of
+// https://eprint.iacr.org/2020/777.pdf
+func (mw *MembershipWitness) ApplyDelta(delta *Delta) (*MembershipWitness, error) {
+	if mw.c == nil || mw.y == nil || delta == nil {
+		return nil, fmt.Errorf("y, c or delta should not be nil")
+	}
+
+	// C' = dA(y)/dD(y)*C + 1/dD(y) * <Gamma_y, Omega>
+	mw.c = mw.c.Mul(delta.d).Add(delta.p)
+	return mw, nil
+}
+
+// BatchUpdate performs batch update as described in section 4
+func (mw *MembershipWitness) BatchUpdate(additions []Element, deletions []Element, coefficients []Coefficient) (*MembershipWitness, error) {
+	delta, err := evaluateDelta(mw.y, additions, deletions, coefficients)
+	if err != nil {
+		return nil, err
+	}
+	mw, err = mw.ApplyDelta(delta)
+	if err != nil {
+		return nil, fmt.Errorf("applyDelta fails")
+	}
+	return mw, nil
+}
+
+// MultiBatchUpdate performs multi-batch update using epoch as described in section 4.2
+func (mw *MembershipWitness) MultiBatchUpdate(A [][]Element, D [][]Element, C [][]Coefficient) (*MembershipWitness, error) {
+	delta, err := evaluateDeltas(mw.y, A, D, C)
+	if err != nil {
+		return nil, fmt.Errorf("evaluateDeltas fails")
+	}
+	mw, err = mw.ApplyDelta(delta)
+	if err != nil {
+		return nil, err
+	}
+	return mw, nil
+}
+
+// MarshalBinary converts a membership witness to bytes
+func (mw MembershipWitness) MarshalBinary() ([]byte, error) {
+	if mw.c == nil || mw.y == nil {
+		return nil, fmt.Errorf("c and y value should not be nil")
+	}
+
+	result := append(mw.c.ToAffineCompressed(), mw.y.Bytes()...)
+	tv := &structMarshal{
+		Value: result,
+		Curve: mw.c.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary converts bytes into MembershipWitness
+func (mw *MembershipWitness) UnmarshalBinary(data []byte) error {
+	if data == nil {
+		return fmt.Errorf("input data should not be nil")
+	}
+	tv := new(structMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+
+	ptLength := len(curve.Point.ToAffineCompressed())
+	scLength := len(curve.Scalar.Bytes())
+	expectedLength := ptLength + scLength
+	if len(tv.Value) != expectedLength {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	cValue, err := curve.Point.FromAffineCompressed(tv.Value[:ptLength])
+	if err != nil {
+		return err
+	}
+	yValue, err := curve.Scalar.SetBytes(tv.Value[ptLength:])
+	if err != nil {
+		return err
+	}
+	mw.c = cValue
+	mw.y = yValue
+	return nil
+}
+
+// Delta contains values d and p, where d should be the division dA(y)/dD(y) on some value y
+// p should be equal to 1/dD * <Gamma_y, Omega>
+type Delta struct {
+	d curves.Scalar
+	p curves.Point
+}
+
+// MarshalBinary converts Delta into bytes
+func (d *Delta) MarshalBinary() ([]byte, error) {
+	if d.d == nil || d.p == nil {
+		return nil, fmt.Errorf("d and p should not be nil")
+	}
+	var result []byte
+	result = append(result, d.p.ToAffineCompressed()...)
+	result = append(result, d.d.Bytes()...)
+	tv := &structMarshal{
+		Value: result,
+		Curve: d.p.CurveName(),
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary converts data into Delta
+func (d *Delta) UnmarshalBinary(data []byte) error {
+	if data == nil {
+		return fmt.Errorf("expected non-zero byte sequence")
+	}
+
+	tv := new(structMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("invalid curve")
+	}
+
+	ptLength := len(curve.Point.ToAffineCompressed())
+	scLength := len(curve.Scalar.Bytes())
+	expectedLength := ptLength + scLength
+	if len(tv.Value) != expectedLength {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	pValue, err := curve.NewIdentityPoint().FromAffineCompressed(tv.Value[:ptLength])
+	if err != nil {
+		return err
+	}
+	dValue, err := curve.NewScalar().SetBytes(tv.Value[ptLength:])
+	if err != nil {
+		return err
+	}
+	if err != nil {
+		return err
+	}
+	d.d = dValue
+	d.p = pValue
+	return nil
+}
+
+// evaluateDeltas compute values used for membership witness batch update with epoch
+// as described in section 4.2, page 11 of https://eprint.iacr.org/2020/777.pdf
+func evaluateDeltas(y Element, A [][]Element, D [][]Element, C [][]Coefficient) (*Delta, error) {
+	if len(A) != len(D) || len(A) != len(C) {
+		return nil, fmt.Errorf("a, d, c should have same length")
+	}
+
+	one := y.One()
+	size := len(A)
+
+	// dA(x) =  ∏ 1..n (yA_i - x)
+	aa := make([]curves.Scalar, 0)
+	// dD(x) = ∏ 1..m (yD_i - x)
+	dd := make([]curves.Scalar, 0)
+
+	a := one
+	d := one
+
+	// dA_{a->b}(y) = ∏ a..b dAs(y)
+	// dD_{a->b}(y) = ∏ a..b dDs(y)
+	for i := 0; i < size; i++ {
+		adds := A[i]
+		dels := D[i]
+
+		// ta = dAs(y)
+		ta, err := dad(adds, y)
+		if err != nil {
+			return nil, fmt.Errorf("dad on additions fails")
+		}
+		// td = dDs(y)
+		td, err := dad(dels, y)
+		if err != nil {
+			return nil, fmt.Errorf("dad on deletions fails")
+		}
+		// ∏ a..b dAs(y)
+		a = a.Mul(ta)
+		// ∏ a..b dDs(y)
+		d = d.Mul(td)
+
+		aa = append(aa, ta)
+		dd = append(dd, td)
+	}
+
+	// If this fails, then this value was removed.
+	d, err := d.Invert()
+	if err != nil {
+		return nil, fmt.Errorf("no inverse exists")
+	}
+
+	// <Gamma_y, Omega>
+	p := make(polynomialPoint, 0, size)
+
+	// Ωi->j+1 = ∑ 1..t (dAt * dDt-1) · Ω
+	for i := 0; i < size; i++ {
+		// t = i+1
+		// ∏^(t-1)_(h=i+1)
+		ddh := one
+
+		// dDi→t−1 (y)
+		for h := 0; h < i; h++ {
+			ddh = ddh.Mul(dd[h])
+		}
+
+		// ∏^(j+1)_(k=t+1)
+		dak := one
+		// dAt->j(y)
+		for k := i + 1; k < size; k++ {
+			dak = dak.Mul(aa[k])
+		}
+
+		// dDi->t-1(y) * dAt->j(y)
+		dak = dak.Mul(ddh)
+		pp := make(polynomialPoint, len(C[i]))
+		for j := 0; j < len(pp); j++ {
+			pp[j] = C[i][j]
+		}
+
+		// dDi->t-1(y) * dAt->j(y) · Ω
+		pp, err := pp.Mul(dak)
+		if err != nil {
+			return nil, fmt.Errorf("pp.Mul fails")
+		}
+
+		p, err = p.Add(pp)
+		if err != nil {
+			return nil, fmt.Errorf("pp.Add fails")
+		}
+	}
+	// dAi->j(y)/dDi->j(y)
+	a = a.Mul(d)
+
+	// Ωi->j(y)
+	v, err := p.evaluate(y)
+	if err != nil {
+		return nil, fmt.Errorf("p.evaluate fails")
+	}
+
+	// (1/dDi->j(y)) * Ωi->j(y)
+	v = v.Mul(d)
+
+	// return
+	return &Delta{d: a, p: v}, nil
+}
+
+// evaluateDelta computes values used for membership witness batch update
+// as described in section 4.1 of https://eprint.iacr.org/2020/777.pdf
+func evaluateDelta(y Element, additions []Element, deletions []Element, coefficients []Coefficient) (*Delta, error) {
+	// dD(y) = ∏ 1..m (yD_i - y), d = 1/dD(y)
+	var err error
+	d, err := dad(deletions, y)
+	if err != nil {
+		return nil, fmt.Errorf("dad fails on deletions")
+	}
+	d, err = d.Invert()
+	if err != nil {
+		return nil, fmt.Errorf("no inverse exists")
+	}
+
+	//dA(y) =  ∏ 1..n (yA_i - y)
+	a, err := dad(additions, y)
+	if err != nil {
+		return nil, fmt.Errorf("dad fails on additions")
+	}
+	// dA(y)/dD(y)
+	a = a.Mul(d)
+
+	// Create a PolynomialG1 from coefficients
+	p := make(polynomialPoint, len(coefficients))
+	for i := 0; i < len(coefficients); i++ {
+		p[i] = coefficients[i]
+	}
+
+	// <Gamma_y, Omega>
+	v, err := p.evaluate(y)
+	if err != nil {
+		return nil, fmt.Errorf("p.evaluate fails")
+	}
+	// 1/dD * <Gamma_y, Omega>
+	v = v.Mul(d)
+
+	return &Delta{d: a, p: v}, nil
+}
diff --git a/pkg/accumulator/witness_test.go b/pkg/accumulator/witness_test.go
new file mode 100644
index 00000000..827da2cb
--- /dev/null
+++ b/pkg/accumulator/witness_test.go
@@ -0,0 +1,227 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package accumulator
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func Test_Membership_Witness_New(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	var seed [32]byte
+	key, _ := new(SecretKey).New(curve, seed[:])
+	acc, _ := new(Accumulator).New(curve)
+	e := curve.Scalar.New(2)
+	mw, err := new(MembershipWitness).New(e, acc, key)
+	require.NoError(t, err)
+	require.NotNil(t, mw.c)
+	require.NotNil(t, mw.y)
+}
+
+func Test_Membership_Witness_Marshal(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	mw := &MembershipWitness{
+		curve.PointG1.Generator().Mul(curve.Scalar.New(10)),
+		curve.Scalar.New(15),
+	}
+	data, err := mw.MarshalBinary()
+	require.NoError(t, err)
+	require.NotNil(t, data)
+	newMW := &MembershipWitness{}
+	err = newMW.UnmarshalBinary(data)
+	require.NoError(t, err)
+	require.Equal(t, mw.c, newMW.c)
+	require.Equal(t, mw.y, newMW.y)
+}
+
+func Test_Membership(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+
+	element1 := curve.Scalar.Hash([]byte("3"))
+	element2 := curve.Scalar.Hash([]byte("4"))
+	element3 := curve.Scalar.Hash([]byte("5"))
+	element4 := curve.Scalar.Hash([]byte("6"))
+	element5 := curve.Scalar.Hash([]byte("7"))
+	element6 := curve.Scalar.Hash([]byte("8"))
+	element7 := curve.Scalar.Hash([]byte("9"))
+	elements := []Element{element1, element2, element3, element4, element5, element6, element7}
+
+	// nm_witness_max works as well if set to value larger than 0 for this test.x
+	acc, err := new(Accumulator).WithElements(curve, sk, elements)
+	require.NoError(t, err)
+	require.NotNil(t, acc.value)
+	require.False(t, acc.value.IsIdentity())
+	require.True(t, acc.value.IsOnCurve())
+	require.NotEqual(t, acc.value, curve.NewG1GeneratorPoint())
+
+	wit, err := new(MembershipWitness).New(elements[3], acc, sk)
+	require.NoError(t, err)
+	require.Equal(t, wit.y, elements[3])
+
+	err = wit.Verify(pk, acc)
+	require.NoError(t, err)
+
+	// Test wrong cases, forge a wrong witness
+	wrongWit := MembershipWitness{
+		curve.PointG1.Identity(),
+		curve.Scalar.One(),
+	}
+	err = wrongWit.Verify(pk, acc)
+	require.Error(t, err)
+
+	// Test wrong cases, forge a wrong accumulator
+	wrongAcc := &Accumulator{
+		curve.PointG1.Generator(),
+	}
+	err = wit.Verify(pk, wrongAcc)
+	require.Error(t, err)
+}
+
+func Test_Membership_Batch_Update(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+
+	element1 := curve.Scalar.Hash([]byte("3"))
+	element2 := curve.Scalar.Hash([]byte("4"))
+	element3 := curve.Scalar.Hash([]byte("5"))
+	element4 := curve.Scalar.Hash([]byte("6"))
+	element5 := curve.Scalar.Hash([]byte("7"))
+	element6 := curve.Scalar.Hash([]byte("8"))
+	element7 := curve.Scalar.Hash([]byte("9"))
+	elements := []Element{element1, element2, element3, element4, element5, element6, element7}
+
+	// nm_witness_max works as well if set to value larger than 0 for this test.
+	acc, err := new(Accumulator).WithElements(curve, sk, elements)
+	require.NoError(t, err)
+	require.NotNil(t, acc.value)
+
+	wit, err := new(MembershipWitness).New(elements[3], acc, sk)
+	require.NoError(t, err)
+	require.Equal(t, wit.y, elements[3])
+
+	err = wit.Verify(pk, acc)
+	require.Nil(t, err)
+
+	data1 := curve.Scalar.Hash([]byte("1"))
+	data2 := curve.Scalar.Hash([]byte("2"))
+	data3 := curve.Scalar.Hash([]byte("3"))
+	data4 := curve.Scalar.Hash([]byte("4"))
+	data5 := curve.Scalar.Hash([]byte("5"))
+	data := []Element{data1, data2, data3, data4, data5}
+	additions := data[0:2]
+	deletions := data[2:5]
+	_, coefficients, err := acc.Update(sk, additions, deletions)
+	require.NoError(t, err)
+	require.NotNil(t, coefficients)
+
+	_, err = wit.BatchUpdate(additions, deletions, coefficients)
+	require.NoError(t, err)
+	err = wit.Verify(pk, acc)
+	require.Nil(t, err)
+}
+
+func Test_Membership_Multi_Batch_Update(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+
+	element1 := curve.Scalar.Hash([]byte("3"))
+	element2 := curve.Scalar.Hash([]byte("4"))
+	element3 := curve.Scalar.Hash([]byte("5"))
+	element4 := curve.Scalar.Hash([]byte("6"))
+	element5 := curve.Scalar.Hash([]byte("7"))
+	element6 := curve.Scalar.Hash([]byte("8"))
+	element7 := curve.Scalar.Hash([]byte("9"))
+	element8 := curve.Scalar.Hash([]byte("10"))
+	element9 := curve.Scalar.Hash([]byte("11"))
+	element10 := curve.Scalar.Hash([]byte("12"))
+	element11 := curve.Scalar.Hash([]byte("13"))
+	element12 := curve.Scalar.Hash([]byte("14"))
+	element13 := curve.Scalar.Hash([]byte("15"))
+	element14 := curve.Scalar.Hash([]byte("16"))
+	element15 := curve.Scalar.Hash([]byte("17"))
+	element16 := curve.Scalar.Hash([]byte("18"))
+	element17 := curve.Scalar.Hash([]byte("19"))
+	element18 := curve.Scalar.Hash([]byte("20"))
+	elements := []Element{
+		element1,
+		element2,
+		element3,
+		element4,
+		element5,
+		element6,
+		element7,
+		element8,
+		element9,
+		element10,
+		element11,
+		element12,
+		element13,
+		element14,
+		element15,
+		element16,
+		element17,
+		element18,
+	}
+	acc, err := new(Accumulator).WithElements(curve, sk, elements)
+	require.NoError(t, err)
+	require.NotNil(t, acc.value)
+
+	wit, err := new(MembershipWitness).New(elements[3], acc, sk)
+	require.NoError(t, err)
+
+	err = wit.Verify(pk, acc)
+	require.Nil(t, err)
+
+	data1 := curve.Scalar.Hash([]byte("1"))
+	data2 := curve.Scalar.Hash([]byte("2"))
+	data3 := curve.Scalar.Hash([]byte("3"))
+	data4 := curve.Scalar.Hash([]byte("4"))
+	data5 := curve.Scalar.Hash([]byte("5"))
+	data := []Element{data1, data2, data3, data4, data5}
+	adds1 := data[0:2]
+	dels1 := data[2:5]
+	_, coeffs1, err := acc.Update(sk, adds1, dels1)
+	require.NoError(t, err)
+	require.NotNil(t, coeffs1)
+
+	dels2 := elements[8:10]
+	_, coeffs2, err := acc.Update(sk, []Element{}, dels2)
+	require.NoError(t, err)
+	require.NotNil(t, coeffs2)
+
+	dels3 := elements[11:14]
+	_, coeffs3, err := acc.Update(sk, []Element{}, dels3)
+	require.NoError(t, err)
+	require.NotNil(t, coeffs3)
+
+	a := make([][]Element, 3)
+	a[0] = adds1
+	a[1] = []Element{}
+	a[2] = []Element{}
+
+	d := make([][]Element, 3)
+	d[0] = dels1
+	d[1] = dels2
+	d[2] = dels3
+
+	c := make([][]Coefficient, 3)
+	c[0] = coeffs1
+	c[1] = coeffs2
+	c[2] = coeffs3
+
+	_, err = wit.MultiBatchUpdate(a, d, c)
+	require.NoError(t, err)
+
+	err = wit.Verify(pk, acc)
+	require.Nil(t, err)
+}
diff --git a/pkg/core/README.md b/pkg/core/README.md
new file mode 100644
index 00000000..24fbd4e9
--- /dev/null
+++ b/pkg/core/README.md
@@ -0,0 +1,274 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# core
+
+```go
+import "github.com/coinbase/kryptology/pkg/core"
+```
+
+## Index
+
+- [Constants](<#constants>)
+- [Variables](<#variables>)
+- [func Add(x, y, m *big.Int) (*big.Int, error)](<#func-add>)
+- [func AnyNil(values ...*big.Int) bool](<#func-anynil>)
+- [func Commit(msg []byte) (Commitment, *Witness, error)](<#func-commit>)
+- [func ComputeHMAC(f func() hash.Hash, msg []byte, k []byte) ([]byte, error)](<#func-computehmac>)
+- [func ConstantTimeEq(a, b *big.Int) bool](<#func-constanttimeeq>)
+- [func ConstantTimeEqByte(a, b *big.Int) byte](<#func-constanttimeeqbyte>)
+- [func Exp(x, y, m *big.Int) (*big.Int, error)](<#func-exp>)
+- [func ExpandMessageXmd(f func() hash.Hash, msg, DST []byte, lenInBytes int) ([]byte, error)](<#func-expandmessagexmd>)
+- [func FiatShamir(values ...*big.Int) ([]byte, error)](<#func-fiatshamir>)
+- [func GenerateSafePrime(bits uint) (*big.Int, error)](<#func-generatesafeprime>)
+- [func Hash(msg []byte, curve elliptic.Curve) (*big.Int, error)](<#func-hash>)
+- [func I2OSP(b, n int) []byte](<#func-i2osp>)
+- [func In(x, m *big.Int) error](<#func-in>)
+- [func Inv(x, m *big.Int) (*big.Int, error)](<#func-inv>)
+- [func Mul(x, y, m *big.Int) (*big.Int, error)](<#func-mul>)
+- [func Neg(x, m *big.Int) (*big.Int, error)](<#func-neg>)
+- [func OS2IP(os []byte) *big.Int](<#func-os2ip>)
+- [func Open(c Commitment, d Witness) (bool, error)](<#func-open>)
+- [func Rand(m *big.Int) (*big.Int, error)](<#func-rand>)
+- [type Commitment](<#type-commitment>)
+- [type HashField](<#type-hashfield>)
+- [type Params](<#type-params>)
+- [type Witness](<#type-witness>)
+  - [func (w Witness) MarshalJSON() ([]byte, error)](<#func-witness-marshaljson>)
+  - [func (w *Witness) UnmarshalJSON(data []byte) error](<#func-witness-unmarshaljson>)
+
+
+## Constants
+
+Size of random values and hash outputs are determined by our hash function
+
+```go
+const Size = sha256.Size
+```
+
+## Variables
+
+```go
+var (
+    // Zero is additive identity in the set of integers
+    Zero = big.NewInt(0)
+
+    // One is the multiplicative identity in the set of integers
+    One = big.NewInt(1)
+
+    // Two is the odd prime
+    Two = big.NewInt(2)
+)
+```
+
+## func [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L85>)
+
+```go
+func Add(x, y, m *big.Int) (*big.Int, error)
+```
+
+Add \(modular addition\): z = x\+y \(modulo m\)
+
+## func [AnyNil](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L168>)
+
+```go
+func AnyNil(values ...*big.Int) bool
+```
+
+AnyNil determines if any of values are nil
+
+## func [Commit](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L60>)
+
+```go
+func Commit(msg []byte) (Commitment, *Witness, error)
+```
+
+Commit to a given message\. Uses SHA256 as the hash function\.
+
+## func [ComputeHMAC](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L101>)
+
+```go
+func ComputeHMAC(f func() hash.Hash, msg []byte, k []byte) ([]byte, error)
+```
+
+ComputeHMAC computes HMAC\(hash\_fn\, msg\, key\) Takes in a hash function to use for HMAC
+
+## func [ConstantTimeEq](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L65>)
+
+```go
+func ConstantTimeEq(a, b *big.Int) bool
+```
+
+ConstantTimeEq determines if a\, b have identical byte serialization and uses the crypto/subtle package to get a constant time comparison over byte representations\.
+
+## func [ConstantTimeEqByte](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L35>)
+
+```go
+func ConstantTimeEqByte(a, b *big.Int) byte
+```
+
+ConstantTimeEqByte determines if a\, b have identical byte serialization and signs\. It uses the crypto/subtle package to get a constant time comparison over byte representations\. Return value is a byte which may be useful in bitwise operations\. Returns 0x1 if the two values have the identical sign and byte representation; 0x0 otherwise\.
+
+## func [Exp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L114>)
+
+```go
+func Exp(x, y, m *big.Int) (*big.Int, error)
+```
+
+Exp \(modular exponentiation\): z = x^y \(modulo m\)
+
+## func [ExpandMessageXmd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L123>)
+
+```go
+func ExpandMessageXmd(f func() hash.Hash, msg, DST []byte, lenInBytes int) ([]byte, error)
+```
+
+## func [FiatShamir](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L247>)
+
+```go
+func FiatShamir(values ...*big.Int) ([]byte, error)
+```
+
+fiatShamir computes the HKDF over many values iteratively such that each value is hashed separately and based on preceding values
+
+### The first value is computed as okm\_0 = KDF\(f || value\) where
+f is a byte slice of 32 0xFF
+salt is zero\-filled byte slice with length equal to the hash output length
+info is the protocol name
+okm is the 32 byte output
+
+The each subsequent iteration is computed by as okm\_i = KDF\(f\_i || value || okm\_\{i\-1\}\) where f\_i = 2^b \- 1 \- i such that there are 0xFF bytes prior to the value\. f\_1 changes the first byte to 0xFE\, f\_2 to 0xFD\. The previous okm is appended to the value to provide cryptographic domain separation See https://signal.org/docs/specifications/x3dh/#cryptographic-notation and https://signal.org/docs/specifications/xeddsa/#hash-functions for more details\. This uses the KDF function similar to X3DH for each \`value\` But changes the key just like XEdDSA where the prefix bytes change by a single bit
+
+## func [GenerateSafePrime](<https://github.com/coinbase/kryptology/blob/master/pkg/core/primes.go#L18>)
+
+```go
+func GenerateSafePrime(bits uint) (*big.Int, error)
+```
+
+GenerateSafePrime creates a prime number \`p\` where \(\`p\`\-1\)/2 is also prime with at least \`bits\`
+
+## func [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L220>)
+
+```go
+func Hash(msg []byte, curve elliptic.Curve) (*big.Int, error)
+```
+
+## func [I2OSP](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L78>)
+
+```go
+func I2OSP(b, n int) []byte
+```
+
+## func [In](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L71>)
+
+```go
+func In(x, m *big.Int) error
+```
+
+In determines ring membership before modular reduction: x ∈ Z\_m returns nil if 0 ≤ x \< m
+
+## func [Inv](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L133>)
+
+```go
+func Inv(x, m *big.Int) (*big.Int, error)
+```
+
+Inv \(modular inverse\): returns y such that xy = 1 \(modulo m\)\.
+
+## func [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L99>)
+
+```go
+func Mul(x, y, m *big.Int) (*big.Int, error)
+```
+
+Mul \(modular multiplication\): z = x\*y \(modulo m\)
+
+## func [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L123>)
+
+```go
+func Neg(x, m *big.Int) (*big.Int, error)
+```
+
+Neg \(modular negation\): z = \-x \(modulo m\)
+
+## func [OS2IP](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L89>)
+
+```go
+func OS2IP(os []byte) *big.Int
+```
+
+## func [Open](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L85>)
+
+```go
+func Open(c Commitment, d Witness) (bool, error)
+```
+
+Open a commitment and return true if the commitment/decommitment pair are valid\. reference: spec\.§2\.4: Commitment Scheme
+
+## func [Rand](<https://github.com/coinbase/kryptology/blob/master/pkg/core/mod.go#L145>)
+
+```go
+func Rand(m *big.Int) (*big.Int, error)
+```
+
+Rand generates a cryptographically secure random integer in the range: 1 \< r \< m\.
+
+## type [Commitment](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L26>)
+
+Commitment to a given message which can be later revealed\. This is sent to and held by a verifier until the corresponding witness is provided\.
+
+```go
+type Commitment []byte
+```
+
+## type [HashField](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L24-L29>)
+
+```go
+type HashField struct {
+    // F_p^k
+    Order           *big.Int // p^k
+    Characteristic  *big.Int // p
+    ExtensionDegree *big.Int // k
+}
+```
+
+## type [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/core/hash.go#L31-L36>)
+
+```go
+type Params struct {
+    F                 *HashField
+    SecurityParameter int
+    Hash              func() hash.Hash
+    L                 int
+}
+```
+
+## type [Witness](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L30-L33>)
+
+Witness is sent to and opened by the verifier\. This proves that committed message hasn't been altered by later information\.
+
+```go
+type Witness struct {
+    Msg []byte
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Witness\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L43>)
+
+```go
+func (w Witness) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON encodes Witness in JSON
+
+### func \(\*Witness\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/commit.go#L48>)
+
+```go
+func (w *Witness) UnmarshalJSON(data []byte) error
+```
+
+UnmarshalJSON decodes JSON into a Witness struct
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/commit.go b/pkg/core/commit.go
new file mode 100644
index 00000000..8cfe0423
--- /dev/null
+++ b/pkg/core/commit.go
@@ -0,0 +1,115 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"crypto/hmac"
+	crand "crypto/rand"
+	"crypto/sha256"
+	"crypto/subtle"
+	"encoding/json"
+	"fmt"
+	"hash"
+)
+
+// Size of random values and hash outputs are determined by our hash function
+const Size = sha256.Size
+
+type (
+	// Commitment to a given message which can be later revealed.
+	// This is sent to and held by a verifier until the corresponding
+	// witness is provided.
+	Commitment []byte
+
+	// Witness is sent to and opened by the verifier. This proves that
+	// committed message hasn't been altered by later information.
+	Witness struct {
+		Msg []byte
+		r   [Size]byte
+	}
+
+	// witnessJSON is used for un/marshaling.
+	witnessJSON struct {
+		Msg []byte
+		R   [Size]byte
+	}
+)
+
+// MarshalJSON encodes Witness in JSON
+func (w Witness) MarshalJSON() ([]byte, error) {
+	return json.Marshal(witnessJSON{w.Msg, w.r})
+}
+
+// UnmarshalJSON decodes JSON into a Witness struct
+func (w *Witness) UnmarshalJSON(data []byte) error {
+	witness := &witnessJSON{}
+	err := json.Unmarshal(data, witness)
+	if err != nil {
+		return err
+	}
+	w.Msg = witness.Msg
+	w.r = witness.R
+	return nil
+}
+
+// Commit to a given message. Uses SHA256 as the hash function.
+func Commit(msg []byte) (Commitment, *Witness, error) {
+	// Initialize our decommitment
+	d := Witness{msg, [Size]byte{}}
+
+	// Generate a random nonce of the required length
+	n, err := crand.Read(d.r[:])
+	// Ensure no errors retrieving nonce
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Ensure we read all the bytes expected
+	if n != Size {
+		return nil, nil, fmt.Errorf("failed to read %v bytes from crypto/rand: received %v bytes", Size, n)
+	}
+	// Compute the commitment: HMAC(Sha2, msg, key)
+	c, err := ComputeHMAC(sha256.New, msg, d.r[:])
+	if err != nil {
+		return nil, nil, err
+	}
+	return c, &d, nil
+}
+
+// Open a commitment and return true if the commitment/decommitment pair are valid.
+// reference: spec.§2.4: Commitment Scheme
+func Open(c Commitment, d Witness) (bool, error) {
+	// Ensure commitment is well-formed.
+	if len(c) != Size {
+		return false, fmt.Errorf("invalid commitment, wrong length. %v != %v", len(c), Size)
+	}
+
+	// Re-compute the commitment: HMAC(Sha2, msg, key)
+	cʹ, err := ComputeHMAC(sha256.New, d.Msg, d.r[:])
+	if err != nil {
+		return false, err
+	}
+	return subtle.ConstantTimeCompare(cʹ, c) == 1, nil
+}
+
+// ComputeHMAC computes HMAC(hash_fn, msg, key)
+// Takes in a hash function to use for HMAC
+func ComputeHMAC(f func() hash.Hash, msg []byte, k []byte) ([]byte, error) {
+	if f == nil {
+		return nil, fmt.Errorf("hash function cannot be nil")
+	}
+
+	mac := hmac.New(f, k)
+	w, err := mac.Write(msg)
+
+	if w != len(msg) {
+		return nil, fmt.Errorf("bytes written to hash doesn't match expected: %v != %v", w, len(msg))
+	} else if err != nil {
+		return nil, err
+	}
+	return mac.Sum(nil), nil
+}
diff --git a/pkg/core/commit_test.go b/pkg/core/commit_test.go
new file mode 100644
index 00000000..863cf5bd
--- /dev/null
+++ b/pkg/core/commit_test.go
@@ -0,0 +1,374 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"bytes"
+	"encoding/json"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+// An entry into our test table
+type entry struct {
+	// Input
+	msg []byte
+
+	// Result (actual, not expected)
+	commit   Commitment
+	decommit *Witness
+	err      error
+}
+
+// Test inputs and placeholders for results that will be filled in
+// during init()
+var testResults = []entry{
+	{[]byte("This is a test message"), nil, nil, nil},
+	{[]byte("short msg"), nil, nil, nil},
+	{[]byte("This input field is intentionally longer than the SHA256 block size to ensure that the entire message is processed"),
+		nil, nil, nil},
+	{[]byte{0xFB, 0x1A, 0x18, 0x47, 0x39, 0x3C, 0x9F, 0x45, 0x5F, 0x29, 0x4C, 0x51, 0x42, 0x30, 0xA6, 0xB9},
+		nil, nil, nil},
+	// msg = \epsilon (empty string)
+	{[]byte{}, nil, nil, nil},
+	// msg == nil
+	{nil, nil, nil, nil},
+}
+
+// Run our inputs through commit and record the outputs
+func init() {
+	for i := range testResults {
+		entry := &testResults[i]
+		entry.commit, entry.decommit, entry.err = Commit(entry.msg)
+	}
+}
+
+// Computing commitments should never produce errors
+func TestCommitWithoutErrors(t *testing.T) {
+	for _, entry := range testResults {
+		if entry.err != nil {
+			t.Errorf("received Commit(%v): %v", entry.msg, entry.err)
+		}
+	}
+}
+
+// Commitments should be 256b == 64B in length
+func TestCommitmentsAreExpectedLength(t *testing.T) {
+	const expLen = 256 / 8
+	for _, entry := range testResults {
+		if len(entry.commit) != expLen {
+			t.Errorf("commitment is not expected length: %v != %v", len(entry.commit), expLen)
+		}
+	}
+}
+
+// Decommit cannot be nil
+func TestCommmitProducesDecommit(t *testing.T) {
+	for _, entry := range testResults {
+		if entry.decommit == nil {
+			t.Errorf("decommit cannot be nil: Commit(%v)", entry.msg)
+		}
+	}
+}
+
+// Decommit value should contain the same message
+func TestCommmitProducesDecommitWithSameMessage(t *testing.T) {
+	for _, entry := range testResults {
+		if !bytes.Equal(entry.msg, entry.decommit.Msg) {
+			t.Errorf("decommit.msg != msg: %v != %v", entry.msg, entry.decommit.Msg)
+		}
+	}
+}
+
+// Commitments should be unique
+func TestCommmitProducesDistinctCommitments(t *testing.T) {
+	seen := make(map[[Size]byte]bool)
+
+	// Check the pre-computed commitments for uniquness
+	for _, entry := range testResults {
+
+		// Slices cannot be used as hash keys, so we need to copy into
+		// an array. Oh, go-lang.
+		var cee [Size]byte
+		copy(cee[:], entry.commit)
+
+		// Ensure each commit is unique
+		if seen[cee] {
+			t.Errorf("duplicate commit found: %v", cee)
+		}
+		seen[cee] = true
+	}
+}
+
+// Commitments should be unique even for the same message since the nonce is
+// randomly selected
+func TestCommmitDistinctCommitments(t *testing.T) {
+	seen := make(map[[Size]byte]bool)
+	msg := []byte("black lives matter")
+	const iterations = 1000
+
+	// Check the pre-computed commitments for uniquness
+	for i := 0; i < iterations; i++ {
+		// Compute a commitment
+		c, _, err := Commit(msg)
+		if err != nil {
+			t.Error(err)
+		}
+
+		// Slices cannot be used as hash keys, so copy into an array
+		var cee [Size]byte
+		copy(cee[:], []byte(c))
+
+		// Ensure each commit is unique
+		if seen[cee] {
+			t.Errorf("duplicate commit found: %v", cee)
+		}
+		seen[cee] = true
+	}
+}
+
+// Nonces must be 256b = 64B
+func TestCommmitNonceIsExpectedLength(t *testing.T) {
+	const expLen = 256 / 8
+
+	// Check the pre-computed nonces
+	for _, entry := range testResults {
+		if len(entry.decommit.r) != expLen {
+			t.Errorf("nonce is not expected length: %v != %v", len(entry.decommit.r), expLen)
+		}
+	}
+}
+
+// Randomly selected nonces will be unique with overwhelming probability
+func TestCommmitProducesDistinctNonces(t *testing.T) {
+	seen := make(map[[Size]byte]bool)
+	msg := []byte("black lives matter")
+	const iterations = 1000
+
+	// Check the pre-computed commitments for uniquness
+	for i := 0; i < iterations; i++ {
+		// Compute a commitment
+		_, dee, err := Commit(msg)
+		if err != nil {
+			t.Error(err)
+		}
+
+		// Ensure each nonce is unique
+		if seen[dee.r] {
+			t.Errorf("duplicate nonce found: %v", dee.r)
+		}
+		seen[dee.r] = true
+	}
+}
+
+func TestOpenOnValidCommitments(t *testing.T) {
+	for _, entry := range testResults {
+
+		// Open each commitment
+		ok, err := Open(entry.commit, *entry.decommit)
+
+		// There should be no error
+		if err != nil {
+			t.Error(err)
+		}
+
+		// The commitments should verify
+		if !ok {
+			t.Errorf("commitment failed to open: %v", entry.msg)
+		}
+	}
+}
+
+func TestOpenOnModifiedNonce(t *testing.T) {
+	for _, entry := range testResults {
+		dʹ := copyWitness(entry.decommit)
+
+		// Modify the nonce
+		dʹ.r[0] ^= 0x40
+
+		// Open and check for failure
+		ok, err := Open(entry.commit, *dʹ)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+func TestOpenOnZeroPrefixNonce(t *testing.T) {
+	for _, entry := range testResults {
+		dʹ := copyWitness(entry.decommit)
+
+		// Modify the nonce
+		dʹ.r[0] = 0x00
+		dʹ.r[1] = 0x00
+		dʹ.r[2] = 0x00
+		dʹ.r[3] = 0x00
+		dʹ.r[4] = 0x00
+		dʹ.r[5] = 0x00
+		dʹ.r[6] = 0x00
+		dʹ.r[7] = 0x00
+		dʹ.r[8] = 0x00
+		dʹ.r[9] = 0x00
+		dʹ.r[10] = 0x00
+
+		// Open and check for failure
+		ok, err := Open(entry.commit, *dʹ)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// Makes a deep copy of a Witness
+func copyWitness(d *Witness) *Witness {
+	msg := make([]byte, len(d.Msg))
+	var r [Size]byte
+
+	copy(msg, d.Msg)
+	copy(r[:], d.r[:])
+	return &Witness{msg, r}
+}
+
+// Asserts that err != nil, and ok == false.
+func assertFailedOpen(t *testing.T, ok bool, err error) {
+	// There should be no error
+	if err != nil {
+		t.Error(err)
+	}
+
+	// But the commitments should fail
+	if ok {
+		t.Error("commitment was verified but was expected to fail")
+	}
+}
+
+// An unrelated message should fail on open
+func TestOpenOnNewMessage(t *testing.T) {
+	for _, entry := range testResults {
+		dʹ := copyWitness(entry.decommit)
+
+		// Use a distinct message
+		dʹ.Msg = []byte("no one expects the spanish inquisition")
+
+		// Open and check for failure
+		ok, err := Open(entry.commit, *dʹ)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// An appended message should fail on open
+func TestOpenOnAppendedMessage(t *testing.T) {
+	for _, entry := range testResults {
+		dʹ := copyWitness(entry.decommit)
+
+		// Modify the message
+		dʹ.Msg = []byte("no one expects the spanish inquisition")
+
+		// Open and check for failure
+		ok, err := Open(entry.commit, *dʹ)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// A modified message should fail on open
+func TestOpenOnModifiedMessage(t *testing.T) {
+	for _, entry := range testResults {
+		// Skip the empty string message for this test case
+		if len(entry.msg) == 0 {
+			continue
+		}
+
+		// Modify the message _in situ_
+		dʹ := copyWitness(entry.decommit)
+		dʹ.Msg[1] ^= 0x99
+
+		// Open and check for failure
+		ok, err := Open(entry.commit, *dʹ)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// A modified commitment should fail on open
+func TestOpenOnModifiedCommitment(t *testing.T) {
+	for _, entry := range testResults {
+		// Copy and then modify the commitment
+		cʹ := make([]byte, Size)
+		copy(cʹ[:], entry.commit)
+		cʹ[6] ^= 0x33
+
+		// Open and check for failure
+		ok, err := Open(cʹ, *entry.decommit)
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// An empty decommit should fail to open
+func TestOpenOnDefaultDecommitObject(t *testing.T) {
+	for _, entry := range testResults {
+		// Open and check for failure
+		ok, err := Open(entry.commit, Witness{})
+		assertFailedOpen(t, ok, err)
+	}
+}
+
+// A nil commit should return an error
+func TestOpenOnNilCommitment(t *testing.T) {
+	_, err := Open(nil, Witness{})
+	assertError(t, err)
+}
+
+// Verifies that err != nil
+func assertError(t *testing.T, err error) {
+	if err == nil {
+		t.Error("expected an error but received nil")
+	}
+}
+
+// Ill-formed commitment should produce an error
+func TestOpenOnLongCommitment(t *testing.T) {
+	tooLong := make([]byte, Size+1)
+	_, err := Open(tooLong, Witness{})
+	assertError(t, err)
+}
+
+// Ill-formed commitment should produce an error
+func TestOpenOnShortCommitment(t *testing.T) {
+	tooShort := make([]byte, Size-1)
+	_, err := Open(tooShort, Witness{})
+	assertError(t, err)
+}
+
+// Tests that marshal-unmarshal is the identity function
+func TestWitnessMarshalRoundTrip(t *testing.T) {
+	expected := &Witness{
+		[]byte("I'm the dude. So that's what you call me"),
+		[Size]byte{0xAC},
+	}
+
+	// Marhal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	actual := &Witness{}
+	assert.NoError(t, json.Unmarshal(jsonBytes, actual))
+	assert.Equal(t, expected.Msg, actual.Msg)
+	assert.Equal(t, expected.r, actual.r)
+}
+
+// Tests that marshal-unmarshal is the identity function
+func TestCommitmentMarshalRoundTrip(t *testing.T) {
+	expected := Commitment([]byte("That or uh his-dudeness or duder or el duderino."))
+
+	// Marhal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	actual := Commitment{}
+	assert.NoError(t, json.Unmarshal(jsonBytes, &actual))
+	assert.Equal(t, []byte(expected), []byte(actual))
+}
diff --git a/pkg/core/curves/README.md b/pkg/core/curves/README.md
new file mode 100755
index 00000000..84369852
--- /dev/null
+++ b/pkg/core/curves/README.md
@@ -0,0 +1,5329 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# curves
+
+```go
+import "github.com/coinbase/kryptology/pkg/core/curves"
+```
+
+This implementation IS NOT constant time as it leverages math/big for big number operations\.
+
+## Index
+
+- [Constants](<#constants>)
+- [func Ed25519Order() *big.Int](<#func-ed25519order>)
+- [func VerifyEcdsa(pk *EcPoint, hash []byte, sig *EcdsaSignature) bool](<#func-verifyecdsa>)
+- [type Bls12381Scalar](<#type-bls12381scalar>)
+  - [func NewBls12381Scalar() *Bls12381Scalar](<#func-newbls12381scalar>)
+  - [func (k Bls12381Scalar) Add(x, y *big.Int) *big.Int](<#func-bls12381scalar-add>)
+  - [func (k Bls12381Scalar) Bytes(x *big.Int) []byte](<#func-bls12381scalar-bytes>)
+  - [func (k Bls12381Scalar) Div(x, y *big.Int) *big.Int](<#func-bls12381scalar-div>)
+  - [func (k Bls12381Scalar) Hash(input []byte) *big.Int](<#func-bls12381scalar-hash>)
+  - [func (k Bls12381Scalar) IsValid(x *big.Int) bool](<#func-bls12381scalar-isvalid>)
+  - [func (k Bls12381Scalar) Mul(x, y *big.Int) *big.Int](<#func-bls12381scalar-mul>)
+  - [func (k Bls12381Scalar) Neg(x *big.Int) *big.Int](<#func-bls12381scalar-neg>)
+  - [func (k Bls12381Scalar) Random() (*big.Int, error)](<#func-bls12381scalar-random>)
+  - [func (k Bls12381Scalar) Sub(x, y *big.Int) *big.Int](<#func-bls12381scalar-sub>)
+- [type Curve](<#type-curve>)
+  - [func BLS12377G1() *Curve](<#func-bls12377g1>)
+  - [func BLS12377G2() *Curve](<#func-bls12377g2>)
+  - [func BLS12381G1() *Curve](<#func-bls12381g1>)
+  - [func BLS12381G2() *Curve](<#func-bls12381g2>)
+  - [func ED25519() *Curve](<#func-ed25519>)
+  - [func GetCurveByName(name string) *Curve](<#func-getcurvebyname>)
+  - [func K256() *Curve](<#func-k256>)
+  - [func P256() *Curve](<#func-p256>)
+  - [func PALLAS() *Curve](<#func-pallas>)
+  - [func (c Curve) NewGeneratorPoint() Point](<#func-curve-newgeneratorpoint>)
+  - [func (c Curve) NewIdentityPoint() Point](<#func-curve-newidentitypoint>)
+  - [func (c Curve) NewScalar() Scalar](<#func-curve-newscalar>)
+  - [func (c Curve) ScalarBaseMult(sc Scalar) Point](<#func-curve-scalarbasemult>)
+- [type EcPoint](<#type-ecpoint>)
+  - [func NewScalarBaseMult(curve elliptic.Curve, k *big.Int) (*EcPoint, error)](<#func-newscalarbasemult>)
+  - [func PointFromBytesUncompressed(curve elliptic.Curve, b []byte) (*EcPoint, error)](<#func-pointfrombytesuncompressed>)
+  - [func (a *EcPoint) Add(b *EcPoint) (*EcPoint, error)](<#func-ecpoint-add>)
+  - [func (a EcPoint) Bytes() []byte](<#func-ecpoint-bytes>)
+  - [func (a EcPoint) Equals(b *EcPoint) bool](<#func-ecpoint-equals>)
+  - [func (a EcPoint) IsBasePoint() bool](<#func-ecpoint-isbasepoint>)
+  - [func (a EcPoint) IsIdentity() bool](<#func-ecpoint-isidentity>)
+  - [func (a EcPoint) IsOnCurve() bool](<#func-ecpoint-isoncurve>)
+  - [func (a EcPoint) IsValid() bool](<#func-ecpoint-isvalid>)
+  - [func (a *EcPoint) MarshalBinary() ([]byte, error)](<#func-ecpoint-marshalbinary>)
+  - [func (a EcPoint) MarshalJSON() ([]byte, error)](<#func-ecpoint-marshaljson>)
+  - [func (a *EcPoint) Neg() (*EcPoint, error)](<#func-ecpoint-neg>)
+  - [func (a *EcPoint) ScalarMult(k *big.Int) (*EcPoint, error)](<#func-ecpoint-scalarmult>)
+  - [func (a *EcPoint) UnmarshalBinary(data []byte) error](<#func-ecpoint-unmarshalbinary>)
+  - [func (a *EcPoint) UnmarshalJSON(bytes []byte) error](<#func-ecpoint-unmarshaljson>)
+- [type EcPointJson](<#type-ecpointjson>)
+- [type EcScalar](<#type-ecscalar>)
+- [type EcdsaSignature](<#type-ecdsasignature>)
+- [type EcdsaVerify](<#type-ecdsaverify>)
+- [type Ed25519Scalar](<#type-ed25519scalar>)
+  - [func NewEd25519Scalar() *Ed25519Scalar](<#func-newed25519scalar>)
+  - [func (k Ed25519Scalar) Add(x, y *big.Int) *big.Int](<#func-ed25519scalar-add>)
+  - [func (k Ed25519Scalar) Bytes(x *big.Int) []byte](<#func-ed25519scalar-bytes>)
+  - [func (k Ed25519Scalar) Div(x, y *big.Int) *big.Int](<#func-ed25519scalar-div>)
+  - [func (k Ed25519Scalar) Hash(input []byte) *big.Int](<#func-ed25519scalar-hash>)
+  - [func (k Ed25519Scalar) IsValid(x *big.Int) bool](<#func-ed25519scalar-isvalid>)
+  - [func (k Ed25519Scalar) Mul(x, y *big.Int) *big.Int](<#func-ed25519scalar-mul>)
+  - [func (k Ed25519Scalar) Neg(x *big.Int) *big.Int](<#func-ed25519scalar-neg>)
+  - [func (k Ed25519Scalar) Random() (*big.Int, error)](<#func-ed25519scalar-random>)
+  - [func (k Ed25519Scalar) RandomWithReader(r io.Reader) (*big.Int, error)](<#func-ed25519scalar-randomwithreader>)
+  - [func (k Ed25519Scalar) Sub(x, y *big.Int) *big.Int](<#func-ed25519scalar-sub>)
+- [type Element](<#type-element>)
+  - [func (x Element) Add(y *Element) *Element](<#func-element-add>)
+  - [func (x Element) BigInt() *big.Int](<#func-element-bigint>)
+  - [func (x Element) Bytes() []byte](<#func-element-bytes>)
+  - [func (x Element) Clone() *Element](<#func-element-clone>)
+  - [func (x Element) Div(y *Element) *Element](<#func-element-div>)
+  - [func (x Element) Field() *Field](<#func-element-field>)
+  - [func (x Element) Invert() *Element](<#func-element-invert>)
+  - [func (x Element) IsEqual(y *Element) bool](<#func-element-isequal>)
+  - [func (x *Element) MarshalJSON() ([]byte, error)](<#func-element-marshaljson>)
+  - [func (x Element) Mul(y *Element) *Element](<#func-element-mul>)
+  - [func (x Element) Neg() *Element](<#func-element-neg>)
+  - [func (x Element) Pow(y *Element) *Element](<#func-element-pow>)
+  - [func (x Element) Sqrt() *Element](<#func-element-sqrt>)
+  - [func (x Element) Sub(y *Element) *Element](<#func-element-sub>)
+  - [func (x *Element) UnmarshalJSON(bytes []byte) error](<#func-element-unmarshaljson>)
+- [type ElementJSON](<#type-elementjson>)
+- [type Ep](<#type-ep>)
+  - [func (p *Ep) Add(lhs *Ep, rhs *Ep) *Ep](<#func-ep-add>)
+  - [func (p *Ep) CMove(lhs, rhs *Ep, condition int) *Ep](<#func-ep-cmove>)
+  - [func (p Ep) CurveName() string](<#func-ep-curvename>)
+  - [func (p *Ep) Double(other *Ep) *Ep](<#func-ep-double>)
+  - [func (p *Ep) Equal(other *Ep) bool](<#func-ep-equal>)
+  - [func (p *Ep) FromAffineCompressed(bytes []byte) (*Ep, error)](<#func-ep-fromaffinecompressed>)
+  - [func (p *Ep) FromAffineUncompressed(bytes []byte) (*Ep, error)](<#func-ep-fromaffineuncompressed>)
+  - [func (p *Ep) Generator() *Ep](<#func-ep-generator>)
+  - [func (p *Ep) Hash(bytes []byte) *Ep](<#func-ep-hash>)
+  - [func (p *Ep) Identity() *Ep](<#func-ep-identity>)
+  - [func (p *Ep) IsIdentity() bool](<#func-ep-isidentity>)
+  - [func (p *Ep) IsOnCurve() bool](<#func-ep-isoncurve>)
+  - [func (p *Ep) Mul(point *Ep, scalar *fq.Fq) *Ep](<#func-ep-mul>)
+  - [func (p *Ep) Neg(other *Ep) *Ep](<#func-ep-neg>)
+  - [func (p *Ep) Random(reader io.Reader) *Ep](<#func-ep-random>)
+  - [func (p *Ep) Set(other *Ep) *Ep](<#func-ep-set>)
+  - [func (p *Ep) Sub(lhs, rhs *Ep) *Ep](<#func-ep-sub>)
+  - [func (p Ep) SumOfProducts(points []*Ep, scalars []Scalar) *Ep](<#func-ep-sumofproducts>)
+  - [func (p *Ep) ToAffineCompressed() []byte](<#func-ep-toaffinecompressed>)
+  - [func (p *Ep) ToAffineUncompressed() []byte](<#func-ep-toaffineuncompressed>)
+  - [func (p *Ep) X() *fp.Fp](<#func-ep-x>)
+  - [func (p *Ep) Y() *fp.Fp](<#func-ep-y>)
+- [type Field](<#type-field>)
+  - [func NewField(modulus *big.Int) *Field](<#func-newfield>)
+  - [func (f Field) ElementFromBytes(bytes []byte) *Element](<#func-field-elementfrombytes>)
+  - [func (f Field) IsValid(value *big.Int) bool](<#func-field-isvalid>)
+  - [func (f Field) NewElement(value *big.Int) *Element](<#func-field-newelement>)
+  - [func (f Field) One() *Element](<#func-field-one>)
+  - [func (f Field) RandomElement(r io.Reader) (*Element, error)](<#func-field-randomelement>)
+  - [func (f Field) ReducedElementFromBytes(bytes []byte) *Element](<#func-field-reducedelementfrombytes>)
+  - [func (f Field) Zero() *Element](<#func-field-zero>)
+- [type K256Scalar](<#type-k256scalar>)
+  - [func NewK256Scalar() *K256Scalar](<#func-newk256scalar>)
+  - [func (k K256Scalar) Add(x, y *big.Int) *big.Int](<#func-k256scalar-add>)
+  - [func (k K256Scalar) Bytes(x *big.Int) []byte](<#func-k256scalar-bytes>)
+  - [func (k K256Scalar) Div(x, y *big.Int) *big.Int](<#func-k256scalar-div>)
+  - [func (k K256Scalar) Hash(input []byte) *big.Int](<#func-k256scalar-hash>)
+  - [func (k K256Scalar) IsValid(x *big.Int) bool](<#func-k256scalar-isvalid>)
+  - [func (k K256Scalar) Mul(x, y *big.Int) *big.Int](<#func-k256scalar-mul>)
+  - [func (k K256Scalar) Neg(x *big.Int) *big.Int](<#func-k256scalar-neg>)
+  - [func (k K256Scalar) Random() (*big.Int, error)](<#func-k256scalar-random>)
+  - [func (k K256Scalar) Sub(x, y *big.Int) *big.Int](<#func-k256scalar-sub>)
+- [type P256Scalar](<#type-p256scalar>)
+  - [func NewP256Scalar() *P256Scalar](<#func-newp256scalar>)
+  - [func (k P256Scalar) Add(x, y *big.Int) *big.Int](<#func-p256scalar-add>)
+  - [func (k P256Scalar) Bytes(x *big.Int) []byte](<#func-p256scalar-bytes>)
+  - [func (k P256Scalar) Div(x, y *big.Int) *big.Int](<#func-p256scalar-div>)
+  - [func (k P256Scalar) Hash(input []byte) *big.Int](<#func-p256scalar-hash>)
+  - [func (k P256Scalar) IsValid(x *big.Int) bool](<#func-p256scalar-isvalid>)
+  - [func (k P256Scalar) Mul(x, y *big.Int) *big.Int](<#func-p256scalar-mul>)
+  - [func (k P256Scalar) Neg(x *big.Int) *big.Int](<#func-p256scalar-neg>)
+  - [func (k P256Scalar) Random() (*big.Int, error)](<#func-p256scalar-random>)
+  - [func (k P256Scalar) Sub(x, y *big.Int) *big.Int](<#func-p256scalar-sub>)
+- [type PairingCurve](<#type-pairingcurve>)
+  - [func BLS12381(preferredPoint Point) *PairingCurve](<#func-bls12381>)
+  - [func GetPairingCurveByName(name string) *PairingCurve](<#func-getpairingcurvebyname>)
+  - [func (c PairingCurve) NewG1GeneratorPoint() PairingPoint](<#func-pairingcurve-newg1generatorpoint>)
+  - [func (c PairingCurve) NewG1IdentityPoint() PairingPoint](<#func-pairingcurve-newg1identitypoint>)
+  - [func (c PairingCurve) NewG2GeneratorPoint() PairingPoint](<#func-pairingcurve-newg2generatorpoint>)
+  - [func (c PairingCurve) NewG2IdentityPoint() PairingPoint](<#func-pairingcurve-newg2identitypoint>)
+  - [func (c PairingCurve) NewScalar() PairingScalar](<#func-pairingcurve-newscalar>)
+  - [func (c PairingCurve) ScalarG1BaseMult(sc Scalar) PairingPoint](<#func-pairingcurve-scalarg1basemult>)
+  - [func (c PairingCurve) ScalarG2BaseMult(sc Scalar) PairingPoint](<#func-pairingcurve-scalarg2basemult>)
+- [type PairingPoint](<#type-pairingpoint>)
+- [type PairingScalar](<#type-pairingscalar>)
+- [type PallasCurve](<#type-pallascurve>)
+  - [func Pallas() *PallasCurve](<#func-pallas>)
+  - [func (curve *PallasCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)](<#func-pallascurve-add>)
+  - [func (curve *PallasCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)](<#func-pallascurve-double>)
+  - [func (curve *PallasCurve) IsOnCurve(x, y *big.Int) bool](<#func-pallascurve-isoncurve>)
+  - [func (curve *PallasCurve) Params() *elliptic.CurveParams](<#func-pallascurve-params>)
+  - [func (curve *PallasCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)](<#func-pallascurve-scalarbasemult>)
+  - [func (curve *PallasCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)](<#func-pallascurve-scalarmult>)
+- [type PallasScalar](<#type-pallasscalar>)
+  - [func NewPallasScalar() *PallasScalar](<#func-newpallasscalar>)
+  - [func (k PallasScalar) Add(x, y *big.Int) *big.Int](<#func-pallasscalar-add>)
+  - [func (k PallasScalar) Bytes(x *big.Int) []byte](<#func-pallasscalar-bytes>)
+  - [func (k PallasScalar) Div(x, y *big.Int) *big.Int](<#func-pallasscalar-div>)
+  - [func (k PallasScalar) Hash(input []byte) *big.Int](<#func-pallasscalar-hash>)
+  - [func (k PallasScalar) IsValid(x *big.Int) bool](<#func-pallasscalar-isvalid>)
+  - [func (k PallasScalar) Mul(x, y *big.Int) *big.Int](<#func-pallasscalar-mul>)
+  - [func (k PallasScalar) Neg(x *big.Int) *big.Int](<#func-pallasscalar-neg>)
+  - [func (k PallasScalar) Random() (*big.Int, error)](<#func-pallasscalar-random>)
+  - [func (k PallasScalar) Sub(x, y *big.Int) *big.Int](<#func-pallasscalar-sub>)
+- [type Point](<#type-point>)
+- [type PointBls12377G1](<#type-pointbls12377g1>)
+  - [func (p *PointBls12377G1) Add(rhs Point) Point](<#func-pointbls12377g1-add>)
+  - [func (p *PointBls12377G1) CurveName() string](<#func-pointbls12377g1-curvename>)
+  - [func (p *PointBls12377G1) Double() Point](<#func-pointbls12377g1-double>)
+  - [func (p *PointBls12377G1) Equal(rhs Point) bool](<#func-pointbls12377g1-equal>)
+  - [func (p *PointBls12377G1) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointbls12377g1-fromaffinecompressed>)
+  - [func (p *PointBls12377G1) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointbls12377g1-fromaffineuncompressed>)
+  - [func (p *PointBls12377G1) Generator() Point](<#func-pointbls12377g1-generator>)
+  - [func (p *PointBls12377G1) Hash(bytes []byte) Point](<#func-pointbls12377g1-hash>)
+  - [func (p *PointBls12377G1) Identity() Point](<#func-pointbls12377g1-identity>)
+  - [func (p *PointBls12377G1) IsIdentity() bool](<#func-pointbls12377g1-isidentity>)
+  - [func (p *PointBls12377G1) IsNegative() bool](<#func-pointbls12377g1-isnegative>)
+  - [func (p *PointBls12377G1) IsOnCurve() bool](<#func-pointbls12377g1-isoncurve>)
+  - [func (p *PointBls12377G1) MarshalBinary() ([]byte, error)](<#func-pointbls12377g1-marshalbinary>)
+  - [func (p *PointBls12377G1) MarshalJSON() ([]byte, error)](<#func-pointbls12377g1-marshaljson>)
+  - [func (p *PointBls12377G1) MarshalText() ([]byte, error)](<#func-pointbls12377g1-marshaltext>)
+  - [func (p *PointBls12377G1) Modulus() *big.Int](<#func-pointbls12377g1-modulus>)
+  - [func (p *PointBls12377G1) Mul(rhs Scalar) Point](<#func-pointbls12377g1-mul>)
+  - [func (p *PointBls12377G1) MultiPairing(points ...PairingPoint) Scalar](<#func-pointbls12377g1-multipairing>)
+  - [func (p *PointBls12377G1) Neg() Point](<#func-pointbls12377g1-neg>)
+  - [func (p *PointBls12377G1) OtherGroup() PairingPoint](<#func-pointbls12377g1-othergroup>)
+  - [func (p *PointBls12377G1) Pairing(rhs PairingPoint) Scalar](<#func-pointbls12377g1-pairing>)
+  - [func (p *PointBls12377G1) Random(reader io.Reader) Point](<#func-pointbls12377g1-random>)
+  - [func (p *PointBls12377G1) Scalar() Scalar](<#func-pointbls12377g1-scalar>)
+  - [func (p *PointBls12377G1) Set(x, y *big.Int) (Point, error)](<#func-pointbls12377g1-set>)
+  - [func (p *PointBls12377G1) Sub(rhs Point) Point](<#func-pointbls12377g1-sub>)
+  - [func (p *PointBls12377G1) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointbls12377g1-sumofproducts>)
+  - [func (p *PointBls12377G1) ToAffineCompressed() []byte](<#func-pointbls12377g1-toaffinecompressed>)
+  - [func (p *PointBls12377G1) ToAffineUncompressed() []byte](<#func-pointbls12377g1-toaffineuncompressed>)
+  - [func (p *PointBls12377G1) UnmarshalBinary(input []byte) error](<#func-pointbls12377g1-unmarshalbinary>)
+  - [func (p *PointBls12377G1) UnmarshalJSON(input []byte) error](<#func-pointbls12377g1-unmarshaljson>)
+  - [func (p *PointBls12377G1) UnmarshalText(input []byte) error](<#func-pointbls12377g1-unmarshaltext>)
+  - [func (p *PointBls12377G1) X() *big.Int](<#func-pointbls12377g1-x>)
+  - [func (p *PointBls12377G1) Y() *big.Int](<#func-pointbls12377g1-y>)
+- [type PointBls12377G2](<#type-pointbls12377g2>)
+  - [func (p *PointBls12377G2) Add(rhs Point) Point](<#func-pointbls12377g2-add>)
+  - [func (p *PointBls12377G2) CurveName() string](<#func-pointbls12377g2-curvename>)
+  - [func (p *PointBls12377G2) Double() Point](<#func-pointbls12377g2-double>)
+  - [func (p *PointBls12377G2) Equal(rhs Point) bool](<#func-pointbls12377g2-equal>)
+  - [func (p *PointBls12377G2) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointbls12377g2-fromaffinecompressed>)
+  - [func (p *PointBls12377G2) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointbls12377g2-fromaffineuncompressed>)
+  - [func (p *PointBls12377G2) Generator() Point](<#func-pointbls12377g2-generator>)
+  - [func (p *PointBls12377G2) Hash(bytes []byte) Point](<#func-pointbls12377g2-hash>)
+  - [func (p *PointBls12377G2) Identity() Point](<#func-pointbls12377g2-identity>)
+  - [func (p *PointBls12377G2) IsIdentity() bool](<#func-pointbls12377g2-isidentity>)
+  - [func (p *PointBls12377G2) IsNegative() bool](<#func-pointbls12377g2-isnegative>)
+  - [func (p *PointBls12377G2) IsOnCurve() bool](<#func-pointbls12377g2-isoncurve>)
+  - [func (p *PointBls12377G2) MarshalBinary() ([]byte, error)](<#func-pointbls12377g2-marshalbinary>)
+  - [func (p *PointBls12377G2) MarshalJSON() ([]byte, error)](<#func-pointbls12377g2-marshaljson>)
+  - [func (p *PointBls12377G2) MarshalText() ([]byte, error)](<#func-pointbls12377g2-marshaltext>)
+  - [func (p *PointBls12377G2) Modulus() *big.Int](<#func-pointbls12377g2-modulus>)
+  - [func (p *PointBls12377G2) Mul(rhs Scalar) Point](<#func-pointbls12377g2-mul>)
+  - [func (p *PointBls12377G2) MultiPairing(points ...PairingPoint) Scalar](<#func-pointbls12377g2-multipairing>)
+  - [func (p *PointBls12377G2) Neg() Point](<#func-pointbls12377g2-neg>)
+  - [func (p *PointBls12377G2) OtherGroup() PairingPoint](<#func-pointbls12377g2-othergroup>)
+  - [func (p *PointBls12377G2) Pairing(rhs PairingPoint) Scalar](<#func-pointbls12377g2-pairing>)
+  - [func (p *PointBls12377G2) Random(reader io.Reader) Point](<#func-pointbls12377g2-random>)
+  - [func (p *PointBls12377G2) Scalar() Scalar](<#func-pointbls12377g2-scalar>)
+  - [func (p *PointBls12377G2) Set(x, y *big.Int) (Point, error)](<#func-pointbls12377g2-set>)
+  - [func (p *PointBls12377G2) Sub(rhs Point) Point](<#func-pointbls12377g2-sub>)
+  - [func (p *PointBls12377G2) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointbls12377g2-sumofproducts>)
+  - [func (p *PointBls12377G2) ToAffineCompressed() []byte](<#func-pointbls12377g2-toaffinecompressed>)
+  - [func (p *PointBls12377G2) ToAffineUncompressed() []byte](<#func-pointbls12377g2-toaffineuncompressed>)
+  - [func (p *PointBls12377G2) UnmarshalBinary(input []byte) error](<#func-pointbls12377g2-unmarshalbinary>)
+  - [func (p *PointBls12377G2) UnmarshalJSON(input []byte) error](<#func-pointbls12377g2-unmarshaljson>)
+  - [func (p *PointBls12377G2) UnmarshalText(input []byte) error](<#func-pointbls12377g2-unmarshaltext>)
+  - [func (p *PointBls12377G2) X() *big.Int](<#func-pointbls12377g2-x>)
+  - [func (p *PointBls12377G2) Y() *big.Int](<#func-pointbls12377g2-y>)
+- [type PointBls12381G1](<#type-pointbls12381g1>)
+  - [func (p *PointBls12381G1) Add(rhs Point) Point](<#func-pointbls12381g1-add>)
+  - [func (p *PointBls12381G1) CurveName() string](<#func-pointbls12381g1-curvename>)
+  - [func (p *PointBls12381G1) Double() Point](<#func-pointbls12381g1-double>)
+  - [func (p *PointBls12381G1) Equal(rhs Point) bool](<#func-pointbls12381g1-equal>)
+  - [func (p *PointBls12381G1) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointbls12381g1-fromaffinecompressed>)
+  - [func (p *PointBls12381G1) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointbls12381g1-fromaffineuncompressed>)
+  - [func (p *PointBls12381G1) Generator() Point](<#func-pointbls12381g1-generator>)
+  - [func (p *PointBls12381G1) Hash(bytes []byte) Point](<#func-pointbls12381g1-hash>)
+  - [func (p *PointBls12381G1) Identity() Point](<#func-pointbls12381g1-identity>)
+  - [func (p *PointBls12381G1) IsIdentity() bool](<#func-pointbls12381g1-isidentity>)
+  - [func (p *PointBls12381G1) IsNegative() bool](<#func-pointbls12381g1-isnegative>)
+  - [func (p *PointBls12381G1) IsOnCurve() bool](<#func-pointbls12381g1-isoncurve>)
+  - [func (p *PointBls12381G1) MarshalBinary() ([]byte, error)](<#func-pointbls12381g1-marshalbinary>)
+  - [func (p *PointBls12381G1) MarshalJSON() ([]byte, error)](<#func-pointbls12381g1-marshaljson>)
+  - [func (p *PointBls12381G1) MarshalText() ([]byte, error)](<#func-pointbls12381g1-marshaltext>)
+  - [func (p *PointBls12381G1) Modulus() *big.Int](<#func-pointbls12381g1-modulus>)
+  - [func (p *PointBls12381G1) Mul(rhs Scalar) Point](<#func-pointbls12381g1-mul>)
+  - [func (p *PointBls12381G1) MultiPairing(points ...PairingPoint) Scalar](<#func-pointbls12381g1-multipairing>)
+  - [func (p *PointBls12381G1) Neg() Point](<#func-pointbls12381g1-neg>)
+  - [func (p *PointBls12381G1) OtherGroup() PairingPoint](<#func-pointbls12381g1-othergroup>)
+  - [func (p *PointBls12381G1) Pairing(rhs PairingPoint) Scalar](<#func-pointbls12381g1-pairing>)
+  - [func (p *PointBls12381G1) Random(reader io.Reader) Point](<#func-pointbls12381g1-random>)
+  - [func (p *PointBls12381G1) Scalar() Scalar](<#func-pointbls12381g1-scalar>)
+  - [func (p *PointBls12381G1) Set(x, y *big.Int) (Point, error)](<#func-pointbls12381g1-set>)
+  - [func (p *PointBls12381G1) Sub(rhs Point) Point](<#func-pointbls12381g1-sub>)
+  - [func (p *PointBls12381G1) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointbls12381g1-sumofproducts>)
+  - [func (p *PointBls12381G1) ToAffineCompressed() []byte](<#func-pointbls12381g1-toaffinecompressed>)
+  - [func (p *PointBls12381G1) ToAffineUncompressed() []byte](<#func-pointbls12381g1-toaffineuncompressed>)
+  - [func (p *PointBls12381G1) UnmarshalBinary(input []byte) error](<#func-pointbls12381g1-unmarshalbinary>)
+  - [func (p *PointBls12381G1) UnmarshalJSON(input []byte) error](<#func-pointbls12381g1-unmarshaljson>)
+  - [func (p *PointBls12381G1) UnmarshalText(input []byte) error](<#func-pointbls12381g1-unmarshaltext>)
+  - [func (p *PointBls12381G1) X() *big.Int](<#func-pointbls12381g1-x>)
+  - [func (p *PointBls12381G1) Y() *big.Int](<#func-pointbls12381g1-y>)
+- [type PointBls12381G2](<#type-pointbls12381g2>)
+  - [func (p *PointBls12381G2) Add(rhs Point) Point](<#func-pointbls12381g2-add>)
+  - [func (p *PointBls12381G2) CurveName() string](<#func-pointbls12381g2-curvename>)
+  - [func (p *PointBls12381G2) Double() Point](<#func-pointbls12381g2-double>)
+  - [func (p *PointBls12381G2) Equal(rhs Point) bool](<#func-pointbls12381g2-equal>)
+  - [func (p *PointBls12381G2) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointbls12381g2-fromaffinecompressed>)
+  - [func (p *PointBls12381G2) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointbls12381g2-fromaffineuncompressed>)
+  - [func (p *PointBls12381G2) Generator() Point](<#func-pointbls12381g2-generator>)
+  - [func (p *PointBls12381G2) Hash(bytes []byte) Point](<#func-pointbls12381g2-hash>)
+  - [func (p *PointBls12381G2) Identity() Point](<#func-pointbls12381g2-identity>)
+  - [func (p *PointBls12381G2) IsIdentity() bool](<#func-pointbls12381g2-isidentity>)
+  - [func (p *PointBls12381G2) IsNegative() bool](<#func-pointbls12381g2-isnegative>)
+  - [func (p *PointBls12381G2) IsOnCurve() bool](<#func-pointbls12381g2-isoncurve>)
+  - [func (p *PointBls12381G2) MarshalBinary() ([]byte, error)](<#func-pointbls12381g2-marshalbinary>)
+  - [func (p *PointBls12381G2) MarshalJSON() ([]byte, error)](<#func-pointbls12381g2-marshaljson>)
+  - [func (p *PointBls12381G2) MarshalText() ([]byte, error)](<#func-pointbls12381g2-marshaltext>)
+  - [func (p *PointBls12381G2) Modulus() *big.Int](<#func-pointbls12381g2-modulus>)
+  - [func (p *PointBls12381G2) Mul(rhs Scalar) Point](<#func-pointbls12381g2-mul>)
+  - [func (p *PointBls12381G2) MultiPairing(points ...PairingPoint) Scalar](<#func-pointbls12381g2-multipairing>)
+  - [func (p *PointBls12381G2) Neg() Point](<#func-pointbls12381g2-neg>)
+  - [func (p *PointBls12381G2) OtherGroup() PairingPoint](<#func-pointbls12381g2-othergroup>)
+  - [func (p *PointBls12381G2) Pairing(rhs PairingPoint) Scalar](<#func-pointbls12381g2-pairing>)
+  - [func (p *PointBls12381G2) Random(reader io.Reader) Point](<#func-pointbls12381g2-random>)
+  - [func (p *PointBls12381G2) Scalar() Scalar](<#func-pointbls12381g2-scalar>)
+  - [func (p *PointBls12381G2) Set(x, y *big.Int) (Point, error)](<#func-pointbls12381g2-set>)
+  - [func (p *PointBls12381G2) Sub(rhs Point) Point](<#func-pointbls12381g2-sub>)
+  - [func (p *PointBls12381G2) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointbls12381g2-sumofproducts>)
+  - [func (p *PointBls12381G2) ToAffineCompressed() []byte](<#func-pointbls12381g2-toaffinecompressed>)
+  - [func (p *PointBls12381G2) ToAffineUncompressed() []byte](<#func-pointbls12381g2-toaffineuncompressed>)
+  - [func (p *PointBls12381G2) UnmarshalBinary(input []byte) error](<#func-pointbls12381g2-unmarshalbinary>)
+  - [func (p *PointBls12381G2) UnmarshalJSON(input []byte) error](<#func-pointbls12381g2-unmarshaljson>)
+  - [func (p *PointBls12381G2) UnmarshalText(input []byte) error](<#func-pointbls12381g2-unmarshaltext>)
+  - [func (p *PointBls12381G2) X() *big.Int](<#func-pointbls12381g2-x>)
+  - [func (p *PointBls12381G2) Y() *big.Int](<#func-pointbls12381g2-y>)
+- [type PointEd25519](<#type-pointed25519>)
+  - [func (p *PointEd25519) Add(rhs Point) Point](<#func-pointed25519-add>)
+  - [func (p *PointEd25519) CurveName() string](<#func-pointed25519-curvename>)
+  - [func (p *PointEd25519) Double() Point](<#func-pointed25519-double>)
+  - [func (p *PointEd25519) Equal(rhs Point) bool](<#func-pointed25519-equal>)
+  - [func (p *PointEd25519) FromAffineCompressed(inBytes []byte) (Point, error)](<#func-pointed25519-fromaffinecompressed>)
+  - [func (p *PointEd25519) FromAffineUncompressed(inBytes []byte) (Point, error)](<#func-pointed25519-fromaffineuncompressed>)
+  - [func (p *PointEd25519) Generator() Point](<#func-pointed25519-generator>)
+  - [func (p *PointEd25519) GetEdwardsPoint() *edwards25519.Point](<#func-pointed25519-getedwardspoint>)
+  - [func (p *PointEd25519) Hash(bytes []byte) Point](<#func-pointed25519-hash>)
+  - [func (p *PointEd25519) Identity() Point](<#func-pointed25519-identity>)
+  - [func (p *PointEd25519) IsIdentity() bool](<#func-pointed25519-isidentity>)
+  - [func (p *PointEd25519) IsNegative() bool](<#func-pointed25519-isnegative>)
+  - [func (p *PointEd25519) IsOnCurve() bool](<#func-pointed25519-isoncurve>)
+  - [func (p *PointEd25519) MangleScalarBitsAndMulByBasepointToProducePublicKey(rhs *ScalarEd25519) *PointEd25519](<#func-pointed25519-manglescalarbitsandmulbybasepointtoproducepublickey>)
+  - [func (p *PointEd25519) MarshalBinary() ([]byte, error)](<#func-pointed25519-marshalbinary>)
+  - [func (p *PointEd25519) MarshalJSON() ([]byte, error)](<#func-pointed25519-marshaljson>)
+  - [func (p *PointEd25519) MarshalText() ([]byte, error)](<#func-pointed25519-marshaltext>)
+  - [func (p *PointEd25519) Mul(rhs Scalar) Point](<#func-pointed25519-mul>)
+  - [func (p *PointEd25519) Neg() Point](<#func-pointed25519-neg>)
+  - [func (p *PointEd25519) Random(reader io.Reader) Point](<#func-pointed25519-random>)
+  - [func (p *PointEd25519) Scalar() Scalar](<#func-pointed25519-scalar>)
+  - [func (p *PointEd25519) Set(x, y *big.Int) (Point, error)](<#func-pointed25519-set>)
+  - [func (p *PointEd25519) SetEdwardsPoint(pt *edwards25519.Point) *PointEd25519](<#func-pointed25519-setedwardspoint>)
+  - [func (p *PointEd25519) Sub(rhs Point) Point](<#func-pointed25519-sub>)
+  - [func (p *PointEd25519) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointed25519-sumofproducts>)
+  - [func (p *PointEd25519) ToAffineCompressed() []byte](<#func-pointed25519-toaffinecompressed>)
+  - [func (p *PointEd25519) ToAffineUncompressed() []byte](<#func-pointed25519-toaffineuncompressed>)
+  - [func (p *PointEd25519) UnmarshalBinary(input []byte) error](<#func-pointed25519-unmarshalbinary>)
+  - [func (p *PointEd25519) UnmarshalJSON(input []byte) error](<#func-pointed25519-unmarshaljson>)
+  - [func (p *PointEd25519) UnmarshalText(input []byte) error](<#func-pointed25519-unmarshaltext>)
+  - [func (p *PointEd25519) VarTimeDoubleScalarBaseMult(a Scalar, A Point, b Scalar) Point](<#func-pointed25519-vartimedoublescalarbasemult>)
+- [type PointK256](<#type-pointk256>)
+  - [func (p *PointK256) Add(rhs Point) Point](<#func-pointk256-add>)
+  - [func (p *PointK256) CurveName() string](<#func-pointk256-curvename>)
+  - [func (p *PointK256) Double() Point](<#func-pointk256-double>)
+  - [func (p *PointK256) Equal(rhs Point) bool](<#func-pointk256-equal>)
+  - [func (p *PointK256) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointk256-fromaffinecompressed>)
+  - [func (p *PointK256) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointk256-fromaffineuncompressed>)
+  - [func (p *PointK256) Generator() Point](<#func-pointk256-generator>)
+  - [func (p *PointK256) Hash(bytes []byte) Point](<#func-pointk256-hash>)
+  - [func (p *PointK256) Identity() Point](<#func-pointk256-identity>)
+  - [func (p *PointK256) IsIdentity() bool](<#func-pointk256-isidentity>)
+  - [func (p *PointK256) IsNegative() bool](<#func-pointk256-isnegative>)
+  - [func (p *PointK256) IsOnCurve() bool](<#func-pointk256-isoncurve>)
+  - [func (p *PointK256) MarshalBinary() ([]byte, error)](<#func-pointk256-marshalbinary>)
+  - [func (p *PointK256) MarshalJSON() ([]byte, error)](<#func-pointk256-marshaljson>)
+  - [func (p *PointK256) MarshalText() ([]byte, error)](<#func-pointk256-marshaltext>)
+  - [func (p *PointK256) Mul(rhs Scalar) Point](<#func-pointk256-mul>)
+  - [func (p *PointK256) Neg() Point](<#func-pointk256-neg>)
+  - [func (p *PointK256) Params() *elliptic.CurveParams](<#func-pointk256-params>)
+  - [func (p *PointK256) Random(reader io.Reader) Point](<#func-pointk256-random>)
+  - [func (p *PointK256) Scalar() Scalar](<#func-pointk256-scalar>)
+  - [func (p *PointK256) Set(x, y *big.Int) (Point, error)](<#func-pointk256-set>)
+  - [func (p *PointK256) Sub(rhs Point) Point](<#func-pointk256-sub>)
+  - [func (p *PointK256) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointk256-sumofproducts>)
+  - [func (p *PointK256) ToAffineCompressed() []byte](<#func-pointk256-toaffinecompressed>)
+  - [func (p *PointK256) ToAffineUncompressed() []byte](<#func-pointk256-toaffineuncompressed>)
+  - [func (p *PointK256) UnmarshalBinary(input []byte) error](<#func-pointk256-unmarshalbinary>)
+  - [func (p *PointK256) UnmarshalJSON(input []byte) error](<#func-pointk256-unmarshaljson>)
+  - [func (p *PointK256) UnmarshalText(input []byte) error](<#func-pointk256-unmarshaltext>)
+  - [func (p *PointK256) X() *big.Int](<#func-pointk256-x>)
+  - [func (p *PointK256) Y() *big.Int](<#func-pointk256-y>)
+- [type PointP256](<#type-pointp256>)
+  - [func (p *PointP256) Add(rhs Point) Point](<#func-pointp256-add>)
+  - [func (p *PointP256) CurveName() string](<#func-pointp256-curvename>)
+  - [func (p *PointP256) Double() Point](<#func-pointp256-double>)
+  - [func (p *PointP256) Equal(rhs Point) bool](<#func-pointp256-equal>)
+  - [func (p *PointP256) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointp256-fromaffinecompressed>)
+  - [func (p *PointP256) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointp256-fromaffineuncompressed>)
+  - [func (p *PointP256) Generator() Point](<#func-pointp256-generator>)
+  - [func (p *PointP256) Hash(bytes []byte) Point](<#func-pointp256-hash>)
+  - [func (p *PointP256) Identity() Point](<#func-pointp256-identity>)
+  - [func (p *PointP256) IsIdentity() bool](<#func-pointp256-isidentity>)
+  - [func (p *PointP256) IsNegative() bool](<#func-pointp256-isnegative>)
+  - [func (p *PointP256) IsOnCurve() bool](<#func-pointp256-isoncurve>)
+  - [func (p *PointP256) MarshalBinary() ([]byte, error)](<#func-pointp256-marshalbinary>)
+  - [func (p *PointP256) MarshalJSON() ([]byte, error)](<#func-pointp256-marshaljson>)
+  - [func (p *PointP256) MarshalText() ([]byte, error)](<#func-pointp256-marshaltext>)
+  - [func (p *PointP256) Mul(rhs Scalar) Point](<#func-pointp256-mul>)
+  - [func (p *PointP256) Neg() Point](<#func-pointp256-neg>)
+  - [func (p *PointP256) Params() *elliptic.CurveParams](<#func-pointp256-params>)
+  - [func (p *PointP256) Random(reader io.Reader) Point](<#func-pointp256-random>)
+  - [func (p *PointP256) Scalar() Scalar](<#func-pointp256-scalar>)
+  - [func (p *PointP256) Set(x, y *big.Int) (Point, error)](<#func-pointp256-set>)
+  - [func (p *PointP256) Sub(rhs Point) Point](<#func-pointp256-sub>)
+  - [func (p *PointP256) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointp256-sumofproducts>)
+  - [func (p *PointP256) ToAffineCompressed() []byte](<#func-pointp256-toaffinecompressed>)
+  - [func (p *PointP256) ToAffineUncompressed() []byte](<#func-pointp256-toaffineuncompressed>)
+  - [func (p *PointP256) UnmarshalBinary(input []byte) error](<#func-pointp256-unmarshalbinary>)
+  - [func (p *PointP256) UnmarshalJSON(input []byte) error](<#func-pointp256-unmarshaljson>)
+  - [func (p *PointP256) UnmarshalText(input []byte) error](<#func-pointp256-unmarshaltext>)
+  - [func (p *PointP256) X() *big.Int](<#func-pointp256-x>)
+  - [func (p *PointP256) Y() *big.Int](<#func-pointp256-y>)
+- [type PointPallas](<#type-pointpallas>)
+  - [func (p *PointPallas) Add(rhs Point) Point](<#func-pointpallas-add>)
+  - [func (p *PointPallas) CurveName() string](<#func-pointpallas-curvename>)
+  - [func (p *PointPallas) Double() Point](<#func-pointpallas-double>)
+  - [func (p *PointPallas) Equal(rhs Point) bool](<#func-pointpallas-equal>)
+  - [func (p *PointPallas) FromAffineCompressed(bytes []byte) (Point, error)](<#func-pointpallas-fromaffinecompressed>)
+  - [func (p *PointPallas) FromAffineUncompressed(bytes []byte) (Point, error)](<#func-pointpallas-fromaffineuncompressed>)
+  - [func (p *PointPallas) Generator() Point](<#func-pointpallas-generator>)
+  - [func (p *PointPallas) GetEp() *Ep](<#func-pointpallas-getep>)
+  - [func (p *PointPallas) Hash(bytes []byte) Point](<#func-pointpallas-hash>)
+  - [func (p *PointPallas) Identity() Point](<#func-pointpallas-identity>)
+  - [func (p *PointPallas) IsIdentity() bool](<#func-pointpallas-isidentity>)
+  - [func (p *PointPallas) IsNegative() bool](<#func-pointpallas-isnegative>)
+  - [func (p *PointPallas) IsOnCurve() bool](<#func-pointpallas-isoncurve>)
+  - [func (p *PointPallas) MarshalBinary() ([]byte, error)](<#func-pointpallas-marshalbinary>)
+  - [func (p *PointPallas) MarshalJSON() ([]byte, error)](<#func-pointpallas-marshaljson>)
+  - [func (p *PointPallas) MarshalText() ([]byte, error)](<#func-pointpallas-marshaltext>)
+  - [func (p *PointPallas) Mul(rhs Scalar) Point](<#func-pointpallas-mul>)
+  - [func (p *PointPallas) Neg() Point](<#func-pointpallas-neg>)
+  - [func (p *PointPallas) Random(reader io.Reader) Point](<#func-pointpallas-random>)
+  - [func (p *PointPallas) Scalar() Scalar](<#func-pointpallas-scalar>)
+  - [func (p *PointPallas) Set(x, y *big.Int) (Point, error)](<#func-pointpallas-set>)
+  - [func (p *PointPallas) Sub(rhs Point) Point](<#func-pointpallas-sub>)
+  - [func (p *PointPallas) SumOfProducts(points []Point, scalars []Scalar) Point](<#func-pointpallas-sumofproducts>)
+  - [func (p *PointPallas) ToAffineCompressed() []byte](<#func-pointpallas-toaffinecompressed>)
+  - [func (p *PointPallas) ToAffineUncompressed() []byte](<#func-pointpallas-toaffineuncompressed>)
+  - [func (p *PointPallas) UnmarshalBinary(input []byte) error](<#func-pointpallas-unmarshalbinary>)
+  - [func (p *PointPallas) UnmarshalJSON(input []byte) error](<#func-pointpallas-unmarshaljson>)
+  - [func (p *PointPallas) UnmarshalText(input []byte) error](<#func-pointpallas-unmarshaltext>)
+  - [func (p *PointPallas) X() *fp.Fp](<#func-pointpallas-x>)
+  - [func (p *PointPallas) Y() *fp.Fp](<#func-pointpallas-y>)
+- [type Scalar](<#type-scalar>)
+- [type ScalarBls12377](<#type-scalarbls12377>)
+  - [func (s *ScalarBls12377) Add(rhs Scalar) Scalar](<#func-scalarbls12377-add>)
+  - [func (s *ScalarBls12377) BigInt() *big.Int](<#func-scalarbls12377-bigint>)
+  - [func (s *ScalarBls12377) Bytes() []byte](<#func-scalarbls12377-bytes>)
+  - [func (s *ScalarBls12377) Clone() Scalar](<#func-scalarbls12377-clone>)
+  - [func (s *ScalarBls12377) Cmp(rhs Scalar) int](<#func-scalarbls12377-cmp>)
+  - [func (s *ScalarBls12377) Cube() Scalar](<#func-scalarbls12377-cube>)
+  - [func (s *ScalarBls12377) Div(rhs Scalar) Scalar](<#func-scalarbls12377-div>)
+  - [func (s *ScalarBls12377) Double() Scalar](<#func-scalarbls12377-double>)
+  - [func (s *ScalarBls12377) Hash(bytes []byte) Scalar](<#func-scalarbls12377-hash>)
+  - [func (s *ScalarBls12377) Invert() (Scalar, error)](<#func-scalarbls12377-invert>)
+  - [func (s *ScalarBls12377) IsEven() bool](<#func-scalarbls12377-iseven>)
+  - [func (s *ScalarBls12377) IsOdd() bool](<#func-scalarbls12377-isodd>)
+  - [func (s *ScalarBls12377) IsOne() bool](<#func-scalarbls12377-isone>)
+  - [func (s *ScalarBls12377) IsZero() bool](<#func-scalarbls12377-iszero>)
+  - [func (s *ScalarBls12377) MarshalBinary() ([]byte, error)](<#func-scalarbls12377-marshalbinary>)
+  - [func (s *ScalarBls12377) MarshalJSON() ([]byte, error)](<#func-scalarbls12377-marshaljson>)
+  - [func (s *ScalarBls12377) MarshalText() ([]byte, error)](<#func-scalarbls12377-marshaltext>)
+  - [func (s *ScalarBls12377) Mul(rhs Scalar) Scalar](<#func-scalarbls12377-mul>)
+  - [func (s *ScalarBls12377) MulAdd(y, z Scalar) Scalar](<#func-scalarbls12377-muladd>)
+  - [func (s *ScalarBls12377) Neg() Scalar](<#func-scalarbls12377-neg>)
+  - [func (s *ScalarBls12377) New(value int) Scalar](<#func-scalarbls12377-new>)
+  - [func (s *ScalarBls12377) One() Scalar](<#func-scalarbls12377-one>)
+  - [func (s *ScalarBls12377) Order() *big.Int](<#func-scalarbls12377-order>)
+  - [func (s *ScalarBls12377) Point() Point](<#func-scalarbls12377-point>)
+  - [func (s *ScalarBls12377) Random(reader io.Reader) Scalar](<#func-scalarbls12377-random>)
+  - [func (s *ScalarBls12377) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarbls12377-setbigint>)
+  - [func (s *ScalarBls12377) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarbls12377-setbytes>)
+  - [func (s *ScalarBls12377) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarbls12377-setbyteswide>)
+  - [func (s *ScalarBls12377) SetPoint(p Point) PairingScalar](<#func-scalarbls12377-setpoint>)
+  - [func (s *ScalarBls12377) Sqrt() (Scalar, error)](<#func-scalarbls12377-sqrt>)
+  - [func (s *ScalarBls12377) Square() Scalar](<#func-scalarbls12377-square>)
+  - [func (s *ScalarBls12377) Sub(rhs Scalar) Scalar](<#func-scalarbls12377-sub>)
+  - [func (s *ScalarBls12377) UnmarshalBinary(input []byte) error](<#func-scalarbls12377-unmarshalbinary>)
+  - [func (s *ScalarBls12377) UnmarshalJSON(input []byte) error](<#func-scalarbls12377-unmarshaljson>)
+  - [func (s *ScalarBls12377) UnmarshalText(input []byte) error](<#func-scalarbls12377-unmarshaltext>)
+  - [func (s *ScalarBls12377) Zero() Scalar](<#func-scalarbls12377-zero>)
+- [type ScalarBls12377Gt](<#type-scalarbls12377gt>)
+  - [func (s *ScalarBls12377Gt) Add(rhs Scalar) Scalar](<#func-scalarbls12377gt-add>)
+  - [func (s *ScalarBls12377Gt) BigInt() *big.Int](<#func-scalarbls12377gt-bigint>)
+  - [func (s *ScalarBls12377Gt) Bytes() []byte](<#func-scalarbls12377gt-bytes>)
+  - [func (s *ScalarBls12377Gt) Clone() Scalar](<#func-scalarbls12377gt-clone>)
+  - [func (s *ScalarBls12377Gt) Cmp(rhs Scalar) int](<#func-scalarbls12377gt-cmp>)
+  - [func (s *ScalarBls12377Gt) Cube() Scalar](<#func-scalarbls12377gt-cube>)
+  - [func (s *ScalarBls12377Gt) Div(rhs Scalar) Scalar](<#func-scalarbls12377gt-div>)
+  - [func (s *ScalarBls12377Gt) Double() Scalar](<#func-scalarbls12377gt-double>)
+  - [func (s *ScalarBls12377Gt) Hash(bytes []byte) Scalar](<#func-scalarbls12377gt-hash>)
+  - [func (s *ScalarBls12377Gt) Invert() (Scalar, error)](<#func-scalarbls12377gt-invert>)
+  - [func (s *ScalarBls12377Gt) IsEven() bool](<#func-scalarbls12377gt-iseven>)
+  - [func (s *ScalarBls12377Gt) IsOdd() bool](<#func-scalarbls12377gt-isodd>)
+  - [func (s *ScalarBls12377Gt) IsOne() bool](<#func-scalarbls12377gt-isone>)
+  - [func (s *ScalarBls12377Gt) IsZero() bool](<#func-scalarbls12377gt-iszero>)
+  - [func (s *ScalarBls12377Gt) MarshalBinary() ([]byte, error)](<#func-scalarbls12377gt-marshalbinary>)
+  - [func (s *ScalarBls12377Gt) MarshalJSON() ([]byte, error)](<#func-scalarbls12377gt-marshaljson>)
+  - [func (s *ScalarBls12377Gt) MarshalText() ([]byte, error)](<#func-scalarbls12377gt-marshaltext>)
+  - [func (s *ScalarBls12377Gt) Mul(rhs Scalar) Scalar](<#func-scalarbls12377gt-mul>)
+  - [func (s *ScalarBls12377Gt) MulAdd(y, z Scalar) Scalar](<#func-scalarbls12377gt-muladd>)
+  - [func (s *ScalarBls12377Gt) Neg() Scalar](<#func-scalarbls12377gt-neg>)
+  - [func (s *ScalarBls12377Gt) New(input int) Scalar](<#func-scalarbls12377gt-new>)
+  - [func (s *ScalarBls12377Gt) One() Scalar](<#func-scalarbls12377gt-one>)
+  - [func (s *ScalarBls12377Gt) Point() Point](<#func-scalarbls12377gt-point>)
+  - [func (s *ScalarBls12377Gt) Random(reader io.Reader) Scalar](<#func-scalarbls12377gt-random>)
+  - [func (s *ScalarBls12377Gt) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarbls12377gt-setbigint>)
+  - [func (s *ScalarBls12377Gt) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarbls12377gt-setbytes>)
+  - [func (s *ScalarBls12377Gt) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarbls12377gt-setbyteswide>)
+  - [func (s *ScalarBls12377Gt) Sqrt() (Scalar, error)](<#func-scalarbls12377gt-sqrt>)
+  - [func (s *ScalarBls12377Gt) Square() Scalar](<#func-scalarbls12377gt-square>)
+  - [func (s *ScalarBls12377Gt) Sub(rhs Scalar) Scalar](<#func-scalarbls12377gt-sub>)
+  - [func (s *ScalarBls12377Gt) UnmarshalBinary(input []byte) error](<#func-scalarbls12377gt-unmarshalbinary>)
+  - [func (s *ScalarBls12377Gt) UnmarshalJSON(input []byte) error](<#func-scalarbls12377gt-unmarshaljson>)
+  - [func (s *ScalarBls12377Gt) UnmarshalText(input []byte) error](<#func-scalarbls12377gt-unmarshaltext>)
+  - [func (s *ScalarBls12377Gt) Zero() Scalar](<#func-scalarbls12377gt-zero>)
+- [type ScalarBls12381](<#type-scalarbls12381>)
+  - [func (s *ScalarBls12381) Add(rhs Scalar) Scalar](<#func-scalarbls12381-add>)
+  - [func (s *ScalarBls12381) BigInt() *big.Int](<#func-scalarbls12381-bigint>)
+  - [func (s *ScalarBls12381) Bytes() []byte](<#func-scalarbls12381-bytes>)
+  - [func (s *ScalarBls12381) Clone() Scalar](<#func-scalarbls12381-clone>)
+  - [func (s *ScalarBls12381) Cmp(rhs Scalar) int](<#func-scalarbls12381-cmp>)
+  - [func (s *ScalarBls12381) Cube() Scalar](<#func-scalarbls12381-cube>)
+  - [func (s *ScalarBls12381) Div(rhs Scalar) Scalar](<#func-scalarbls12381-div>)
+  - [func (s *ScalarBls12381) Double() Scalar](<#func-scalarbls12381-double>)
+  - [func (s *ScalarBls12381) Hash(bytes []byte) Scalar](<#func-scalarbls12381-hash>)
+  - [func (s *ScalarBls12381) Invert() (Scalar, error)](<#func-scalarbls12381-invert>)
+  - [func (s *ScalarBls12381) IsEven() bool](<#func-scalarbls12381-iseven>)
+  - [func (s *ScalarBls12381) IsOdd() bool](<#func-scalarbls12381-isodd>)
+  - [func (s *ScalarBls12381) IsOne() bool](<#func-scalarbls12381-isone>)
+  - [func (s *ScalarBls12381) IsZero() bool](<#func-scalarbls12381-iszero>)
+  - [func (s *ScalarBls12381) MarshalBinary() ([]byte, error)](<#func-scalarbls12381-marshalbinary>)
+  - [func (s *ScalarBls12381) MarshalJSON() ([]byte, error)](<#func-scalarbls12381-marshaljson>)
+  - [func (s *ScalarBls12381) MarshalText() ([]byte, error)](<#func-scalarbls12381-marshaltext>)
+  - [func (s *ScalarBls12381) Mul(rhs Scalar) Scalar](<#func-scalarbls12381-mul>)
+  - [func (s *ScalarBls12381) MulAdd(y, z Scalar) Scalar](<#func-scalarbls12381-muladd>)
+  - [func (s *ScalarBls12381) Neg() Scalar](<#func-scalarbls12381-neg>)
+  - [func (s *ScalarBls12381) New(value int) Scalar](<#func-scalarbls12381-new>)
+  - [func (s *ScalarBls12381) One() Scalar](<#func-scalarbls12381-one>)
+  - [func (s *ScalarBls12381) Order() *big.Int](<#func-scalarbls12381-order>)
+  - [func (s *ScalarBls12381) Point() Point](<#func-scalarbls12381-point>)
+  - [func (s *ScalarBls12381) Random(reader io.Reader) Scalar](<#func-scalarbls12381-random>)
+  - [func (s *ScalarBls12381) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarbls12381-setbigint>)
+  - [func (s *ScalarBls12381) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarbls12381-setbytes>)
+  - [func (s *ScalarBls12381) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarbls12381-setbyteswide>)
+  - [func (s *ScalarBls12381) SetPoint(p Point) PairingScalar](<#func-scalarbls12381-setpoint>)
+  - [func (s *ScalarBls12381) Sqrt() (Scalar, error)](<#func-scalarbls12381-sqrt>)
+  - [func (s *ScalarBls12381) Square() Scalar](<#func-scalarbls12381-square>)
+  - [func (s *ScalarBls12381) Sub(rhs Scalar) Scalar](<#func-scalarbls12381-sub>)
+  - [func (s *ScalarBls12381) UnmarshalBinary(input []byte) error](<#func-scalarbls12381-unmarshalbinary>)
+  - [func (s *ScalarBls12381) UnmarshalJSON(input []byte) error](<#func-scalarbls12381-unmarshaljson>)
+  - [func (s *ScalarBls12381) UnmarshalText(input []byte) error](<#func-scalarbls12381-unmarshaltext>)
+  - [func (s *ScalarBls12381) Zero() Scalar](<#func-scalarbls12381-zero>)
+- [type ScalarBls12381Gt](<#type-scalarbls12381gt>)
+  - [func (s *ScalarBls12381Gt) Add(rhs Scalar) Scalar](<#func-scalarbls12381gt-add>)
+  - [func (s *ScalarBls12381Gt) BigInt() *big.Int](<#func-scalarbls12381gt-bigint>)
+  - [func (s *ScalarBls12381Gt) Bytes() []byte](<#func-scalarbls12381gt-bytes>)
+  - [func (s *ScalarBls12381Gt) Clone() Scalar](<#func-scalarbls12381gt-clone>)
+  - [func (s *ScalarBls12381Gt) Cmp(rhs Scalar) int](<#func-scalarbls12381gt-cmp>)
+  - [func (s *ScalarBls12381Gt) Cube() Scalar](<#func-scalarbls12381gt-cube>)
+  - [func (s *ScalarBls12381Gt) Div(rhs Scalar) Scalar](<#func-scalarbls12381gt-div>)
+  - [func (s *ScalarBls12381Gt) Double() Scalar](<#func-scalarbls12381gt-double>)
+  - [func (s *ScalarBls12381Gt) Hash(bytes []byte) Scalar](<#func-scalarbls12381gt-hash>)
+  - [func (s *ScalarBls12381Gt) Invert() (Scalar, error)](<#func-scalarbls12381gt-invert>)
+  - [func (s *ScalarBls12381Gt) IsEven() bool](<#func-scalarbls12381gt-iseven>)
+  - [func (s *ScalarBls12381Gt) IsOdd() bool](<#func-scalarbls12381gt-isodd>)
+  - [func (s *ScalarBls12381Gt) IsOne() bool](<#func-scalarbls12381gt-isone>)
+  - [func (s *ScalarBls12381Gt) IsZero() bool](<#func-scalarbls12381gt-iszero>)
+  - [func (s *ScalarBls12381Gt) MarshalBinary() ([]byte, error)](<#func-scalarbls12381gt-marshalbinary>)
+  - [func (s *ScalarBls12381Gt) MarshalJSON() ([]byte, error)](<#func-scalarbls12381gt-marshaljson>)
+  - [func (s *ScalarBls12381Gt) MarshalText() ([]byte, error)](<#func-scalarbls12381gt-marshaltext>)
+  - [func (s *ScalarBls12381Gt) Mul(rhs Scalar) Scalar](<#func-scalarbls12381gt-mul>)
+  - [func (s *ScalarBls12381Gt) MulAdd(y, z Scalar) Scalar](<#func-scalarbls12381gt-muladd>)
+  - [func (s *ScalarBls12381Gt) Neg() Scalar](<#func-scalarbls12381gt-neg>)
+  - [func (s *ScalarBls12381Gt) New(input int) Scalar](<#func-scalarbls12381gt-new>)
+  - [func (s *ScalarBls12381Gt) One() Scalar](<#func-scalarbls12381gt-one>)
+  - [func (s *ScalarBls12381Gt) Point() Point](<#func-scalarbls12381gt-point>)
+  - [func (s *ScalarBls12381Gt) Random(reader io.Reader) Scalar](<#func-scalarbls12381gt-random>)
+  - [func (s *ScalarBls12381Gt) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarbls12381gt-setbigint>)
+  - [func (s *ScalarBls12381Gt) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarbls12381gt-setbytes>)
+  - [func (s *ScalarBls12381Gt) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarbls12381gt-setbyteswide>)
+  - [func (s *ScalarBls12381Gt) Sqrt() (Scalar, error)](<#func-scalarbls12381gt-sqrt>)
+  - [func (s *ScalarBls12381Gt) Square() Scalar](<#func-scalarbls12381gt-square>)
+  - [func (s *ScalarBls12381Gt) Sub(rhs Scalar) Scalar](<#func-scalarbls12381gt-sub>)
+  - [func (s *ScalarBls12381Gt) UnmarshalBinary(input []byte) error](<#func-scalarbls12381gt-unmarshalbinary>)
+  - [func (s *ScalarBls12381Gt) UnmarshalJSON(input []byte) error](<#func-scalarbls12381gt-unmarshaljson>)
+  - [func (s *ScalarBls12381Gt) UnmarshalText(input []byte) error](<#func-scalarbls12381gt-unmarshaltext>)
+  - [func (s *ScalarBls12381Gt) Zero() Scalar](<#func-scalarbls12381gt-zero>)
+- [type ScalarEd25519](<#type-scalared25519>)
+  - [func (s *ScalarEd25519) Add(rhs Scalar) Scalar](<#func-scalared25519-add>)
+  - [func (s *ScalarEd25519) BigInt() *big.Int](<#func-scalared25519-bigint>)
+  - [func (s *ScalarEd25519) Bytes() []byte](<#func-scalared25519-bytes>)
+  - [func (s *ScalarEd25519) Clone() Scalar](<#func-scalared25519-clone>)
+  - [func (s *ScalarEd25519) Cmp(rhs Scalar) int](<#func-scalared25519-cmp>)
+  - [func (s *ScalarEd25519) Cube() Scalar](<#func-scalared25519-cube>)
+  - [func (s *ScalarEd25519) Div(rhs Scalar) Scalar](<#func-scalared25519-div>)
+  - [func (s *ScalarEd25519) Double() Scalar](<#func-scalared25519-double>)
+  - [func (s *ScalarEd25519) GetEdwardsScalar() *edwards25519.Scalar](<#func-scalared25519-getedwardsscalar>)
+  - [func (s *ScalarEd25519) Hash(bytes []byte) Scalar](<#func-scalared25519-hash>)
+  - [func (s *ScalarEd25519) Invert() (Scalar, error)](<#func-scalared25519-invert>)
+  - [func (s *ScalarEd25519) IsEven() bool](<#func-scalared25519-iseven>)
+  - [func (s *ScalarEd25519) IsOdd() bool](<#func-scalared25519-isodd>)
+  - [func (s *ScalarEd25519) IsOne() bool](<#func-scalared25519-isone>)
+  - [func (s *ScalarEd25519) IsZero() bool](<#func-scalared25519-iszero>)
+  - [func (s *ScalarEd25519) MarshalBinary() ([]byte, error)](<#func-scalared25519-marshalbinary>)
+  - [func (s *ScalarEd25519) MarshalJSON() ([]byte, error)](<#func-scalared25519-marshaljson>)
+  - [func (s *ScalarEd25519) MarshalText() ([]byte, error)](<#func-scalared25519-marshaltext>)
+  - [func (s *ScalarEd25519) Mul(rhs Scalar) Scalar](<#func-scalared25519-mul>)
+  - [func (s *ScalarEd25519) MulAdd(y, z Scalar) Scalar](<#func-scalared25519-muladd>)
+  - [func (s *ScalarEd25519) Neg() Scalar](<#func-scalared25519-neg>)
+  - [func (s *ScalarEd25519) New(input int) Scalar](<#func-scalared25519-new>)
+  - [func (s *ScalarEd25519) One() Scalar](<#func-scalared25519-one>)
+  - [func (s *ScalarEd25519) Point() Point](<#func-scalared25519-point>)
+  - [func (s *ScalarEd25519) Random(reader io.Reader) Scalar](<#func-scalared25519-random>)
+  - [func (s *ScalarEd25519) SetBigInt(x *big.Int) (Scalar, error)](<#func-scalared25519-setbigint>)
+  - [func (s *ScalarEd25519) SetBytes(input []byte) (Scalar, error)](<#func-scalared25519-setbytes>)
+  - [func (s *ScalarEd25519) SetBytesCanonical(bytes []byte) (Scalar, error)](<#func-scalared25519-setbytescanonical>)
+  - [func (s *ScalarEd25519) SetBytesClamping(bytes []byte) (Scalar, error)](<#func-scalared25519-setbytesclamping>)
+  - [func (s *ScalarEd25519) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalared25519-setbyteswide>)
+  - [func (s *ScalarEd25519) SetEdwardsScalar(sc *edwards25519.Scalar) *ScalarEd25519](<#func-scalared25519-setedwardsscalar>)
+  - [func (s *ScalarEd25519) Sqrt() (Scalar, error)](<#func-scalared25519-sqrt>)
+  - [func (s *ScalarEd25519) Square() Scalar](<#func-scalared25519-square>)
+  - [func (s *ScalarEd25519) Sub(rhs Scalar) Scalar](<#func-scalared25519-sub>)
+  - [func (s *ScalarEd25519) UnmarshalBinary(input []byte) error](<#func-scalared25519-unmarshalbinary>)
+  - [func (s *ScalarEd25519) UnmarshalJSON(input []byte) error](<#func-scalared25519-unmarshaljson>)
+  - [func (s *ScalarEd25519) UnmarshalText(input []byte) error](<#func-scalared25519-unmarshaltext>)
+  - [func (s *ScalarEd25519) Zero() Scalar](<#func-scalared25519-zero>)
+- [type ScalarK256](<#type-scalark256>)
+  - [func (s *ScalarK256) Add(rhs Scalar) Scalar](<#func-scalark256-add>)
+  - [func (s *ScalarK256) BigInt() *big.Int](<#func-scalark256-bigint>)
+  - [func (s *ScalarK256) Bytes() []byte](<#func-scalark256-bytes>)
+  - [func (s *ScalarK256) Clone() Scalar](<#func-scalark256-clone>)
+  - [func (s *ScalarK256) Cmp(rhs Scalar) int](<#func-scalark256-cmp>)
+  - [func (s *ScalarK256) Cube() Scalar](<#func-scalark256-cube>)
+  - [func (s *ScalarK256) Div(rhs Scalar) Scalar](<#func-scalark256-div>)
+  - [func (s *ScalarK256) Double() Scalar](<#func-scalark256-double>)
+  - [func (s *ScalarK256) Hash(bytes []byte) Scalar](<#func-scalark256-hash>)
+  - [func (s *ScalarK256) Invert() (Scalar, error)](<#func-scalark256-invert>)
+  - [func (s *ScalarK256) IsEven() bool](<#func-scalark256-iseven>)
+  - [func (s *ScalarK256) IsOdd() bool](<#func-scalark256-isodd>)
+  - [func (s *ScalarK256) IsOne() bool](<#func-scalark256-isone>)
+  - [func (s *ScalarK256) IsZero() bool](<#func-scalark256-iszero>)
+  - [func (s *ScalarK256) MarshalBinary() ([]byte, error)](<#func-scalark256-marshalbinary>)
+  - [func (s *ScalarK256) MarshalJSON() ([]byte, error)](<#func-scalark256-marshaljson>)
+  - [func (s *ScalarK256) MarshalText() ([]byte, error)](<#func-scalark256-marshaltext>)
+  - [func (s *ScalarK256) Mul(rhs Scalar) Scalar](<#func-scalark256-mul>)
+  - [func (s *ScalarK256) MulAdd(y, z Scalar) Scalar](<#func-scalark256-muladd>)
+  - [func (s *ScalarK256) Neg() Scalar](<#func-scalark256-neg>)
+  - [func (s *ScalarK256) New(value int) Scalar](<#func-scalark256-new>)
+  - [func (s *ScalarK256) One() Scalar](<#func-scalark256-one>)
+  - [func (s *ScalarK256) Point() Point](<#func-scalark256-point>)
+  - [func (s *ScalarK256) Random(reader io.Reader) Scalar](<#func-scalark256-random>)
+  - [func (s *ScalarK256) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalark256-setbigint>)
+  - [func (s *ScalarK256) SetBytes(bytes []byte) (Scalar, error)](<#func-scalark256-setbytes>)
+  - [func (s *ScalarK256) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalark256-setbyteswide>)
+  - [func (s *ScalarK256) Sqrt() (Scalar, error)](<#func-scalark256-sqrt>)
+  - [func (s *ScalarK256) Square() Scalar](<#func-scalark256-square>)
+  - [func (s *ScalarK256) Sub(rhs Scalar) Scalar](<#func-scalark256-sub>)
+  - [func (s *ScalarK256) UnmarshalBinary(input []byte) error](<#func-scalark256-unmarshalbinary>)
+  - [func (s *ScalarK256) UnmarshalJSON(input []byte) error](<#func-scalark256-unmarshaljson>)
+  - [func (s *ScalarK256) UnmarshalText(input []byte) error](<#func-scalark256-unmarshaltext>)
+  - [func (s *ScalarK256) Zero() Scalar](<#func-scalark256-zero>)
+- [type ScalarP256](<#type-scalarp256>)
+  - [func (s *ScalarP256) Add(rhs Scalar) Scalar](<#func-scalarp256-add>)
+  - [func (s *ScalarP256) BigInt() *big.Int](<#func-scalarp256-bigint>)
+  - [func (s *ScalarP256) Bytes() []byte](<#func-scalarp256-bytes>)
+  - [func (s *ScalarP256) Clone() Scalar](<#func-scalarp256-clone>)
+  - [func (s *ScalarP256) Cmp(rhs Scalar) int](<#func-scalarp256-cmp>)
+  - [func (s *ScalarP256) Cube() Scalar](<#func-scalarp256-cube>)
+  - [func (s *ScalarP256) Div(rhs Scalar) Scalar](<#func-scalarp256-div>)
+  - [func (s *ScalarP256) Double() Scalar](<#func-scalarp256-double>)
+  - [func (s *ScalarP256) Hash(bytes []byte) Scalar](<#func-scalarp256-hash>)
+  - [func (s *ScalarP256) Invert() (Scalar, error)](<#func-scalarp256-invert>)
+  - [func (s *ScalarP256) IsEven() bool](<#func-scalarp256-iseven>)
+  - [func (s *ScalarP256) IsOdd() bool](<#func-scalarp256-isodd>)
+  - [func (s *ScalarP256) IsOne() bool](<#func-scalarp256-isone>)
+  - [func (s *ScalarP256) IsZero() bool](<#func-scalarp256-iszero>)
+  - [func (s *ScalarP256) MarshalBinary() ([]byte, error)](<#func-scalarp256-marshalbinary>)
+  - [func (s *ScalarP256) MarshalJSON() ([]byte, error)](<#func-scalarp256-marshaljson>)
+  - [func (s *ScalarP256) MarshalText() ([]byte, error)](<#func-scalarp256-marshaltext>)
+  - [func (s *ScalarP256) Mul(rhs Scalar) Scalar](<#func-scalarp256-mul>)
+  - [func (s *ScalarP256) MulAdd(y, z Scalar) Scalar](<#func-scalarp256-muladd>)
+  - [func (s *ScalarP256) Neg() Scalar](<#func-scalarp256-neg>)
+  - [func (s *ScalarP256) New(value int) Scalar](<#func-scalarp256-new>)
+  - [func (s *ScalarP256) One() Scalar](<#func-scalarp256-one>)
+  - [func (s *ScalarP256) Point() Point](<#func-scalarp256-point>)
+  - [func (s *ScalarP256) Random(reader io.Reader) Scalar](<#func-scalarp256-random>)
+  - [func (s *ScalarP256) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarp256-setbigint>)
+  - [func (s *ScalarP256) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarp256-setbytes>)
+  - [func (s *ScalarP256) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarp256-setbyteswide>)
+  - [func (s *ScalarP256) Sqrt() (Scalar, error)](<#func-scalarp256-sqrt>)
+  - [func (s *ScalarP256) Square() Scalar](<#func-scalarp256-square>)
+  - [func (s *ScalarP256) Sub(rhs Scalar) Scalar](<#func-scalarp256-sub>)
+  - [func (s *ScalarP256) UnmarshalBinary(input []byte) error](<#func-scalarp256-unmarshalbinary>)
+  - [func (s *ScalarP256) UnmarshalJSON(input []byte) error](<#func-scalarp256-unmarshaljson>)
+  - [func (s *ScalarP256) UnmarshalText(input []byte) error](<#func-scalarp256-unmarshaltext>)
+  - [func (s *ScalarP256) Zero() Scalar](<#func-scalarp256-zero>)
+- [type ScalarPallas](<#type-scalarpallas>)
+  - [func (s *ScalarPallas) Add(rhs Scalar) Scalar](<#func-scalarpallas-add>)
+  - [func (s *ScalarPallas) BigInt() *big.Int](<#func-scalarpallas-bigint>)
+  - [func (s *ScalarPallas) Bytes() []byte](<#func-scalarpallas-bytes>)
+  - [func (s *ScalarPallas) Clone() Scalar](<#func-scalarpallas-clone>)
+  - [func (s *ScalarPallas) Cmp(rhs Scalar) int](<#func-scalarpallas-cmp>)
+  - [func (s *ScalarPallas) Cube() Scalar](<#func-scalarpallas-cube>)
+  - [func (s *ScalarPallas) Div(rhs Scalar) Scalar](<#func-scalarpallas-div>)
+  - [func (s *ScalarPallas) Double() Scalar](<#func-scalarpallas-double>)
+  - [func (s *ScalarPallas) GetFq() *fq.Fq](<#func-scalarpallas-getfq>)
+  - [func (s *ScalarPallas) Hash(bytes []byte) Scalar](<#func-scalarpallas-hash>)
+  - [func (s *ScalarPallas) Invert() (Scalar, error)](<#func-scalarpallas-invert>)
+  - [func (s *ScalarPallas) IsEven() bool](<#func-scalarpallas-iseven>)
+  - [func (s *ScalarPallas) IsOdd() bool](<#func-scalarpallas-isodd>)
+  - [func (s *ScalarPallas) IsOne() bool](<#func-scalarpallas-isone>)
+  - [func (s *ScalarPallas) IsZero() bool](<#func-scalarpallas-iszero>)
+  - [func (s *ScalarPallas) MarshalBinary() ([]byte, error)](<#func-scalarpallas-marshalbinary>)
+  - [func (s *ScalarPallas) MarshalJSON() ([]byte, error)](<#func-scalarpallas-marshaljson>)
+  - [func (s *ScalarPallas) MarshalText() ([]byte, error)](<#func-scalarpallas-marshaltext>)
+  - [func (s *ScalarPallas) Mul(rhs Scalar) Scalar](<#func-scalarpallas-mul>)
+  - [func (s *ScalarPallas) MulAdd(y, z Scalar) Scalar](<#func-scalarpallas-muladd>)
+  - [func (s *ScalarPallas) Neg() Scalar](<#func-scalarpallas-neg>)
+  - [func (s *ScalarPallas) New(value int) Scalar](<#func-scalarpallas-new>)
+  - [func (s *ScalarPallas) One() Scalar](<#func-scalarpallas-one>)
+  - [func (s *ScalarPallas) Point() Point](<#func-scalarpallas-point>)
+  - [func (s *ScalarPallas) Random(reader io.Reader) Scalar](<#func-scalarpallas-random>)
+  - [func (s *ScalarPallas) SetBigInt(v *big.Int) (Scalar, error)](<#func-scalarpallas-setbigint>)
+  - [func (s *ScalarPallas) SetBytes(bytes []byte) (Scalar, error)](<#func-scalarpallas-setbytes>)
+  - [func (s *ScalarPallas) SetBytesWide(bytes []byte) (Scalar, error)](<#func-scalarpallas-setbyteswide>)
+  - [func (s *ScalarPallas) SetFq(fq *fq.Fq) *ScalarPallas](<#func-scalarpallas-setfq>)
+  - [func (s *ScalarPallas) Sqrt() (Scalar, error)](<#func-scalarpallas-sqrt>)
+  - [func (s *ScalarPallas) Square() Scalar](<#func-scalarpallas-square>)
+  - [func (s *ScalarPallas) Sub(rhs Scalar) Scalar](<#func-scalarpallas-sub>)
+  - [func (s *ScalarPallas) UnmarshalBinary(input []byte) error](<#func-scalarpallas-unmarshalbinary>)
+  - [func (s *ScalarPallas) UnmarshalJSON(input []byte) error](<#func-scalarpallas-unmarshaljson>)
+  - [func (s *ScalarPallas) UnmarshalText(input []byte) error](<#func-scalarpallas-unmarshaltext>)
+  - [func (s *ScalarPallas) Zero() Scalar](<#func-scalarpallas-zero>)
+
+
+## Constants
+
+```go
+const (
+    K256Name       = "secp256k1"
+    BLS12381G1Name = "BLS12381G1"
+    BLS12381G2Name = "BLS12381G2"
+    BLS12831Name   = "BLS12831"
+    P256Name       = "P-256"
+    ED25519Name    = "ed25519"
+    PallasName     = "pallas"
+    BLS12377G1Name = "BLS12377G1"
+    BLS12377G2Name = "BLS12377G2"
+    BLS12377Name   = "BLS12377"
+)
+```
+
+## func [Ed25519Order](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L267>)
+
+```go
+func Ed25519Order() *big.Int
+```
+
+SubgroupOrder returns the order of the Ed25519 base Point\.
+
+## func [VerifyEcdsa](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ecdsa.go#L30>)
+
+```go
+func VerifyEcdsa(pk *EcPoint, hash []byte, sig *EcdsaSignature) bool
+```
+
+Verifies ECDSA signature using core types\.
+
+## type [Bls12381Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L171>)
+
+```go
+type Bls12381Scalar struct{}
+```
+
+### func [NewBls12381Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L176>)
+
+```go
+func NewBls12381Scalar() *Bls12381Scalar
+```
+
+### func \(Bls12381Scalar\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L180>)
+
+```go
+func (k Bls12381Scalar) Add(x, y *big.Int) *big.Int
+```
+
+### func \(Bls12381Scalar\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L232>)
+
+```go
+func (k Bls12381Scalar) Bytes(x *big.Int) []byte
+```
+
+### func \(Bls12381Scalar\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L207>)
+
+```go
+func (k Bls12381Scalar) Div(x, y *big.Int) *big.Int
+```
+
+### func \(Bls12381Scalar\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L213>)
+
+```go
+func (k Bls12381Scalar) Hash(input []byte) *big.Int
+```
+
+### func \(Bls12381Scalar\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L238>)
+
+```go
+func (k Bls12381Scalar) IsValid(x *big.Int) bool
+```
+
+### func \(Bls12381Scalar\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L200>)
+
+```go
+func (k Bls12381Scalar) Mul(x, y *big.Int) *big.Int
+```
+
+### func \(Bls12381Scalar\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L194>)
+
+```go
+func (k Bls12381Scalar) Neg(x *big.Int) *big.Int
+```
+
+### func \(Bls12381Scalar\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L217>)
+
+```go
+func (k Bls12381Scalar) Random() (*big.Int, error)
+```
+
+### func \(Bls12381Scalar\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L187>)
+
+```go
+func (k Bls12381Scalar) Sub(x, y *big.Int) *big.Int
+```
+
+## type [Curve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L382-L386>)
+
+Curve represents a named elliptic curve with a scalar field and point group
+
+```go
+type Curve struct {
+    Scalar Scalar
+    Point  Point
+    Name   string
+}
+```
+
+### func [BLS12377G1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L537>)
+
+```go
+func BLS12377G1() *Curve
+```
+
+BLS12377G1 returns the BLS12\-377 curve with points in G1
+
+### func [BLS12377G2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L554>)
+
+```go
+func BLS12377G2() *Curve
+```
+
+BLS12377G2 returns the BLS12\-377 curve with points in G2
+
+### func [BLS12381G1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L484>)
+
+```go
+func BLS12381G1() *Curve
+```
+
+BLS12381G1 returns the BLS12\-381 curve with points in G1
+
+### func [BLS12381G2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L501>)
+
+```go
+func BLS12381G2() *Curve
+```
+
+BLS12381G2 returns the BLS12\-381 curve with points in G2
+
+### func [ED25519](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L597>)
+
+```go
+func ED25519() *Curve
+```
+
+### func [GetCurveByName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L443>)
+
+```go
+func GetCurveByName(name string) *Curve
+```
+
+GetCurveByName returns the correct \`Curve\` given the name
+
+### func [K256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L571>)
+
+```go
+func K256() *Curve
+```
+
+K256 returns the secp256k1 curve
+
+### func [P256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L584>)
+
+```go
+func P256() *Curve
+```
+
+### func [PALLAS](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L610>)
+
+```go
+func PALLAS() *Curve
+```
+
+### func \(Curve\) [NewGeneratorPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L392>)
+
+```go
+func (c Curve) NewGeneratorPoint() Point
+```
+
+### func \(Curve\) [NewIdentityPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L396>)
+
+```go
+func (c Curve) NewIdentityPoint() Point
+```
+
+### func \(Curve\) [NewScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L400>)
+
+```go
+func (c Curve) NewScalar() Scalar
+```
+
+### func \(Curve\) [ScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L388>)
+
+```go
+func (c Curve) ScalarBaseMult(sc Scalar) Point
+```
+
+## type [EcPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L45-L48>)
+
+EcPoint represents an elliptic curve Point
+
+```go
+type EcPoint struct {
+    Curve elliptic.Curve
+    X, Y  *big.Int
+}
+```
+
+### func [NewScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L190>)
+
+```go
+func NewScalarBaseMult(curve elliptic.Curve, k *big.Int) (*EcPoint, error)
+```
+
+NewScalarBaseMult creates a Point from the base Point multiplied by a field element
+
+### func [PointFromBytesUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L216>)
+
+```go
+func PointFromBytesUncompressed(curve elliptic.Curve, b []byte) (*EcPoint, error)
+```
+
+PointFromBytesUncompressed outputs uncompressed X || Y similar to https://www.secg.org/sec1-v1.99.dif.pdf section 2\.2 and 2\.3
+
+### func \(\*EcPoint\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L143>)
+
+```go
+func (a *EcPoint) Add(b *EcPoint) (*EcPoint, error)
+```
+
+Add performs elliptic curve addition on two points
+
+### func \(EcPoint\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L205>)
+
+```go
+func (a EcPoint) Bytes() []byte
+```
+
+Bytes returns the bytes represented by this Point with x || y
+
+### func \(EcPoint\) [Equals](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L119>)
+
+```go
+func (a EcPoint) Equals(b *EcPoint) bool
+```
+
+Equals return true if a \+ b have the same x\,y coordinates
+
+### func \(EcPoint\) [IsBasePoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L130>)
+
+```go
+func (a EcPoint) IsBasePoint() bool
+```
+
+IsBasePoint returns true if this Point is curve's base Point
+
+### func \(EcPoint\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L112>)
+
+```go
+func (a EcPoint) IsIdentity() bool
+```
+
+IsIdentity returns true if this Point is the Point at infinity
+
+### func \(EcPoint\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L107>)
+
+```go
+func (a EcPoint) IsOnCurve() bool
+```
+
+### func \(EcPoint\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L103>)
+
+```go
+func (a EcPoint) IsValid() bool
+```
+
+### func \(\*EcPoint\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L82>)
+
+```go
+func (a *EcPoint) MarshalBinary() ([]byte, error)
+```
+
+### func \(EcPoint\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L59>)
+
+```go
+func (a EcPoint) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON serializes
+
+### func \(\*EcPoint\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L161>)
+
+```go
+func (a *EcPoint) Neg() (*EcPoint, error)
+```
+
+Neg returns the negation of a Weierstrass Point\.
+
+### func \(\*EcPoint\) [ScalarMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L175>)
+
+```go
+func (a *EcPoint) ScalarMult(k *big.Int) (*EcPoint, error)
+```
+
+ScalarMult multiplies this Point by a Scalar
+
+### func \(\*EcPoint\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L93>)
+
+```go
+func (a *EcPoint) UnmarshalBinary(data []byte) error
+```
+
+### func \(\*EcPoint\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L67>)
+
+```go
+func (a *EcPoint) UnmarshalJSON(bytes []byte) error
+```
+
+## type [EcPointJson](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_point.go#L53-L56>)
+
+EcPointJson encapsulates the data that is serialized to JSON used internally and not for external use\. Public so other pieces can use for serialization
+
+```go
+type EcPointJson struct {
+    CurveName string
+    X, Y      *big.Int
+}
+```
+
+## type [EcScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L25-L35>)
+
+```go
+type EcScalar interface {
+    Add(x, y *big.Int) *big.Int
+    Sub(x, y *big.Int) *big.Int
+    Neg(x *big.Int) *big.Int
+    Mul(x, y *big.Int) *big.Int
+    Hash(input []byte) *big.Int
+    Div(x, y *big.Int) *big.Int
+    Random() (*big.Int, error)
+    IsValid(x *big.Int) bool
+    Bytes(x *big.Int) []byte // fixed-length byte array
+}
+```
+
+## type [EcdsaSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ecdsa.go#L21-L24>)
+
+EcdsaSignature represents a \(composite\) digital signature
+
+```go
+type EcdsaSignature struct {
+    V    int
+    R, S *big.Int
+}
+```
+
+## type [EcdsaVerify](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ecdsa.go#L18>)
+
+EcdsaVerify runs a curve\- or algorithm\-specific ECDSA verification function on input an ECDSA public \(verification\) key\, a message digest\, and an ECDSA signature\. It must return true if all the parameters are sane and the ECDSA signature is valid\, and false otherwise
+
+```go
+type EcdsaVerify func(pubKey *EcPoint, hash []byte, signature *EcdsaSignature) bool
+```
+
+## type [Ed25519Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L246>)
+
+```go
+type Ed25519Scalar struct{}
+```
+
+### func [NewEd25519Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L251>)
+
+```go
+func NewEd25519Scalar() *Ed25519Scalar
+```
+
+### func \(Ed25519Scalar\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L255>)
+
+```go
+func (k Ed25519Scalar) Add(x, y *big.Int) *big.Int
+```
+
+### func \(Ed25519Scalar\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L324>)
+
+```go
+func (k Ed25519Scalar) Bytes(x *big.Int) []byte
+```
+
+### func \(Ed25519Scalar\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L303>)
+
+```go
+func (k Ed25519Scalar) Div(x, y *big.Int) *big.Int
+```
+
+### func \(Ed25519Scalar\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L317>)
+
+```go
+func (k Ed25519Scalar) Hash(input []byte) *big.Int
+```
+
+### func \(Ed25519Scalar\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L355>)
+
+```go
+func (k Ed25519Scalar) IsValid(x *big.Int) bool
+```
+
+### func \(Ed25519Scalar\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L290>)
+
+```go
+func (k Ed25519Scalar) Mul(x, y *big.Int) *big.Int
+```
+
+### func \(Ed25519Scalar\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L281>)
+
+```go
+func (k Ed25519Scalar) Neg(x *big.Int) *big.Int
+```
+
+### func \(Ed25519Scalar\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L332>)
+
+```go
+func (k Ed25519Scalar) Random() (*big.Int, error)
+```
+
+### func \(Ed25519Scalar\) [RandomWithReader](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L336>)
+
+```go
+func (k Ed25519Scalar) RandomWithReader(r io.Reader) (*big.Int, error)
+```
+
+### func \(Ed25519Scalar\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L268>)
+
+```go
+func (k Ed25519Scalar) Sub(x, y *big.Int) *big.Int
+```
+
+## type [Element](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L28-L31>)
+
+Element is a group element within a finite field\.
+
+```go
+type Element struct {
+    Modulus *Field   `json:"modulus"`
+    Value   *big.Int `json:"value"`
+}
+```
+
+### func \(Element\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L174>)
+
+```go
+func (x Element) Add(y *Element) *Element
+```
+
+Add returns the sum x\+y
+
+### func \(Element\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L233>)
+
+```go
+func (x Element) BigInt() *big.Int
+```
+
+BigInt returns value as a big\.Int
+
+### func \(Element\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L238>)
+
+```go
+func (x Element) Bytes() []byte
+```
+
+Bytes returns the value as bytes
+
+### func \(Element\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L252>)
+
+```go
+func (x Element) Clone() *Element
+```
+
+Clone returns a new copy of the element
+
+### func \(Element\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L208>)
+
+```go
+func (x Element) Div(y *Element) *Element
+```
+
+Div returns the quotient x/y
+
+### func \(Element\) [Field](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L169>)
+
+```go
+func (x Element) Field() *Field
+```
+
+### func \(Element\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L224>)
+
+```go
+func (x Element) Invert() *Element
+```
+
+### func \(Element\) [IsEqual](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L243>)
+
+```go
+func (x Element) IsEqual(y *Element) bool
+```
+
+IsEqual returns x == y
+
+### func \(\*Element\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L42>)
+
+```go
+func (x *Element) MarshalJSON() ([]byte, error)
+```
+
+Marshal Element to JSON
+
+### func \(Element\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L199>)
+
+```go
+func (x Element) Mul(y *Element) *Element
+```
+
+Mul returns the product x\*y
+
+### func \(Element\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L192>)
+
+```go
+func (x Element) Neg() *Element
+```
+
+Neg returns the field negation
+
+### func \(Element\) [Pow](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L218>)
+
+```go
+func (x Element) Pow(y *Element) *Element
+```
+
+Pow computes x^y reduced by the modulus
+
+### func \(Element\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L228>)
+
+```go
+func (x Element) Sqrt() *Element
+```
+
+### func \(Element\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L183>)
+
+```go
+func (x Element) Sub(y *Element) *Element
+```
+
+Sub returns the difference x\-y
+
+### func \(\*Element\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L49>)
+
+```go
+func (x *Element) UnmarshalJSON(bytes []byte) error
+```
+
+## type [ElementJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L36-L39>)
+
+ElementJSON is used in JSON\<\>Element conversions\. For years\, big\.Int hasn't properly supported JSON unmarshaling https://github.com/golang/go/issues/28154
+
+```go
+type ElementJSON struct {
+    Modulus string `json:"modulus"`
+    Value   string `json:"value"`
+}
+```
+
+## type [Ep](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L687-L691>)
+
+```go
+type Ep struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*Ep\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L772>)
+
+```go
+func (p *Ep) Add(lhs *Ep, rhs *Ep) *Ep
+```
+
+### func \(\*Ep\) [CMove](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L1010>)
+
+```go
+func (p *Ep) CMove(lhs, rhs *Ep, condition int) *Ep
+```
+
+### func \(Ep\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L965>)
+
+```go
+func (p Ep) CurveName() string
+```
+
+### func \(\*Ep\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L736>)
+
+```go
+func (p *Ep) Double(other *Ep) *Ep
+```
+
+### func \(\*Ep\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L847>)
+
+```go
+func (p *Ep) Equal(other *Ep) bool
+```
+
+### func \(\*Ep\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L906>)
+
+```go
+func (p *Ep) FromAffineCompressed(bytes []byte) (*Ep, error)
+```
+
+### func \(\*Ep\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L936>)
+
+```go
+func (p *Ep) FromAffineUncompressed(bytes []byte) (*Ep, error)
+```
+
+### func \(\*Ep\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L725>)
+
+```go
+func (p *Ep) Generator() *Ep
+```
+
+### func \(\*Ep\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L699>)
+
+```go
+func (p *Ep) Hash(bytes []byte) *Ep
+```
+
+### func \(\*Ep\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L718>)
+
+```go
+func (p *Ep) Identity() *Ep
+```
+
+### func \(\*Ep\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L732>)
+
+```go
+func (p *Ep) IsIdentity() bool
+```
+
+### func \(\*Ep\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L993>)
+
+```go
+func (p *Ep) IsOnCurve() bool
+```
+
+### func \(\*Ep\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L826>)
+
+```go
+func (p *Ep) Mul(point *Ep, scalar *fq.Fq) *Ep
+```
+
+### func \(\*Ep\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L765>)
+
+```go
+func (p *Ep) Neg(other *Ep) *Ep
+```
+
+### func \(\*Ep\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L693>)
+
+```go
+func (p *Ep) Random(reader io.Reader) *Ep
+```
+
+### func \(\*Ep\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L859>)
+
+```go
+func (p *Ep) Set(other *Ep) *Ep
+```
+
+### func \(\*Ep\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L822>)
+
+```go
+func (p *Ep) Sub(lhs, rhs *Ep) *Ep
+```
+
+### func \(Ep\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L969>)
+
+```go
+func (p Ep) SumOfProducts(points []*Ep, scalars []Scalar) *Ep
+```
+
+### func \(\*Ep\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L885>)
+
+```go
+func (p *Ep) ToAffineCompressed() []byte
+```
+
+### func \(\*Ep\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L898>)
+
+```go
+func (p *Ep) ToAffineUncompressed() []byte
+```
+
+### func \(\*Ep\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L981>)
+
+```go
+func (p *Ep) X() *fp.Fp
+```
+
+### func \(\*Ep\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L987>)
+
+```go
+func (p *Ep) Y() *fp.Fp
+```
+
+## type [Field](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L23-L25>)
+
+Field is a finite field\.
+
+```go
+type Field struct {
+    *big.Int
+}
+```
+
+### func [NewField](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L74>)
+
+```go
+func NewField(modulus *big.Int) *Field
+```
+
+New is a constructor for a Field\.
+
+### func \(Field\) [ElementFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L134>)
+
+```go
+func (f Field) ElementFromBytes(bytes []byte) *Element
+```
+
+ElementFromBytes initializes a new field element from big\-endian bytes
+
+### func \(Field\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L93>)
+
+```go
+func (f Field) IsValid(value *big.Int) bool
+```
+
+IsValid returns whether or not the value is within \[0\, modulus\)
+
+### func \(Field\) [NewElement](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L98>)
+
+```go
+func (f Field) NewElement(value *big.Int) *Element
+```
+
+### func \(Field\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L106>)
+
+```go
+func (f Field) One() *Element
+```
+
+### func \(Field\) [RandomElement](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L110>)
+
+```go
+func (f Field) RandomElement(r io.Reader) (*Element, error)
+```
+
+### func \(Field\) [ReducedElementFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L163>)
+
+```go
+func (f Field) ReducedElementFromBytes(bytes []byte) *Element
+```
+
+ReducedElementFromBytes initializes a new field element from big\-endian bytes and reduces it by the modulus of the field\.
+
+WARNING: If this is used with cryptographic constructions which rely on a uniform distribution of values\, this may introduce a bias to the value of the returned field element\. This happens when the integer range of the provided bytes is not an integer multiple of the field order\.
+
+Assume we are working in field which a modulus of 3 and the range of the uniform random bytes we provide as input is 5\. Thus\, the set of field elements is \{0\, 1\, 2\} and the set of integer values for the input bytes is: \{0\, 1\, 2\, 3\, 4\}\. What is the distribution of the output values produced by this function?
+
+```
+ReducedElementFromBytes(0) => 0
+ReducedElementFromBytes(1) => 1
+ReducedElementFromBytes(2) => 2
+ReducedElementFromBytes(3) => 0
+ReducedElementFromBytes(4) => 1
+```
+
+For a value space V and random value v\, a uniform distribution is defined as P\[V = v\] = 1/|V| where |V| is to the order of the field\. Using the results from above\, we see that P\[v = 0\] = 2/5\, P\[v = 1\] = 2/5\, and P\[v = 2\] = 1/5\. For a uniform distribution we would expect these to each be equal to 1/3\. As they do not\, this does not return uniform output for that example\.
+
+To see why this is okay if the range is a multiple of the field order\, change the input range to 6 and notice that now each output has a probability of 2/6 = 1/3\, and the output is uniform\.
+
+### func \(Field\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/field.go#L102>)
+
+```go
+func (f Field) Zero() *Element
+```
+
+## type [K256Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L37>)
+
+```go
+type K256Scalar struct{}
+```
+
+### func [NewK256Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L44>)
+
+```go
+func NewK256Scalar() *K256Scalar
+```
+
+### func \(K256Scalar\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L48>)
+
+```go
+func (k K256Scalar) Add(x, y *big.Int) *big.Int
+```
+
+### func \(K256Scalar\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L99>)
+
+```go
+func (k K256Scalar) Bytes(x *big.Int) []byte
+```
+
+### func \(K256Scalar\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L72>)
+
+```go
+func (k K256Scalar) Div(x, y *big.Int) *big.Int
+```
+
+### func \(K256Scalar\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L77>)
+
+```go
+func (k K256Scalar) Hash(input []byte) *big.Int
+```
+
+### func \(K256Scalar\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L95>)
+
+```go
+func (k K256Scalar) IsValid(x *big.Int) bool
+```
+
+### func \(K256Scalar\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L66>)
+
+```go
+func (k K256Scalar) Mul(x, y *big.Int) *big.Int
+```
+
+### func \(K256Scalar\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L60>)
+
+```go
+func (k K256Scalar) Neg(x *big.Int) *big.Int
+```
+
+### func \(K256Scalar\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L81>)
+
+```go
+func (k K256Scalar) Random() (*big.Int, error)
+```
+
+### func \(K256Scalar\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L54>)
+
+```go
+func (k K256Scalar) Sub(x, y *big.Int) *big.Int
+```
+
+## type [P256Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L105>)
+
+```go
+type P256Scalar struct{}
+```
+
+### func [NewP256Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L110>)
+
+```go
+func NewP256Scalar() *P256Scalar
+```
+
+### func \(P256Scalar\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L114>)
+
+```go
+func (k P256Scalar) Add(x, y *big.Int) *big.Int
+```
+
+### func \(P256Scalar\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L165>)
+
+```go
+func (k P256Scalar) Bytes(x *big.Int) []byte
+```
+
+### func \(P256Scalar\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L138>)
+
+```go
+func (k P256Scalar) Div(x, y *big.Int) *big.Int
+```
+
+### func \(P256Scalar\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L143>)
+
+```go
+func (k P256Scalar) Hash(input []byte) *big.Int
+```
+
+### func \(P256Scalar\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L161>)
+
+```go
+func (k P256Scalar) IsValid(x *big.Int) bool
+```
+
+### func \(P256Scalar\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L132>)
+
+```go
+func (k P256Scalar) Mul(x, y *big.Int) *big.Int
+```
+
+### func \(P256Scalar\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L126>)
+
+```go
+func (k P256Scalar) Neg(x *big.Int) *big.Int
+```
+
+### func \(P256Scalar\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L147>)
+
+```go
+func (k P256Scalar) Random() (*big.Int, error)
+```
+
+### func \(P256Scalar\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ec_scalar.go#L120>)
+
+```go
+func (k P256Scalar) Sub(x, y *big.Int) *big.Int
+```
+
+## type [PairingCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L406-L412>)
+
+PairingCurve represents a named elliptic curve that supports pairings
+
+```go
+type PairingCurve struct {
+    Scalar  PairingScalar
+    PointG1 PairingPoint
+    PointG2 PairingPoint
+    GT      Scalar
+    Name    string
+}
+```
+
+### func [BLS12381](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L517>)
+
+```go
+func BLS12381(preferredPoint Point) *PairingCurve
+```
+
+### func [GetPairingCurveByName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L470>)
+
+```go
+func GetPairingCurveByName(name string) *PairingCurve
+```
+
+### func \(PairingCurve\) [NewG1GeneratorPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L422>)
+
+```go
+func (c PairingCurve) NewG1GeneratorPoint() PairingPoint
+```
+
+### func \(PairingCurve\) [NewG1IdentityPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L430>)
+
+```go
+func (c PairingCurve) NewG1IdentityPoint() PairingPoint
+```
+
+### func \(PairingCurve\) [NewG2GeneratorPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L426>)
+
+```go
+func (c PairingCurve) NewG2GeneratorPoint() PairingPoint
+```
+
+### func \(PairingCurve\) [NewG2IdentityPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L434>)
+
+```go
+func (c PairingCurve) NewG2IdentityPoint() PairingPoint
+```
+
+### func \(PairingCurve\) [NewScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L438>)
+
+```go
+func (c PairingCurve) NewScalar() PairingScalar
+```
+
+### func \(PairingCurve\) [ScalarG1BaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L414>)
+
+```go
+func (c PairingCurve) ScalarG1BaseMult(sc Scalar) PairingPoint
+```
+
+### func \(PairingCurve\) [ScalarG2BaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L418>)
+
+```go
+func (c PairingCurve) ScalarG2BaseMult(sc Scalar) PairingPoint
+```
+
+## type [PairingPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L274-L279>)
+
+```go
+type PairingPoint interface {
+    Point
+    OtherGroup() PairingPoint
+    Pairing(rhs PairingPoint) Scalar
+    MultiPairing(...PairingPoint) Scalar
+}
+```
+
+## type [PairingScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L137-L140>)
+
+```go
+type PairingScalar interface {
+    Scalar
+    SetPoint(p Point) PairingScalar
+}
+```
+
+## type [PallasCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L52-L54>)
+
+```go
+type PallasCurve struct {
+    *elliptic.CurveParams
+}
+```
+
+### func [Pallas](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L78>)
+
+```go
+func Pallas() *PallasCurve
+```
+
+### func \(\*PallasCurve\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L96>)
+
+```go
+func (curve *PallasCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*PallasCurve\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L117>)
+
+```go
+func (curve *PallasCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*PallasCurve\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L87>)
+
+```go
+func (curve *PallasCurve) IsOnCurve(x, y *big.Int) bool
+```
+
+### func \(\*PallasCurve\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L83>)
+
+```go
+func (curve *PallasCurve) Params() *elliptic.CurveParams
+```
+
+### func \(\*PallasCurve\) [ScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L147>)
+
+```go
+func (curve *PallasCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
+```
+
+### func \(\*PallasCurve\) [ScalarMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L130>)
+
+```go
+func (curve *PallasCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)
+```
+
+## type [PallasScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L159>)
+
+PallasScalar \- Old interface
+
+```go
+type PallasScalar struct{}
+```
+
+### func [NewPallasScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L161>)
+
+```go
+func NewPallasScalar() *PallasScalar
+```
+
+### func \(PallasScalar\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L165>)
+
+```go
+func (k PallasScalar) Add(x, y *big.Int) *big.Int
+```
+
+### func \(PallasScalar\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L195>)
+
+```go
+func (k PallasScalar) Bytes(x *big.Int) []byte
+```
+
+### func \(PallasScalar\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L185>)
+
+```go
+func (k PallasScalar) Div(x, y *big.Int) *big.Int
+```
+
+### func \(PallasScalar\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L191>)
+
+```go
+func (k PallasScalar) Hash(input []byte) *big.Int
+```
+
+### func \(PallasScalar\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L204>)
+
+```go
+func (k PallasScalar) IsValid(x *big.Int) bool
+```
+
+### func \(PallasScalar\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L180>)
+
+```go
+func (k PallasScalar) Mul(x, y *big.Int) *big.Int
+```
+
+### func \(PallasScalar\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L175>)
+
+```go
+func (k PallasScalar) Neg(x *big.Int) *big.Int
+```
+
+### func \(PallasScalar\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L199>)
+
+```go
+func (k PallasScalar) Random() (*big.Int, error)
+```
+
+### func \(PallasScalar\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L170>)
+
+```go
+func (k PallasScalar) Sub(x, y *big.Int) *big.Int
+```
+
+## type [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L244-L272>)
+
+Point represents an elliptic curve point
+
+```go
+type Point interface {
+    encoding.BinaryMarshaler
+    encoding.BinaryUnmarshaler
+    encoding.TextMarshaler
+    encoding.TextUnmarshaler
+    json.Marshaler
+    json.Unmarshaler
+    Random(reader io.Reader) Point
+    Hash(bytes []byte) Point
+    Identity() Point
+    Generator() Point
+    IsIdentity() bool
+    IsNegative() bool
+    IsOnCurve() bool
+    Double() Point
+    Scalar() Scalar
+    Neg() Point
+    Add(rhs Point) Point
+    Sub(rhs Point) Point
+    Mul(rhs Scalar) Point
+    Equal(rhs Point) bool
+    Set(x, y *big.Int) (Point, error)
+    ToAffineCompressed() []byte
+    ToAffineUncompressed() []byte
+    FromAffineCompressed(bytes []byte) (Point, error)
+    FromAffineUncompressed(bytes []byte) (Point, error)
+    CurveName() string
+    SumOfProducts(points []Point, scalars []Scalar) Point
+}
+```
+
+## type [PointBls12377G1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L33-L35>)
+
+```go
+type PointBls12377G1 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointBls12377G1\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L405>)
+
+```go
+func (p *PointBls12377G1) Add(rhs Point) Point
+```
+
+### func \(\*PointBls12377G1\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L503>)
+
+```go
+func (p *PointBls12377G1) CurveName() string
+```
+
+### func \(\*PointBls12377G1\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L384>)
+
+```go
+func (p *PointBls12377G1) Double() Point
+```
+
+### func \(\*PointBls12377G1\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L444>)
+
+```go
+func (p *PointBls12377G1) Equal(rhs Point) bool
+```
+
+### func \(\*PointBls12377G1\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L479>)
+
+```go
+func (p *PointBls12377G1) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12377G1\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L491>)
+
+```go
+func (p *PointBls12377G1) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12377G1\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L361>)
+
+```go
+func (p *PointBls12377G1) Generator() Point
+```
+
+### func \(\*PointBls12377G1\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L345>)
+
+```go
+func (p *PointBls12377G1) Hash(bytes []byte) Point
+```
+
+### func \(\*PointBls12377G1\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L354>)
+
+```go
+func (p *PointBls12377G1) Identity() Point
+```
+
+### func \(\*PointBls12377G1\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L369>)
+
+```go
+func (p *PointBls12377G1) IsIdentity() bool
+```
+
+### func \(\*PointBls12377G1\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L373>)
+
+```go
+func (p *PointBls12377G1) IsNegative() bool
+```
+
+### func \(\*PointBls12377G1\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L380>)
+
+```go
+func (p *PointBls12377G1) IsOnCurve() bool
+```
+
+### func \(\*PointBls12377G1\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L562>)
+
+```go
+func (p *PointBls12377G1) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointBls12377G1\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L596>)
+
+```go
+func (p *PointBls12377G1) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointBls12377G1\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L579>)
+
+```go
+func (p *PointBls12377G1) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointBls12377G1\) [Modulus](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L558>)
+
+```go
+func (p *PointBls12377G1) Modulus() *big.Int
+```
+
+### func \(\*PointBls12377G1\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L431>)
+
+```go
+func (p *PointBls12377G1) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointBls12377G1\) [MultiPairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L544>)
+
+```go
+func (p *PointBls12377G1) MultiPairing(points ...PairingPoint) Scalar
+```
+
+### func \(\*PointBls12377G1\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L399>)
+
+```go
+func (p *PointBls12377G1) Neg() Point
+```
+
+### func \(\*PointBls12377G1\) [OtherGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L519>)
+
+```go
+func (p *PointBls12377G1) OtherGroup() PairingPoint
+```
+
+### func \(\*PointBls12377G1\) [Pairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L523>)
+
+```go
+func (p *PointBls12377G1) Pairing(rhs PairingPoint) Scalar
+```
+
+### func \(\*PointBls12377G1\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L339>)
+
+```go
+func (p *PointBls12377G1) Random(reader io.Reader) Point
+```
+
+### func \(\*PointBls12377G1\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L392>)
+
+```go
+func (p *PointBls12377G1) Scalar() Scalar
+```
+
+### func \(\*PointBls12377G1\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L453>)
+
+```go
+func (p *PointBls12377G1) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointBls12377G1\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L418>)
+
+```go
+func (p *PointBls12377G1) Sub(rhs Point) Point
+```
+
+### func \(\*PointBls12377G1\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L507>)
+
+```go
+func (p *PointBls12377G1) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointBls12377G1\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L469>)
+
+```go
+func (p *PointBls12377G1) ToAffineCompressed() []byte
+```
+
+### func \(\*PointBls12377G1\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L474>)
+
+```go
+func (p *PointBls12377G1) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointBls12377G1\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L566>)
+
+```go
+func (p *PointBls12377G1) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointBls12377G1\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L600>)
+
+```go
+func (p *PointBls12377G1) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointBls12377G1\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L583>)
+
+```go
+func (p *PointBls12377G1) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointBls12377G1\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L548>)
+
+```go
+func (p *PointBls12377G1) X() *big.Int
+```
+
+### func \(\*PointBls12377G1\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L553>)
+
+```go
+func (p *PointBls12377G1) Y() *big.Int
+```
+
+## type [PointBls12377G2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L37-L39>)
+
+```go
+type PointBls12377G2 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointBls12377G2\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L678>)
+
+```go
+func (p *PointBls12377G2) Add(rhs Point) Point
+```
+
+### func \(\*PointBls12377G2\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L776>)
+
+```go
+func (p *PointBls12377G2) CurveName() string
+```
+
+### func \(\*PointBls12377G2\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L657>)
+
+```go
+func (p *PointBls12377G2) Double() Point
+```
+
+### func \(\*PointBls12377G2\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L717>)
+
+```go
+func (p *PointBls12377G2) Equal(rhs Point) bool
+```
+
+### func \(\*PointBls12377G2\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L752>)
+
+```go
+func (p *PointBls12377G2) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12377G2\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L764>)
+
+```go
+func (p *PointBls12377G2) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12377G2\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L635>)
+
+```go
+func (p *PointBls12377G2) Generator() Point
+```
+
+### func \(\*PointBls12377G2\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L619>)
+
+```go
+func (p *PointBls12377G2) Hash(bytes []byte) Point
+```
+
+### func \(\*PointBls12377G2\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L628>)
+
+```go
+func (p *PointBls12377G2) Identity() Point
+```
+
+### func \(\*PointBls12377G2\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L643>)
+
+```go
+func (p *PointBls12377G2) IsIdentity() bool
+```
+
+### func \(\*PointBls12377G2\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L647>)
+
+```go
+func (p *PointBls12377G2) IsNegative() bool
+```
+
+### func \(\*PointBls12377G2\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L653>)
+
+```go
+func (p *PointBls12377G2) IsOnCurve() bool
+```
+
+### func \(\*PointBls12377G2\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L835>)
+
+```go
+func (p *PointBls12377G2) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointBls12377G2\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L869>)
+
+```go
+func (p *PointBls12377G2) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointBls12377G2\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L852>)
+
+```go
+func (p *PointBls12377G2) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointBls12377G2\) [Modulus](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L831>)
+
+```go
+func (p *PointBls12377G2) Modulus() *big.Int
+```
+
+### func \(\*PointBls12377G2\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L704>)
+
+```go
+func (p *PointBls12377G2) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointBls12377G2\) [MultiPairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L817>)
+
+```go
+func (p *PointBls12377G2) MultiPairing(points ...PairingPoint) Scalar
+```
+
+### func \(\*PointBls12377G2\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L672>)
+
+```go
+func (p *PointBls12377G2) Neg() Point
+```
+
+### func \(\*PointBls12377G2\) [OtherGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L792>)
+
+```go
+func (p *PointBls12377G2) OtherGroup() PairingPoint
+```
+
+### func \(\*PointBls12377G2\) [Pairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L796>)
+
+```go
+func (p *PointBls12377G2) Pairing(rhs PairingPoint) Scalar
+```
+
+### func \(\*PointBls12377G2\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L613>)
+
+```go
+func (p *PointBls12377G2) Random(reader io.Reader) Point
+```
+
+### func \(\*PointBls12377G2\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L665>)
+
+```go
+func (p *PointBls12377G2) Scalar() Scalar
+```
+
+### func \(\*PointBls12377G2\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L726>)
+
+```go
+func (p *PointBls12377G2) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointBls12377G2\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L691>)
+
+```go
+func (p *PointBls12377G2) Sub(rhs Point) Point
+```
+
+### func \(\*PointBls12377G2\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L780>)
+
+```go
+func (p *PointBls12377G2) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointBls12377G2\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L742>)
+
+```go
+func (p *PointBls12377G2) ToAffineCompressed() []byte
+```
+
+### func \(\*PointBls12377G2\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L747>)
+
+```go
+func (p *PointBls12377G2) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointBls12377G2\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L839>)
+
+```go
+func (p *PointBls12377G2) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointBls12377G2\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L873>)
+
+```go
+func (p *PointBls12377G2) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointBls12377G2\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L856>)
+
+```go
+func (p *PointBls12377G2) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointBls12377G2\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L821>)
+
+```go
+func (p *PointBls12377G2) X() *big.Int
+```
+
+### func \(\*PointBls12377G2\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L826>)
+
+```go
+func (p *PointBls12377G2) Y() *big.Int
+```
+
+## type [PointBls12381G1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L31-L33>)
+
+```go
+type PointBls12381G1 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointBls12381G1\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L396>)
+
+```go
+func (p *PointBls12381G1) Add(rhs Point) Point
+```
+
+### func \(\*PointBls12381G1\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L487>)
+
+```go
+func (p *PointBls12381G1) CurveName() string
+```
+
+### func \(\*PointBls12381G1\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L379>)
+
+```go
+func (p *PointBls12381G1) Double() Point
+```
+
+### func \(\*PointBls12381G1\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L435>)
+
+```go
+func (p *PointBls12381G1) Equal(rhs Point) bool
+```
+
+### func \(\*PointBls12381G1\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L471>)
+
+```go
+func (p *PointBls12381G1) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12381G1\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L479>)
+
+```go
+func (p *PointBls12381G1) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12381G1\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L359>)
+
+```go
+func (p *PointBls12381G1) Generator() Point
+```
+
+### func \(\*PointBls12381G1\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L344>)
+
+```go
+func (p *PointBls12381G1) Hash(bytes []byte) Point
+```
+
+### func \(\*PointBls12381G1\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L353>)
+
+```go
+func (p *PointBls12381G1) Identity() Point
+```
+
+### func \(\*PointBls12381G1\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L365>)
+
+```go
+func (p *PointBls12381G1) IsIdentity() bool
+```
+
+### func \(\*PointBls12381G1\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L369>)
+
+```go
+func (p *PointBls12381G1) IsNegative() bool
+```
+
+### func \(\*PointBls12381G1\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L375>)
+
+```go
+func (p *PointBls12381G1) IsOnCurve() bool
+```
+
+### func \(\*PointBls12381G1\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L563>)
+
+```go
+func (p *PointBls12381G1) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointBls12381G1\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L597>)
+
+```go
+func (p *PointBls12381G1) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointBls12381G1\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L580>)
+
+```go
+func (p *PointBls12381G1) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointBls12381G1\) [Modulus](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L559>)
+
+```go
+func (p *PointBls12381G1) Modulus() *big.Int
+```
+
+### func \(\*PointBls12381G1\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L422>)
+
+```go
+func (p *PointBls12381G1) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointBls12381G1\) [MultiPairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L545>)
+
+```go
+func (p *PointBls12381G1) MultiPairing(points ...PairingPoint) Scalar
+```
+
+### func \(\*PointBls12381G1\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L391>)
+
+```go
+func (p *PointBls12381G1) Neg() Point
+```
+
+### func \(\*PointBls12381G1\) [OtherGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L516>)
+
+```go
+func (p *PointBls12381G1) OtherGroup() PairingPoint
+```
+
+### func \(\*PointBls12381G1\) [Pairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L520>)
+
+```go
+func (p *PointBls12381G1) Pairing(rhs PairingPoint) Scalar
+```
+
+### func \(\*PointBls12381G1\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L338>)
+
+```go
+func (p *PointBls12381G1) Random(reader io.Reader) Point
+```
+
+### func \(\*PointBls12381G1\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L384>)
+
+```go
+func (p *PointBls12381G1) Scalar() Scalar
+```
+
+### func \(\*PointBls12381G1\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L444>)
+
+```go
+func (p *PointBls12381G1) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointBls12381G1\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L409>)
+
+```go
+func (p *PointBls12381G1) Sub(rhs Point) Point
+```
+
+### func \(\*PointBls12381G1\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L491>)
+
+```go
+func (p *PointBls12381G1) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointBls12381G1\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L459>)
+
+```go
+func (p *PointBls12381G1) ToAffineCompressed() []byte
+```
+
+### func \(\*PointBls12381G1\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L463>)
+
+```go
+func (p *PointBls12381G1) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointBls12381G1\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L567>)
+
+```go
+func (p *PointBls12381G1) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointBls12381G1\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L601>)
+
+```go
+func (p *PointBls12381G1) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointBls12381G1\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L584>)
+
+```go
+func (p *PointBls12381G1) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointBls12381G1\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L549>)
+
+```go
+func (p *PointBls12381G1) X() *big.Int
+```
+
+### func \(\*PointBls12381G1\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L554>)
+
+```go
+func (p *PointBls12381G1) Y() *big.Int
+```
+
+## type [PointBls12381G2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L35-L37>)
+
+```go
+type PointBls12381G2 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointBls12381G2\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L672>)
+
+```go
+func (p *PointBls12381G2) Add(rhs Point) Point
+```
+
+### func \(\*PointBls12381G2\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L763>)
+
+```go
+func (p *PointBls12381G2) CurveName() string
+```
+
+### func \(\*PointBls12381G2\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L655>)
+
+```go
+func (p *PointBls12381G2) Double() Point
+```
+
+### func \(\*PointBls12381G2\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L711>)
+
+```go
+func (p *PointBls12381G2) Equal(rhs Point) bool
+```
+
+### func \(\*PointBls12381G2\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L747>)
+
+```go
+func (p *PointBls12381G2) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12381G2\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L755>)
+
+```go
+func (p *PointBls12381G2) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointBls12381G2\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L635>)
+
+```go
+func (p *PointBls12381G2) Generator() Point
+```
+
+### func \(\*PointBls12381G2\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L620>)
+
+```go
+func (p *PointBls12381G2) Hash(bytes []byte) Point
+```
+
+### func \(\*PointBls12381G2\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L629>)
+
+```go
+func (p *PointBls12381G2) Identity() Point
+```
+
+### func \(\*PointBls12381G2\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L641>)
+
+```go
+func (p *PointBls12381G2) IsIdentity() bool
+```
+
+### func \(\*PointBls12381G2\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L645>)
+
+```go
+func (p *PointBls12381G2) IsNegative() bool
+```
+
+### func \(\*PointBls12381G2\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L651>)
+
+```go
+func (p *PointBls12381G2) IsOnCurve() bool
+```
+
+### func \(\*PointBls12381G2\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L839>)
+
+```go
+func (p *PointBls12381G2) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointBls12381G2\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L873>)
+
+```go
+func (p *PointBls12381G2) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointBls12381G2\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L856>)
+
+```go
+func (p *PointBls12381G2) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointBls12381G2\) [Modulus](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L835>)
+
+```go
+func (p *PointBls12381G2) Modulus() *big.Int
+```
+
+### func \(\*PointBls12381G2\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L698>)
+
+```go
+func (p *PointBls12381G2) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointBls12381G2\) [MultiPairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L821>)
+
+```go
+func (p *PointBls12381G2) MultiPairing(points ...PairingPoint) Scalar
+```
+
+### func \(\*PointBls12381G2\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L667>)
+
+```go
+func (p *PointBls12381G2) Neg() Point
+```
+
+### func \(\*PointBls12381G2\) [OtherGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L792>)
+
+```go
+func (p *PointBls12381G2) OtherGroup() PairingPoint
+```
+
+### func \(\*PointBls12381G2\) [Pairing](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L796>)
+
+```go
+func (p *PointBls12381G2) Pairing(rhs PairingPoint) Scalar
+```
+
+### func \(\*PointBls12381G2\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L614>)
+
+```go
+func (p *PointBls12381G2) Random(reader io.Reader) Point
+```
+
+### func \(\*PointBls12381G2\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L660>)
+
+```go
+func (p *PointBls12381G2) Scalar() Scalar
+```
+
+### func \(\*PointBls12381G2\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L720>)
+
+```go
+func (p *PointBls12381G2) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointBls12381G2\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L685>)
+
+```go
+func (p *PointBls12381G2) Sub(rhs Point) Point
+```
+
+### func \(\*PointBls12381G2\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L767>)
+
+```go
+func (p *PointBls12381G2) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointBls12381G2\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L735>)
+
+```go
+func (p *PointBls12381G2) ToAffineCompressed() []byte
+```
+
+### func \(\*PointBls12381G2\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L739>)
+
+```go
+func (p *PointBls12381G2) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointBls12381G2\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L843>)
+
+```go
+func (p *PointBls12381G2) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointBls12381G2\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L877>)
+
+```go
+func (p *PointBls12381G2) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointBls12381G2\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L860>)
+
+```go
+func (p *PointBls12381G2) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointBls12381G2\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L825>)
+
+```go
+func (p *PointBls12381G2) X() *big.Int
+```
+
+### func \(\*PointBls12381G2\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L830>)
+
+```go
+func (p *PointBls12381G2) Y() *big.Int
+```
+
+## type [PointEd25519](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L27-L29>)
+
+```go
+type PointEd25519 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointEd25519\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L416>)
+
+```go
+func (p *PointEd25519) Add(rhs Point) Point
+```
+
+### func \(\*PointEd25519\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L606>)
+
+```go
+func (p *PointEd25519) CurveName() string
+```
+
+### func \(\*PointEd25519\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L404>)
+
+```go
+func (p *PointEd25519) Double() Point
+```
+
+### func \(\*PointEd25519\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L468>)
+
+```go
+func (p *PointEd25519) Equal(rhs Point) bool
+```
+
+### func \(\*PointEd25519\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L574>)
+
+```go
+func (p *PointEd25519) FromAffineCompressed(inBytes []byte) (Point, error)
+```
+
+### func \(\*PointEd25519\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L582>)
+
+```go
+func (p *PointEd25519) FromAffineUncompressed(inBytes []byte) (Point, error)
+```
+
+### func \(\*PointEd25519\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L384>)
+
+```go
+func (p *PointEd25519) Generator() Point
+```
+
+### func \(\*PointEd25519\) [GetEdwardsPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L699>)
+
+```go
+func (p *PointEd25519) GetEdwardsPoint() *edwards25519.Point
+```
+
+### func \(\*PointEd25519\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L363>)
+
+```go
+func (p *PointEd25519) Hash(bytes []byte) Point
+```
+
+### func \(\*PointEd25519\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L378>)
+
+```go
+func (p *PointEd25519) Identity() Point
+```
+
+### func \(\*PointEd25519\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L390>)
+
+```go
+func (p *PointEd25519) IsIdentity() bool
+```
+
+### func \(\*PointEd25519\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L394>)
+
+```go
+func (p *PointEd25519) IsNegative() bool
+```
+
+### func \(\*PointEd25519\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L399>)
+
+```go
+func (p *PointEd25519) IsOnCurve() bool
+```
+
+### func \(\*PointEd25519\) [MangleScalarBitsAndMulByBasepointToProducePublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L458>)
+
+```go
+func (p *PointEd25519) MangleScalarBitsAndMulByBasepointToProducePublicKey(rhs *ScalarEd25519) *PointEd25519
+```
+
+MangleScalarBitsAndMulByBasepointToProducePublicKey is a function for mangling the bits of a \(formerly mathematically well\-defined\) "scalar" and multiplying it to produce a public key\.
+
+### func \(\*PointEd25519\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L648>)
+
+```go
+func (p *PointEd25519) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointEd25519\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L682>)
+
+```go
+func (p *PointEd25519) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointEd25519\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L665>)
+
+```go
+func (p *PointEd25519) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointEd25519\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L441>)
+
+```go
+func (p *PointEd25519) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointEd25519\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L412>)
+
+```go
+func (p *PointEd25519) Neg() Point
+```
+
+### func \(\*PointEd25519\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L357>)
+
+```go
+func (p *PointEd25519) Random(reader io.Reader) Point
+```
+
+### func \(\*PointEd25519\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L408>)
+
+```go
+func (p *PointEd25519) Scalar() Scalar
+```
+
+### func \(\*PointEd25519\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L488>)
+
+```go
+func (p *PointEd25519) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointEd25519\) [SetEdwardsPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L703>)
+
+```go
+func (p *PointEd25519) SetEdwardsPoint(pt *edwards25519.Point) *PointEd25519
+```
+
+### func \(\*PointEd25519\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L428>)
+
+```go
+func (p *PointEd25519) Sub(rhs Point) Point
+```
+
+### func \(\*PointEd25519\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L610>)
+
+```go
+func (p *PointEd25519) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointEd25519\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L559>)
+
+```go
+func (p *PointEd25519) ToAffineCompressed() []byte
+```
+
+### func \(\*PointEd25519\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L563>)
+
+```go
+func (p *PointEd25519) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointEd25519\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L652>)
+
+```go
+func (p *PointEd25519) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointEd25519\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L686>)
+
+```go
+func (p *PointEd25519) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointEd25519\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L669>)
+
+```go
+func (p *PointEd25519) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointEd25519\) [VarTimeDoubleScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L631>)
+
+```go
+func (p *PointEd25519) VarTimeDoubleScalarBaseMult(a Scalar, A Point, b Scalar) Point
+```
+
+## type [PointK256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L24-L26>)
+
+```go
+type PointK256 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointK256\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L367>)
+
+```go
+func (p *PointK256) Add(rhs Point) Point
+```
+
+### func \(\*PointK256\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L489>)
+
+```go
+func (p *PointK256) CurveName() string
+```
+
+### func \(\*PointK256\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L352>)
+
+```go
+func (p *PointK256) Double() Point
+```
+
+### func \(\*PointK256\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L406>)
+
+```go
+func (p *PointK256) Equal(rhs Point) bool
+```
+
+### func \(\*PointK256\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L447>)
+
+```go
+func (p *PointK256) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointK256\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L477>)
+
+```go
+func (p *PointK256) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointK256\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L330>)
+
+```go
+func (p *PointK256) Generator() Point
+```
+
+### func \(\*PointK256\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L298>)
+
+```go
+func (p *PointK256) Hash(bytes []byte) Point
+```
+
+### func \(\*PointK256\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L324>)
+
+```go
+func (p *PointK256) Identity() Point
+```
+
+### func \(\*PointK256\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L338>)
+
+```go
+func (p *PointK256) IsIdentity() bool
+```
+
+### func \(\*PointK256\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L344>)
+
+```go
+func (p *PointK256) IsNegative() bool
+```
+
+### func \(\*PointK256\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L348>)
+
+```go
+func (p *PointK256) IsOnCurve() bool
+```
+
+### func \(\*PointK256\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L517>)
+
+```go
+func (p *PointK256) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointK256\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L553>)
+
+```go
+func (p *PointK256) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointK256\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L535>)
+
+```go
+func (p *PointK256) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointK256\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L393>)
+
+```go
+func (p *PointK256) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointK256\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L361>)
+
+```go
+func (p *PointK256) Neg() Point
+```
+
+### func \(\*PointK256\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L513>)
+
+```go
+func (p *PointK256) Params() *elliptic.CurveParams
+```
+
+### func \(\*PointK256\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L292>)
+
+```go
+func (p *PointK256) Random(reader io.Reader) Point
+```
+
+### func \(\*PointK256\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L357>)
+
+```go
+func (p *PointK256) Scalar() Scalar
+```
+
+### func \(\*PointK256\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L417>)
+
+```go
+func (p *PointK256) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointK256\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L380>)
+
+```go
+func (p *PointK256) Sub(rhs Point) Point
+```
+
+### func \(\*PointK256\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L493>)
+
+```go
+func (p *PointK256) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointK256\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L431>)
+
+```go
+func (p *PointK256) ToAffineCompressed() []byte
+```
+
+### func \(\*PointK256\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L439>)
+
+```go
+func (p *PointK256) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointK256\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L521>)
+
+```go
+func (p *PointK256) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointK256\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L557>)
+
+```go
+func (p *PointK256) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointK256\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L539>)
+
+```go
+func (p *PointK256) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointK256\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L505>)
+
+```go
+func (p *PointK256) X() *big.Int
+```
+
+### func \(\*PointK256\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L509>)
+
+```go
+func (p *PointK256) Y() *big.Int
+```
+
+## type [PointP256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L23-L25>)
+
+```go
+type PointP256 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointP256\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L365>)
+
+```go
+func (p *PointP256) Add(rhs Point) Point
+```
+
+### func \(\*PointP256\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L487>)
+
+```go
+func (p *PointP256) CurveName() string
+```
+
+### func \(\*PointP256\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L349>)
+
+```go
+func (p *PointP256) Double() Point
+```
+
+### func \(\*PointP256\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L404>)
+
+```go
+func (p *PointP256) Equal(rhs Point) bool
+```
+
+### func \(\*PointP256\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L445>)
+
+```go
+func (p *PointP256) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointP256\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L475>)
+
+```go
+func (p *PointP256) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointP256\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L327>)
+
+```go
+func (p *PointP256) Generator() Point
+```
+
+### func \(\*PointP256\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L297>)
+
+```go
+func (p *PointP256) Hash(bytes []byte) Point
+```
+
+### func \(\*PointP256\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L321>)
+
+```go
+func (p *PointP256) Identity() Point
+```
+
+### func \(\*PointP256\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L335>)
+
+```go
+func (p *PointP256) IsIdentity() bool
+```
+
+### func \(\*PointP256\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L341>)
+
+```go
+func (p *PointP256) IsNegative() bool
+```
+
+### func \(\*PointP256\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L345>)
+
+```go
+func (p *PointP256) IsOnCurve() bool
+```
+
+### func \(\*PointP256\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L515>)
+
+```go
+func (p *PointP256) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointP256\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L551>)
+
+```go
+func (p *PointP256) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointP256\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L533>)
+
+```go
+func (p *PointP256) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointP256\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L391>)
+
+```go
+func (p *PointP256) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointP256\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L359>)
+
+```go
+func (p *PointP256) Neg() Point
+```
+
+### func \(\*PointP256\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L511>)
+
+```go
+func (p *PointP256) Params() *elliptic.CurveParams
+```
+
+### func \(\*PointP256\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L291>)
+
+```go
+func (p *PointP256) Random(reader io.Reader) Point
+```
+
+### func \(\*PointP256\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L355>)
+
+```go
+func (p *PointP256) Scalar() Scalar
+```
+
+### func \(\*PointP256\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L415>)
+
+```go
+func (p *PointP256) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointP256\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L378>)
+
+```go
+func (p *PointP256) Sub(rhs Point) Point
+```
+
+### func \(\*PointP256\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L491>)
+
+```go
+func (p *PointP256) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointP256\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L429>)
+
+```go
+func (p *PointP256) ToAffineCompressed() []byte
+```
+
+### func \(\*PointP256\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L437>)
+
+```go
+func (p *PointP256) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointP256\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L519>)
+
+```go
+func (p *PointP256) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointP256\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L555>)
+
+```go
+func (p *PointP256) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointP256\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L537>)
+
+```go
+func (p *PointP256) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointP256\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L503>)
+
+```go
+func (p *PointP256) X() *big.Int
+```
+
+### func \(\*PointP256\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L507>)
+
+```go
+func (p *PointP256) Y() *big.Int
+```
+
+## type [PointPallas](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L487-L489>)
+
+```go
+type PointPallas struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PointPallas\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L531>)
+
+```go
+func (p *PointPallas) Add(rhs Point) Point
+```
+
+### func \(\*PointPallas\) [CurveName](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L607>)
+
+```go
+func (p *PointPallas) CurveName() string
+```
+
+### func \(\*PointPallas\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L519>)
+
+```go
+func (p *PointPallas) Double() Point
+```
+
+### func \(\*PointPallas\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L555>)
+
+```go
+func (p *PointPallas) Equal(rhs Point) bool
+```
+
+### func \(\*PointPallas\) [FromAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L591>)
+
+```go
+func (p *PointPallas) FromAffineCompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointPallas\) [FromAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L599>)
+
+```go
+func (p *PointPallas) FromAffineUncompressed(bytes []byte) (Point, error)
+```
+
+### func \(\*PointPallas\) [Generator](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L503>)
+
+```go
+func (p *PointPallas) Generator() Point
+```
+
+### func \(\*PointPallas\) [GetEp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L683>)
+
+```go
+func (p *PointPallas) GetEp() *Ep
+```
+
+### func \(\*PointPallas\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L495>)
+
+```go
+func (p *PointPallas) Hash(bytes []byte) Point
+```
+
+### func \(\*PointPallas\) [Identity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L499>)
+
+```go
+func (p *PointPallas) Identity() Point
+```
+
+### func \(\*PointPallas\) [IsIdentity](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L507>)
+
+```go
+func (p *PointPallas) IsIdentity() bool
+```
+
+### func \(\*PointPallas\) [IsNegative](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L511>)
+
+```go
+func (p *PointPallas) IsNegative() bool
+```
+
+### func \(\*PointPallas\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L515>)
+
+```go
+func (p *PointPallas) IsOnCurve() bool
+```
+
+### func \(\*PointPallas\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L624>)
+
+```go
+func (p *PointPallas) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PointPallas\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L658>)
+
+```go
+func (p *PointPallas) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PointPallas\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L641>)
+
+```go
+func (p *PointPallas) MarshalText() ([]byte, error)
+```
+
+### func \(\*PointPallas\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L547>)
+
+```go
+func (p *PointPallas) Mul(rhs Scalar) Point
+```
+
+### func \(\*PointPallas\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L527>)
+
+```go
+func (p *PointPallas) Neg() Point
+```
+
+### func \(\*PointPallas\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L491>)
+
+```go
+func (p *PointPallas) Random(reader io.Reader) Point
+```
+
+### func \(\*PointPallas\) [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L523>)
+
+```go
+func (p *PointPallas) Scalar() Scalar
+```
+
+### func \(\*PointPallas\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L563>)
+
+```go
+func (p *PointPallas) Set(x, y *big.Int) (Point, error)
+```
+
+### func \(\*PointPallas\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L539>)
+
+```go
+func (p *PointPallas) Sub(rhs Point) Point
+```
+
+### func \(\*PointPallas\) [SumOfProducts](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L611>)
+
+```go
+func (p *PointPallas) SumOfProducts(points []Point, scalars []Scalar) Point
+```
+
+### func \(\*PointPallas\) [ToAffineCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L583>)
+
+```go
+func (p *PointPallas) ToAffineCompressed() []byte
+```
+
+### func \(\*PointPallas\) [ToAffineUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L587>)
+
+```go
+func (p *PointPallas) ToAffineUncompressed() []byte
+```
+
+### func \(\*PointPallas\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L628>)
+
+```go
+func (p *PointPallas) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*PointPallas\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L662>)
+
+```go
+func (p *PointPallas) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*PointPallas\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L645>)
+
+```go
+func (p *PointPallas) UnmarshalText(input []byte) error
+```
+
+### func \(\*PointPallas\) [X](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L675>)
+
+```go
+func (p *PointPallas) X() *fp.Fp
+```
+
+### func \(\*PointPallas\) [Y](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L679>)
+
+```go
+func (p *PointPallas) Y() *fp.Fp
+```
+
+## type [Scalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/curve.go#L66-L135>)
+
+Scalar represents an element of the scalar field \\mathbb\{F\}\_q of the elliptic curve construction\.
+
+```go
+type Scalar interface {
+    encoding.BinaryMarshaler
+    encoding.BinaryUnmarshaler
+    encoding.TextMarshaler
+    encoding.TextUnmarshaler
+    json.Marshaler
+    json.Unmarshaler
+    // Random returns a random scalar using the provided reader
+    // to retrieve bytes
+    Random(reader io.Reader) Scalar
+    // Hash the specific bytes in a manner to yield a
+    // uniformly distributed scalar
+    Hash(bytes []byte) Scalar
+    // Zero returns the additive identity element
+    Zero() Scalar
+    // One returns the multiplicative identity element
+    One() Scalar
+    // IsZero returns true if this element is the additive identity element
+    IsZero() bool
+    // IsOne returns true if this element is the multiplicative identity element
+    IsOne() bool
+    // IsOdd returns true if this element is odd
+    IsOdd() bool
+    // IsEven returns true if this element is even
+    IsEven() bool
+    // New returns an element with the value equal to `value`
+    New(value int) Scalar
+    // Cmp returns
+    // -2 if this element is in a different field than rhs
+    // -1 if this element is less than rhs
+    // 0 if this element is equal to rhs
+    // 1 if this element is greater than rhs
+    Cmp(rhs Scalar) int
+    // Square returns element*element
+    Square() Scalar
+    // Double returns element+element
+    Double() Scalar
+    // Invert returns element^-1 mod p
+    Invert() (Scalar, error)
+    // Sqrt computes the square root of this element if it exists.
+    Sqrt() (Scalar, error)
+    // Cube returns element*element*element
+    Cube() Scalar
+    // Add returns element+rhs
+    Add(rhs Scalar) Scalar
+    // Sub returns element-rhs
+    Sub(rhs Scalar) Scalar
+    // Mul returns element*rhs
+    Mul(rhs Scalar) Scalar
+    // MulAdd returns element * y + z mod p
+    MulAdd(y, z Scalar) Scalar
+    // Div returns element*rhs^-1 mod p
+    Div(rhs Scalar) Scalar
+    // Neg returns -element mod p
+    Neg() Scalar
+    // SetBigInt returns this element set to the value of v
+    SetBigInt(v *big.Int) (Scalar, error)
+    // BigInt returns this element as a big integer
+    BigInt() *big.Int
+    // Point returns the associated point for this scalar
+    Point() Point
+    // Bytes returns the canonical byte representation of this scalar
+    Bytes() []byte
+    // SetBytes creates a scalar from the canonical representation expecting the exact number of bytes needed to represent the scalar
+    SetBytes(bytes []byte) (Scalar, error)
+    // SetBytesWide creates a scalar expecting double the exact number of bytes needed to represent the scalar which is reduced by the modulus
+    SetBytesWide(bytes []byte) (Scalar, error)
+    // Clone returns a cloned Scalar of this value
+    Clone() Scalar
+}
+```
+
+## type [ScalarBls12377](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L28-L31>)
+
+```go
+type ScalarBls12377 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarBls12377\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L152>)
+
+```go
+func (s *ScalarBls12377) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L231>)
+
+```go
+func (s *ScalarBls12377) BigInt() *big.Int
+```
+
+### func \(\*ScalarBls12377\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L235>)
+
+```go
+func (s *ScalarBls12377) Bytes() []byte
+```
+
+### func \(\*ScalarBls12377\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L268>)
+
+```go
+func (s *ScalarBls12377) Clone() Scalar
+```
+
+### func \(\*ScalarBls12377\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L107>)
+
+```go
+func (s *ScalarBls12377) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarBls12377\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L145>)
+
+```go
+func (s *ScalarBls12377) Cube() Scalar
+```
+
+### func \(\*ScalarBls12377\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L195>)
+
+```go
+func (s *ScalarBls12377) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L123>)
+
+```go
+func (s *ScalarBls12377) Double() Scalar
+```
+
+### func \(\*ScalarBls12377\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L54>)
+
+```go
+func (s *ScalarBls12377) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarBls12377\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L131>)
+
+```go
+func (s *ScalarBls12377) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarBls12377\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L92>)
+
+```go
+func (s *ScalarBls12377) IsEven() bool
+```
+
+### func \(\*ScalarBls12377\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L88>)
+
+```go
+func (s *ScalarBls12377) IsOdd() bool
+```
+
+### func \(\*ScalarBls12377\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L84>)
+
+```go
+func (s *ScalarBls12377) IsOne() bool
+```
+
+### func \(\*ScalarBls12377\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L80>)
+
+```go
+func (s *ScalarBls12377) IsZero() bool
+```
+
+### func \(\*ScalarBls12377\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L286>)
+
+```go
+func (s *ScalarBls12377) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L322>)
+
+```go
+func (s *ScalarBls12377) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L304>)
+
+```go
+func (s *ScalarBls12377) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L178>)
+
+```go
+func (s *ScalarBls12377) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L191>)
+
+```go
+func (s *ScalarBls12377) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L209>)
+
+```go
+func (s *ScalarBls12377) Neg() Scalar
+```
+
+### func \(\*ScalarBls12377\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L96>)
+
+```go
+func (s *ScalarBls12377) New(value int) Scalar
+```
+
+### func \(\*ScalarBls12377\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L73>)
+
+```go
+func (s *ScalarBls12377) One() Scalar
+```
+
+### func \(\*ScalarBls12377\) [Order](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L282>)
+
+```go
+func (s *ScalarBls12377) Order() *big.Int
+```
+
+### func \(\*ScalarBls12377\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L264>)
+
+```go
+func (s *ScalarBls12377) Point() Point
+```
+
+### func \(\*ScalarBls12377\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L45>)
+
+```go
+func (s *ScalarBls12377) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarBls12377\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L217>)
+
+```go
+func (s *ScalarBls12377) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L240>)
+
+```go
+func (s *ScalarBls12377) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L252>)
+
+```go
+func (s *ScalarBls12377) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377\) [SetPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L275>)
+
+```go
+func (s *ScalarBls12377) SetPoint(p Point) PairingScalar
+```
+
+### func \(\*ScalarBls12377\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L138>)
+
+```go
+func (s *ScalarBls12377) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarBls12377\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L116>)
+
+```go
+func (s *ScalarBls12377) Square() Scalar
+```
+
+### func \(\*ScalarBls12377\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L165>)
+
+```go
+func (s *ScalarBls12377) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L290>)
+
+```go
+func (s *ScalarBls12377) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarBls12377\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L326>)
+
+```go
+func (s *ScalarBls12377) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarBls12377\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L308>)
+
+```go
+func (s *ScalarBls12377) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarBls12377\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L66>)
+
+```go
+func (s *ScalarBls12377) Zero() Scalar
+```
+
+## type [ScalarBls12377Gt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L41-L43>)
+
+```go
+type ScalarBls12377Gt struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarBls12377Gt\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1097>)
+
+```go
+func (s *ScalarBls12377Gt) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1168>)
+
+```go
+func (s *ScalarBls12377Gt) BigInt() *big.Int
+```
+
+### func \(\*ScalarBls12377Gt\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1178>)
+
+```go
+func (s *ScalarBls12377Gt) Bytes() []byte
+```
+
+### func \(\*ScalarBls12377Gt\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1211>)
+
+```go
+func (s *ScalarBls12377Gt) Clone() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1053>)
+
+```go
+func (s *ScalarBls12377Gt) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarBls12377Gt\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1088>)
+
+```go
+func (s *ScalarBls12377Gt) Cube() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1137>)
+
+```go
+func (s *ScalarBls12377Gt) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1069>)
+
+```go
+func (s *ScalarBls12377Gt) Double() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L939>)
+
+```go
+func (s *ScalarBls12377Gt) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1076>)
+
+```go
+func (s *ScalarBls12377Gt) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1033>)
+
+```go
+func (s *ScalarBls12377Gt) IsEven() bool
+```
+
+### func \(\*ScalarBls12377Gt\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1028>)
+
+```go
+func (s *ScalarBls12377Gt) IsOdd() bool
+```
+
+### func \(\*ScalarBls12377Gt\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L972>)
+
+```go
+func (s *ScalarBls12377Gt) IsOne() bool
+```
+
+### func \(\*ScalarBls12377Gt\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L963>)
+
+```go
+func (s *ScalarBls12377Gt) IsZero() bool
+```
+
+### func \(\*ScalarBls12377Gt\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L977>)
+
+```go
+func (s *ScalarBls12377Gt) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1011>)
+
+```go
+func (s *ScalarBls12377Gt) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L994>)
+
+```go
+func (s *ScalarBls12377Gt) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1121>)
+
+```go
+func (s *ScalarBls12377Gt) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1133>)
+
+```go
+func (s *ScalarBls12377Gt) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1151>)
+
+```go
+func (s *ScalarBls12377Gt) Neg() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1038>)
+
+```go
+func (s *ScalarBls12377Gt) New(input int) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L958>)
+
+```go
+func (s *ScalarBls12377Gt) One() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1173>)
+
+```go
+func (s *ScalarBls12377Gt) Point() Point
+```
+
+### func \(\*ScalarBls12377Gt\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L919>)
+
+```go
+func (s *ScalarBls12377Gt) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1162>)
+
+```go
+func (s *ScalarBls12377Gt) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1183>)
+
+```go
+func (s *ScalarBls12377Gt) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1192>)
+
+```go
+func (s *ScalarBls12377Gt) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1083>)
+
+```go
+func (s *ScalarBls12377Gt) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarBls12377Gt\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1062>)
+
+```go
+func (s *ScalarBls12377Gt) Square() Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1109>)
+
+```go
+func (s *ScalarBls12377Gt) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12377Gt\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L981>)
+
+```go
+func (s *ScalarBls12377Gt) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarBls12377Gt\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L1015>)
+
+```go
+func (s *ScalarBls12377Gt) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarBls12377Gt\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L998>)
+
+```go
+func (s *ScalarBls12377Gt) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarBls12377Gt\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12377_curve.go#L948>)
+
+```go
+func (s *ScalarBls12377Gt) Zero() Scalar
+```
+
+## type [ScalarBls12381](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L26-L29>)
+
+```go
+type ScalarBls12381 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarBls12381\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L150>)
+
+```go
+func (s *ScalarBls12381) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L230>)
+
+```go
+func (s *ScalarBls12381) BigInt() *big.Int
+```
+
+### func \(\*ScalarBls12381\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L234>)
+
+```go
+func (s *ScalarBls12381) Bytes() []byte
+```
+
+### func \(\*ScalarBls12381\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L267>)
+
+```go
+func (s *ScalarBls12381) Clone() Scalar
+```
+
+### func \(\*ScalarBls12381\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L105>)
+
+```go
+func (s *ScalarBls12381) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarBls12381\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L143>)
+
+```go
+func (s *ScalarBls12381) Cube() Scalar
+```
+
+### func \(\*ScalarBls12381\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L193>)
+
+```go
+func (s *ScalarBls12381) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L121>)
+
+```go
+func (s *ScalarBls12381) Double() Scalar
+```
+
+### func \(\*ScalarBls12381\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L52>)
+
+```go
+func (s *ScalarBls12381) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarBls12381\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L129>)
+
+```go
+func (s *ScalarBls12381) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarBls12381\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L90>)
+
+```go
+func (s *ScalarBls12381) IsEven() bool
+```
+
+### func \(\*ScalarBls12381\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L86>)
+
+```go
+func (s *ScalarBls12381) IsOdd() bool
+```
+
+### func \(\*ScalarBls12381\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L82>)
+
+```go
+func (s *ScalarBls12381) IsOne() bool
+```
+
+### func \(\*ScalarBls12381\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L78>)
+
+```go
+func (s *ScalarBls12381) IsZero() bool
+```
+
+### func \(\*ScalarBls12381\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L285>)
+
+```go
+func (s *ScalarBls12381) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L321>)
+
+```go
+func (s *ScalarBls12381) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L303>)
+
+```go
+func (s *ScalarBls12381) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L176>)
+
+```go
+func (s *ScalarBls12381) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L189>)
+
+```go
+func (s *ScalarBls12381) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L208>)
+
+```go
+func (s *ScalarBls12381) Neg() Scalar
+```
+
+### func \(\*ScalarBls12381\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L94>)
+
+```go
+func (s *ScalarBls12381) New(value int) Scalar
+```
+
+### func \(\*ScalarBls12381\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L71>)
+
+```go
+func (s *ScalarBls12381) One() Scalar
+```
+
+### func \(\*ScalarBls12381\) [Order](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L281>)
+
+```go
+func (s *ScalarBls12381) Order() *big.Int
+```
+
+### func \(\*ScalarBls12381\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L263>)
+
+```go
+func (s *ScalarBls12381) Point() Point
+```
+
+### func \(\*ScalarBls12381\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L43>)
+
+```go
+func (s *ScalarBls12381) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarBls12381\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L216>)
+
+```go
+func (s *ScalarBls12381) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L239>)
+
+```go
+func (s *ScalarBls12381) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L251>)
+
+```go
+func (s *ScalarBls12381) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381\) [SetPoint](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L274>)
+
+```go
+func (s *ScalarBls12381) SetPoint(p Point) PairingScalar
+```
+
+### func \(\*ScalarBls12381\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L136>)
+
+```go
+func (s *ScalarBls12381) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarBls12381\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L114>)
+
+```go
+func (s *ScalarBls12381) Square() Scalar
+```
+
+### func \(\*ScalarBls12381\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L163>)
+
+```go
+func (s *ScalarBls12381) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L289>)
+
+```go
+func (s *ScalarBls12381) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarBls12381\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L325>)
+
+```go
+func (s *ScalarBls12381) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarBls12381\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L307>)
+
+```go
+func (s *ScalarBls12381) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarBls12381\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L64>)
+
+```go
+func (s *ScalarBls12381) Zero() Scalar
+```
+
+## type [ScalarBls12381Gt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L39-L41>)
+
+```go
+type ScalarBls12381Gt struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarBls12381Gt\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1115>)
+
+```go
+func (s *ScalarBls12381Gt) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1186>)
+
+```go
+func (s *ScalarBls12381Gt) BigInt() *big.Int
+```
+
+### func \(\*ScalarBls12381Gt\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1194>)
+
+```go
+func (s *ScalarBls12381Gt) Bytes() []byte
+```
+
+### func \(\*ScalarBls12381Gt\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1223>)
+
+```go
+func (s *ScalarBls12381Gt) Clone() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1068>)
+
+```go
+func (s *ScalarBls12381Gt) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarBls12381Gt\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1106>)
+
+```go
+func (s *ScalarBls12381Gt) Cube() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1158>)
+
+```go
+func (s *ScalarBls12381Gt) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1085>)
+
+```go
+func (s *ScalarBls12381Gt) Double() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L940>)
+
+```go
+func (s *ScalarBls12381Gt) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1093>)
+
+```go
+func (s *ScalarBls12381Gt) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1049>)
+
+```go
+func (s *ScalarBls12381Gt) IsEven() bool
+```
+
+### func \(\*ScalarBls12381Gt\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1044>)
+
+```go
+func (s *ScalarBls12381Gt) IsOdd() bool
+```
+
+### func \(\*ScalarBls12381Gt\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L989>)
+
+```go
+func (s *ScalarBls12381Gt) IsOne() bool
+```
+
+### func \(\*ScalarBls12381Gt\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L985>)
+
+```go
+func (s *ScalarBls12381Gt) IsZero() bool
+```
+
+### func \(\*ScalarBls12381Gt\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L993>)
+
+```go
+func (s *ScalarBls12381Gt) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1027>)
+
+```go
+func (s *ScalarBls12381Gt) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1010>)
+
+```go
+func (s *ScalarBls12381Gt) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1141>)
+
+```go
+func (s *ScalarBls12381Gt) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1154>)
+
+```go
+func (s *ScalarBls12381Gt) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1172>)
+
+```go
+func (s *ScalarBls12381Gt) Neg() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1054>)
+
+```go
+func (s *ScalarBls12381Gt) New(input int) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L981>)
+
+```go
+func (s *ScalarBls12381Gt) One() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1190>)
+
+```go
+func (s *ScalarBls12381Gt) Point() Point
+```
+
+### func \(\*ScalarBls12381Gt\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L921>)
+
+```go
+func (s *ScalarBls12381Gt) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1180>)
+
+```go
+func (s *ScalarBls12381Gt) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1198>)
+
+```go
+func (s *ScalarBls12381Gt) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1206>)
+
+```go
+func (s *ScalarBls12381Gt) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1101>)
+
+```go
+func (s *ScalarBls12381Gt) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarBls12381Gt\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1077>)
+
+```go
+func (s *ScalarBls12381Gt) Square() Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1128>)
+
+```go
+func (s *ScalarBls12381Gt) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarBls12381Gt\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L997>)
+
+```go
+func (s *ScalarBls12381Gt) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarBls12381Gt\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1031>)
+
+```go
+func (s *ScalarBls12381Gt) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarBls12381Gt\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L1014>)
+
+```go
+func (s *ScalarBls12381Gt) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarBls12381Gt\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/bls12381_curve.go#L977>)
+
+```go
+func (s *ScalarBls12381Gt) Zero() Scalar
+```
+
+## type [ScalarEd25519](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L23-L25>)
+
+```go
+type ScalarEd25519 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarEd25519\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L152>)
+
+```go
+func (s *ScalarEd25519) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarEd25519\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L233>)
+
+```go
+func (s *ScalarEd25519) BigInt() *big.Int
+```
+
+### func \(\*ScalarEd25519\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L239>)
+
+```go
+func (s *ScalarEd25519) Bytes() []byte
+```
+
+### func \(\*ScalarEd25519\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L292>)
+
+```go
+func (s *ScalarEd25519) Clone() Scalar
+```
+
+### func \(\*ScalarEd25519\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L113>)
+
+```go
+func (s *ScalarEd25519) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarEd25519\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L146>)
+
+```go
+func (s *ScalarEd25519) Cube() Scalar
+```
+
+### func \(\*ScalarEd25519\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L197>)
+
+```go
+func (s *ScalarEd25519) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarEd25519\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L127>)
+
+```go
+func (s *ScalarEd25519) Double() Scalar
+```
+
+### func \(\*ScalarEd25519\) [GetEdwardsScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L332>)
+
+```go
+func (s *ScalarEd25519) GetEdwardsScalar() *edwards25519.Scalar
+```
+
+### func \(\*ScalarEd25519\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L42>)
+
+```go
+func (s *ScalarEd25519) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarEd25519\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L133>)
+
+```go
+func (s *ScalarEd25519) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarEd25519\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L86>)
+
+```go
+func (s *ScalarEd25519) IsEven() bool
+```
+
+### func \(\*ScalarEd25519\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L82>)
+
+```go
+func (s *ScalarEd25519) IsOdd() bool
+```
+
+### func \(\*ScalarEd25519\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L73>)
+
+```go
+func (s *ScalarEd25519) IsOne() bool
+```
+
+### func \(\*ScalarEd25519\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L65>)
+
+```go
+func (s *ScalarEd25519) IsZero() bool
+```
+
+### func \(\*ScalarEd25519\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L298>)
+
+```go
+func (s *ScalarEd25519) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarEd25519\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L340>)
+
+```go
+func (s *ScalarEd25519) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarEd25519\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L315>)
+
+```go
+func (s *ScalarEd25519) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarEd25519\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L174>)
+
+```go
+func (s *ScalarEd25519) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarEd25519\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L185>)
+
+```go
+func (s *ScalarEd25519) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarEd25519\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L208>)
+
+```go
+func (s *ScalarEd25519) Neg() Scalar
+```
+
+### func \(\*ScalarEd25519\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L90>)
+
+```go
+func (s *ScalarEd25519) New(input int) Scalar
+```
+
+### func \(\*ScalarEd25519\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L59>)
+
+```go
+func (s *ScalarEd25519) One() Scalar
+```
+
+### func \(\*ScalarEd25519\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L288>)
+
+```go
+func (s *ScalarEd25519) Point() Point
+```
+
+### func \(\*ScalarEd25519\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L33>)
+
+```go
+func (s *ScalarEd25519) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarEd25519\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L214>)
+
+```go
+func (s *ScalarEd25519) SetBigInt(x *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarEd25519\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L245>)
+
+```go
+func (s *ScalarEd25519) SetBytes(input []byte) (Scalar, error)
+```
+
+SetBytes takes input a 32\-byte long array and returns a ed25519 scalar\. The input must be 32\-byte long and must be a reduced bytes\.
+
+### func \(\*ScalarEd25519\) [SetBytesCanonical](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L284>)
+
+```go
+func (s *ScalarEd25519) SetBytesCanonical(bytes []byte) (Scalar, error)
+```
+
+SetBytesCanonical uses SetCanonicalBytes of fillipo\.io/edwards25519\. https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L98 This function takes an input x and sets s = x\, where x is a 32\-byte little\-endian encoding of s\, then it returns the corresponding ed25519 scalar\. If the input is not a canonical encoding of s\, it returns nil and an error\.
+
+### func \(\*ScalarEd25519\) [SetBytesClamping](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L271>)
+
+```go
+func (s *ScalarEd25519) SetBytesClamping(bytes []byte) (Scalar, error)
+```
+
+SetBytesClamping uses SetBytesWithClamping of fillipo\.io/edwards25519\- https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L135 which applies the buffer pruning described in RFC 8032\, Section 5\.1\.5 \(also known as clamping\) and sets bytes to the result\. The input must be 32\-byte long\, and it is not modified\. If bytes is not of the right length\, SetBytesWithClamping returns nil and an error\, and the receiver is unchanged\.
+
+### func \(\*ScalarEd25519\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L259>)
+
+```go
+func (s *ScalarEd25519) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+SetBytesWide takes input a 64\-byte long byte array\, reduce it and return an ed25519 scalar\. It uses SetUniformBytes of fillipo\.io/edwards25519 \- https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L85 If bytes is not of the right length\, it returns nil and an error
+
+### func \(\*ScalarEd25519\) [SetEdwardsScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L336>)
+
+```go
+func (s *ScalarEd25519) SetEdwardsScalar(sc *edwards25519.Scalar) *ScalarEd25519
+```
+
+### func \(\*ScalarEd25519\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L139>)
+
+```go
+func (s *ScalarEd25519) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarEd25519\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L122>)
+
+```go
+func (s *ScalarEd25519) Square() Scalar
+```
+
+### func \(\*ScalarEd25519\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L163>)
+
+```go
+func (s *ScalarEd25519) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarEd25519\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L302>)
+
+```go
+func (s *ScalarEd25519) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarEd25519\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L344>)
+
+```go
+func (s *ScalarEd25519) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarEd25519\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L319>)
+
+```go
+func (s *ScalarEd25519) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarEd25519\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/ed25519_curve.go#L53>)
+
+```go
+func (s *ScalarEd25519) Zero() Scalar
+```
+
+## type [ScalarK256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L20-L22>)
+
+```go
+type ScalarK256 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarK256\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L126>)
+
+```go
+func (s *ScalarK256) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarK256\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L200>)
+
+```go
+func (s *ScalarK256) BigInt() *big.Int
+```
+
+### func \(\*ScalarK256\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L204>)
+
+```go
+func (s *ScalarK256) Bytes() []byte
+```
+
+### func \(\*ScalarK256\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L235>)
+
+```go
+func (s *ScalarK256) Clone() Scalar
+```
+
+### func \(\*ScalarK256\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L86>)
+
+```go
+func (s *ScalarK256) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarK256\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L120>)
+
+```go
+func (s *ScalarK256) Cube() Scalar
+```
+
+### func \(\*ScalarK256\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L166>)
+
+```go
+func (s *ScalarK256) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarK256\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L101>)
+
+```go
+func (s *ScalarK256) Double() Scalar
+```
+
+### func \(\*ScalarK256\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L37>)
+
+```go
+func (s *ScalarK256) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarK256\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L108>)
+
+```go
+func (s *ScalarK256) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarK256\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L72>)
+
+```go
+func (s *ScalarK256) IsEven() bool
+```
+
+### func \(\*ScalarK256\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L68>)
+
+```go
+func (s *ScalarK256) IsOdd() bool
+```
+
+### func \(\*ScalarK256\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L64>)
+
+```go
+func (s *ScalarK256) IsOne() bool
+```
+
+### func \(\*ScalarK256\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L60>)
+
+```go
+func (s *ScalarK256) IsZero() bool
+```
+
+### func \(\*ScalarK256\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L241>)
+
+```go
+func (s *ScalarK256) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarK256\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L275>)
+
+```go
+func (s *ScalarK256) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarK256\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L258>)
+
+```go
+func (s *ScalarK256) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarK256\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L150>)
+
+```go
+func (s *ScalarK256) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarK256\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L162>)
+
+```go
+func (s *ScalarK256) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarK256\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L180>)
+
+```go
+func (s *ScalarK256) Neg() Scalar
+```
+
+### func \(\*ScalarK256\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L76>)
+
+```go
+func (s *ScalarK256) New(value int) Scalar
+```
+
+### func \(\*ScalarK256\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L54>)
+
+```go
+func (s *ScalarK256) One() Scalar
+```
+
+### func \(\*ScalarK256\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L231>)
+
+```go
+func (s *ScalarK256) Point() Point
+```
+
+### func \(\*ScalarK256\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L28>)
+
+```go
+func (s *ScalarK256) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarK256\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L187>)
+
+```go
+func (s *ScalarK256) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarK256\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L209>)
+
+```go
+func (s *ScalarK256) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarK256\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L220>)
+
+```go
+func (s *ScalarK256) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarK256\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L114>)
+
+```go
+func (s *ScalarK256) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarK256\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L95>)
+
+```go
+func (s *ScalarK256) Square() Scalar
+```
+
+### func \(\*ScalarK256\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L138>)
+
+```go
+func (s *ScalarK256) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarK256\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L245>)
+
+```go
+func (s *ScalarK256) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarK256\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L279>)
+
+```go
+func (s *ScalarK256) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarK256\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L262>)
+
+```go
+func (s *ScalarK256) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarK256\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/k256_curve.go#L48>)
+
+```go
+func (s *ScalarK256) Zero() Scalar
+```
+
+## type [ScalarP256](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L19-L21>)
+
+```go
+type ScalarP256 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarP256\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L125>)
+
+```go
+func (s *ScalarP256) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarP256\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L199>)
+
+```go
+func (s *ScalarP256) BigInt() *big.Int
+```
+
+### func \(\*ScalarP256\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L203>)
+
+```go
+func (s *ScalarP256) Bytes() []byte
+```
+
+### func \(\*ScalarP256\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L234>)
+
+```go
+func (s *ScalarP256) Clone() Scalar
+```
+
+### func \(\*ScalarP256\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L85>)
+
+```go
+func (s *ScalarP256) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarP256\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L119>)
+
+```go
+func (s *ScalarP256) Cube() Scalar
+```
+
+### func \(\*ScalarP256\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L165>)
+
+```go
+func (s *ScalarP256) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarP256\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L100>)
+
+```go
+func (s *ScalarP256) Double() Scalar
+```
+
+### func \(\*ScalarP256\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L36>)
+
+```go
+func (s *ScalarP256) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarP256\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L107>)
+
+```go
+func (s *ScalarP256) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarP256\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L71>)
+
+```go
+func (s *ScalarP256) IsEven() bool
+```
+
+### func \(\*ScalarP256\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L67>)
+
+```go
+func (s *ScalarP256) IsOdd() bool
+```
+
+### func \(\*ScalarP256\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L63>)
+
+```go
+func (s *ScalarP256) IsOne() bool
+```
+
+### func \(\*ScalarP256\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L59>)
+
+```go
+func (s *ScalarP256) IsZero() bool
+```
+
+### func \(\*ScalarP256\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L240>)
+
+```go
+func (s *ScalarP256) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarP256\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L274>)
+
+```go
+func (s *ScalarP256) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarP256\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L257>)
+
+```go
+func (s *ScalarP256) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarP256\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L149>)
+
+```go
+func (s *ScalarP256) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarP256\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L161>)
+
+```go
+func (s *ScalarP256) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarP256\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L179>)
+
+```go
+func (s *ScalarP256) Neg() Scalar
+```
+
+### func \(\*ScalarP256\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L75>)
+
+```go
+func (s *ScalarP256) New(value int) Scalar
+```
+
+### func \(\*ScalarP256\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L53>)
+
+```go
+func (s *ScalarP256) One() Scalar
+```
+
+### func \(\*ScalarP256\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L230>)
+
+```go
+func (s *ScalarP256) Point() Point
+```
+
+### func \(\*ScalarP256\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L27>)
+
+```go
+func (s *ScalarP256) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarP256\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L186>)
+
+```go
+func (s *ScalarP256) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarP256\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L208>)
+
+```go
+func (s *ScalarP256) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarP256\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L219>)
+
+```go
+func (s *ScalarP256) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarP256\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L113>)
+
+```go
+func (s *ScalarP256) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarP256\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L94>)
+
+```go
+func (s *ScalarP256) Square() Scalar
+```
+
+### func \(\*ScalarP256\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L137>)
+
+```go
+func (s *ScalarP256) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarP256\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L244>)
+
+```go
+func (s *ScalarP256) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarP256\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L278>)
+
+```go
+func (s *ScalarP256) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarP256\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L261>)
+
+```go
+func (s *ScalarP256) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarP256\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/p256_curve.go#L47>)
+
+```go
+func (s *ScalarP256) Zero() Scalar
+```
+
+## type [ScalarPallas](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L209-L211>)
+
+ScalarPallas \- New interface
+
+```go
+type ScalarPallas struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*ScalarPallas\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L319>)
+
+```go
+func (s *ScalarPallas) Add(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarPallas\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L382>)
+
+```go
+func (s *ScalarPallas) BigInt() *big.Int
+```
+
+### func \(\*ScalarPallas\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L386>)
+
+```go
+func (s *ScalarPallas) Bytes() []byte
+```
+
+### func \(\*ScalarPallas\) [Clone](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L421>)
+
+```go
+func (s *ScalarPallas) Clone() Scalar
+```
+
+### func \(\*ScalarPallas\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L270>)
+
+```go
+func (s *ScalarPallas) Cmp(rhs Scalar) int
+```
+
+### func \(\*ScalarPallas\) [Cube](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L311>)
+
+```go
+func (s *ScalarPallas) Cube() Scalar
+```
+
+### func \(\*ScalarPallas\) [Div](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L356>)
+
+```go
+func (s *ScalarPallas) Div(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarPallas\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L285>)
+
+```go
+func (s *ScalarPallas) Double() Scalar
+```
+
+### func \(\*ScalarPallas\) [GetFq](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L427>)
+
+```go
+func (s *ScalarPallas) GetFq() *fq.Fq
+```
+
+### func \(\*ScalarPallas\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L222>)
+
+```go
+func (s *ScalarPallas) Hash(bytes []byte) Scalar
+```
+
+### func \(\*ScalarPallas\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L291>)
+
+```go
+func (s *ScalarPallas) Invert() (Scalar, error)
+```
+
+### func \(\*ScalarPallas\) [IsEven](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L259>)
+
+```go
+func (s *ScalarPallas) IsEven() bool
+```
+
+### func \(\*ScalarPallas\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L255>)
+
+```go
+func (s *ScalarPallas) IsOdd() bool
+```
+
+### func \(\*ScalarPallas\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L251>)
+
+```go
+func (s *ScalarPallas) IsOne() bool
+```
+
+### func \(\*ScalarPallas\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L247>)
+
+```go
+func (s *ScalarPallas) IsZero() bool
+```
+
+### func \(\*ScalarPallas\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L436>)
+
+```go
+func (s *ScalarPallas) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ScalarPallas\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L470>)
+
+```go
+func (s *ScalarPallas) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ScalarPallas\) [MarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L453>)
+
+```go
+func (s *ScalarPallas) MarshalText() ([]byte, error)
+```
+
+### func \(\*ScalarPallas\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L341>)
+
+```go
+func (s *ScalarPallas) Mul(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarPallas\) [MulAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L352>)
+
+```go
+func (s *ScalarPallas) MulAdd(y, z Scalar) Scalar
+```
+
+### func \(\*ScalarPallas\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L370>)
+
+```go
+func (s *ScalarPallas) Neg() Scalar
+```
+
+### func \(\*ScalarPallas\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L263>)
+
+```go
+func (s *ScalarPallas) New(value int) Scalar
+```
+
+### func \(\*ScalarPallas\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L241>)
+
+```go
+func (s *ScalarPallas) One() Scalar
+```
+
+### func \(\*ScalarPallas\) [Point](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L417>)
+
+```go
+func (s *ScalarPallas) Point() Point
+```
+
+### func \(\*ScalarPallas\) [Random](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L213>)
+
+```go
+func (s *ScalarPallas) Random(reader io.Reader) Scalar
+```
+
+### func \(\*ScalarPallas\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L376>)
+
+```go
+func (s *ScalarPallas) SetBigInt(v *big.Int) (Scalar, error)
+```
+
+### func \(\*ScalarPallas\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L391>)
+
+```go
+func (s *ScalarPallas) SetBytes(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarPallas\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L406>)
+
+```go
+func (s *ScalarPallas) SetBytesWide(bytes []byte) (Scalar, error)
+```
+
+### func \(\*ScalarPallas\) [SetFq](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L431>)
+
+```go
+func (s *ScalarPallas) SetFq(fq *fq.Fq) *ScalarPallas
+```
+
+### func \(\*ScalarPallas\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L301>)
+
+```go
+func (s *ScalarPallas) Sqrt() (Scalar, error)
+```
+
+### func \(\*ScalarPallas\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L279>)
+
+```go
+func (s *ScalarPallas) Square() Scalar
+```
+
+### func \(\*ScalarPallas\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L330>)
+
+```go
+func (s *ScalarPallas) Sub(rhs Scalar) Scalar
+```
+
+### func \(\*ScalarPallas\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L440>)
+
+```go
+func (s *ScalarPallas) UnmarshalBinary(input []byte) error
+```
+
+### func \(\*ScalarPallas\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L474>)
+
+```go
+func (s *ScalarPallas) UnmarshalJSON(input []byte) error
+```
+
+### func \(\*ScalarPallas\) [UnmarshalText](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L457>)
+
+```go
+func (s *ScalarPallas) UnmarshalText(input []byte) error
+```
+
+### func \(\*ScalarPallas\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/pallas_curve.go#L235>)
+
+```go
+func (s *ScalarPallas) Zero() Scalar
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/curves/bls12377_curve.go b/pkg/core/curves/bls12377_curve.go
new file mode 100644
index 00000000..3aba8a57
--- /dev/null
+++ b/pkg/core/curves/bls12377_curve.go
@@ -0,0 +1,1216 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377"
+	"io"
+	"math/big"
+)
+
+// See 'r' = https://eprint.iacr.org/2018/962.pdf Figure 16
+var bls12377modulus = bhex("12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001")
+var g1Inf = bls12377.G1Affine{X: [6]uint64{}, Y: [6]uint64{}}
+var g2Inf = bls12377.G2Affine{
+	X: bls12377.E2{A0: [6]uint64{}, A1: [6]uint64{}},
+	Y: bls12377.E2{A0: [6]uint64{}, A1: [6]uint64{}},
+}
+
+type ScalarBls12377 struct {
+	value *big.Int
+	point Point
+}
+
+type PointBls12377G1 struct {
+	value *bls12377.G1Affine
+}
+
+type PointBls12377G2 struct {
+	value *bls12377.G2Affine
+}
+
+type ScalarBls12377Gt struct {
+	value *bls12377.GT
+}
+
+func (s *ScalarBls12377) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarBls12377) Hash(bytes []byte) Scalar {
+	xmd, err := expandMsgXmd(sha256.New(), bytes, []byte("BLS12377_XMD:SHA-256_SSWU_RO_"), 48)
+	if err != nil {
+		return nil
+	}
+	v := new(big.Int).SetBytes(xmd)
+	return &ScalarBls12377{
+		value: v.Mod(v, bls12377modulus),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) Zero() Scalar {
+	return &ScalarBls12377{
+		value: big.NewInt(0),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) One() Scalar {
+	return &ScalarBls12377{
+		value: big.NewInt(1),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) IsZero() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{}) == 1
+}
+
+func (s *ScalarBls12377) IsOne() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{1}) == 1
+}
+
+func (s *ScalarBls12377) IsOdd() bool {
+	return s.value.Bit(0) == 1
+}
+
+func (s *ScalarBls12377) IsEven() bool {
+	return s.value.Bit(0) == 0
+}
+
+func (s *ScalarBls12377) New(value int) Scalar {
+	v := big.NewInt(int64(value))
+	if value < 0 {
+		v.Mod(v, bls12377modulus)
+	}
+	return &ScalarBls12377{
+		value: v,
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		return s.value.Cmp(r.value)
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarBls12377) Square() Scalar {
+	return &ScalarBls12377{
+		value: new(big.Int).Exp(s.value, big.NewInt(2), bls12377modulus),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) Double() Scalar {
+	v := new(big.Int).Add(s.value, s.value)
+	return &ScalarBls12377{
+		value: v.Mod(v, bls12377modulus),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) Invert() (Scalar, error) {
+	return &ScalarBls12377{
+		value: new(big.Int).ModInverse(s.value, bls12377modulus),
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12377) Sqrt() (Scalar, error) {
+	return &ScalarBls12377{
+		value: new(big.Int).ModSqrt(s.value, bls12377modulus),
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12377) Cube() Scalar {
+	return &ScalarBls12377{
+		value: new(big.Int).Exp(s.value, big.NewInt(3), bls12377modulus),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		v := new(big.Int).Add(s.value, r.value)
+		return &ScalarBls12377{
+			value: v.Mod(v, bls12377modulus),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		v := new(big.Int).Sub(s.value, r.value)
+		return &ScalarBls12377{
+			value: v.Mod(v, bls12377modulus),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		v := new(big.Int).Mul(s.value, r.value)
+		return &ScalarBls12377{
+			value: v.Mod(v, bls12377modulus),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarBls12377) Div(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		v := new(big.Int).ModInverse(r.value, bls12377modulus)
+		v.Mul(v, s.value)
+		return &ScalarBls12377{
+			value: v.Mod(v, bls12377modulus),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377) Neg() Scalar {
+	z := new(big.Int).Neg(s.value)
+	return &ScalarBls12377{
+		value: z.Mod(z, bls12377modulus),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) SetBigInt(v *big.Int) (Scalar, error) {
+	if v == nil {
+		return nil, fmt.Errorf("invalid value")
+	}
+	t := new(big.Int).Mod(v, bls12377modulus)
+	if t.Cmp(v) != 0 {
+		return nil, fmt.Errorf("invalid value")
+	}
+	return &ScalarBls12377{
+		value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12377) BigInt() *big.Int {
+	return new(big.Int).Set(s.value)
+}
+
+func (s *ScalarBls12377) Bytes() []byte {
+	var out [32]byte
+	return s.value.FillBytes(out[:])
+}
+
+func (s *ScalarBls12377) SetBytes(bytes []byte) (Scalar, error) {
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, bls12377modulus)
+	if t.Cmp(value) != 0 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	return &ScalarBls12377{
+		value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12377) SetBytesWide(bytes []byte) (Scalar, error) {
+	if len(bytes) < 32 || len(bytes) > 128 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, bls12377modulus)
+	return &ScalarBls12377{
+		value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12377) Point() Point {
+	return s.point.Identity()
+}
+
+func (s *ScalarBls12377) Clone() Scalar {
+	return &ScalarBls12377{
+		value: new(big.Int).Set(s.value),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12377) SetPoint(p Point) PairingScalar {
+	return &ScalarBls12377{
+		value: new(big.Int).Set(s.value),
+		point: p,
+	}
+}
+
+func (s *ScalarBls12377) Order() *big.Int {
+	return bls12377modulus
+}
+
+func (s *ScalarBls12377) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarBls12377) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12377)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	s.point = ss.point
+	return nil
+}
+
+func (s *ScalarBls12377) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarBls12377) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12377)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	s.point = ss.point
+	return nil
+}
+
+func (s *ScalarBls12377) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarBls12377) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarBls12377)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+func (p *PointBls12377G1) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointBls12377G1) Hash(bytes []byte) Point {
+	var domain = []byte("BLS12377G1_XMD:SHA-256_SVDW_RO_")
+	pt, err := bls12377.HashToCurveG1Svdw(bytes, domain)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12377G1{value: &pt}
+}
+
+func (p *PointBls12377G1) Identity() Point {
+	t := bls12377.G1Affine{}
+	return &PointBls12377G1{
+		value: t.Set(&g1Inf),
+	}
+}
+
+func (p *PointBls12377G1) Generator() Point {
+	t := bls12377.G1Affine{}
+	_, _, g1Aff, _ := bls12377.Generators()
+	return &PointBls12377G1{
+		value: t.Set(&g1Aff),
+	}
+}
+
+func (p *PointBls12377G1) IsIdentity() bool {
+	return p.value.IsInfinity()
+}
+
+func (p *PointBls12377G1) IsNegative() bool {
+	// According to https://github.com/zcash/librustzcash/blob/6e0364cd42a2b3d2b958a54771ef51a8db79dd29/pairing/src/bls12_381/README.md#serialization
+	// This bit represents the sign of the `y` coordinate which is what we want
+
+	return (p.value.Bytes()[0]>>5)&1 == 1
+}
+
+func (p *PointBls12377G1) IsOnCurve() bool {
+	return p.value.IsOnCurve()
+}
+
+func (p *PointBls12377G1) Double() Point {
+	t := &bls12377.G1Jac{}
+	t.FromAffine(p.value)
+	t.DoubleAssign()
+	value := bls12377.G1Affine{}
+	return &PointBls12377G1{value.FromJacobian(t)}
+}
+
+func (p *PointBls12377G1) Scalar() Scalar {
+	return &ScalarBls12377{
+		value: new(big.Int),
+		point: new(PointBls12377G1),
+	}
+}
+
+func (p *PointBls12377G1) Neg() Point {
+	value := &bls12377.G1Affine{}
+	value.Neg(p.value)
+	return &PointBls12377G1{value}
+}
+
+func (p *PointBls12377G1) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12377G1)
+	if ok {
+		value := &bls12377.G1Affine{}
+		return &PointBls12377G1{value.Add(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G1) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12377G1)
+	if ok {
+		value := &bls12377.G1Affine{}
+		return &PointBls12377G1{value.Sub(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G1) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		value := &bls12377.G1Affine{}
+		return &PointBls12377G1{value.ScalarMultiplication(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G1) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointBls12377G1)
+	if ok {
+		return p.value.Equal(r.value)
+	} else {
+		return false
+	}
+}
+
+func (p *PointBls12377G1) Set(x, y *big.Int) (Point, error) {
+	if x.Cmp(core.Zero) == 0 &&
+		y.Cmp(core.Zero) == 0 {
+		return p.Identity(), nil
+	}
+	var data [96]byte
+	x.FillBytes(data[:48])
+	y.FillBytes(data[48:])
+	value := &bls12377.G1Affine{}
+	_, err := value.SetBytes(data[:])
+	if err != nil {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	return &PointBls12377G1{value}, nil
+}
+
+func (p *PointBls12377G1) ToAffineCompressed() []byte {
+	v := p.value.Bytes()
+	return v[:]
+}
+
+func (p *PointBls12377G1) ToAffineUncompressed() []byte {
+	v := p.value.RawBytes()
+	return v[:]
+}
+
+func (p *PointBls12377G1) FromAffineCompressed(bytes []byte) (Point, error) {
+	if len(bytes) != bls12377.SizeOfG1AffineCompressed {
+		return nil, fmt.Errorf("invalid point")
+	}
+	value := &bls12377.G1Affine{}
+	_, err := value.SetBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12377G1{value}, nil
+}
+
+func (p *PointBls12377G1) FromAffineUncompressed(bytes []byte) (Point, error) {
+	if len(bytes) != bls12377.SizeOfG1AffineUncompressed {
+		return nil, fmt.Errorf("invalid point")
+	}
+	value := &bls12377.G1Affine{}
+	_, err := value.SetBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12377G1{value}, nil
+}
+
+func (p *PointBls12377G1) CurveName() string {
+	return "BLS12377G1"
+}
+
+func (p *PointBls12377G1) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nScalars := make([]*big.Int, len(scalars))
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarBls12377)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.value
+	}
+	return sumOfProductsPippenger(points, nScalars)
+}
+
+func (p *PointBls12377G1) OtherGroup() PairingPoint {
+	return new(PointBls12377G2).Identity().(PairingPoint)
+}
+
+func (p *PointBls12377G1) Pairing(rhs PairingPoint) Scalar {
+	pt, ok := rhs.(*PointBls12377G2)
+	if !ok {
+		return nil
+	}
+	if !p.value.IsInSubGroup() ||
+		!pt.value.IsInSubGroup() {
+		return nil
+	}
+	value := bls12377.GT{}
+	if p.value.IsInfinity() || pt.value.IsInfinity() {
+		return &ScalarBls12377Gt{&value}
+	}
+	value, err := bls12377.Pair([]bls12377.G1Affine{*p.value}, []bls12377.G2Affine{*pt.value})
+	if err != nil {
+		return nil
+	}
+
+	return &ScalarBls12377Gt{&value}
+}
+
+func (p *PointBls12377G1) MultiPairing(points ...PairingPoint) Scalar {
+	return multiPairingBls12377(points...)
+}
+
+func (p *PointBls12377G1) X() *big.Int {
+	b := p.value.RawBytes()
+	return new(big.Int).SetBytes(b[:48])
+}
+
+func (p *PointBls12377G1) Y() *big.Int {
+	b := p.value.RawBytes()
+	return new(big.Int).SetBytes(b[48:])
+}
+
+func (p *PointBls12377G1) Modulus() *big.Int {
+	return bls12377modulus
+}
+
+func (p *PointBls12377G1) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointBls12377G1) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12377G1)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointBls12377G1) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointBls12377G1) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12377G1)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointBls12377G1) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointBls12377G1) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointBls12377G1)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.value = P.value
+	return nil
+}
+
+func (p *PointBls12377G2) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointBls12377G2) Hash(bytes []byte) Point {
+	var domain = []byte("BLS12377G2_XMD:SHA-256_SVDW_RO_")
+	pt, err := bls12377.HashToCurveG2Svdw(bytes, domain)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12377G2{value: &pt}
+}
+
+func (p *PointBls12377G2) Identity() Point {
+	t := bls12377.G2Affine{}
+	return &PointBls12377G2{
+		value: t.Set(&g2Inf),
+	}
+}
+
+func (p *PointBls12377G2) Generator() Point {
+	t := bls12377.G2Affine{}
+	_, _, _, g2Aff := bls12377.Generators()
+	return &PointBls12377G2{
+		value: t.Set(&g2Aff),
+	}
+}
+
+func (p *PointBls12377G2) IsIdentity() bool {
+	return p.value.IsInfinity()
+}
+
+func (p *PointBls12377G2) IsNegative() bool {
+	// According to https://github.com/zcash/librustzcash/blob/6e0364cd42a2b3d2b958a54771ef51a8db79dd29/pairing/src/bls12_381/README.md#serialization
+	// This bit represents the sign of the `y` coordinate which is what we want
+	return (p.value.Bytes()[0]>>5)&1 == 1
+}
+
+func (p *PointBls12377G2) IsOnCurve() bool {
+	return p.value.IsOnCurve()
+}
+
+func (p *PointBls12377G2) Double() Point {
+	t := &bls12377.G2Jac{}
+	t.FromAffine(p.value)
+	t.DoubleAssign()
+	value := bls12377.G2Affine{}
+	return &PointBls12377G2{value.FromJacobian(t)}
+}
+
+func (p *PointBls12377G2) Scalar() Scalar {
+	return &ScalarBls12377{
+		value: new(big.Int),
+		point: new(PointBls12377G2),
+	}
+}
+
+func (p *PointBls12377G2) Neg() Point {
+	value := &bls12377.G2Affine{}
+	value.Neg(p.value)
+	return &PointBls12377G2{value}
+}
+
+func (p *PointBls12377G2) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12377G2)
+	if ok {
+		value := &bls12377.G2Affine{}
+		return &PointBls12377G2{value.Add(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G2) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12377G2)
+	if ok {
+		value := &bls12377.G2Affine{}
+		return &PointBls12377G2{value.Sub(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G2) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarBls12377)
+	if ok {
+		value := &bls12377.G2Affine{}
+		return &PointBls12377G2{value.ScalarMultiplication(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12377G2) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointBls12377G2)
+	if ok {
+		return p.value.Equal(r.value)
+	} else {
+		return false
+	}
+}
+
+func (p *PointBls12377G2) Set(x, y *big.Int) (Point, error) {
+	if x.Cmp(core.Zero) == 0 &&
+		y.Cmp(core.Zero) == 0 {
+		return p.Identity(), nil
+	}
+	var data [192]byte
+	x.FillBytes(data[:96])
+	y.FillBytes(data[96:])
+	value := &bls12377.G2Affine{}
+	_, err := value.SetBytes(data[:])
+	if err != nil {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	return &PointBls12377G2{value}, nil
+}
+
+func (p *PointBls12377G2) ToAffineCompressed() []byte {
+	v := p.value.Bytes()
+	return v[:]
+}
+
+func (p *PointBls12377G2) ToAffineUncompressed() []byte {
+	v := p.value.RawBytes()
+	return v[:]
+}
+
+func (p *PointBls12377G2) FromAffineCompressed(bytes []byte) (Point, error) {
+	if len(bytes) != bls12377.SizeOfG2AffineCompressed {
+		return nil, fmt.Errorf("invalid point")
+	}
+	value := &bls12377.G2Affine{}
+	_, err := value.SetBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12377G2{value}, nil
+}
+
+func (p *PointBls12377G2) FromAffineUncompressed(bytes []byte) (Point, error) {
+	if len(bytes) != bls12377.SizeOfG2AffineUncompressed {
+		return nil, fmt.Errorf("invalid point")
+	}
+	value := &bls12377.G2Affine{}
+	_, err := value.SetBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12377G2{value}, nil
+}
+
+func (p *PointBls12377G2) CurveName() string {
+	return "BLS12377G2"
+}
+
+func (p *PointBls12377G2) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nScalars := make([]*big.Int, len(scalars))
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarBls12377)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.value
+	}
+	return sumOfProductsPippenger(points, nScalars)
+}
+
+func (p *PointBls12377G2) OtherGroup() PairingPoint {
+	return new(PointBls12377G1).Identity().(PairingPoint)
+}
+
+func (p *PointBls12377G2) Pairing(rhs PairingPoint) Scalar {
+	pt, ok := rhs.(*PointBls12377G1)
+	if !ok {
+		return nil
+	}
+	if !p.value.IsInSubGroup() ||
+		!pt.value.IsInSubGroup() {
+		return nil
+	}
+	value := bls12377.GT{}
+	if p.value.IsInfinity() || pt.value.IsInfinity() {
+		return &ScalarBls12377Gt{&value}
+	}
+	value, err := bls12377.Pair([]bls12377.G1Affine{*pt.value}, []bls12377.G2Affine{*p.value})
+	if err != nil {
+		return nil
+	}
+
+	return &ScalarBls12377Gt{&value}
+}
+
+func (p *PointBls12377G2) MultiPairing(points ...PairingPoint) Scalar {
+	return multiPairingBls12377(points...)
+}
+
+func (p *PointBls12377G2) X() *big.Int {
+	b := p.value.RawBytes()
+	return new(big.Int).SetBytes(b[:96])
+}
+
+func (p *PointBls12377G2) Y() *big.Int {
+	b := p.value.RawBytes()
+	return new(big.Int).SetBytes(b[96:])
+}
+
+func (p *PointBls12377G2) Modulus() *big.Int {
+	return bls12377modulus
+}
+
+func (p *PointBls12377G2) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointBls12377G2) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12377G2)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointBls12377G2) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointBls12377G2) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12377G2)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointBls12377G2) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointBls12377G2) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointBls12377G2)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.value = P.value
+	return nil
+}
+
+func multiPairingBls12377(points ...PairingPoint) Scalar {
+	if len(points)%2 != 0 {
+		return nil
+	}
+	g1Arr := make([]bls12377.G1Affine, 0, len(points)/2)
+	g2Arr := make([]bls12377.G2Affine, 0, len(points)/2)
+	valid := true
+	for i := 0; i < len(points); i += 2 {
+		pt1, ok := points[i].(*PointBls12377G1)
+		valid = valid && ok
+		pt2, ok := points[i+1].(*PointBls12377G2)
+		valid = valid && ok
+		if valid {
+			valid = valid && pt1.value.IsInSubGroup()
+			valid = valid && pt2.value.IsInSubGroup()
+		}
+		if valid {
+			g1Arr = append(g1Arr, *pt1.value)
+			g2Arr = append(g2Arr, *pt2.value)
+		}
+	}
+	if !valid {
+		return nil
+	}
+
+	value, err := bls12377.Pair(g1Arr, g2Arr)
+	if err != nil {
+		return nil
+	}
+
+	return &ScalarBls12377Gt{&value}
+}
+
+func (s *ScalarBls12377Gt) Random(reader io.Reader) Scalar {
+	const width = 48
+	offset := 0
+	var data [bls12377.SizeOfGT]byte
+	for i := 0; i < 12; i++ {
+		tv, err := rand.Int(reader, bls12377modulus)
+		if err != nil {
+			return nil
+		}
+		tv.FillBytes(data[offset*width : (offset+1)*width])
+		offset++
+	}
+	value := bls12377.GT{}
+	err := value.SetBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarBls12377Gt{&value}
+}
+
+func (s *ScalarBls12377Gt) Hash(bytes []byte) Scalar {
+	reader := new(chachaReader)
+	err := reader.Seed(bytes)
+	if err != nil {
+		return nil
+	}
+	return s.Random(reader)
+}
+
+func (s *ScalarBls12377Gt) Zero() Scalar {
+	var t [bls12377.SizeOfGT]byte
+	value := bls12377.GT{}
+	err := value.SetBytes(t[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarBls12377Gt{&value}
+}
+
+func (s *ScalarBls12377Gt) One() Scalar {
+	value := bls12377.GT{}
+	return &ScalarBls12377Gt{value.SetOne()}
+}
+
+func (s *ScalarBls12377Gt) IsZero() bool {
+	r := byte(0)
+	b := s.value.Bytes()
+	for _, i := range b {
+		r |= i
+	}
+	return r == 0
+}
+
+func (s *ScalarBls12377Gt) IsOne() bool {
+	o := bls12377.GT{}
+	return s.value.Equal(o.SetOne())
+}
+
+func (s *ScalarBls12377Gt) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarBls12377Gt) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12377Gt)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarBls12377Gt) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarBls12377Gt) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12377Gt)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarBls12377Gt) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarBls12377Gt) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarBls12377Gt)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+func (s *ScalarBls12377Gt) IsOdd() bool {
+	data := s.value.Bytes()
+	return data[len(data)-1]&1 == 1
+}
+
+func (s *ScalarBls12377Gt) IsEven() bool {
+	data := s.value.Bytes()
+	return data[len(data)-1]&1 == 0
+}
+
+func (s *ScalarBls12377Gt) New(input int) Scalar {
+	var data [576]byte
+	data[3] = byte(input >> 24 & 0xFF)
+	data[2] = byte(input >> 16 & 0xFF)
+	data[1] = byte(input >> 8 & 0xFF)
+	data[0] = byte(input & 0xFF)
+
+	value := bls12377.GT{}
+	err := value.SetBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarBls12377Gt{&value}
+}
+
+func (s *ScalarBls12377Gt) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarBls12377Gt)
+	if ok && s.value.Equal(r.value) {
+		return 0
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarBls12377Gt) Square() Scalar {
+	value := bls12377.GT{}
+	return &ScalarBls12377Gt{
+		value.Square(s.value),
+	}
+}
+
+func (s *ScalarBls12377Gt) Double() Scalar {
+	value := &bls12377.GT{}
+	return &ScalarBls12377Gt{
+		value.Add(s.value, s.value),
+	}
+}
+
+func (s *ScalarBls12377Gt) Invert() (Scalar, error) {
+	value := &bls12377.GT{}
+	return &ScalarBls12377Gt{
+		value.Inverse(s.value),
+	}, nil
+}
+
+func (s *ScalarBls12377Gt) Sqrt() (Scalar, error) {
+	// Not implemented
+	return nil, nil
+}
+
+func (s *ScalarBls12377Gt) Cube() Scalar {
+	value := &bls12377.GT{}
+	value.Square(s.value)
+	value.Mul(value, s.value)
+	return &ScalarBls12377Gt{
+		value,
+	}
+}
+
+func (s *ScalarBls12377Gt) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377Gt)
+	if ok {
+		value := &bls12377.GT{}
+		return &ScalarBls12377Gt{
+			value.Add(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377Gt) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377Gt)
+	if ok {
+		value := &bls12377.GT{}
+		return &ScalarBls12377Gt{
+			value.Sub(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377Gt) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377Gt)
+	if ok {
+		value := &bls12377.GT{}
+		return &ScalarBls12377Gt{
+			value.Mul(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377Gt) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarBls12377Gt) Div(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12377Gt)
+	if ok {
+		value := &bls12377.GT{}
+		value.Inverse(r.value)
+		value.Mul(value, s.value)
+		return &ScalarBls12377Gt{
+			value,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12377Gt) Neg() Scalar {
+	sValue := &bls12377.GT{}
+	sValue.SetOne()
+	value := &bls12377.GT{}
+	value.SetOne()
+	value.Sub(value, sValue)
+	return &ScalarBls12377Gt{
+		value.Sub(value, s.value),
+	}
+}
+
+func (s *ScalarBls12377Gt) SetBigInt(v *big.Int) (Scalar, error) {
+	var bytes [576]byte
+	v.FillBytes(bytes[:])
+	return s.SetBytes(bytes[:])
+}
+
+func (s *ScalarBls12377Gt) BigInt() *big.Int {
+	b := s.value.Bytes()
+	return new(big.Int).SetBytes(b[:])
+}
+
+func (s *ScalarBls12377Gt) Point() Point {
+	p := &PointBls12377G1{}
+	return p.Identity()
+}
+
+func (s *ScalarBls12377Gt) Bytes() []byte {
+	b := s.value.Bytes()
+	return b[:]
+}
+
+func (s *ScalarBls12377Gt) SetBytes(bytes []byte) (Scalar, error) {
+	value := &bls12377.GT{}
+	err := value.SetBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarBls12377Gt{value}, nil
+}
+
+func (s *ScalarBls12377Gt) SetBytesWide(bytes []byte) (Scalar, error) {
+	l := len(bytes)
+	if l != 1152 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value := &bls12377.GT{}
+	err := value.SetBytes(bytes[:l/2])
+	if err != nil {
+		return nil, err
+	}
+	value2 := &bls12377.GT{}
+	err = value2.SetBytes(bytes[l/2:])
+	if err != nil {
+		return nil, err
+	}
+	value.Add(value, value2)
+	return &ScalarBls12377Gt{value}, nil
+}
+
+func (s *ScalarBls12377Gt) Clone() Scalar {
+	value := &bls12377.GT{}
+	return &ScalarBls12377Gt{
+		value.Set(s.value),
+	}
+}
diff --git a/pkg/core/curves/bls12377_curve_test.go b/pkg/core/curves/bls12377_curve_test.go
new file mode 100644
index 00000000..4517d769
--- /dev/null
+++ b/pkg/core/curves/bls12377_curve_test.go
@@ -0,0 +1,516 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	crand "crypto/rand"
+	bls12377 "github.com/consensys/gnark-crypto/ecc/bls12-377"
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"testing"
+)
+
+func TestScalarBls12377G1Random(t *testing.T) {
+	bls12377g1 := BLS12377G1()
+	sc := bls12377g1.Scalar.Random(testRng())
+	s, ok := sc.(*ScalarBls12377)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("022a7db6fad5d5ff49108230818187de316bd0b3e5e96f190397bbb9f28e7a8b", 16)
+	assert.Equal(t, s.value, expected)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12377g1.Scalar.Random(crand.Reader)
+		_, ok := sc.(*ScalarBls12377)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsZero())
+	}
+}
+
+func TestScalarBls12377G1Hash(t *testing.T) {
+	var b [32]byte
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Scalar.Hash(b[:])
+	s, ok := sc.(*ScalarBls12377)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("0c043edae82bf279180b9353139711c1fda5fa64a1f085b80760edaee8f0baca", 16)
+	assert.Equal(t, s.value, expected)
+}
+
+func TestScalarBls12377G1Zero(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Scalar.Zero()
+	assert.True(t, sc.IsZero())
+	assert.True(t, sc.IsEven())
+}
+
+func TestScalarBls12377G1One(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Scalar.One()
+	assert.True(t, sc.IsOne())
+	assert.True(t, sc.IsOdd())
+}
+
+func TestScalarBls12377G1New(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	three := bls12377G1.Scalar.New(3)
+	assert.True(t, three.IsOdd())
+	four := bls12377G1.Scalar.New(4)
+	assert.True(t, four.IsEven())
+	neg1 := bls12377G1.Scalar.New(-1)
+	assert.True(t, neg1.IsEven())
+	neg2 := bls12377G1.Scalar.New(-2)
+	assert.True(t, neg2.IsOdd())
+}
+
+func TestScalarBls12377G1Square(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	three := bls12377G1.Scalar.New(3)
+	nine := bls12377G1.Scalar.New(9)
+	assert.Equal(t, three.Square().Cmp(nine), 0)
+}
+
+func TestScalarBls12377G1Cube(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	three := bls12377G1.Scalar.New(3)
+	twentySeven := bls12377G1.Scalar.New(27)
+	assert.Equal(t, three.Cube().Cmp(twentySeven), 0)
+}
+
+func TestScalarBls12377G1Double(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	three := bls12377G1.Scalar.New(3)
+	six := bls12377G1.Scalar.New(6)
+	assert.Equal(t, three.Double().Cmp(six), 0)
+}
+
+func TestScalarBls12377G1Neg(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	one := bls12377G1.Scalar.One()
+	neg1 := bls12377G1.Scalar.New(-1)
+	assert.Equal(t, one.Neg().Cmp(neg1), 0)
+	lotsOfThrees := bls12377G1.Scalar.New(333333)
+	expected := bls12377G1.Scalar.New(-333333)
+	assert.Equal(t, lotsOfThrees.Neg().Cmp(expected), 0)
+}
+
+func TestScalarBls12377G1Invert(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	actual, _ := nine.Invert()
+	sa, _ := actual.(*ScalarBls12377)
+	expected, err := bls12377G1.Scalar.SetBigInt(bhex("0a5f38510051b12ffcd5f1f46c1ef000c0095e8d9000000093d0d55555555556"))
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarBls12377G1Sqrt(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	actual, err := nine.Sqrt()
+	assert.NoError(t, err)
+	sa, _ := actual.(*ScalarBls12377)
+	expected, err := bls12377G1.Scalar.SetBigInt(bhex("12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a117ffffffffffe"))
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarBls12377G1Add(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	six := bls12377G1.Scalar.New(6)
+	fifteen := nine.Add(six)
+	assert.NotNil(t, fifteen)
+	expected := bls12377G1.Scalar.New(15)
+	assert.Equal(t, expected.Cmp(fifteen), 0)
+	n := new(big.Int).Set(bls12377modulus)
+	n.Sub(n, big.NewInt(3))
+
+	upper, err := bls12377G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := upper.Add(nine)
+	assert.NotNil(t, actual)
+	assert.Equal(t, actual.Cmp(six), 0)
+}
+
+func TestScalarBls12377G1Sub(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	six := bls12377G1.Scalar.New(6)
+	n := new(big.Int).Set(bls12377modulus)
+	n.Sub(n, big.NewInt(3))
+
+	expected, err := bls12377G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := six.Sub(nine)
+	assert.Equal(t, expected.Cmp(actual), 0)
+
+	actual = nine.Sub(six)
+	assert.Equal(t, actual.Cmp(bls12377G1.Scalar.New(3)), 0)
+}
+
+func TestScalarBls12377G1Mul(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	six := bls12377G1.Scalar.New(6)
+	actual := nine.Mul(six)
+	assert.Equal(t, actual.Cmp(bls12377G1.Scalar.New(54)), 0)
+	n := new(big.Int).Set(bls12377modulus)
+	n.Sub(n, big.NewInt(1))
+	upper, err := bls12377G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	assert.Equal(t, upper.Mul(upper).Cmp(bls12377G1.Scalar.New(1)), 0)
+}
+
+func TestScalarBls12377G1Div(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	nine := bls12377G1.Scalar.New(9)
+	actual := nine.Div(nine)
+	assert.Equal(t, actual.Cmp(bls12377G1.Scalar.New(1)), 0)
+	assert.Equal(t, bls12377G1.Scalar.New(54).Div(nine).Cmp(bls12377G1.Scalar.New(6)), 0)
+}
+
+func TestScalarBls12377G1Serialize(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Scalar.New(255)
+	sequence := sc.Bytes()
+	assert.Equal(t, len(sequence), 32)
+	assert.Equal(t, sequence, []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0xff})
+	ret, err := bls12377G1.Scalar.SetBytes(sequence)
+	assert.NoError(t, err)
+	assert.Equal(t, ret.Cmp(sc), 0)
+
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc = bls12377G1.Scalar.Random(crand.Reader)
+		sequence = sc.Bytes()
+		assert.Equal(t, len(sequence), 32)
+		ret, err = bls12377G1.Scalar.SetBytes(sequence)
+		assert.NoError(t, err)
+		assert.Equal(t, ret.Cmp(sc), 0)
+	}
+}
+
+func TestScalarBls12377G1Nil(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	one := bls12377G1.Scalar.New(1)
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, one.Div(nil))
+	assert.Nil(t, bls12377G1.Scalar.Random(nil))
+	assert.Equal(t, one.Cmp(nil), -2)
+	_, err := bls12377G1.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestScalarBls12377Point(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	_, ok := bls12377G1.Scalar.Point().(*PointBls12377G1)
+	assert.True(t, ok)
+	bls12377G2 := BLS12377G2()
+	_, ok = bls12377G2.Scalar.Point().(*PointBls12377G2)
+	assert.True(t, ok)
+}
+
+func TestPointBls12377G2Random(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	sc := bls12377G2.Point.Random(testRng())
+	s, ok := sc.(*PointBls12377G2)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("2deeb99988cc46605a5e8eeb50b2c52fc4a12b4537aa8a149431ca85bac2017a32d2a3bf8411d5145bdf587f162a1b01a106e89ebf3210c0926ba07681cd84fc8ae2409b396b24730a8b851d05ba3293b82ae341c472d626c1f55da16ba46d", 16)
+	expectedY, _ := new(big.Int).SetString("b17be752bc4a8ff05824fcf974d232cebe07ee333ce879bf8c7b88ce18813cb190e8a45eddbd7cc5a4b68993ed17770094ab97b85b70b0b80e89c854336b85e46c7259070fb6606b03bcab12d96438f9a79353fafe11733aed51bfa4e798b8", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12377G2.Point.Random(crand.Reader)
+		_, ok := sc.(*PointBls12377G2)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointBls12377G2Hash(t *testing.T) {
+	var b [32]byte
+	bls12377G2 := BLS12377G2()
+	sc := bls12377G2.Point.Hash(b[:])
+	s, ok := sc.(*PointBls12377G2)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("014eec1848d84be62f3a5778353ea6c2b0db859508bc40ff2c1387f0a4b2a167fedbe6b10f946f33c600623d7b96dc8200ef8b67c1e07c4dc522f25deb617ad8251199d235da8bc7700332c8416aa204f81e6bebd914e46acea095d3083b7723", 16)
+	expectedY, _ := new(big.Int).SetString("015c17fb5e37ce1284fa5f10cca9a55be5a5e4d821649294ab820a6f044f55337665df04a940ee7f5d937aff69196b010168d9090eb791d4b21752622f1fd5fb0f4c44bfd83e2cf6d332b02343999fac3de660ca84aff40b428f25b5378fe648", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+}
+
+func TestPointBls12377G2Identity(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	sc := bls12377G2.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{0xc0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0})
+}
+
+func TestPointBls12377G2Generator(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	sc := bls12377G2.Point.Generator()
+	s, ok := sc.(*PointBls12377G2)
+	assert.True(t, ok)
+	_, _, _, g2Aff := bls12377.Generators()
+	assert.True(t, s.value.Equal(&g2Aff))
+}
+
+func TestPointBls12377G2Set(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	iden, err := bls12377G2.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	_, _, _, g2Aff := bls12377.Generators()
+	generator := g2Aff.Bytes()
+	_, err = bls12377G2.Point.Set(new(big.Int).SetBytes(generator[:96]), new(big.Int).SetBytes(generator[96:]))
+	assert.NoError(t, err)
+}
+
+func TestPointBls12377G2Double(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	g := bls12377G2.Point.Generator()
+	gg2 := g.Double()
+	assert.True(t, gg2.Equal(g.Mul(bls12377G2.Scalar.New(2))))
+	i := bls12377G2.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointBls12377G2Neg(t *testing.T) {
+	bls12377G2 := BLS12377G1()
+	g := bls12377G2.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(bls12377G2.Point.Generator()))
+	assert.True(t, bls12377G2.Point.Identity().Neg().Equal(bls12377G2.Point.Identity()))
+}
+
+func TestPointBls12377G2Add(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	pt := bls12377G2.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(bls12377G2.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointBls12377G2Sub(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	g := bls12377G2.Point.Generator()
+	pt := bls12377G2.Point.Generator().Mul(bls12377G2.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointBls12377G2Mul(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	g := bls12377G2.Point.Generator()
+	pt := bls12377G2.Point.Generator().Mul(bls12377G2.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointBls12377G2Serialize(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	ss := bls12377G2.Scalar.Random(testRng())
+	g := bls12377G2.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0x81, 0x88, 0xf4, 0x32, 0xec, 0x60, 0x72, 0xd3, 0x76, 0x77, 0x86, 0xcd, 0x44, 0xce, 0x91, 0x5a, 0x3a, 0xb5, 0x13, 0xe2, 0x81, 0x10, 0x41, 0xa1, 0x39, 0x1e, 0xe2, 0x8a, 0x5f, 0x5f, 0xf1, 0x2e, 0x72, 0xab, 0xc5, 0x62, 0x5c, 0x99, 0x56, 0x5d, 0xd4, 0x33, 0x9a, 0x61, 0x63, 0xd4, 0x8e, 0x7c, 0x0, 0xec, 0x46, 0xb, 0xc4, 0x22, 0xd9, 0xe0, 0x74, 0xe6, 0x79, 0x7b, 0x55, 0x8d, 0x8f, 0x9b, 0xf7, 0x59, 0x65, 0x10, 0x97, 0xe3, 0x12, 0x18, 0xd3, 0x76, 0x3, 0x58, 0x87, 0xc7, 0x82, 0x4c, 0x42, 0x80, 0xa2, 0xa, 0x3d, 0x66, 0xfe, 0xb6, 0xed, 0xd9, 0x38, 0x45, 0x5, 0xbe, 0x40, 0x32})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x1, 0x88, 0xf4, 0x32, 0xec, 0x60, 0x72, 0xd3, 0x76, 0x77, 0x86, 0xcd, 0x44, 0xce, 0x91, 0x5a, 0x3a, 0xb5, 0x13, 0xe2, 0x81, 0x10, 0x41, 0xa1, 0x39, 0x1e, 0xe2, 0x8a, 0x5f, 0x5f, 0xf1, 0x2e, 0x72, 0xab, 0xc5, 0x62, 0x5c, 0x99, 0x56, 0x5d, 0xd4, 0x33, 0x9a, 0x61, 0x63, 0xd4, 0x8e, 0x7c, 0x0, 0xec, 0x46, 0xb, 0xc4, 0x22, 0xd9, 0xe0, 0x74, 0xe6, 0x79, 0x7b, 0x55, 0x8d, 0x8f, 0x9b, 0xf7, 0x59, 0x65, 0x10, 0x97, 0xe3, 0x12, 0x18, 0xd3, 0x76, 0x3, 0x58, 0x87, 0xc7, 0x82, 0x4c, 0x42, 0x80, 0xa2, 0xa, 0x3d, 0x66, 0xfe, 0xb6, 0xed, 0xd9, 0x38, 0x45, 0x5, 0xbe, 0x40, 0x32, 0x0, 0xd, 0x69, 0x94, 0x48, 0x5e, 0x3, 0xd4, 0x51, 0x2a, 0xf6, 0xa, 0xf0, 0x4b, 0xd8, 0x42, 0xc4, 0xc3, 0x66, 0xb8, 0x77, 0x15, 0xaf, 0x8b, 0xee, 0x68, 0xc3, 0xfe, 0x16, 0x4d, 0xd0, 0x5b, 0x97, 0xc, 0x16, 0x6c, 0xfe, 0x9e, 0xc, 0xe0, 0xe3, 0x15, 0x33, 0x6c, 0x81, 0xc1, 0x93, 0x1e, 0x1, 0x13, 0xfc, 0x17, 0xf2, 0x9c, 0xe0, 0x61, 0xe4, 0x58, 0x3a, 0xba, 0xed, 0xd9, 0x2f, 0x54, 0xdd, 0xc3, 0x7f, 0xdf, 0xc0, 0x31, 0x89, 0x1f, 0xf3, 0xcf, 0x9c, 0xac, 0x7c, 0xd, 0x91, 0x8a, 0x84, 0xf8, 0xab, 0xcc, 0x77, 0x55, 0xb6, 0x72, 0xf4, 0xb0, 0x13, 0x45, 0xbb, 0x3d, 0x44, 0xfe})
+
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := bls12377G2.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 96)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 192)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointBls12377G2Nil(t *testing.T) {
+	bls12377G2 := BLS12377G2()
+	one := bls12377G2.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, bls12377G2.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := bls12377G2.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointBls12377G1Random(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Point.Random(testRng())
+	s, ok := sc.(*PointBls12377G1)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("facd83174df271a2dbd7d84f02f4d1b6a61850a926e7ec5ca34e558378feb146231e5e105fa27310843db23a49ca53", 16)
+	expectedY, _ := new(big.Int).SetString("4fa90bd4c90a2d4afd01bf0f561ab112bc13bb7c0faa87a2324febab2c3fa1ff47b2ed1dd9e38b1c660dd6d2ec0a7b", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12377G1.Point.Random(crand.Reader)
+		_, ok := sc.(*PointBls12377G1)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointBls12377G1Hash(t *testing.T) {
+	var b [32]byte
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Point.Hash(b[:])
+	s, ok := sc.(*PointBls12377G1)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("8c1f4dd215430f2a1c01e1f50eded8de37033e5b70b9987c93547e0b8ec87ca918039d41e5e634773e1bcbe1e2d836", 16)
+	expectedY, _ := new(big.Int).SetString("552b0bde9c7b051118a5619cf409cd9d2b25a1ebb5e35b7c7bd031f8c15f1d08979e634d2acd1b7be4ccb43a064393", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+}
+
+func TestPointBls12377G1Identity(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{0xc0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+}
+
+func TestPointBls12377G1Generator(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	sc := bls12377G1.Point.Generator()
+	s, ok := sc.(*PointBls12377G1)
+	assert.True(t, ok)
+	_, _, g1Aff, _ := bls12377.Generators()
+	assert.True(t, s.value.Equal(&g1Aff))
+}
+
+func TestPointBls12377G1Set(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	iden, err := bls12377G1.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	_, _, g1Aff, _ := bls12377.Generators()
+	generator := g1Aff.Bytes()
+	_, err = bls12377G1.Point.Set(new(big.Int).SetBytes(generator[:48]), new(big.Int).SetBytes(generator[48:]))
+	assert.NoError(t, err)
+}
+
+func TestPointBls12377G1Double(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	g := bls12377G1.Point.Generator()
+	g2 := g.Double()
+	assert.True(t, g2.Equal(g.Mul(bls12377G1.Scalar.New(2))))
+	i := bls12377G1.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointBls12377G1Neg(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	g := bls12377G1.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(bls12377G1.Point.Generator()))
+	assert.True(t, bls12377G1.Point.Identity().Neg().Equal(bls12377G1.Point.Identity()))
+}
+
+func TestPointBls12377G1Add(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	pt := bls12377G1.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(bls12377G1.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointBls12377G1Sub(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	g := bls12377G1.Point.Generator()
+	pt := bls12377G1.Point.Generator().Mul(bls12377G1.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointBls12377G1Mul(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	g := bls12377G1.Point.Generator()
+	pt := bls12377G1.Point.Generator().Mul(bls12377G1.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointBls12377G1Serialize(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	ss := bls12377G1.Scalar.Random(testRng())
+	g := bls12377G1.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0xa0, 0xd0, 0xae, 0xea, 0xaa, 0xf1, 0xf6, 0x0, 0x59, 0x39, 0x33, 0x3c, 0x60, 0x16, 0xaf, 0x68, 0x86, 0x2d, 0x3a, 0xc1, 0x73, 0x24, 0xdd, 0x2, 0xb6, 0x49, 0xde, 0xf, 0xe7, 0x42, 0xe8, 0x10, 0xf, 0xab, 0xd1, 0x63, 0xed, 0x13, 0xda, 0x0, 0x69, 0x1b, 0x20, 0x7d, 0xcd, 0x71, 0x7, 0xef})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x0, 0xd0, 0xae, 0xea, 0xaa, 0xf1, 0xf6, 0x0, 0x59, 0x39, 0x33, 0x3c, 0x60, 0x16, 0xaf, 0x68, 0x86, 0x2d, 0x3a, 0xc1, 0x73, 0x24, 0xdd, 0x2, 0xb6, 0x49, 0xde, 0xf, 0xe7, 0x42, 0xe8, 0x10, 0xf, 0xab, 0xd1, 0x63, 0xed, 0x13, 0xda, 0x0, 0x69, 0x1b, 0x20, 0x7d, 0xcd, 0x71, 0x7, 0xef, 0x1, 0x78, 0x3f, 0xbd, 0xd4, 0xbd, 0x7c, 0xf5, 0x7a, 0xfd, 0x33, 0x45, 0x7, 0x39, 0xf2, 0xb7, 0x10, 0x4c, 0x1e, 0xc5, 0x2b, 0x93, 0x4, 0x67, 0x54, 0x88, 0x8b, 0x57, 0x69, 0xf, 0x74, 0x40, 0xf4, 0x58, 0x5b, 0xd7, 0x76, 0x63, 0x58, 0xd9, 0x7b, 0x6d, 0x46, 0x8e, 0x50, 0x89, 0xc4, 0x7d})
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := bls12377G1.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 48)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 96)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointBls12377G1Nil(t *testing.T) {
+	bls12377G1 := BLS12377G1()
+	one := bls12377G1.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, bls12377G1.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := bls12377G1.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointBls12377G1SumOfProducts(t *testing.T) {
+	lhs := new(PointBls12377G1).Generator().Mul(new(ScalarBls12377).New(50))
+	points := make([]Point, 5)
+	for i := range points {
+		points[i] = new(PointBls12377G1).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarBls12377).New(8),
+		new(ScalarBls12377).New(9),
+		new(ScalarBls12377).New(10),
+		new(ScalarBls12377).New(11),
+		new(ScalarBls12377).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
diff --git a/pkg/core/curves/bls12381_curve.go b/pkg/core/curves/bls12381_curve.go
new file mode 100644
index 00000000..2e716ffc
--- /dev/null
+++ b/pkg/core/curves/bls12381_curve.go
@@ -0,0 +1,1227 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+	cc20rand "github.com/nixberg/chacha-rng-go"
+	"io"
+	"math/big"
+)
+
+var g1 = bls12381.NewG1()
+var g2 = bls12381.NewG2()
+var gt = bls12381.NewEngine().GT()
+var bls12381modulus = bhex("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab")
+
+type ScalarBls12381 struct {
+	Value *big.Int
+	point Point
+}
+
+type PointBls12381G1 struct {
+	Value *bls12381.PointG1
+}
+
+type PointBls12381G2 struct {
+	Value *bls12381.PointG2
+}
+
+type ScalarBls12381Gt struct {
+	Value *bls12381.E
+}
+
+func (s *ScalarBls12381) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarBls12381) Hash(bytes []byte) Scalar {
+	xmd, err := expandMsgXmd(sha256.New(), bytes, []byte("BLS12381_XMD:SHA-256_SSWU_RO_"), 48)
+	if err != nil {
+		return nil
+	}
+	v := new(big.Int).SetBytes(xmd)
+	return &ScalarBls12381{
+		Value: v.Mod(v, g1.Q()),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) Zero() Scalar {
+	return &ScalarBls12381{
+		Value: big.NewInt(0),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) One() Scalar {
+	return &ScalarBls12381{
+		Value: big.NewInt(1),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) IsZero() bool {
+	return subtle.ConstantTimeCompare(s.Value.Bytes(), []byte{}) == 1
+}
+
+func (s *ScalarBls12381) IsOne() bool {
+	return subtle.ConstantTimeCompare(s.Value.Bytes(), []byte{1}) == 1
+}
+
+func (s *ScalarBls12381) IsOdd() bool {
+	return s.Value.Bit(0) == 1
+}
+
+func (s *ScalarBls12381) IsEven() bool {
+	return s.Value.Bit(0) == 0
+}
+
+func (s *ScalarBls12381) New(value int) Scalar {
+	v := big.NewInt(int64(value))
+	if value < 0 {
+		v.Mod(v, g1.Q())
+	}
+	return &ScalarBls12381{
+		Value: v,
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		return s.Value.Cmp(r.Value)
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarBls12381) Square() Scalar {
+	return &ScalarBls12381{
+		Value: new(big.Int).Exp(s.Value, big.NewInt(2), g1.Q()),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) Double() Scalar {
+	v := new(big.Int).Add(s.Value, s.Value)
+	return &ScalarBls12381{
+		Value: v.Mod(v, g1.Q()),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) Invert() (Scalar, error) {
+	return &ScalarBls12381{
+		Value: new(big.Int).ModInverse(s.Value, g1.Q()),
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12381) Sqrt() (Scalar, error) {
+	return &ScalarBls12381{
+		Value: new(big.Int).ModSqrt(s.Value, g1.Q()),
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12381) Cube() Scalar {
+	return &ScalarBls12381{
+		Value: new(big.Int).Exp(s.Value, big.NewInt(3), g1.Q()),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		v := new(big.Int).Add(s.Value, r.Value)
+		return &ScalarBls12381{
+			Value: v.Mod(v, g1.Q()),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		v := new(big.Int).Sub(s.Value, r.Value)
+		return &ScalarBls12381{
+			Value: v.Mod(v, g1.Q()),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		v := new(big.Int).Mul(s.Value, r.Value)
+		return &ScalarBls12381{
+			Value: v.Mod(v, g1.Q()),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarBls12381) Div(rhs Scalar) Scalar {
+	n := g1.Q()
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		v := new(big.Int).ModInverse(r.Value, n)
+		v.Mul(v, s.Value)
+		return &ScalarBls12381{
+			Value: v.Mod(v, n),
+			point: s.point,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381) Neg() Scalar {
+	z := new(big.Int).Neg(s.Value)
+	return &ScalarBls12381{
+		Value: z.Mod(z, g1.Q()),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) SetBigInt(v *big.Int) (Scalar, error) {
+	if v == nil {
+		return nil, fmt.Errorf("invalid value")
+	}
+	t := new(big.Int).Mod(v, g1.Q())
+	if t.Cmp(v) != 0 {
+		return nil, fmt.Errorf("invalid value")
+	}
+	return &ScalarBls12381{
+		Value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12381) BigInt() *big.Int {
+	return new(big.Int).Set(s.Value)
+}
+
+func (s *ScalarBls12381) Bytes() []byte {
+	var out [32]byte
+	return s.Value.FillBytes(out[:])
+}
+
+func (s *ScalarBls12381) SetBytes(bytes []byte) (Scalar, error) {
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, g1.Q())
+	if t.Cmp(value) != 0 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	return &ScalarBls12381{
+		Value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12381) SetBytesWide(bytes []byte) (Scalar, error) {
+	if len(bytes) < 32 || len(bytes) > 128 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, g1.Q())
+	return &ScalarBls12381{
+		Value: t,
+		point: s.point,
+	}, nil
+}
+
+func (s *ScalarBls12381) Point() Point {
+	return s.point.Identity()
+}
+
+func (s *ScalarBls12381) Clone() Scalar {
+	return &ScalarBls12381{
+		Value: new(big.Int).Set(s.Value),
+		point: s.point,
+	}
+}
+
+func (s *ScalarBls12381) SetPoint(p Point) PairingScalar {
+	return &ScalarBls12381{
+		Value: new(big.Int).Set(s.Value),
+		point: p,
+	}
+}
+
+func (s *ScalarBls12381) Order() *big.Int {
+	return g1.Q()
+}
+
+func (s *ScalarBls12381) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarBls12381) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12381)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.Value = ss.Value
+	s.point = ss.point
+	return nil
+}
+
+func (s *ScalarBls12381) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarBls12381) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12381)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.Value = ss.Value
+	s.point = ss.point
+	return nil
+}
+
+func (s *ScalarBls12381) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarBls12381) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarBls12381)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.Value = S.Value
+	return nil
+}
+
+func (p *PointBls12381G1) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointBls12381G1) Hash(bytes []byte) Point {
+	var domain = []byte("BLS12381G1_XMD:SHA-256_SSWU_RO_")
+	pt, err := g1.HashToCurve(sha256.New, bytes, domain)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12381G1{Value: pt}
+}
+
+func (p *PointBls12381G1) Identity() Point {
+	return &PointBls12381G1{
+		Value: g1.New(),
+	}
+}
+
+func (p *PointBls12381G1) Generator() Point {
+	return &PointBls12381G1{
+		Value: g1.One(),
+	}
+}
+
+func (p *PointBls12381G1) IsIdentity() bool {
+	return g1.IsZero(p.Value)
+}
+
+func (p *PointBls12381G1) IsNegative() bool {
+	// According to https://github.com/zcash/librustzcash/blob/6e0364cd42a2b3d2b958a54771ef51a8db79dd29/pairing/src/bls12_381/README.md#serialization
+	// This bit represents the sign of the `y` coordinate which is what we want
+	return (g1.ToCompressed(p.Value)[0]>>5)&1 == 1
+}
+
+func (p *PointBls12381G1) IsOnCurve() bool {
+	return g1.IsOnCurve(p.Value)
+}
+
+func (p *PointBls12381G1) Double() Point {
+	value := g1.Double(g1.New(), p.Value)
+	return &PointBls12381G1{value}
+}
+
+func (p *PointBls12381G1) Scalar() Scalar {
+	return &ScalarBls12381{
+		Value: new(big.Int),
+		point: new(PointBls12381G1),
+	}
+}
+
+func (p *PointBls12381G1) Neg() Point {
+	value := g1.Neg(g1.New(), p.Value)
+	return &PointBls12381G1{value}
+}
+
+func (p *PointBls12381G1) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12381G1)
+	if ok {
+		value := g1.Add(g1.New(), p.Value, r.Value)
+		return &PointBls12381G1{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G1) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12381G1)
+	if ok {
+		value := g1.Sub(g1.New(), p.Value, r.Value)
+		return &PointBls12381G1{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G1) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		value := g1.MulScalar(g1.New(), p.Value, r.Value)
+		return &PointBls12381G1{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G1) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointBls12381G1)
+	if ok {
+		return g1.Equal(p.Value, r.Value)
+	} else {
+		return false
+	}
+}
+
+func (p *PointBls12381G1) Set(x, y *big.Int) (Point, error) {
+	if x.Cmp(core.Zero) == 0 &&
+		y.Cmp(core.Zero) == 0 {
+		return p.Identity(), nil
+	}
+	var data [96]byte
+	x.FillBytes(data[:48])
+	y.FillBytes(data[48:])
+	value, err := g1.FromUncompressed(data[:])
+	if err != nil {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	return &PointBls12381G1{value}, nil
+}
+
+func (p *PointBls12381G1) ToAffineCompressed() []byte {
+	return g1.ToCompressed(p.Value)
+}
+
+func (p *PointBls12381G1) ToAffineUncompressed() []byte {
+	bytes, err := g1.ToUncompressed(p.Value)
+	if err != nil {
+		panic(err)
+	}
+	return bytes
+}
+
+func (p *PointBls12381G1) FromAffineCompressed(bytes []byte) (Point, error) {
+	value, err := g1.FromCompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12381G1{value}, nil
+}
+
+func (p *PointBls12381G1) FromAffineUncompressed(bytes []byte) (Point, error) {
+	value, err := g1.FromUncompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12381G1{value}, nil
+}
+
+func (p *PointBls12381G1) CurveName() string {
+	return "BLS12381G1"
+}
+
+func (p *PointBls12381G1) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nPoints := make([]*bls12381.PointG1, len(points))
+	nScalars := make([]*big.Int, len(scalars))
+	for i, pt := range points {
+		pp, ok := pt.(*PointBls12381G1)
+		if !ok {
+			return nil
+		}
+		nPoints[i] = pp.Value
+	}
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarBls12381)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.Value
+	}
+	value := g1.New()
+	_, err := g1.MultiExp(value, nPoints, nScalars)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12381G1{value}
+}
+
+func (p *PointBls12381G1) OtherGroup() PairingPoint {
+	return new(PointBls12381G2).Identity().(PairingPoint)
+}
+
+func (p *PointBls12381G1) Pairing(rhs PairingPoint) Scalar {
+	var err error
+	pt, ok := rhs.(*PointBls12381G2)
+	if !ok {
+		return nil
+	}
+	if !g1.InCorrectSubgroup(p.Value) ||
+		!g2.InCorrectSubgroup(pt.Value) {
+		return nil
+	}
+	value := &bls12381.E{}
+	if g1.IsZero(p.Value) || g2.IsZero(pt.Value) {
+		return &ScalarBls12381Gt{value}
+	}
+	eng := bls12381.NewEngine()
+	eng.AddPair(p.Value, pt.Value)
+
+	value, err = eng.Result()
+	if err != nil {
+		panic(err)
+	}
+
+	return &ScalarBls12381Gt{value}
+}
+
+func (p *PointBls12381G1) MultiPairing(points ...PairingPoint) Scalar {
+	return multiPairing(points...)
+}
+
+func (p *PointBls12381G1) X() *big.Int {
+	bytes := g1.ToBytes(p.Value)
+	return new(big.Int).SetBytes(bytes[:48])
+}
+
+func (p *PointBls12381G1) Y() *big.Int {
+	bytes := g1.ToBytes(p.Value)
+	return new(big.Int).SetBytes(bytes[48:])
+}
+
+func (p *PointBls12381G1) Modulus() *big.Int {
+	return bls12381modulus
+}
+
+func (p *PointBls12381G1) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointBls12381G1) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12381G1)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.Value = ppt.Value
+	return nil
+}
+
+func (p *PointBls12381G1) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointBls12381G1) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12381G1)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.Value = ppt.Value
+	return nil
+}
+
+func (p *PointBls12381G1) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointBls12381G1) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointBls12381G1)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.Value = P.Value
+	return nil
+}
+
+func (p *PointBls12381G2) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointBls12381G2) Hash(bytes []byte) Point {
+	var domain = []byte("BLS12381G2_XMD:SHA-256_SSWU_RO_")
+	pt, err := g2.HashToCurve(sha256.New, bytes, domain)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12381G2{Value: pt}
+}
+
+func (p *PointBls12381G2) Identity() Point {
+	return &PointBls12381G2{
+		Value: g2.New(),
+	}
+}
+
+func (p *PointBls12381G2) Generator() Point {
+	return &PointBls12381G2{
+		Value: g2.One(),
+	}
+}
+
+func (p *PointBls12381G2) IsIdentity() bool {
+	return g2.IsZero(p.Value)
+}
+
+func (p *PointBls12381G2) IsNegative() bool {
+	// According to https://github.com/zcash/librustzcash/blob/6e0364cd42a2b3d2b958a54771ef51a8db79dd29/pairing/src/bls12_381/README.md#serialization
+	// This bit represents the sign of the `y` coordinate which is what we want
+	return (g2.ToCompressed(p.Value)[0]>>5)&1 == 1
+}
+
+func (p *PointBls12381G2) IsOnCurve() bool {
+	return g2.IsOnCurve(p.Value)
+}
+
+func (p *PointBls12381G2) Double() Point {
+	value := g2.Double(g2.New(), p.Value)
+	return &PointBls12381G2{value}
+}
+
+func (p *PointBls12381G2) Scalar() Scalar {
+	return &ScalarBls12381{
+		Value: new(big.Int),
+		point: new(PointBls12381G2),
+	}
+}
+
+func (p *PointBls12381G2) Neg() Point {
+	value := g2.Neg(g2.New(), p.Value)
+	return &PointBls12381G2{value}
+}
+
+func (p *PointBls12381G2) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12381G2)
+	if ok {
+		value := g2.Add(g2.New(), p.Value, r.Value)
+		return &PointBls12381G2{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G2) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointBls12381G2)
+	if ok {
+		value := g2.Sub(g2.New(), p.Value, r.Value)
+		return &PointBls12381G2{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G2) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarBls12381)
+	if ok {
+		value := g2.MulScalar(g2.New(), p.Value, r.Value)
+		return &PointBls12381G2{value}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointBls12381G2) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointBls12381G2)
+	if ok {
+		return g2.Equal(p.Value, r.Value)
+	} else {
+		return false
+	}
+}
+
+func (p *PointBls12381G2) Set(x, y *big.Int) (Point, error) {
+	if x.Cmp(core.Zero) == 0 &&
+		y.Cmp(core.Zero) == 0 {
+		return p.Identity(), nil
+	}
+	var data [192]byte
+	x.FillBytes(data[:96])
+	y.FillBytes(data[96:])
+	value, err := g2.FromUncompressed(data[:])
+	if err != nil {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	return &PointBls12381G2{value}, nil
+}
+
+func (p *PointBls12381G2) ToAffineCompressed() []byte {
+	return g2.ToCompressed(p.Value)
+}
+
+func (p *PointBls12381G2) ToAffineUncompressed() []byte {
+	bytes, err := g2.ToUncompressed(p.Value)
+	if err != nil {
+		panic(err)
+	}
+	return bytes
+}
+
+func (p *PointBls12381G2) FromAffineCompressed(bytes []byte) (Point, error) {
+	value, err := g2.FromCompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12381G2{value}, nil
+}
+
+func (p *PointBls12381G2) FromAffineUncompressed(bytes []byte) (Point, error) {
+	value, err := g2.FromUncompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointBls12381G2{value}, nil
+}
+
+func (p *PointBls12381G2) CurveName() string {
+	return "BLS12381G2"
+}
+
+func (p *PointBls12381G2) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nPoints := make([]*bls12381.PointG2, len(points))
+	nScalars := make([]*big.Int, len(scalars))
+	for i, pt := range points {
+		pp, ok := pt.(*PointBls12381G2)
+		if !ok {
+			return nil
+		}
+		nPoints[i] = pp.Value
+	}
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarBls12381)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.Value
+	}
+	value := g2.New()
+	_, err := g2.MultiExp(value, nPoints, nScalars)
+	if err != nil {
+		return nil
+	}
+	return &PointBls12381G2{value}
+}
+
+func (p *PointBls12381G2) OtherGroup() PairingPoint {
+	return new(PointBls12381G1).Identity().(PairingPoint)
+}
+
+func (p *PointBls12381G2) Pairing(rhs PairingPoint) Scalar {
+	var err error
+	pt, ok := rhs.(*PointBls12381G1)
+	if !ok {
+		return nil
+	}
+	if !g2.InCorrectSubgroup(p.Value) ||
+		!g1.InCorrectSubgroup(pt.Value) {
+		return nil
+	}
+	value := &bls12381.E{}
+	if g2.IsZero(p.Value) || g1.IsZero(pt.Value) {
+		return &ScalarBls12381Gt{value}
+	}
+	eng := bls12381.NewEngine()
+	eng.AddPair(pt.Value, p.Value)
+
+	value, err = eng.Result()
+	if err != nil {
+		panic(err)
+	}
+
+	return &ScalarBls12381Gt{value}
+}
+
+func (p *PointBls12381G2) MultiPairing(points ...PairingPoint) Scalar {
+	return multiPairing(points...)
+}
+
+func (p *PointBls12381G2) X() *big.Int {
+	bytes := g2.ToBytes(p.Value)
+	return new(big.Int).SetBytes(bytes[:96])
+}
+
+func (p *PointBls12381G2) Y() *big.Int {
+	bytes := g2.ToBytes(p.Value)
+	return new(big.Int).SetBytes(bytes[96:])
+}
+
+func (p *PointBls12381G2) Modulus() *big.Int {
+	return bls12381modulus
+}
+
+func (p *PointBls12381G2) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointBls12381G2) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12381G2)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.Value = ppt.Value
+	return nil
+}
+
+func (p *PointBls12381G2) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointBls12381G2) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointBls12381G2)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.Value = ppt.Value
+	return nil
+}
+
+func (p *PointBls12381G2) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointBls12381G2) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointBls12381G2)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.Value = P.Value
+	return nil
+}
+
+func multiPairing(points ...PairingPoint) Scalar {
+	if len(points)%2 != 0 {
+		return nil
+	}
+	valid := true
+	eng := bls12381.NewEngine()
+	for i := 0; i < len(points); i += 2 {
+		pt1, ok := points[i].(*PointBls12381G1)
+		valid = valid && ok
+		pt2, ok := points[i+1].(*PointBls12381G2)
+		valid = valid && ok
+		if valid {
+			valid = valid && g1.InCorrectSubgroup(pt1.Value)
+			valid = valid && g2.InCorrectSubgroup(pt2.Value)
+		}
+		if valid {
+			eng.AddPair(pt1.Value, pt2.Value)
+		}
+	}
+	if !valid {
+		return nil
+	}
+
+	value, err := eng.Result()
+	if err != nil {
+		panic(err)
+	}
+
+	return &ScalarBls12381Gt{value}
+}
+
+func (s *ScalarBls12381Gt) Random(reader io.Reader) Scalar {
+	const width = 48
+	offset := 0
+	var data [576]byte
+	for i := 0; i < 12; i++ {
+		tv, err := rand.Int(reader, bls12381modulus)
+		if err != nil {
+			return nil
+		}
+		tv.FillBytes(data[offset*width : (offset+1)*width])
+		offset++
+	}
+	value, err := gt.FromBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarBls12381Gt{value}
+}
+
+func (s *ScalarBls12381Gt) Hash(bytes []byte) Scalar {
+	reader := new(chachaReader)
+	err := reader.Seed(bytes)
+	if err != nil {
+		return nil
+	}
+	return s.Random(reader)
+}
+
+type chachaReader struct {
+	rng *cc20rand.ChaCha
+}
+
+func (cc20 *chachaReader) Seed(bytes []byte) error {
+	var seed [8]uint32
+	output, err := core.FiatShamir(new(big.Int).SetBytes(bytes))
+	if err != nil {
+		return err
+	}
+	j := 0
+	for i := 0; i < len(output); i += 4 {
+		seed[j] = uint32(output[i]) << 24
+		seed[j] |= uint32(output[i+1]) << 16
+		seed[j] |= uint32(output[i+2]) << 8
+		seed[j] |= uint32(output[i+2])
+	}
+	cc20.rng = cc20rand.Seeded20(seed, 0)
+	return nil
+}
+
+func (cc20 *chachaReader) Read(bytes []byte) (n int, err error) {
+	cc20.rng.FillUint8(bytes)
+	n = 0
+	err = nil
+	return
+}
+
+func (s *ScalarBls12381Gt) Zero() Scalar {
+	return &ScalarBls12381Gt{gt.New()}
+}
+
+func (s *ScalarBls12381Gt) One() Scalar {
+	return &ScalarBls12381Gt{gt.New().One()}
+}
+
+func (s *ScalarBls12381Gt) IsZero() bool {
+	return s.Value.Equal(gt.New())
+}
+
+func (s *ScalarBls12381Gt) IsOne() bool {
+	return s.Value.IsOne()
+}
+
+func (s *ScalarBls12381Gt) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarBls12381Gt) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12381Gt)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.Value = ss.Value
+	return nil
+}
+
+func (s *ScalarBls12381Gt) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarBls12381Gt) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarBls12381Gt)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.Value = ss.Value
+	return nil
+}
+
+func (s *ScalarBls12381Gt) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarBls12381Gt) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarBls12381Gt)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.Value = S.Value
+	return nil
+}
+
+func (s *ScalarBls12381Gt) IsOdd() bool {
+	data := gt.ToBytes(s.Value)
+	return data[0]&1 == 1
+}
+
+func (s *ScalarBls12381Gt) IsEven() bool {
+	data := gt.ToBytes(s.Value)
+	return data[0]&1 == 0
+}
+
+func (s *ScalarBls12381Gt) New(input int) Scalar {
+	var data [576]byte
+	data[3] = byte(input >> 24 & 0xFF)
+	data[2] = byte(input >> 16 & 0xFF)
+	data[1] = byte(input >> 8 & 0xFF)
+	data[0] = byte(input & 0xFF)
+
+	value, err := gt.FromBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarBls12381Gt{value}
+}
+
+func (s *ScalarBls12381Gt) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarBls12381Gt)
+	if ok && s.Value.Equal(r.Value) {
+		return 0
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarBls12381Gt) Square() Scalar {
+	value := gt.New()
+	gt.Square(value, s.Value)
+	return &ScalarBls12381Gt{
+		value,
+	}
+}
+
+func (s *ScalarBls12381Gt) Double() Scalar {
+	value := gt.New()
+	gt.Add(value, s.Value, s.Value)
+	return &ScalarBls12381Gt{
+		value,
+	}
+}
+
+func (s *ScalarBls12381Gt) Invert() (Scalar, error) {
+	value := gt.New()
+	gt.Inverse(value, s.Value)
+	return &ScalarBls12381Gt{
+		value,
+	}, nil
+}
+
+func (s *ScalarBls12381Gt) Sqrt() (Scalar, error) {
+	// Not implemented
+	return nil, nil
+}
+
+func (s *ScalarBls12381Gt) Cube() Scalar {
+	value := gt.New()
+	gt.Square(value, s.Value)
+	gt.Mul(value, value, s.Value)
+	return &ScalarBls12381Gt{
+		value,
+	}
+}
+
+func (s *ScalarBls12381Gt) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381Gt)
+	if ok {
+		value := gt.New()
+		gt.Add(value, s.Value, r.Value)
+		return &ScalarBls12381Gt{
+			value,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381Gt) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381Gt)
+	if ok {
+		value := gt.New()
+		gt.Sub(value, s.Value, r.Value)
+		return &ScalarBls12381Gt{
+			value,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381Gt) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381Gt)
+	if ok {
+		value := gt.New()
+		gt.Mul(value, s.Value, r.Value)
+		return &ScalarBls12381Gt{
+			value,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381Gt) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarBls12381Gt) Div(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarBls12381Gt)
+	if ok {
+		value := gt.New()
+		gt.Inverse(value, r.Value)
+		gt.Mul(value, value, s.Value)
+		return &ScalarBls12381Gt{
+			value,
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarBls12381Gt) Neg() Scalar {
+	value := gt.New()
+	gt.Sub(value, value, s.Value)
+	return &ScalarBls12381Gt{
+		value,
+	}
+}
+
+func (s *ScalarBls12381Gt) SetBigInt(v *big.Int) (Scalar, error) {
+	var bytes [576]byte
+	v.FillBytes(bytes[:])
+	return s.SetBytes(bytes[:])
+}
+
+func (s *ScalarBls12381Gt) BigInt() *big.Int {
+	return new(big.Int).SetBytes(gt.ToBytes(s.Value))
+}
+
+func (s *ScalarBls12381Gt) Point() Point {
+	return &PointBls12381G1{Value: g1.New()}
+}
+
+func (s *ScalarBls12381Gt) Bytes() []byte {
+	return gt.ToBytes(s.Value)
+}
+
+func (s *ScalarBls12381Gt) SetBytes(bytes []byte) (Scalar, error) {
+	value, err := gt.FromBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarBls12381Gt{value}, nil
+}
+
+func (s *ScalarBls12381Gt) SetBytesWide(bytes []byte) (Scalar, error) {
+	l := len(bytes)
+	if l != 1152 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value, err := gt.FromBytes(bytes[:l/2])
+	if err != nil {
+		return nil, err
+	}
+	value2, err := gt.FromBytes(bytes[l/2:])
+	if err != nil {
+		return nil, err
+	}
+	gt.Add(value, value2, value)
+	return &ScalarBls12381Gt{value}, nil
+}
+
+func (s *ScalarBls12381Gt) Clone() Scalar {
+	return &ScalarBls12381Gt{
+		Value: gt.New().Set(s.Value),
+	}
+}
diff --git a/pkg/core/curves/bls12381_curve_test.go b/pkg/core/curves/bls12381_curve_test.go
new file mode 100644
index 00000000..8164e309
--- /dev/null
+++ b/pkg/core/curves/bls12381_curve_test.go
@@ -0,0 +1,510 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	crand "crypto/rand"
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"testing"
+)
+
+func TestScalarBls12381G1Random(t *testing.T) {
+	bls12381g1 := BLS12381G1()
+	sc := bls12381g1.Scalar.Random(testRng())
+	s, ok := sc.(*ScalarBls12381)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("1208bca85f538782d3941c7e805b239d181247a3c0ab58db6b1c8848804df8c8", 16)
+	assert.Equal(t, s.Value, expected)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12381g1.Scalar.Random(crand.Reader)
+		_, ok := sc.(*ScalarBls12381)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsZero())
+	}
+}
+
+func TestScalarBls12381G1Hash(t *testing.T) {
+	var b [32]byte
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Scalar.Hash(b[:])
+	s, ok := sc.(*ScalarBls12381)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("07ec86a2ab79613fc0294e058151ddc74db38b0cde95a4678eb91f1258f31b40", 16)
+	assert.Equal(t, s.Value, expected)
+}
+
+func TestScalarBls12381G1Zero(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Scalar.Zero()
+	assert.True(t, sc.IsZero())
+	assert.True(t, sc.IsEven())
+}
+
+func TestScalarBls12381G1One(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Scalar.One()
+	assert.True(t, sc.IsOne())
+	assert.True(t, sc.IsOdd())
+}
+
+func TestScalarBls12381G1New(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	three := bls12381G1.Scalar.New(3)
+	assert.True(t, three.IsOdd())
+	four := bls12381G1.Scalar.New(4)
+	assert.True(t, four.IsEven())
+	neg1 := bls12381G1.Scalar.New(-1)
+	assert.True(t, neg1.IsEven())
+	neg2 := bls12381G1.Scalar.New(-2)
+	assert.True(t, neg2.IsOdd())
+}
+
+func TestScalarBls12381G1Square(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	three := bls12381G1.Scalar.New(3)
+	nine := bls12381G1.Scalar.New(9)
+	assert.Equal(t, three.Square().Cmp(nine), 0)
+}
+
+func TestScalarBls12381G1Cube(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	three := bls12381G1.Scalar.New(3)
+	twentySeven := bls12381G1.Scalar.New(27)
+	assert.Equal(t, three.Cube().Cmp(twentySeven), 0)
+}
+
+func TestScalarBls12381G1Double(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	three := bls12381G1.Scalar.New(3)
+	six := bls12381G1.Scalar.New(6)
+	assert.Equal(t, three.Double().Cmp(six), 0)
+}
+
+func TestScalarBls12381G1Neg(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	one := bls12381G1.Scalar.One()
+	neg1 := bls12381G1.Scalar.New(-1)
+	assert.Equal(t, one.Neg().Cmp(neg1), 0)
+	lotsOfThrees := bls12381G1.Scalar.New(333333)
+	expected := bls12381G1.Scalar.New(-333333)
+	assert.Equal(t, lotsOfThrees.Neg().Cmp(expected), 0)
+}
+
+func TestScalarBls12381G1Invert(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	actual, _ := nine.Invert()
+	sa, _ := actual.(*ScalarBls12381)
+	expected, err := bls12381G1.Scalar.SetBigInt(bhex("19c308bd25b13848eef068e557794c72f62a247271c6bf1c38e38e38aaaaaaab"))
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarBls12381G1Sqrt(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	actual, err := nine.Sqrt()
+	assert.NoError(t, err)
+	sa, _ := actual.(*ScalarBls12381)
+	expected, err := bls12381G1.Scalar.SetBigInt(bhex("73eda753299d7d483339d80809a1d80553bda402fffe5bfefffffffefffffffe"))
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarBls12381G1Add(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	six := bls12381G1.Scalar.New(6)
+	fifteen := nine.Add(six)
+	assert.NotNil(t, fifteen)
+	expected := bls12381G1.Scalar.New(15)
+	assert.Equal(t, expected.Cmp(fifteen), 0)
+	n := new(big.Int).Set(g1.Q())
+	n.Sub(n, big.NewInt(3))
+
+	upper, err := bls12381G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := upper.Add(nine)
+	assert.NotNil(t, actual)
+	assert.Equal(t, actual.Cmp(six), 0)
+}
+
+func TestScalarBls12381G1Sub(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	six := bls12381G1.Scalar.New(6)
+	n := new(big.Int).Set(g1.Q())
+	n.Sub(n, big.NewInt(3))
+
+	expected, err := bls12381G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := six.Sub(nine)
+	assert.Equal(t, expected.Cmp(actual), 0)
+
+	actual = nine.Sub(six)
+	assert.Equal(t, actual.Cmp(bls12381G1.Scalar.New(3)), 0)
+}
+
+func TestScalarBls12381G1Mul(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	six := bls12381G1.Scalar.New(6)
+	actual := nine.Mul(six)
+	assert.Equal(t, actual.Cmp(bls12381G1.Scalar.New(54)), 0)
+	n := new(big.Int).Set(g1.Q())
+	n.Sub(n, big.NewInt(1))
+	upper, err := bls12381G1.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	assert.Equal(t, upper.Mul(upper).Cmp(bls12381G1.Scalar.New(1)), 0)
+}
+
+func TestScalarBls12381G1Div(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	nine := bls12381G1.Scalar.New(9)
+	actual := nine.Div(nine)
+	assert.Equal(t, actual.Cmp(bls12381G1.Scalar.New(1)), 0)
+	assert.Equal(t, bls12381G1.Scalar.New(54).Div(nine).Cmp(bls12381G1.Scalar.New(6)), 0)
+}
+
+func TestScalarBls12381G1Serialize(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Scalar.New(255)
+	sequence := sc.Bytes()
+	assert.Equal(t, len(sequence), 32)
+	assert.Equal(t, sequence, []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0xff})
+	ret, err := bls12381G1.Scalar.SetBytes(sequence)
+	assert.NoError(t, err)
+	assert.Equal(t, ret.Cmp(sc), 0)
+
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc = bls12381G1.Scalar.Random(crand.Reader)
+		sequence = sc.Bytes()
+		assert.Equal(t, len(sequence), 32)
+		ret, err = bls12381G1.Scalar.SetBytes(sequence)
+		assert.NoError(t, err)
+		assert.Equal(t, ret.Cmp(sc), 0)
+	}
+}
+
+func TestScalarBls12381G1Nil(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	one := bls12381G1.Scalar.New(1)
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, one.Div(nil))
+	assert.Nil(t, bls12381G1.Scalar.Random(nil))
+	assert.Equal(t, one.Cmp(nil), -2)
+	_, err := bls12381G1.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestScalarBls12381Point(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	_, ok := bls12381G1.Scalar.Point().(*PointBls12381G1)
+	assert.True(t, ok)
+	bls12381G2 := BLS12381G2()
+	_, ok = bls12381G2.Scalar.Point().(*PointBls12381G2)
+	assert.True(t, ok)
+}
+
+func TestPointBls12381G2Random(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	sc := bls12381G2.Point.Random(testRng())
+	s, ok := sc.(*PointBls12381G2)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("13520facd10fc1cd71384d86b445b0e65ac1bf9205e86cd02837c064d1886b8aa3dc5348845bb06216601de5628315600967df84901b1c4f1fac87f9fc13d02f9c3a0f8cf462c86d2b4bbddf7b8520a3df2a5c541724a2c7ddc9eec45f0b2f74", 16)
+	expectedY, _ := new(big.Int).SetString("0a46cb3d91222e4eb068e1eb41e7ef3efd1c705c1272476d74064541661736bf0910adcfe37fafbabf0989e0c9ae122b0ce11d941d60570a9b39ff332e09f9ba661a4aac019911032b1ddb0dee7ce5a34aebb8cb6f1fa21e5cf565d06dfc7b61", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12381G2.Point.Random(crand.Reader)
+		_, ok := sc.(*PointBls12381G2)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointBls12381G2Hash(t *testing.T) {
+	var b [32]byte
+	bls12381G2 := BLS12381G2()
+	sc := bls12381G2.Point.Hash(b[:])
+	s, ok := sc.(*PointBls12381G2)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("15060db402f549b74be2656006f369e0892a857cd7d16738761ad9ba01bf8da2d1e45f86c4f13fe0850ba1195a2e8aa91914cb4d8eac1e4582a45d92cd2c8fec3d34c11629503dafe60f7910e39eff6f6b6d41d881e9fb2b9857c06de7966077", 16)
+	expectedY, _ := new(big.Int).SetString("0e509ea244e9f57d3a6f5140b39792424fb0889b5a3cad7f65d84cf9f3fccf64bec9ff45fc1f0c8fb7f045930336363217b27f340cd6f8bbf15fb1872a4e137c9655aad86672fa4d7e9973c39eec102069a36c632f7f90e6ec75b23dd6accafc", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+}
+
+func TestPointBls12381G2Identity(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	sc := bls12381G2.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{0xc0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0})
+}
+
+func TestPointBls12381G2Generator(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	sc := bls12381G2.Point.Generator()
+	s, ok := sc.(*PointBls12381G2)
+	assert.True(t, ok)
+	assert.True(t, g2.Equal(s.Value, g2.One()))
+}
+
+func TestPointBls12381G2Set(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	iden, err := bls12381G2.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	generator := g2.ToBytes(g2.One())
+	_, err = bls12381G2.Point.Set(new(big.Int).SetBytes(generator[:96]), new(big.Int).SetBytes(generator[96:]))
+	assert.NoError(t, err)
+}
+
+func TestPointBls12381G2Double(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	g := bls12381G2.Point.Generator()
+	gg2 := g.Double()
+	assert.True(t, gg2.Equal(g.Mul(bls12381G2.Scalar.New(2))))
+	i := bls12381G2.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointBls12381G2Neg(t *testing.T) {
+	bls12381G2 := BLS12381G1()
+	g := bls12381G2.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(bls12381G2.Point.Generator()))
+	assert.True(t, bls12381G2.Point.Identity().Neg().Equal(bls12381G2.Point.Identity()))
+}
+
+func TestPointBls12381G2Add(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	pt := bls12381G2.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(bls12381G2.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointBls12381G2Sub(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	g := bls12381G2.Point.Generator()
+	pt := bls12381G2.Point.Generator().Mul(bls12381G2.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointBls12381G2Mul(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	g := bls12381G2.Point.Generator()
+	pt := bls12381G2.Point.Generator().Mul(bls12381G2.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointBls12381G2Serialize(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	ss := bls12381G2.Scalar.Random(testRng())
+	g := bls12381G2.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0xad, 0x49, 0x42, 0x28, 0xc6, 0x2c, 0x54, 0xb3, 0xfd, 0xb0, 0xed, 0xd1, 0x8f, 0x10, 0x1f, 0x9a, 0x9a, 0xc5, 0x68, 0x57, 0xff, 0x99, 0x93, 0x6e, 0x8d, 0x79, 0x95, 0xc3, 0xc9, 0xa8, 0xdf, 0x99, 0x63, 0xa2, 0x67, 0xe4, 0xaa, 0x62, 0x9c, 0x33, 0xb0, 0x54, 0x5e, 0xb6, 0xd6, 0x36, 0xa4, 0x0, 0x12, 0x9b, 0x9b, 0x7f, 0x27, 0xce, 0x26, 0x29, 0xf3, 0xa4, 0xf0, 0x8d, 0xfb, 0x48, 0x6d, 0xc7, 0x73, 0xa0, 0x18, 0x84, 0xc7, 0x98, 0xb7, 0xa7, 0xb1, 0x8, 0x88, 0xe9, 0x21, 0xe1, 0xed, 0x61, 0x3c, 0x37, 0xf7, 0xf3, 0xc1, 0x4f, 0x95, 0xfa, 0x64, 0xda, 0x39, 0x32, 0x4, 0x95, 0x87, 0x44})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0xd, 0x49, 0x42, 0x28, 0xc6, 0x2c, 0x54, 0xb3, 0xfd, 0xb0, 0xed, 0xd1, 0x8f, 0x10, 0x1f, 0x9a, 0x9a, 0xc5, 0x68, 0x57, 0xff, 0x99, 0x93, 0x6e, 0x8d, 0x79, 0x95, 0xc3, 0xc9, 0xa8, 0xdf, 0x99, 0x63, 0xa2, 0x67, 0xe4, 0xaa, 0x62, 0x9c, 0x33, 0xb0, 0x54, 0x5e, 0xb6, 0xd6, 0x36, 0xa4, 0x0, 0x12, 0x9b, 0x9b, 0x7f, 0x27, 0xce, 0x26, 0x29, 0xf3, 0xa4, 0xf0, 0x8d, 0xfb, 0x48, 0x6d, 0xc7, 0x73, 0xa0, 0x18, 0x84, 0xc7, 0x98, 0xb7, 0xa7, 0xb1, 0x8, 0x88, 0xe9, 0x21, 0xe1, 0xed, 0x61, 0x3c, 0x37, 0xf7, 0xf3, 0xc1, 0x4f, 0x95, 0xfa, 0x64, 0xda, 0x39, 0x32, 0x4, 0x95, 0x87, 0x44, 0x12, 0x37, 0xbe, 0xd8, 0xbf, 0xdb, 0x2a, 0xcc, 0xd, 0x17, 0xcc, 0x6c, 0xfe, 0x7f, 0x49, 0xe4, 0x5d, 0xaf, 0xa3, 0x54, 0xb0, 0xe3, 0xc5, 0x86, 0xff, 0x20, 0x64, 0x30, 0x65, 0xc, 0x7c, 0x7c, 0x2f, 0x80, 0xee, 0x7c, 0x74, 0xd2, 0x8d, 0x2e, 0x92, 0xba, 0x16, 0xe4, 0x13, 0xa6, 0x6, 0xfd, 0x9, 0x3e, 0xd8, 0x59, 0xcc, 0x59, 0x3b, 0xa8, 0x64, 0x44, 0x6b, 0xc, 0xba, 0xd9, 0x9a, 0x2c, 0xed, 0x2d, 0xe4, 0x1e, 0xf1, 0xe6, 0xda, 0x8a, 0xfc, 0x62, 0x1d, 0xf, 0x3b, 0xdf, 0xf6, 0xe5, 0xa3, 0xd1, 0xcd, 0xec, 0x21, 0x73, 0x1f, 0x7d, 0xb2, 0x26, 0x7d, 0x5f, 0xf2, 0xd2, 0xc9, 0x4})
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := bls12381G2.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 96)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 192)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointBls12381G2Nil(t *testing.T) {
+	bls12381G2 := BLS12381G2()
+	one := bls12381G2.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, bls12381G2.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := bls12381G2.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointBls12381G1Random(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Point.Random(testRng())
+	s, ok := sc.(*PointBls12381G1)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("191b78617711a9aca6092c50d8c715db4856b84e48b9aa07dc42719335751b2ef3dfa2f6f15afc6dba2d0fb3be63dd83", 16)
+	expectedY, _ := new(big.Int).SetString("0d7053b5d9b5f23839a0dc4ad18bb55bd6ac20e1e53750c1140e434c61f87033e6338f10955b690eee0efc383d6e6d25", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := bls12381G1.Point.Random(crand.Reader)
+		_, ok := sc.(*PointBls12381G1)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointBls12381G1Hash(t *testing.T) {
+	var b [32]byte
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Point.Hash(b[:])
+	s, ok := sc.(*PointBls12381G1)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("1239150a658a8b04d56f3d14593bb3fa6f791ee221224480b5170da43a4c3602f97be83649c31b2738a606b89c2e9fea", 16)
+	expectedY, _ := new(big.Int).SetString("124af4bc2008ed9be7db7137f8b41e4b65f37cfd34938c4466531dc7ed657e66ff6c6c6912488d9285e0645c6ba62b92", 16)
+	assert.Equal(t, s.X(), expectedX)
+	assert.Equal(t, s.Y(), expectedY)
+}
+
+func TestPointBls12381G1Identity(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{0xc0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+}
+
+func TestPointBls12381G1Generator(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	sc := bls12381G1.Point.Generator()
+	s, ok := sc.(*PointBls12381G1)
+	assert.True(t, ok)
+	assert.True(t, g1.Equal(s.Value, g1.One()))
+}
+
+func TestPointBls12381G1Set(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	iden, err := bls12381G1.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	generator := g1.ToBytes(g1.One())
+	_, err = bls12381G1.Point.Set(new(big.Int).SetBytes(generator[:48]), new(big.Int).SetBytes(generator[48:]))
+	assert.NoError(t, err)
+}
+
+func TestPointBls12381G1Double(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	g := bls12381G1.Point.Generator()
+	g2 := g.Double()
+	assert.True(t, g2.Equal(g.Mul(bls12381G1.Scalar.New(2))))
+	i := bls12381G1.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointBls12381G1Neg(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	g := bls12381G1.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(bls12381G1.Point.Generator()))
+	assert.True(t, bls12381G1.Point.Identity().Neg().Equal(bls12381G1.Point.Identity()))
+}
+
+func TestPointBls12381G1Add(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	pt := bls12381G1.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(bls12381G1.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointBls12381G1Sub(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	g := bls12381G1.Point.Generator()
+	pt := bls12381G1.Point.Generator().Mul(bls12381G1.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointBls12381G1Mul(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	g := bls12381G1.Point.Generator()
+	pt := bls12381G1.Point.Generator().Mul(bls12381G1.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointBls12381G1Serialize(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	ss := bls12381G1.Scalar.Random(testRng())
+	g := bls12381G1.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0xa8, 0x6d, 0xac, 0x3a, 0xd8, 0x6f, 0x6b, 0x1f, 0x6b, 0x47, 0x7f, 0x22, 0x73, 0xa9, 0x5a, 0x5f, 0x4c, 0xff, 0x1a, 0xf7, 0x27, 0xab, 0x73, 0x51, 0xfe, 0xa5, 0xfd, 0x9d, 0x21, 0xcd, 0xaa, 0x40, 0x7f, 0xf9, 0x5, 0xca, 0x2f, 0x9a, 0xdb, 0x5d, 0x5b, 0x6a, 0x86, 0xb3, 0x84, 0xc6, 0xc, 0x37})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x8, 0x6d, 0xac, 0x3a, 0xd8, 0x6f, 0x6b, 0x1f, 0x6b, 0x47, 0x7f, 0x22, 0x73, 0xa9, 0x5a, 0x5f, 0x4c, 0xff, 0x1a, 0xf7, 0x27, 0xab, 0x73, 0x51, 0xfe, 0xa5, 0xfd, 0x9d, 0x21, 0xcd, 0xaa, 0x40, 0x7f, 0xf9, 0x5, 0xca, 0x2f, 0x9a, 0xdb, 0x5d, 0x5b, 0x6a, 0x86, 0xb3, 0x84, 0xc6, 0xc, 0x37, 0x10, 0x5f, 0x99, 0x9a, 0x58, 0x93, 0x4, 0x35, 0x76, 0x91, 0x7c, 0x8e, 0x6a, 0xcb, 0x3c, 0xad, 0xdb, 0x84, 0x3, 0xd9, 0x24, 0xec, 0xa2, 0xa8, 0x4e, 0x99, 0x4f, 0xbb, 0x77, 0x3a, 0x3f, 0x9a, 0xd, 0x64, 0x9d, 0x76, 0xe, 0x61, 0xfb, 0x60, 0x36, 0x55, 0x91, 0x5c, 0x49, 0x20, 0x43, 0x29})
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := bls12381G1.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 48)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 96)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointBls12381G1Nil(t *testing.T) {
+	bls12381G1 := BLS12381G1()
+	one := bls12381G1.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, bls12381G1.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := bls12381G1.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointBls12381G1SumOfProducts(t *testing.T) {
+	lhs := new(PointBls12381G1).Generator().Mul(new(ScalarBls12381).New(50))
+	points := make([]Point, 5)
+	for i := range points {
+		points[i] = new(PointBls12381G1).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarBls12381).New(8),
+		new(ScalarBls12381).New(9),
+		new(ScalarBls12381).New(10),
+		new(ScalarBls12381).New(11),
+		new(ScalarBls12381).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
diff --git a/pkg/core/curves/curve.go b/pkg/core/curves/curve.go
new file mode 100644
index 00000000..14dbc2b2
--- /dev/null
+++ b/pkg/core/curves/curve.go
@@ -0,0 +1,892 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	"encoding/hex"
+	"encoding/json"
+	"fmt"
+	"hash"
+	"io"
+	"math/big"
+	"sync"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+var (
+	k256Initonce sync.Once
+	k256         Curve
+
+	bls12381g1Initonce sync.Once
+	bls12381g1         Curve
+
+	bls12381g2Initonce sync.Once
+	bls12381g2         Curve
+
+	bls12377g1Initonce sync.Once
+	bls12377g1         Curve
+
+	bls12377g2Initonce sync.Once
+	bls12377g2         Curve
+
+	p256Initonce sync.Once
+	p256         Curve
+
+	ed25519Initonce sync.Once
+	ed25519         Curve
+
+	pallasInitonce sync.Once
+	pallas         Curve
+)
+
+const (
+	K256Name       = "secp256k1"
+	BLS12381G1Name = "BLS12381G1"
+	BLS12381G2Name = "BLS12381G2"
+	BLS12831Name   = "BLS12831"
+	P256Name       = "P-256"
+	ED25519Name    = "ed25519"
+	PallasName     = "pallas"
+	BLS12377G1Name = "BLS12377G1"
+	BLS12377G2Name = "BLS12377G2"
+	BLS12377Name   = "BLS12377"
+)
+
+const scalarBytes = 32
+
+// Scalar represents an element of the scalar field \mathbb{F}_q
+// of the elliptic curve construction.
+type Scalar interface {
+	// Random returns a random scalar using the provided reader
+	// to retrieve bytes
+	Random(reader io.Reader) Scalar
+	// Hash the specific bytes in a manner to yield a
+	// uniformly distributed scalar
+	Hash(bytes []byte) Scalar
+	// Zero returns the additive identity element
+	Zero() Scalar
+	// One returns the multiplicative identity element
+	One() Scalar
+	// IsZero returns true if this element is the additive identity element
+	IsZero() bool
+	// IsOne returns true if this element is the multiplicative identity element
+	IsOne() bool
+	// IsOdd returns true if this element is odd
+	IsOdd() bool
+	// IsEven returns true if this element is even
+	IsEven() bool
+	// New returns an element with the value equal to `value`
+	New(value int) Scalar
+	// Cmp returns
+	// -2 if this element is in a different field than rhs
+	// -1 if this element is less than rhs
+	// 0 if this element is equal to rhs
+	// 1 if this element is greater than rhs
+	Cmp(rhs Scalar) int
+	// Square returns element*element
+	Square() Scalar
+	// Double returns element+element
+	Double() Scalar
+	// Invert returns element^-1 mod p
+	Invert() (Scalar, error)
+	// Sqrt computes the square root of this element if it exists.
+	Sqrt() (Scalar, error)
+	// Cube returns element*element*element
+	Cube() Scalar
+	// Add returns element+rhs
+	Add(rhs Scalar) Scalar
+	// Sub returns element-rhs
+	Sub(rhs Scalar) Scalar
+	// Mul returns element*rhs
+	Mul(rhs Scalar) Scalar
+	// MulAdd returns element * y + z mod p
+	MulAdd(y, z Scalar) Scalar
+	// Div returns element*rhs^-1 mod p
+	Div(rhs Scalar) Scalar
+	// Neg returns -element mod p
+	Neg() Scalar
+	// SetBigInt returns this element set to the value of v
+	SetBigInt(v *big.Int) (Scalar, error)
+	// BigInt returns this element as a big integer
+	BigInt() *big.Int
+	// Point returns the associated point for this scalar
+	Point() Point
+	// Bytes returns the canonical byte representation of this scalar
+	Bytes() []byte
+	// SetBytes creates a scalar from the canonical representation expecting the exact number of bytes needed to represent the scalar
+	SetBytes(bytes []byte) (Scalar, error)
+	// SetBytesWide creates a scalar expecting double the exact number of bytes needed to represent the scalar which is reduced by the modulus
+	SetBytesWide(bytes []byte) (Scalar, error)
+	// Clone returns a cloned Scalar of this value
+	Clone() Scalar
+}
+
+type PairingScalar interface {
+	Scalar
+	SetPoint(p Point) PairingScalar
+}
+
+func unmarshalScalar(input []byte) (*Curve, []byte, error) {
+	sep := byte(':')
+	i := 0
+	for ; i < len(input); i++ {
+		if input[i] == sep {
+			break
+		}
+	}
+	name := string(input[:i])
+	curve := GetCurveByName(name)
+	if curve == nil {
+		return nil, nil, fmt.Errorf("unrecognized curve")
+	}
+	return curve, input[i+1:], nil
+}
+
+func scalarMarshalBinary(scalar Scalar) ([]byte, error) {
+	// All scalars are 32 bytes long
+	// The last 32 bytes are the actual value
+	// The first remaining bytes are the curve name
+	// separated by a colon
+	name := []byte(scalar.Point().CurveName())
+	output := make([]byte, len(name)+1+scalarBytes)
+	copy(output[:len(name)], name)
+	output[len(name)] = byte(':')
+	copy(output[len(name)+1:], scalar.Bytes())
+	return output, nil
+}
+
+func scalarUnmarshalBinary(input []byte) (Scalar, error) {
+	// All scalars are 32 bytes long
+	// The first 32 bytes are the actual value
+	// The remaining bytes are the curve name
+	if len(input) < scalarBytes+1+len(P256Name) {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	sc, data, err := unmarshalScalar(input)
+	if err != nil {
+		return nil, err
+	}
+	return sc.Scalar.SetBytes(data)
+}
+
+func scalarMarshalText(scalar Scalar) ([]byte, error) {
+	// All scalars are 32 bytes long
+	// For text encoding we put the curve name first for readability
+	// separated by a colon, then the hex encoding of the scalar
+	// which avoids the base64 weakness with strict mode or not
+	name := []byte(scalar.Point().CurveName())
+	output := make([]byte, len(name)+1+scalarBytes*2)
+	copy(output[:len(name)], name)
+	output[len(name)] = byte(':')
+	_ = hex.Encode(output[len(name)+1:], scalar.Bytes())
+	return output, nil
+}
+
+func scalarUnmarshalText(input []byte) (Scalar, error) {
+	if len(input) < scalarBytes*2+len(P256Name)+1 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	curve, data, err := unmarshalScalar(input)
+	if err != nil {
+		return nil, err
+	}
+	var t [scalarBytes]byte
+	_, err = hex.Decode(t[:], data)
+	if err != nil {
+		return nil, err
+	}
+	return curve.Scalar.SetBytes(t[:])
+}
+
+func scalarMarshalJson(scalar Scalar) ([]byte, error) {
+	m := make(map[string]string, 2)
+	m["type"] = scalar.Point().CurveName()
+	m["value"] = hex.EncodeToString(scalar.Bytes())
+	return json.Marshal(m)
+}
+
+func scalarUnmarshalJson(input []byte) (Scalar, error) {
+	var m map[string]string
+
+	err := json.Unmarshal(input, &m)
+	if err != nil {
+		return nil, err
+	}
+	curve := GetCurveByName(m["type"])
+	if curve == nil {
+		return nil, fmt.Errorf("invalid type")
+	}
+	s, err := hex.DecodeString(m["value"])
+	if err != nil {
+		return nil, err
+	}
+	S, err := curve.Scalar.SetBytes(s)
+	if err != nil {
+		return nil, err
+	}
+	return S, nil
+}
+
+// Point represents an elliptic curve point
+type Point interface {
+	Random(reader io.Reader) Point
+	Hash(bytes []byte) Point
+	Identity() Point
+	Generator() Point
+	IsIdentity() bool
+	IsNegative() bool
+	IsOnCurve() bool
+	Double() Point
+	Scalar() Scalar
+	Neg() Point
+	Add(rhs Point) Point
+	Sub(rhs Point) Point
+	Mul(rhs Scalar) Point
+	Equal(rhs Point) bool
+	Set(x, y *big.Int) (Point, error)
+	ToAffineCompressed() []byte
+	ToAffineUncompressed() []byte
+	FromAffineCompressed(bytes []byte) (Point, error)
+	FromAffineUncompressed(bytes []byte) (Point, error)
+	CurveName() string
+	SumOfProducts(points []Point, scalars []Scalar) Point
+}
+
+type PairingPoint interface {
+	Point
+	OtherGroup() PairingPoint
+	Pairing(rhs PairingPoint) Scalar
+	MultiPairing(...PairingPoint) Scalar
+}
+
+func pointMarshalBinary(point Point) ([]byte, error) {
+	// Always stores points in compressed form
+	// The first bytes are the curve name
+	// separated by a colon followed by the compressed point
+	// bytes
+	t := point.ToAffineCompressed()
+	name := []byte(point.CurveName())
+	output := make([]byte, len(name)+1+len(t))
+	copy(output[:len(name)], name)
+	output[len(name)] = byte(':')
+	copy(output[len(output)-len(t):], t)
+	return output, nil
+}
+
+func pointUnmarshalBinary(input []byte) (Point, error) {
+	if len(input) < scalarBytes+1+len(P256Name) {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	sep := byte(':')
+	i := 0
+	for ; i < len(input); i++ {
+		if input[i] == sep {
+			break
+		}
+	}
+	name := string(input[:i])
+	curve := GetCurveByName(name)
+	if curve == nil {
+		return nil, fmt.Errorf("unrecognized curve")
+	}
+	return curve.Point.FromAffineCompressed(input[i+1:])
+}
+
+func pointMarshalText(point Point) ([]byte, error) {
+	// Always stores points in compressed form
+	// The first bytes are the curve name
+	// separated by a colon followed by the compressed point
+	// bytes
+	t := point.ToAffineCompressed()
+	name := []byte(point.CurveName())
+	output := make([]byte, len(name)+1+len(t)*2)
+	copy(output[:len(name)], name)
+	output[len(name)] = byte(':')
+	hex.Encode(output[len(output)-len(t)*2:], t)
+	return output, nil
+}
+
+func pointUnmarshalText(input []byte) (Point, error) {
+	if len(input) < scalarBytes*2+1+len(P256Name) {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	sep := byte(':')
+	i := 0
+	for ; i < len(input); i++ {
+		if input[i] == sep {
+			break
+		}
+	}
+	name := string(input[:i])
+	curve := GetCurveByName(name)
+	if curve == nil {
+		return nil, fmt.Errorf("unrecognized curve")
+	}
+	buffer := make([]byte, (len(input)-i)/2)
+	_, err := hex.Decode(buffer, input[i+1:])
+	if err != nil {
+		return nil, err
+	}
+	return curve.Point.FromAffineCompressed(buffer)
+}
+
+func pointMarshalJson(point Point) ([]byte, error) {
+	m := make(map[string]string, 2)
+	m["type"] = point.CurveName()
+	m["value"] = hex.EncodeToString(point.ToAffineCompressed())
+	return json.Marshal(m)
+}
+
+func pointUnmarshalJson(input []byte) (Point, error) {
+	var m map[string]string
+
+	err := json.Unmarshal(input, &m)
+	if err != nil {
+		return nil, err
+	}
+	curve := GetCurveByName(m["type"])
+	if curve == nil {
+		return nil, fmt.Errorf("invalid type")
+	}
+	p, err := hex.DecodeString(m["value"])
+	if err != nil {
+		return nil, err
+	}
+	P, err := curve.Point.FromAffineCompressed(p)
+	if err != nil {
+		return nil, err
+	}
+	return P, nil
+}
+
+// Curve represents a named elliptic curve with a scalar field and point group
+type Curve struct {
+	Scalar Scalar
+	Point  Point
+	Name   string
+}
+
+func (c Curve) ScalarBaseMult(sc Scalar) Point {
+	return c.Point.Generator().Mul(sc)
+}
+
+func (c Curve) NewGeneratorPoint() Point {
+	return c.Point.Generator()
+}
+
+func (c Curve) NewIdentityPoint() Point {
+	return c.Point.Identity()
+}
+
+func (c Curve) NewScalar() Scalar {
+	return c.Scalar.Zero()
+}
+
+// PairingCurve represents a named elliptic curve
+// that supports pairings
+type PairingCurve struct {
+	Scalar  PairingScalar
+	PointG1 PairingPoint
+	PointG2 PairingPoint
+	GT      Scalar
+	Name    string
+}
+
+func (c PairingCurve) ScalarG1BaseMult(sc Scalar) PairingPoint {
+	return c.PointG1.Generator().Mul(sc).(PairingPoint)
+}
+
+func (c PairingCurve) ScalarG2BaseMult(sc Scalar) PairingPoint {
+	return c.PointG2.Generator().Mul(sc).(PairingPoint)
+}
+
+func (c PairingCurve) NewG1GeneratorPoint() PairingPoint {
+	return c.PointG1.Generator().(PairingPoint)
+}
+
+func (c PairingCurve) NewG2GeneratorPoint() PairingPoint {
+	return c.PointG2.Generator().(PairingPoint)
+}
+
+func (c PairingCurve) NewG1IdentityPoint() PairingPoint {
+	return c.PointG1.Identity().(PairingPoint)
+}
+
+func (c PairingCurve) NewG2IdentityPoint() PairingPoint {
+	return c.PointG2.Identity().(PairingPoint)
+}
+
+func (c PairingCurve) NewScalar() PairingScalar {
+	return c.Scalar.Zero().(PairingScalar)
+}
+
+// GetCurveByName returns the correct `Curve` given the name
+func GetCurveByName(name string) *Curve {
+	switch name {
+	case K256Name:
+		return K256()
+	case BLS12381G1Name:
+		return BLS12381G1()
+	case BLS12381G2Name:
+		return BLS12381G2()
+	case BLS12831Name:
+		return BLS12381G1()
+	case P256Name:
+		return P256()
+	case ED25519Name:
+		return ED25519()
+	case PallasName:
+		return PALLAS()
+	case BLS12377G1Name:
+		return BLS12377G1()
+	case BLS12377G2Name:
+		return BLS12377G2()
+	case BLS12377Name:
+		return BLS12377G1()
+	default:
+		return nil
+	}
+}
+
+func GetPairingCurveByName(name string) *PairingCurve {
+	switch name {
+	case BLS12381G1Name:
+		return BLS12381(BLS12381G1().NewIdentityPoint())
+	case BLS12381G2Name:
+		return BLS12381(BLS12381G2().NewIdentityPoint())
+	case BLS12831Name:
+		return BLS12381(BLS12381G1().NewIdentityPoint())
+	default:
+		return nil
+	}
+}
+
+// BLS12381G1 returns the BLS12-381 curve with points in G1
+func BLS12381G1() *Curve {
+	bls12381g1Initonce.Do(bls12381g1Init)
+	return &bls12381g1
+}
+
+func bls12381g1Init() {
+	bls12381g1 = Curve{
+		Scalar: &ScalarBls12381{
+			Value: new(big.Int),
+			point: new(PointBls12381G1),
+		},
+		Point: new(PointBls12381G1).Identity(),
+		Name:  BLS12381G1Name,
+	}
+}
+
+// BLS12381G2 returns the BLS12-381 curve with points in G2
+func BLS12381G2() *Curve {
+	bls12381g2Initonce.Do(bls12381g2Init)
+	return &bls12381g2
+}
+
+func bls12381g2Init() {
+	bls12381g2 = Curve{
+		Scalar: &ScalarBls12381{
+			Value: new(big.Int),
+			point: new(PointBls12381G2),
+		},
+		Point: new(PointBls12381G2).Identity(),
+		Name:  BLS12381G2Name,
+	}
+}
+
+func BLS12381(preferredPoint Point) *PairingCurve {
+	return &PairingCurve{
+		Scalar: &ScalarBls12381{
+			Value: new(big.Int),
+			point: preferredPoint,
+		},
+		PointG1: &PointBls12381G1{
+			Value: g1.New(),
+		},
+		PointG2: &PointBls12381G2{
+			Value: g2.New(),
+		},
+		GT: &ScalarBls12381Gt{
+			Value: &bls12381.E{},
+		},
+		Name: BLS12831Name,
+	}
+}
+
+// BLS12377G1 returns the BLS12-377 curve with points in G1
+func BLS12377G1() *Curve {
+	bls12377g1Initonce.Do(bls12377g1Init)
+	return &bls12377g1
+}
+
+func bls12377g1Init() {
+	bls12377g1 = Curve{
+		Scalar: &ScalarBls12377{
+			value: new(big.Int),
+			point: new(PointBls12377G1),
+		},
+		Point: new(PointBls12377G1).Identity(),
+		Name:  BLS12377G1Name,
+	}
+}
+
+// BLS12377G2 returns the BLS12-377 curve with points in G2
+func BLS12377G2() *Curve {
+	bls12377g2Initonce.Do(bls12377g2Init)
+	return &bls12377g2
+}
+
+func bls12377g2Init() {
+	bls12377g2 = Curve{
+		Scalar: &ScalarBls12377{
+			value: new(big.Int),
+			point: new(PointBls12377G2),
+		},
+		Point: new(PointBls12377G2).Identity(),
+		Name:  BLS12377G2Name,
+	}
+}
+
+// K256 returns the secp256k1 curve
+func K256() *Curve {
+	k256Initonce.Do(k256Init)
+	return &k256
+}
+
+func k256Init() {
+	k256 = Curve{
+		Scalar: new(ScalarK256).Zero(),
+		Point:  new(PointK256).Identity(),
+		Name:   K256Name,
+	}
+}
+
+func P256() *Curve {
+	p256Initonce.Do(p256Init)
+	return &p256
+}
+
+func p256Init() {
+	p256 = Curve{
+		Scalar: new(ScalarP256).Zero(),
+		Point:  new(PointP256).Identity(),
+		Name:   P256Name,
+	}
+}
+
+func ED25519() *Curve {
+	ed25519Initonce.Do(ed25519Init)
+	return &ed25519
+}
+
+func ed25519Init() {
+	ed25519 = Curve{
+		Scalar: new(ScalarEd25519).Zero(),
+		Point:  new(PointEd25519).Identity(),
+		Name:   ED25519Name,
+	}
+}
+
+func PALLAS() *Curve {
+	pallasInitonce.Do(pallasInit)
+	return &pallas
+}
+
+func pallasInit() {
+	pallas = Curve{
+		Scalar: new(ScalarPallas).Zero(),
+		Point:  new(PointPallas).Identity(),
+		Name:   PallasName,
+	}
+}
+
+func isogenyMap(inX, inY *big.Int, isoParams *isogenyParams) (x, y *big.Int) {
+	xnumL := len(isoParams.Xnum)
+	xdenL := len(isoParams.Xden)
+	ynumL := len(isoParams.Ynum)
+	ydenL := len(isoParams.Yden)
+
+	degree := 0
+	for _, i := range []int{xnumL, xdenL, ynumL, ydenL} {
+		if degree < i {
+			degree = i
+		}
+	}
+
+	xs := make([]*big.Int, degree)
+	xs[0] = big.NewInt(1)              // x[0] = x^0
+	xs[1] = new(big.Int).Set(inX)      // x[1] = x^1
+	xs[2] = new(big.Int).Mul(inX, inX) // x[2] = x^2
+	xs[2].Mod(xs[2], isoParams.P)
+	for i := 3; i < degree; i++ {
+		// x[i] = x^i
+		xs[i] = new(big.Int).Mul(xs[i-1], inX)
+		xs[i].Mod(xs[i], isoParams.P)
+	}
+
+	xNum := computeIsoK(xs, isoParams.Xnum, isoParams.P)
+	xDen := computeIsoK(xs, isoParams.Xden, isoParams.P)
+	yNum := computeIsoK(xs, isoParams.Ynum, isoParams.P)
+	yDen := computeIsoK(xs, isoParams.Yden, isoParams.P)
+
+	xDen.ModInverse(xDen, isoParams.P)
+	yDen.ModInverse(yDen, isoParams.P)
+
+	x = new(big.Int).Mul(xNum, xDen)
+	x.Mod(x, isoParams.P)
+
+	y = new(big.Int).Mul(yNum, yDen)
+	y.Mul(inY, y)
+	y.Mod(y, isoParams.P)
+
+	return
+}
+
+func computeIsoK(xxs, k []*big.Int, p *big.Int) *big.Int {
+	xx := new(big.Int)
+	for i := range k {
+		t := new(big.Int).Mul(xxs[i], k[i])
+		xx.Add(xx, t)
+		xx.Mod(xx, p)
+	}
+	return xx
+}
+
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.1
+func osswu3mod4(u *big.Int, p *sswuParams) (x, y *big.Int) {
+	params := p.Params
+	field := NewField(p.Params.P)
+
+	tv1 := field.NewElement(u)
+	tv1 = tv1.Mul(tv1)                    // tv1 = u^2
+	tv3 := field.NewElement(p.Z).Mul(tv1) // tv3 = Z * tv1
+	tv2 := tv3.Mul(tv3)                   // tv2 = tv3^2
+	xd := tv2.Add(tv3)                    // xd = tv2 + tv3
+	x1n := xd.Add(field.One())            // x1n = (xd + 1)
+	x1n = x1n.Mul(field.NewElement(p.B))  // x1n * B
+	aNeg := field.NewElement(p.A).Neg()
+	xd = xd.Mul(aNeg) // xd = -A * xd
+
+	if xd.Value.Cmp(big.NewInt(0)) == 0 {
+		xd = field.NewElement(p.Z).Mul(field.NewElement(p.A)) // xd = Z * A
+	}
+
+	tv2 = xd.Mul(xd)                     // tv2 = xd^2
+	gxd := tv2.Mul(xd)                   // gxd = tv2 * xd
+	tv2 = tv2.Mul(field.NewElement(p.A)) // tv2 = A * tv2
+
+	gx1 := x1n.Mul(x1n)                  // gx1 = x1n^2
+	gx1 = gx1.Add(tv2)                   // gx1 = gx1 + tv2
+	gx1 = gx1.Mul(x1n)                   // gx1 = gx1 * x1n
+	tv2 = gxd.Mul(field.NewElement(p.B)) // tv2 = B * gxd
+	gx1 = gx1.Add(tv2)                   // gx1 = gx1 + tv2
+
+	tv4 := gxd.Mul(gxd) // tv4 = gxd^2
+	tv2 = gx1.Mul(gxd)  // tv2 = gx1 * gxd
+	tv4 = tv4.Mul(tv2)  //tv4 = tv4 * tv2
+
+	y1 := tv4.Pow(field.NewElement(p.C1))
+	y1 = y1.Mul(tv2)    //y1 = y1 * tv2
+	x2n := tv3.Mul(x1n) // x2n = tv3 * x1n
+
+	y2 := y1.Mul(field.NewElement(p.C2)) // y2 = y1 * c2
+	y2 = y2.Mul(tv1)                     // y2 = y2 * tv1
+	y2 = y2.Mul(field.NewElement(u))     // y2 = y2 * u
+
+	tv2 = y1.Mul(y1) // tv2 = y1^2
+
+	tv2 = tv2.Mul(gxd) // tv2 = tv2 * gxd
+
+	e2 := tv2.Value.Cmp(gx1.Value) == 0
+
+	// If e2, x = x1, else x = x2
+	if e2 {
+		x = x1n.Value
+	} else {
+		x = x2n.Value
+	}
+	// xn / xd
+	x.Mul(x, new(big.Int).ModInverse(xd.Value, params.P))
+	x.Mod(x, params.P)
+
+	// If e2, y = y1, else y = y2
+	if e2 {
+		y = y1.Value
+	} else {
+		y = y2.Value
+	}
+
+	uBytes := u.Bytes()
+	yBytes := y.Bytes()
+
+	usign := uBytes[len(uBytes)-1] & 1
+	ysign := yBytes[len(yBytes)-1] & 1
+
+	// Fix sign of y
+	if usign != ysign {
+		y.Neg(y)
+		y.Mod(y, params.P)
+	}
+
+	return
+}
+
+func expandMsgXmd(h hash.Hash, msg, domain []byte, outLen int) ([]byte, error) {
+	domainLen := uint8(len(domain))
+	if domainLen > 255 {
+		return nil, fmt.Errorf("invalid domain length")
+	}
+	// DST_prime = DST || I2OSP(len(DST), 1)
+	// b_0 = H(Z_pad || msg || l_i_b_str || I2OSP(0, 1) || DST_prime)
+	_, _ = h.Write(make([]byte, h.BlockSize()))
+	_, _ = h.Write(msg)
+	_, _ = h.Write([]byte{uint8(outLen >> 8), uint8(outLen)})
+	_, _ = h.Write([]byte{0})
+	_, _ = h.Write(domain)
+	_, _ = h.Write([]byte{domainLen})
+	b0 := h.Sum(nil)
+
+	// b_1 = H(b_0 || I2OSP(1, 1) || DST_prime)
+	h.Reset()
+	_, _ = h.Write(b0)
+	_, _ = h.Write([]byte{1})
+	_, _ = h.Write(domain)
+	_, _ = h.Write([]byte{domainLen})
+	b1 := h.Sum(nil)
+
+	// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
+	ell := (outLen + h.Size() - 1) / h.Size()
+	bi := b1
+	out := make([]byte, outLen)
+	for i := 1; i < ell; i++ {
+		h.Reset()
+		// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
+		tmp := make([]byte, h.Size())
+		for j := 0; j < h.Size(); j++ {
+			tmp[j] = b0[j] ^ bi[j]
+		}
+		_, _ = h.Write(tmp)
+		_, _ = h.Write([]byte{1 + uint8(i)})
+		_, _ = h.Write(domain)
+		_, _ = h.Write([]byte{domainLen})
+
+		// b_1 || ... || b_(ell - 1)
+		copy(out[(i-1)*h.Size():i*h.Size()], bi[:])
+		bi = h.Sum(nil)
+	}
+	// b_ell
+	copy(out[(ell-1)*h.Size():], bi[:])
+	return out[:outLen], nil
+}
+
+type isogenyParams struct {
+	P    *big.Int
+	Xnum []*big.Int
+	Xden []*big.Int
+	Ynum []*big.Int
+	Yden []*big.Int
+}
+
+func bhex(s string) *big.Int {
+	r, _ := new(big.Int).SetString(s, 16)
+	return r
+}
+
+type sswuParams struct {
+	Params          *elliptic.CurveParams
+	C1, C2, A, B, Z *big.Int
+}
+
+// sumOfProductsPippenger implements a version of Pippenger's algorithm.
+//
+// The algorithm works as follows:
+//
+// Let `n` be a number of point-scalar pairs.
+// Let `w` be a window of bits (6..8, chosen based on `n`, see cost factor).
+//
+// 1. Prepare `2^(w-1) - 1` buckets with indices `[1..2^(w-1))` initialized with identity points.
+//    Bucket 0 is not needed as it would contain points multiplied by 0.
+// 2. Convert scalars to a radix-`2^w` representation with signed digits in `[-2^w/2, 2^w/2]`.
+//    Note: only the last digit may equal `2^w/2`.
+// 3. Starting with the last window, for each point `i=[0..n)` add it to a a bucket indexed by
+//    the point's scalar's value in the window.
+// 4. Once all points in a window are sorted into buckets, add buckets by multiplying each
+//    by their index. Efficient way of doing it is to start with the last bucket and compute two sums:
+//    intermediate sum from the last to the first, and the full sum made of all intermediate sums.
+// 5. Shift the resulting sum of buckets by `w` bits by using `w` doublings.
+// 6. Add to the return value.
+// 7. Repeat the loop.
+//
+// Approximate cost w/o wNAF optimizations (A = addition, D = doubling):
+//
+// ```ascii
+// cost = (n*A + 2*(2^w/2)*A + w*D + A)*256/w
+//          |          |       |     |   |
+//          |          |       |     |   looping over 256/w windows
+//          |          |       |     adding to the result
+//    sorting points   |       shifting the sum by w bits (to the next window, starting from last window)
+//    one by one       |
+//    into buckets     adding/subtracting all buckets
+//                     multiplied by their indexes
+//                     using a sum of intermediate sums
+// ```
+//
+// For large `n`, dominant factor is (n*256/w) additions.
+// However, if `w` is too big and `n` is not too big, then `(2^w/2)*A` could dominate.
+// Therefore, the optimal choice of `w` grows slowly as `n` grows.
+//
+// For constant time we use a fixed window of 6
+//
+// This algorithm is adapted from section 4 of <https://eprint.iacr.org/2012/549.pdf>.
+// and https://cacr.uwaterloo.ca/techreports/2010/cacr2010-26.pdf
+func sumOfProductsPippenger(points []Point, scalars []*big.Int) Point {
+	if len(points) != len(scalars) {
+		return nil
+	}
+
+	const w = 6
+
+	bucketSize := (1 << w) - 1
+	windows := make([]Point, 255/w+1)
+	for i := range windows {
+		windows[i] = points[0].Identity()
+	}
+	bucket := make([]Point, bucketSize)
+
+	for j := 0; j < len(windows); j++ {
+		for i := 0; i < bucketSize; i++ {
+			bucket[i] = points[0].Identity()
+		}
+
+		for i := 0; i < len(scalars); i++ {
+			index := bucketSize & int(new(big.Int).Rsh(scalars[i], uint(w*j)).Int64())
+			if index != 0 {
+				bucket[index-1] = bucket[index-1].Add(points[i])
+			}
+		}
+
+		acc, sum := windows[j].Identity(), windows[j].Identity()
+
+		for i := bucketSize - 1; i >= 0; i-- {
+			sum = sum.Add(bucket[i])
+			acc = acc.Add(sum)
+		}
+		windows[j] = acc
+	}
+
+	acc := windows[0].Identity()
+	for i := len(windows) - 1; i >= 0; i-- {
+		for j := 0; j < w; j++ {
+			acc = acc.Double()
+		}
+		acc = acc.Add(windows[i])
+	}
+	return acc
+}
diff --git a/pkg/core/curves/ec_point.go b/pkg/core/curves/ec_point.go
new file mode 100644
index 00000000..56fa91b9
--- /dev/null
+++ b/pkg/core/curves/ec_point.go
@@ -0,0 +1,255 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+var curveNameToId = map[string]byte{
+	"secp256k1": 0,
+	"P-224":     1,
+	"P-256":     2,
+	"P-384":     3,
+	"P-521":     4,
+}
+
+var curveIdToName = map[byte]func() elliptic.Curve{
+	0: func() elliptic.Curve { return btcec.S256() },
+	1: elliptic.P224,
+	2: elliptic.P256,
+	3: elliptic.P384,
+	4: elliptic.P521,
+}
+
+var curveMapper = map[string]func() elliptic.Curve{
+	"secp256k1": func() elliptic.Curve { return btcec.S256() },
+	"P-224":     elliptic.P224,
+	"P-256":     elliptic.P256,
+	"P-384":     elliptic.P384,
+	"P-521":     elliptic.P521,
+}
+
+// EcPoint represents an elliptic curve Point
+type EcPoint struct {
+	Curve elliptic.Curve
+	X, Y  *big.Int
+}
+
+// EcPointJson encapsulates the data that is serialized to JSON
+// used internally and not for external use. Public so other pieces
+// can use for serialization
+type EcPointJson struct {
+	CurveName string
+	X, Y      *big.Int
+}
+
+// MarshalJSON serializes
+func (a EcPoint) MarshalJSON() ([]byte, error) {
+	return json.Marshal(EcPointJson{
+		CurveName: a.Curve.Params().Name,
+		X:         a.X,
+		Y:         a.Y,
+	})
+}
+
+func (a *EcPoint) UnmarshalJSON(bytes []byte) error {
+	data := new(EcPointJson)
+	err := json.Unmarshal(bytes, data)
+	if err != nil {
+		return err
+	}
+	if mapper, ok := curveMapper[data.CurveName]; ok {
+		a.Curve = mapper()
+		a.X = data.X
+		a.Y = data.Y
+		return nil
+	}
+	return fmt.Errorf("unknown curve deserialized")
+}
+
+func (a *EcPoint) MarshalBinary() ([]byte, error) {
+	result := [65]byte{}
+	if code, ok := curveNameToId[a.Curve.Params().Name]; ok {
+		result[0] = code
+		a.X.FillBytes(result[1:33])
+		a.Y.FillBytes(result[33:65])
+		return result[:], nil
+	}
+	return nil, fmt.Errorf("unknown curve serialized")
+}
+
+func (a *EcPoint) UnmarshalBinary(data []byte) error {
+	if mapper, ok := curveIdToName[data[0]]; ok {
+		a.Curve = mapper()
+		a.X = new(big.Int).SetBytes(data[1:33])
+		a.Y = new(big.Int).SetBytes(data[33:65])
+		return nil
+	}
+	return fmt.Errorf("unknown curve deserialized")
+}
+
+func (a EcPoint) IsValid() bool {
+	return a.IsOnCurve() || a.IsIdentity()
+}
+
+func (a EcPoint) IsOnCurve() bool {
+	return a.Curve.IsOnCurve(a.X, a.Y)
+}
+
+// IsIdentity returns true if this Point is the Point at infinity
+func (a EcPoint) IsIdentity() bool {
+	x := core.ConstantTimeEqByte(a.X, core.Zero)
+	y := core.ConstantTimeEqByte(a.Y, core.Zero)
+	return (x & y) == 1
+}
+
+// Equals return true if a + b have the same x,y coordinates
+func (a EcPoint) Equals(b *EcPoint) bool {
+	if !sameCurve(&a, b) {
+		return false
+	}
+	// Next, compare coords to determine equality
+	x := core.ConstantTimeEqByte(a.X, b.X)
+	y := core.ConstantTimeEqByte(a.Y, b.Y)
+	return (x & y) == 1
+}
+
+// IsBasePoint returns true if this Point is curve's base Point
+func (a EcPoint) IsBasePoint() bool {
+	p := a.Curve.Params()
+	x := core.ConstantTimeEqByte(a.X, p.Gx)
+	y := core.ConstantTimeEqByte(a.Y, p.Gy)
+	return (x & y) == 1
+}
+
+// Normalizes the Scalar to a positive element smaller than the base Point order.
+func reduceModN(curve elliptic.Curve, k *big.Int) *big.Int {
+	return new(big.Int).Mod(k, curve.Params().N)
+}
+
+// Add performs elliptic curve addition on two points
+func (a *EcPoint) Add(b *EcPoint) (*EcPoint, error) {
+	// Validate parameters
+	if a == nil || b == nil {
+		return nil, internal.ErrNilArguments
+	}
+	// Only add points from the same curve
+	if !sameCurve(a, b) {
+		return nil, internal.ErrPointsDistinctCurves
+	}
+	p := &EcPoint{Curve: a.Curve}
+	p.X, p.Y = a.Curve.Add(a.X, a.Y, b.X, b.Y)
+	if !p.IsValid() {
+		return nil, internal.ErrNotOnCurve
+	}
+	return p, nil
+}
+
+// Neg returns the negation of a Weierstrass Point.
+func (a *EcPoint) Neg() (*EcPoint, error) {
+	// Validate parameters
+	if a == nil {
+		return nil, internal.ErrNilArguments
+	}
+	// Only add points from the same curve
+	p := &EcPoint{Curve: a.Curve, X: a.X, Y: new(big.Int).Sub(a.Curve.Params().P, a.Y)}
+	if !p.IsValid() {
+		return nil, internal.ErrNotOnCurve
+	}
+	return p, nil
+}
+
+// ScalarMult multiplies this Point by a Scalar
+func (a *EcPoint) ScalarMult(k *big.Int) (*EcPoint, error) {
+	if a == nil || k == nil {
+		return nil, fmt.Errorf("cannot multiply nil Point or element")
+	}
+	n := reduceModN(a.Curve, k)
+	p := new(EcPoint)
+	p.Curve = a.Curve
+	p.X, p.Y = a.Curve.ScalarMult(a.X, a.Y, n.Bytes())
+	if !p.IsValid() {
+		return nil, fmt.Errorf("result not on the curve")
+	}
+	return p, nil
+}
+
+// NewScalarBaseMult creates a Point from the base Point multiplied by a field element
+func NewScalarBaseMult(curve elliptic.Curve, k *big.Int) (*EcPoint, error) {
+	if curve == nil || k == nil {
+		return nil, fmt.Errorf("nil parameters are not supported")
+	}
+	n := reduceModN(curve, k)
+	p := new(EcPoint)
+	p.Curve = curve
+	p.X, p.Y = curve.ScalarBaseMult(n.Bytes())
+	if !p.IsValid() {
+		return nil, fmt.Errorf("result not on the curve")
+	}
+	return p, nil
+}
+
+// Bytes returns the bytes represented by this Point with x || y
+func (a EcPoint) Bytes() []byte {
+	fieldSize := internal.CalcFieldSize(a.Curve)
+	out := make([]byte, fieldSize*2)
+
+	a.X.FillBytes(out[0:fieldSize])
+	a.Y.FillBytes(out[fieldSize : fieldSize*2])
+	return out
+}
+
+// PointFromBytesUncompressed outputs uncompressed X || Y similar to
+// https://www.secg.org/sec1-v1.99.dif.pdf section 2.2 and 2.3
+func PointFromBytesUncompressed(curve elliptic.Curve, b []byte) (*EcPoint, error) {
+	fieldSize := internal.CalcFieldSize(curve)
+	if len(b) != fieldSize*2 {
+		return nil, fmt.Errorf("invalid number of bytes")
+	}
+	p := &EcPoint{
+		Curve: curve,
+		X:     new(big.Int).SetBytes(b[:fieldSize]),
+		Y:     new(big.Int).SetBytes(b[fieldSize:]),
+	}
+	if !p.IsValid() {
+		return nil, fmt.Errorf("invalid Point")
+	}
+	return p, nil
+}
+
+// sameCurve determines if points a,b appear to be from the same curve
+func sameCurve(a, b *EcPoint) bool {
+	// Handle identical pointers and double-nil
+	if a == b {
+		return true
+	}
+
+	// Handle one nil pointer
+	if a == nil || b == nil {
+		return false
+	}
+
+	aParams := a.Curve.Params()
+	bParams := b.Curve.Params()
+
+	// Use curve order and name
+	return aParams.P == bParams.P &&
+		aParams.N == bParams.N &&
+		aParams.B == bParams.B &&
+		aParams.BitSize == bParams.BitSize &&
+		aParams.Gx == bParams.Gx &&
+		aParams.Gy == bParams.Gy &&
+		aParams.Name == bParams.Name
+}
diff --git a/pkg/core/curves/ec_point_test.go b/pkg/core/curves/ec_point_test.go
new file mode 100644
index 00000000..dee22b12
--- /dev/null
+++ b/pkg/core/curves/ec_point_test.go
@@ -0,0 +1,371 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"bytes"
+	"crypto/elliptic"
+	"github.com/coinbase/kryptology/pkg/core"
+	"math/big"
+	"testing"
+
+	tt "github.com/coinbase/kryptology/internal"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestIsIdentity(t *testing.T) {
+	// Should be Point at infinity
+	identity := &EcPoint{btcec.S256(), core.Zero, core.Zero}
+	assert.True(t, identity.IsIdentity())
+}
+
+func TestNewScalarBaseMultZero(t *testing.T) {
+	// Should be Point at infinity
+	curve := btcec.S256()
+	num := big.NewInt(0)
+	p, err := NewScalarBaseMult(curve, num)
+	if err != nil {
+		t.Errorf("NewScalarBaseMult failed: %v", err)
+	}
+	if p == nil {
+		t.Errorf("NewScalarBaseMult failed when it should've succeeded.")
+	}
+}
+
+func TestNewScalarBaseMultOne(t *testing.T) {
+	// Should be base Point
+	curve := btcec.S256()
+	num := big.NewInt(1)
+	p, err := NewScalarBaseMult(curve, num)
+	if err != nil {
+		t.Errorf("NewScalarBaseMult failed: %v", err)
+	}
+	if p == nil {
+		t.Errorf("NewScalarBaseMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+	if !bytes.Equal(p.Bytes(), append(curve.Gx.Bytes(), curve.Gy.Bytes()...)) {
+		t.Errorf("NewScalarBaseMult should've returned the base Point.")
+	}
+}
+
+func TestNewScalarBaseMultNeg(t *testing.T) {
+	curve := btcec.S256()
+	num := big.NewInt(-1)
+	p, err := NewScalarBaseMult(curve, num)
+	if err != nil {
+		t.Errorf("NewScalarBaseMult failed: %v", err)
+	}
+	if p == nil {
+		t.Errorf("NewScalarBaseMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+	num.Mod(num, curve.N)
+
+	e, err := NewScalarBaseMult(curve, num)
+	if err != nil {
+		t.Errorf("NewScalarBaseMult failed: %v", err)
+	}
+	if e == nil {
+		t.Errorf("NewScalarBaseMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+
+	if !bytes.Equal(p.Bytes(), e.Bytes()) {
+		t.Errorf("NewScalarBaseMult should've returned the %v, found: %v", e, p)
+	}
+}
+
+func TestScalarMultZero(t *testing.T) {
+	// Should be Point at infinity
+	curve := btcec.S256()
+	p := &EcPoint{
+		Curve: curve,
+		X:     curve.Gx,
+		Y:     curve.Gy,
+	}
+	num := big.NewInt(0)
+	q, err := p.ScalarMult(num)
+	if err != nil {
+		t.Errorf("ScalarMult failed: %v", err)
+	}
+	if q == nil {
+		t.Errorf("ScalarMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+	if !q.IsIdentity() {
+		t.Errorf("ScalarMult should've returned the identity Point.")
+	}
+}
+
+func TestScalarMultOne(t *testing.T) {
+	// Should be base Point
+	curve := btcec.S256()
+	p := &EcPoint{
+		Curve: curve,
+		X:     curve.Gx,
+		Y:     curve.Gy,
+	}
+	num := big.NewInt(1)
+	q, err := p.ScalarMult(num)
+	if err != nil {
+		t.Errorf("ScalarMult failed: %v", err)
+	}
+	if q == nil {
+		t.Errorf("ScalarMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+	if !bytes.Equal(q.Bytes(), append(curve.Gx.Bytes(), curve.Gy.Bytes()...)) {
+		t.Errorf("ScalarMult should've returned the base Point.")
+	}
+}
+
+func TestScalarMultNeg(t *testing.T) {
+	curve := btcec.S256()
+	p := &EcPoint{
+		Curve: curve,
+		X:     curve.Gx,
+		Y:     curve.Gy,
+	}
+	num := big.NewInt(-1)
+	q, err := p.ScalarMult(num)
+	if err != nil {
+		t.Errorf("ScalarMult failed: %v", err)
+	}
+	if q == nil {
+		t.Errorf("ScalarMult failed when it should've succeeded.")
+	}
+	num.Mod(num, curve.N)
+
+	e, err := p.ScalarMult(num)
+	if err != nil {
+		t.Errorf("ScalarMult failed: %v", err)
+	}
+	if e == nil {
+		t.Errorf("ScalarMult failed when it should've succeeded.")
+		t.FailNow()
+	}
+
+	if !bytes.Equal(q.Bytes(), e.Bytes()) {
+		t.Errorf("ScalarMult should've returned the %v, found: %v", e, p)
+	}
+}
+
+func TestEcPointAddSimple(t *testing.T) {
+	curve := btcec.S256()
+	num := big.NewInt(1)
+	p1, _ := NewScalarBaseMult(curve, num)
+
+	p2, _ := NewScalarBaseMult(curve, num)
+	p3, err := p1.Add(p2)
+	if err != nil {
+		t.Errorf("EcPoint.Add failed: %v", err)
+	}
+	num = big.NewInt(2)
+
+	ep, _ := NewScalarBaseMult(curve, num)
+
+	if !bytes.Equal(ep.Bytes(), p3.Bytes()) {
+		t.Errorf("EcPoint.Add failed: should equal %v, found: %v", ep, p3)
+	}
+}
+
+func TestEcPointAddCommunicative(t *testing.T) {
+	curve := btcec.S256()
+	a, _ := core.Rand(curve.Params().N)
+	b, _ := core.Rand(curve.Params().N)
+
+	p1, _ := NewScalarBaseMult(curve, a)
+	p2, _ := NewScalarBaseMult(curve, b)
+	p3, err := p1.Add(p2)
+	if err != nil {
+		t.Errorf("EcPoint.Add failed: %v", err)
+	}
+	p4, err := p2.Add(p1)
+	if err != nil {
+		t.Errorf("EcPoint.Add failed: %v", err)
+	}
+	if !bytes.Equal(p3.Bytes(), p4.Bytes()) {
+		t.Errorf("EcPoint.Add Communicative not valid")
+	}
+}
+
+func TestEcPointAddNeg(t *testing.T) {
+	curve := btcec.S256()
+	num := big.NewInt(-1)
+
+	p1, _ := NewScalarBaseMult(curve, num)
+	num.Abs(num)
+
+	p2, _ := NewScalarBaseMult(curve, num)
+
+	p3, err := p1.Add(p2)
+
+	if err != nil {
+		t.Errorf("EcPoint.Add failed: %v", err)
+	}
+	zero := make([]byte, 64)
+	if !bytes.Equal(zero, p3.Bytes()) {
+		t.Errorf("Expected value to be zero, found: %v", p3)
+	}
+}
+
+func TestEcPointBytes(t *testing.T) {
+	curve := btcec.S256()
+
+	point, err := NewScalarBaseMult(curve, big.NewInt(2))
+	assert.NoError(t, err)
+	data := point.Bytes()
+	point2, err := PointFromBytesUncompressed(curve, data)
+	assert.NoError(t, err)
+	if point.X.Cmp(point2.X) != 0 && point.Y.Cmp(point2.Y) != 0 {
+		t.Errorf("Points are not equal. Expected %v, found %v", point, point2)
+	}
+
+	curve2 := elliptic.P224()
+	p2, err := NewScalarBaseMult(curve2, big.NewInt(2))
+	assert.NoError(t, err)
+	dta := p2.Bytes()
+	point3, err := PointFromBytesUncompressed(curve2, dta)
+	assert.NoError(t, err)
+	if p2.X.Cmp(point3.X) != 0 && p2.Y.Cmp(point3.Y) != 0 {
+		t.Errorf("Points are not equal. Expected %v, found %v", p2, point3)
+	}
+
+	curve3 := elliptic.P521()
+	p3, err := NewScalarBaseMult(curve3, big.NewInt(2))
+	assert.NoError(t, err)
+	data = p3.Bytes()
+	point4, err := PointFromBytesUncompressed(curve3, data)
+	assert.NoError(t, err)
+	if p3.X.Cmp(point4.X) != 0 && p3.Y.Cmp(point4.Y) != 0 {
+		t.Errorf("Points are not equal. Expected %v, found %v", p3, point4)
+	}
+}
+
+func TestEcPointBytesDifferentCurves(t *testing.T) {
+	k256 := btcec.S256()
+	p224 := elliptic.P224()
+	p256 := elliptic.P256()
+
+	kp, err := NewScalarBaseMult(k256, big.NewInt(1))
+	assert.NoError(t, err)
+	data := kp.Bytes()
+	_, err = PointFromBytesUncompressed(p224, data)
+	assert.Error(t, err)
+	_, err = PointFromBytesUncompressed(p256, data)
+	assert.Error(t, err)
+}
+
+func TestEcPointBytesInvalidNumberBytes(t *testing.T) {
+	curve := btcec.S256()
+
+	for i := 1; i < 64; i++ {
+		data := make([]byte, i)
+		_, err := PointFromBytesUncompressed(curve, data)
+		assert.Error(t, err)
+	}
+	for i := 65; i < 128; i++ {
+		data := make([]byte, i)
+		_, err := PointFromBytesUncompressed(curve, data)
+		assert.Error(t, err)
+	}
+}
+
+func TestEcPointMultRandom(t *testing.T) {
+	curve := btcec.S256()
+	r, err := core.Rand(curve.N)
+	assert.NoError(t, err)
+	pt, err := NewScalarBaseMult(curve, r)
+	assert.NoError(t, err)
+	assert.NotNil(t, pt)
+	data := pt.Bytes()
+	pt2, err := PointFromBytesUncompressed(curve, data)
+	assert.NoError(t, err)
+	if pt.X.Cmp(pt2.X) != 0 || pt.Y.Cmp(pt2.Y) != 0 {
+		t.Errorf("Points are not equal. Expected: %v, found: %v", pt, pt2)
+	}
+}
+
+func TestIsBasePoint(t *testing.T) {
+	k256 := btcec.S256()
+	p224 := elliptic.P224()
+	p256 := elliptic.P256()
+
+	notG_p224, err := NewScalarBaseMult(p224, tt.B10("9876453120"))
+	if !assert.NoError(t, err) {
+		t.FailNow()
+	}
+
+	tests := []struct {
+		name     string
+		curve    elliptic.Curve
+		x, y     *big.Int
+		expected bool
+	}{
+		{"k256-positive", k256, k256.Gx, k256.Gy, true},
+		{"p224-positive", p224, p224.Params().Gx, p224.Params().Gy, true},
+		{"p256-positive", p256, p256.Params().Gx, p256.Params().Gy, true},
+
+		{"p224-negative", p224, notG_p224.X, notG_p224.Y, false},
+		{"p256-negative-wrong-curve", p256, notG_p224.X, notG_p224.Y, false},
+		{"k256-negative-doubleGx", k256, k256.Gx, k256.Gx, false},
+		{"k256-negative-doubleGy", k256, k256.Gy, k256.Gy, false},
+		{"k256-negative-xy-swap", k256, k256.Gy, k256.Gx, false},
+		{"k256-negative-oh-oh", k256, core.Zero, core.Zero, false},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			actual := EcPoint{test.curve, test.x, test.y}.IsBasePoint()
+			assert.Equal(t, test.expected, actual)
+		})
+	}
+}
+
+func TestEquals(t *testing.T) {
+	k256 := btcec.S256()
+	p224 := elliptic.P224()
+	p256 := elliptic.P256()
+	P_p224, _ := NewScalarBaseMult(p224, tt.B10("9876453120"))
+	P1_p224, _ := NewScalarBaseMult(p224, tt.B10("9876453120"))
+
+	P_k256 := &EcPoint{k256, P_p224.X, P_p224.Y}
+
+	id_p224 := &EcPoint{p224, core.Zero, core.Zero}
+	id_k256 := &EcPoint{k256, core.Zero, core.Zero}
+	id_p256 := &EcPoint{p256, core.Zero, core.Zero}
+
+	tests := []struct {
+		name     string
+		x, y     *EcPoint
+		expected bool
+	}{
+		{"p224 same pointer", P_p224, P_p224, true},
+		{"p224 same Point", P_p224, P1_p224, true},
+		{"p224 identity", id_p224, id_p224, true},
+		{"p256 identity", id_p256, id_p256, true},
+		{"k256 identity", id_k256, id_k256, true},
+
+		{"negative-same x different y", P_p224, &EcPoint{p224, P_p224.X, core.One}, false},
+		{"negative-same y different x", P_p224, &EcPoint{p224, core.Two, P_k256.Y}, false},
+
+		{"negative-wrong curve", P_p224, P_k256, false},
+		{"negative-wrong curve reversed", P_k256, P_p224, false},
+		{"Point is not the identity", P_p224, id_p224, false},
+		{"negative nil", P1_p224, nil, false},
+		{"identities on wrong curve", id_p256, id_k256, false},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			actual := test.x.Equals(test.y)
+			assert.Equal(t, test.expected, actual)
+		})
+	}
+}
diff --git a/pkg/core/curves/ec_scalar.go b/pkg/core/curves/ec_scalar.go
new file mode 100644
index 00000000..68de41ed
--- /dev/null
+++ b/pkg/core/curves/ec_scalar.go
@@ -0,0 +1,357 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	crand "crypto/rand"
+	"crypto/sha512"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/bwesterb/go-ristretto"
+	"io"
+	"math/big"
+
+	"filippo.io/edwards25519"
+	"github.com/coinbase/kryptology/internal"
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+type EcScalar interface {
+	Add(x, y *big.Int) *big.Int
+	Sub(x, y *big.Int) *big.Int
+	Neg(x *big.Int) *big.Int
+	Mul(x, y *big.Int) *big.Int
+	Hash(input []byte) *big.Int
+	Div(x, y *big.Int) *big.Int
+	Random() (*big.Int, error)
+	IsValid(x *big.Int) bool
+	Bytes(x *big.Int) []byte // fixed-length byte array
+}
+
+type K256Scalar struct{}
+
+// Static interface assertion
+var _ EcScalar = (*K256Scalar)(nil)
+
+// warning: the Euclidean alg which Mod uses is not constant-time.
+
+func NewK256Scalar() *K256Scalar {
+	return &K256Scalar{}
+}
+
+func (k K256Scalar) Add(x, y *big.Int) *big.Int {
+	v := new(big.Int).Add(x, y)
+	v.Mod(v, btcec.S256().N)
+	return v
+}
+
+func (k K256Scalar) Sub(x, y *big.Int) *big.Int {
+	v := new(big.Int).Sub(x, y)
+	v.Mod(v, btcec.S256().N)
+	return v
+}
+
+func (k K256Scalar) Neg(x *big.Int) *big.Int {
+	v := new(big.Int).Sub(btcec.S256().N, x)
+	v.Mod(v, btcec.S256().N)
+	return v
+}
+
+func (k K256Scalar) Mul(x, y *big.Int) *big.Int {
+	v := new(big.Int).Mul(x, y)
+	v.Mod(v, btcec.S256().N)
+	return v
+}
+
+func (k K256Scalar) Div(x, y *big.Int) *big.Int {
+	t := new(big.Int).ModInverse(y, btcec.S256().N)
+	return k.Mul(x, t)
+}
+
+func (k K256Scalar) Hash(input []byte) *big.Int {
+	return new(ScalarK256).Hash(input).BigInt()
+}
+
+func (k K256Scalar) Random() (*big.Int, error) {
+	b := make([]byte, 48)
+	n, err := crand.Read(b)
+	if err != nil {
+		return nil, err
+	}
+	if n != 48 {
+		return nil, fmt.Errorf("insufficient bytes read")
+	}
+	v := new(big.Int).SetBytes(b)
+	v.Mod(v, btcec.S256().N)
+	return v, nil
+}
+
+func (k K256Scalar) IsValid(x *big.Int) bool {
+	return core.In(x, btcec.S256().N) == nil
+}
+
+func (k K256Scalar) Bytes(x *big.Int) []byte {
+	bytes := make([]byte, 32)
+	x.FillBytes(bytes) // big-endian; will left-pad.
+	return bytes
+}
+
+type P256Scalar struct{}
+
+// Static interface assertion
+var _ EcScalar = (*P256Scalar)(nil)
+
+func NewP256Scalar() *P256Scalar {
+	return &P256Scalar{}
+}
+
+func (k P256Scalar) Add(x, y *big.Int) *big.Int {
+	v := new(big.Int).Add(x, y)
+	v.Mod(v, elliptic.P256().Params().N)
+	return v
+}
+
+func (k P256Scalar) Sub(x, y *big.Int) *big.Int {
+	v := new(big.Int).Sub(x, y)
+	v.Mod(v, elliptic.P256().Params().N)
+	return v
+}
+
+func (k P256Scalar) Neg(x *big.Int) *big.Int {
+	v := new(big.Int).Sub(elliptic.P256().Params().N, x)
+	v.Mod(v, elliptic.P256().Params().N)
+	return v
+}
+
+func (k P256Scalar) Mul(x, y *big.Int) *big.Int {
+	v := new(big.Int).Mul(x, y)
+	v.Mod(v, elliptic.P256().Params().N)
+	return v
+}
+
+func (k P256Scalar) Div(x, y *big.Int) *big.Int {
+	t := new(big.Int).ModInverse(y, elliptic.P256().Params().N)
+	return k.Mul(x, t)
+}
+
+func (k P256Scalar) Hash(input []byte) *big.Int {
+	return new(ScalarP256).Hash(input).BigInt()
+}
+
+func (k P256Scalar) Random() (*big.Int, error) {
+	b := make([]byte, 48)
+	n, err := crand.Read(b)
+	if err != nil {
+		return nil, err
+	}
+	if n != 48 {
+		return nil, fmt.Errorf("insufficient bytes read")
+	}
+	v := new(big.Int).SetBytes(b)
+	v.Mod(v, elliptic.P256().Params().N)
+	return v, nil
+}
+
+func (k P256Scalar) IsValid(x *big.Int) bool {
+	return core.In(x, elliptic.P256().Params().N) == nil
+}
+
+func (k P256Scalar) Bytes(x *big.Int) []byte {
+	bytes := make([]byte, 32)
+	x.FillBytes(bytes) // big-endian; will left-pad.
+	return bytes
+}
+
+type Bls12381Scalar struct{}
+
+// Static interface assertion
+var _ EcScalar = (*Bls12381Scalar)(nil)
+
+func NewBls12381Scalar() *Bls12381Scalar {
+	return &Bls12381Scalar{}
+}
+
+func (k Bls12381Scalar) Add(x, y *big.Int) *big.Int {
+	g1 := bls12381.NewG1()
+	v := new(big.Int).Add(x, y)
+	v.Mod(v, g1.Q())
+	return v
+}
+
+func (k Bls12381Scalar) Sub(x, y *big.Int) *big.Int {
+	g1 := bls12381.NewG1()
+	v := new(big.Int).Sub(x, y)
+	v.Mod(v, g1.Q())
+	return v
+}
+
+func (k Bls12381Scalar) Neg(x *big.Int) *big.Int {
+	v := new(big.Int).Sub(bls12381.NewG1().Q(), x)
+	v.Mod(v, bls12381.NewG1().Q())
+	return v
+}
+
+func (k Bls12381Scalar) Mul(x, y *big.Int) *big.Int {
+	g1 := bls12381.NewG1()
+	v := new(big.Int).Mul(x, y)
+	v.Mod(v, g1.Q())
+	return v
+}
+
+func (k Bls12381Scalar) Div(x, y *big.Int) *big.Int {
+	g1 := bls12381.NewG1()
+	t := new(big.Int).ModInverse(y, g1.Q())
+	return k.Mul(x, t)
+}
+
+func (k Bls12381Scalar) Hash(input []byte) *big.Int {
+	return new(ScalarBls12381).Hash(input).BigInt()
+}
+
+func (k Bls12381Scalar) Random() (*big.Int, error) {
+	b := make([]byte, 48)
+	n, err := crand.Read(b)
+	if err != nil {
+		return nil, err
+	}
+	if n != 48 {
+		return nil, fmt.Errorf("insufficient bytes read")
+	}
+	v := new(big.Int).SetBytes(b)
+	g1 := bls12381.NewG1()
+	v.Mod(v, g1.Q())
+	return v, nil
+}
+
+func (k Bls12381Scalar) Bytes(x *big.Int) []byte {
+	bytes := make([]byte, 32)
+	x.FillBytes(bytes) // big-endian; will left-pad.
+	return bytes
+}
+
+func (k Bls12381Scalar) IsValid(x *big.Int) bool {
+	g1 := bls12381.NewG1()
+	return core.In(x, g1.Q()) == nil
+}
+
+// taken from https://datatracker.ietf.org/doc/html/rfc8032
+var ed25519N, _ = new(big.Int).SetString("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16)
+
+type Ed25519Scalar struct{}
+
+// Static interface assertion
+var _ EcScalar = (*Ed25519Scalar)(nil)
+
+func NewEd25519Scalar() *Ed25519Scalar {
+	return &Ed25519Scalar{}
+}
+
+func (k Ed25519Scalar) Add(x, y *big.Int) *big.Int {
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	b, err := internal.BigInt2Ed25519Scalar(y)
+	if err != nil {
+		panic(err)
+	}
+	a.Add(a, b)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(a.Bytes()))
+}
+
+func (k Ed25519Scalar) Sub(x, y *big.Int) *big.Int {
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	b, err := internal.BigInt2Ed25519Scalar(y)
+	if err != nil {
+		panic(err)
+	}
+	a.Subtract(a, b)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(a.Bytes()))
+}
+
+func (k Ed25519Scalar) Neg(x *big.Int) *big.Int {
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	a.Negate(a)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(a.Bytes()))
+}
+
+func (k Ed25519Scalar) Mul(x, y *big.Int) *big.Int {
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	b, err := internal.BigInt2Ed25519Scalar(y)
+	if err != nil {
+		panic(err)
+	}
+	a.Multiply(a, b)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(a.Bytes()))
+}
+
+func (k Ed25519Scalar) Div(x, y *big.Int) *big.Int {
+	b, err := internal.BigInt2Ed25519Scalar(y)
+	if err != nil {
+		panic(err)
+	}
+	b.Invert(b)
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	a.Multiply(a, b)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(a.Bytes()))
+}
+
+func (k Ed25519Scalar) Hash(input []byte) *big.Int {
+	v := new(ristretto.Scalar).Derive(input)
+	var data [32]byte
+	v.BytesInto(&data)
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(data[:]))
+}
+
+func (k Ed25519Scalar) Bytes(x *big.Int) []byte {
+	a, err := internal.BigInt2Ed25519Scalar(x)
+	if err != nil {
+		panic(err)
+	}
+	return internal.ReverseScalarBytes(a.Bytes())
+}
+
+func (k Ed25519Scalar) Random() (*big.Int, error) {
+	return k.RandomWithReader(crand.Reader)
+}
+
+func (k Ed25519Scalar) RandomWithReader(r io.Reader) (*big.Int, error) {
+	b := make([]byte, 64)
+	n, err := r.Read(b)
+	if err != nil {
+		return nil, err
+	}
+	if n != 64 {
+		return nil, fmt.Errorf("insufficient bytes read")
+	}
+	digest := sha512.Sum512(b)
+	var hBytes [32]byte
+	copy(hBytes[:], digest[:])
+	s, err := edwards25519.NewScalar().SetBytesWithClamping(hBytes[:])
+	if err != nil {
+		return nil, err
+	}
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(s.Bytes())), nil
+}
+
+func (k Ed25519Scalar) IsValid(x *big.Int) bool {
+	return x.Cmp(ed25519N) == -1
+}
diff --git a/pkg/core/curves/ecdsa.go b/pkg/core/curves/ecdsa.go
new file mode 100644
index 00000000..2b2e9b4d
--- /dev/null
+++ b/pkg/core/curves/ecdsa.go
@@ -0,0 +1,38 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/ecdsa"
+	"math/big"
+)
+
+// EcdsaVerify runs a curve- or algorithm-specific ECDSA verification function on input
+// an ECDSA public (verification) key, a message digest, and an ECDSA signature.
+// It must return true if all the parameters are sane and the ECDSA signature is valid,
+// and false otherwise
+type EcdsaVerify func(pubKey *EcPoint, hash []byte, signature *EcdsaSignature) bool
+
+// EcdsaSignature represents a (composite) digital signature
+type EcdsaSignature struct {
+	V    int
+	R, S *big.Int
+}
+
+// Static type assertion
+var _ EcdsaVerify = VerifyEcdsa
+
+// Verifies ECDSA signature using core types.
+func VerifyEcdsa(pk *EcPoint, hash []byte, sig *EcdsaSignature) bool {
+	return ecdsa.Verify(
+		&ecdsa.PublicKey{
+			Curve: pk.Curve,
+			X:     pk.X,
+			Y:     pk.Y,
+		},
+		hash, sig.R, sig.S)
+}
diff --git a/pkg/core/curves/ed25519_curve.go b/pkg/core/curves/ed25519_curve.go
new file mode 100644
index 00000000..f3af1abf
--- /dev/null
+++ b/pkg/core/curves/ed25519_curve.go
@@ -0,0 +1,784 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"bytes"
+	"crypto/sha512"
+	"crypto/subtle"
+	"filippo.io/edwards25519"
+	"filippo.io/edwards25519/field"
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/bwesterb/go-ristretto"
+	ed "github.com/bwesterb/go-ristretto/edwards25519"
+	"io"
+	"math/big"
+)
+
+type ScalarEd25519 struct {
+	value *edwards25519.Scalar
+}
+
+type PointEd25519 struct {
+	value *edwards25519.Point
+}
+
+var scOne, _ = edwards25519.NewScalar().SetCanonicalBytes([]byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+
+func (s *ScalarEd25519) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarEd25519) Hash(bytes []byte) Scalar {
+	v := new(ristretto.Scalar).Derive(bytes)
+	var data [32]byte
+	v.BytesInto(&data)
+	value, err := edwards25519.NewScalar().SetCanonicalBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	return &ScalarEd25519{value}
+}
+
+func (s *ScalarEd25519) Zero() Scalar {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar(),
+	}
+}
+
+func (s *ScalarEd25519) One() Scalar {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar().Set(scOne),
+	}
+}
+
+func (s *ScalarEd25519) IsZero() bool {
+	i := byte(0)
+	for _, b := range s.value.Bytes() {
+		i |= b
+	}
+	return i == 0
+}
+
+func (s *ScalarEd25519) IsOne() bool {
+	data := s.value.Bytes()
+	i := byte(0)
+	for j := 1; j < len(data); j++ {
+		i |= data[j]
+	}
+	return i == 0 && data[0] == 1
+}
+
+func (s *ScalarEd25519) IsOdd() bool {
+	return s.value.Bytes()[0]&1 == 1
+}
+
+func (s *ScalarEd25519) IsEven() bool {
+	return s.value.Bytes()[0]&1 == 0
+}
+
+func (s *ScalarEd25519) New(input int) Scalar {
+	var data [64]byte
+	i := input
+	if input < 0 {
+		i = -input
+	}
+	data[0] = byte(i)
+	data[1] = byte(i >> 8)
+	data[2] = byte(i >> 16)
+	data[3] = byte(i >> 24)
+	value, err := edwards25519.NewScalar().SetUniformBytes(data[:])
+	if err != nil {
+		return nil
+	}
+	if input < 0 {
+		value.Negate(value)
+	}
+
+	return &ScalarEd25519{
+		value,
+	}
+}
+
+func (s *ScalarEd25519) Cmp(rhs Scalar) int {
+	r := s.Sub(rhs)
+	if r != nil && r.IsZero() {
+		return 0
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarEd25519) Square() Scalar {
+	value := edwards25519.NewScalar().Multiply(s.value, s.value)
+	return &ScalarEd25519{value}
+}
+
+func (s *ScalarEd25519) Double() Scalar {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar().Add(s.value, s.value),
+	}
+}
+
+func (s *ScalarEd25519) Invert() (Scalar, error) {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar().Invert(s.value),
+	}, nil
+}
+
+func (s *ScalarEd25519) Sqrt() (Scalar, error) {
+	bi25519, _ := new(big.Int).SetString("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16)
+	x := s.BigInt()
+	x.ModSqrt(x, bi25519)
+	return s.SetBigInt(x)
+}
+
+func (s *ScalarEd25519) Cube() Scalar {
+	value := edwards25519.NewScalar().Multiply(s.value, s.value)
+	value.Multiply(value, s.value)
+	return &ScalarEd25519{value}
+}
+
+func (s *ScalarEd25519) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarEd25519)
+	if ok {
+		return &ScalarEd25519{
+			value: edwards25519.NewScalar().Add(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarEd25519) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarEd25519)
+	if ok {
+		return &ScalarEd25519{
+			value: edwards25519.NewScalar().Subtract(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarEd25519) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarEd25519)
+	if ok {
+		return &ScalarEd25519{
+			value: edwards25519.NewScalar().Multiply(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarEd25519) MulAdd(y, z Scalar) Scalar {
+	yy, ok := y.(*ScalarEd25519)
+	if !ok {
+		return nil
+	}
+	zz, ok := z.(*ScalarEd25519)
+	if !ok {
+		return nil
+	}
+	return &ScalarEd25519{value: edwards25519.NewScalar().MultiplyAdd(s.value, yy.value, zz.value)}
+}
+
+func (s *ScalarEd25519) Div(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarEd25519)
+	if ok {
+		value := edwards25519.NewScalar().Invert(r.value)
+		value.Multiply(value, s.value)
+		return &ScalarEd25519{value}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarEd25519) Neg() Scalar {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar().Negate(s.value),
+	}
+}
+
+func (s *ScalarEd25519) SetBigInt(x *big.Int) (Scalar, error) {
+	if x == nil {
+		return nil, fmt.Errorf("invalid value")
+	}
+
+	bi25519, _ := new(big.Int).SetString("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16)
+	var v big.Int
+	buf := v.Mod(x, bi25519).Bytes()
+	var rBuf [32]byte
+	for i := 0; i < len(buf) && i < 32; i++ {
+		rBuf[i] = buf[len(buf)-i-1]
+	}
+	value, err := edwards25519.NewScalar().SetCanonicalBytes(rBuf[:])
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarEd25519{value}, nil
+}
+
+func (s *ScalarEd25519) BigInt() *big.Int {
+	var ret big.Int
+	buf := internal.ReverseScalarBytes(s.value.Bytes())
+	return ret.SetBytes(buf)
+}
+
+func (s *ScalarEd25519) Bytes() []byte {
+	return s.value.Bytes()
+}
+
+// SetBytes takes input a 32-byte long array and returns a ed25519 scalar.
+// The input must be 32-byte long and must be a reduced bytes.
+func (s *ScalarEd25519) SetBytes(input []byte) (Scalar, error) {
+	if len(input) != 32 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value, err := edwards25519.NewScalar().SetCanonicalBytes(input)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarEd25519{value}, nil
+}
+
+// SetBytesWide takes input a 64-byte long byte array, reduce it and return an ed25519 scalar.
+// It uses SetUniformBytes of fillipo.io/edwards25519 - https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L85
+// If bytes is not of the right length, it returns nil and an error
+func (s *ScalarEd25519) SetBytesWide(bytes []byte) (Scalar, error) {
+	value, err := edwards25519.NewScalar().SetUniformBytes(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarEd25519{value}, nil
+}
+
+// SetBytesClamping uses SetBytesWithClamping of fillipo.io/edwards25519- https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L135
+// which applies the buffer pruning described in RFC 8032, Section 5.1.5 (also known as clamping)
+// and sets bytes to the result. The input must be 32-byte long, and it is not modified.
+// If bytes is not of the right length, SetBytesWithClamping returns nil and an error, and the receiver is unchanged.
+func (s *ScalarEd25519) SetBytesClamping(bytes []byte) (Scalar, error) {
+	value, err := edwards25519.NewScalar().SetBytesWithClamping(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarEd25519{value}, nil
+}
+
+// SetBytesCanonical uses SetCanonicalBytes of fillipo.io/edwards25519.
+// https://github.com/FiloSottile/edwards25519/blob/v1.0.0-rc.1/scalar.go#L98
+// This function takes an input x and sets s = x, where x is a 32-byte little-endian
+// encoding of s, then it returns the corresponding ed25519 scalar. If the input is
+// not a canonical encoding of s, it returns nil and an error.
+func (s *ScalarEd25519) SetBytesCanonical(bytes []byte) (Scalar, error) {
+	return s.SetBytes(bytes)
+}
+
+func (s *ScalarEd25519) Point() Point {
+	return new(PointEd25519).Identity()
+}
+
+func (s *ScalarEd25519) Clone() Scalar {
+	return &ScalarEd25519{
+		value: edwards25519.NewScalar().Set(s.value),
+	}
+}
+
+func (s *ScalarEd25519) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarEd25519) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarEd25519)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarEd25519) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarEd25519) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarEd25519)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarEd25519) GetEdwardsScalar() *edwards25519.Scalar {
+	return edwards25519.NewScalar().Set(s.value)
+}
+
+func (s *ScalarEd25519) SetEdwardsScalar(sc *edwards25519.Scalar) *ScalarEd25519 {
+	return &ScalarEd25519{value: edwards25519.NewScalar().Set(sc)}
+}
+
+func (s *ScalarEd25519) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarEd25519) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarEd25519)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+func (p *PointEd25519) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointEd25519) Hash(bytes []byte) Point {
+	/// Perform hashing to the group using the Elligator2 map
+	///
+	/// See https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-11#section-6.7.1
+	h := sha512.Sum512(bytes)
+	var res [32]byte
+	copy(res[:], h[:32])
+	signBit := (res[31] & 0x80) >> 7
+
+	fe := new(ed.FieldElement).SetBytes(&res).BytesInto(&res)
+	m1 := elligatorEncode(fe)
+
+	return toEdwards(m1, signBit)
+}
+
+func (p *PointEd25519) Identity() Point {
+	return &PointEd25519{
+		value: edwards25519.NewIdentityPoint(),
+	}
+}
+
+func (p *PointEd25519) Generator() Point {
+	return &PointEd25519{
+		value: edwards25519.NewGeneratorPoint(),
+	}
+}
+
+func (p *PointEd25519) IsIdentity() bool {
+	return p.Equal(p.Identity())
+}
+
+func (p *PointEd25519) IsNegative() bool {
+	// Negative points don't really exist in ed25519
+	return false
+}
+
+func (p *PointEd25519) IsOnCurve() bool {
+	_, err := edwards25519.NewIdentityPoint().SetBytes(p.ToAffineCompressed())
+	return err == nil
+}
+
+func (p *PointEd25519) Double() Point {
+	return &PointEd25519{value: edwards25519.NewIdentityPoint().Add(p.value, p.value)}
+}
+
+func (p *PointEd25519) Scalar() Scalar {
+	return new(ScalarEd25519).Zero()
+}
+
+func (p *PointEd25519) Neg() Point {
+	return &PointEd25519{value: edwards25519.NewIdentityPoint().Negate(p.value)}
+}
+
+func (p *PointEd25519) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointEd25519)
+	if ok {
+		return &PointEd25519{value: edwards25519.NewIdentityPoint().Add(p.value, r.value)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointEd25519) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointEd25519)
+	if ok {
+		rTmp := edwards25519.NewIdentityPoint().Negate(r.value)
+		return &PointEd25519{value: edwards25519.NewIdentityPoint().Add(p.value, rTmp)}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointEd25519) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarEd25519)
+	if ok {
+		value := edwards25519.NewIdentityPoint().ScalarMult(r.value, p.value)
+		return &PointEd25519{value}
+	} else {
+		return nil
+	}
+}
+
+// MangleScalarBitsAndMulByBasepointToProducePublicKey
+// is a function for mangling the bits of a (formerly
+// mathematically well-defined) "scalar" and multiplying it to produce a
+// public key.
+func (p *PointEd25519) MangleScalarBitsAndMulByBasepointToProducePublicKey(rhs *ScalarEd25519) *PointEd25519 {
+	data := rhs.value.Bytes()
+	s, err := edwards25519.NewScalar().SetBytesWithClamping(data[:])
+	if err != nil {
+		return nil
+	}
+	value := edwards25519.NewIdentityPoint().ScalarBaseMult(s)
+	return &PointEd25519{value}
+}
+
+func (p *PointEd25519) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointEd25519)
+	if ok {
+		// We would like to check that the point (X/Z, Y/Z) is equal to
+		// the point (X'/Z', Y'/Z') without converting into affine
+		// coordinates (x, y) and (x', y'), which requires two inversions.
+		// We have that X = xZ and X' = x'Z'. Thus, x = x' is equivalent to
+		// (xZ)Z' = (x'Z')Z, and similarly for the y-coordinate.
+		return p.value.Equal(r.value) == 1
+		//lhs1 := new(ed.FieldElement).Mul(&p.value.X, &r.value.Z)
+		//rhs1 := new(ed.FieldElement).Mul(&r.value.X, &p.value.Z)
+		//lhs2 := new(ed.FieldElement).Mul(&p.value.Y, &r.value.Z)
+		//rhs2 := new(ed.FieldElement).Mul(&r.value.Y, &p.value.Z)
+		//
+		//return lhs1.Equals(rhs1) && lhs2.Equals(rhs2)
+	} else {
+		return false
+	}
+}
+
+func (p *PointEd25519) Set(x, y *big.Int) (Point, error) {
+	// check is identity
+	xx := subtle.ConstantTimeCompare(x.Bytes(), []byte{})
+	yy := subtle.ConstantTimeCompare(y.Bytes(), []byte{})
+	if (xx | yy) == 1 {
+		return p.Identity(), nil
+	}
+	xElem := new(ed.FieldElement).SetBigInt(x)
+	yElem := new(ed.FieldElement).SetBigInt(y)
+
+	var data [32]byte
+	var affine [64]byte
+	xElem.BytesInto(&data)
+	copy(affine[:32], data[:])
+	yElem.BytesInto(&data)
+	copy(affine[32:], data[:])
+	return p.FromAffineUncompressed(affine[:])
+}
+
+// sqrtRatio sets r to the non-negative square root of the ratio of u and v.
+//
+// If u/v is square, sqrtRatio returns r and 1. If u/v is not square, SqrtRatio
+// sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00,
+// and returns r and 0.
+func sqrtRatio(u, v *ed.FieldElement) (r *ed.FieldElement, wasSquare bool) {
+	var sqrtM1 = ed.FieldElement{
+		533094393274173, 2016890930128738, 18285341111199,
+		134597186663265, 1486323764102114,
+	}
+	a := new(ed.FieldElement)
+	b := new(ed.FieldElement)
+	r = new(ed.FieldElement)
+
+	// r = (u * v3) * (u * v7)^((p-5)/8)
+	v2 := a.Square(v)
+	uv3 := b.Mul(u, b.Mul(v2, v))
+	uv7 := a.Mul(uv3, a.Square(v2))
+	r.Mul(uv3, r.Exp22523(uv7))
+
+	check := a.Mul(v, a.Square(r)) // check = v * r^2
+
+	uNeg := b.Neg(u)
+	correctSignSqrt := check.Equals(u)
+	flippedSignSqrt := check.Equals(uNeg)
+	flippedSignSqrtI := check.Equals(uNeg.Mul(uNeg, &sqrtM1))
+
+	rPrime := b.Mul(r, &sqrtM1) // r_prime = SQRT_M1 * r
+	// r = CT_SELECT(r_prime IF flipped_sign_sqrt | flipped_sign_sqrt_i ELSE r)
+	cselect(r, rPrime, r, flippedSignSqrt || flippedSignSqrtI)
+
+	r.Abs(r) // Choose the nonnegative square root.
+	return r, correctSignSqrt || flippedSignSqrt
+}
+
+// cselect sets v to a if cond == 1, and to b if cond == 0.
+func cselect(v, a, b *ed.FieldElement, cond bool) *ed.FieldElement {
+	const mask64Bits uint64 = (1 << 64) - 1
+
+	m := uint64(0)
+	if cond {
+		m = mask64Bits
+	}
+
+	v[0] = (m & a[0]) | (^m & b[0])
+	v[1] = (m & a[1]) | (^m & b[1])
+	v[2] = (m & a[2]) | (^m & b[2])
+	v[3] = (m & a[3]) | (^m & b[3])
+	v[4] = (m & a[4]) | (^m & b[4])
+	return v
+}
+
+func (p *PointEd25519) ToAffineCompressed() []byte {
+	return p.value.Bytes()
+}
+
+func (p *PointEd25519) ToAffineUncompressed() []byte {
+	x, y, z, _ := p.value.ExtendedCoordinates()
+	recip := new(field.Element).Invert(z)
+	x.Multiply(x, recip)
+	y.Multiply(y, recip)
+	var out [64]byte
+	copy(out[:32], x.Bytes())
+	copy(out[32:], y.Bytes())
+	return out[:]
+}
+
+func (p *PointEd25519) FromAffineCompressed(inBytes []byte) (Point, error) {
+	pt, err := edwards25519.NewIdentityPoint().SetBytes(inBytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointEd25519{value: pt}, nil
+}
+
+func (p *PointEd25519) FromAffineUncompressed(inBytes []byte) (Point, error) {
+	if len(inBytes) != 64 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	if bytes.Equal(inBytes, []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}) {
+		return &PointEd25519{value: edwards25519.NewIdentityPoint()}, nil
+	}
+	x, err := new(field.Element).SetBytes(inBytes[:32])
+	if err != nil {
+		return nil, err
+	}
+	y, err := new(field.Element).SetBytes(inBytes[32:])
+	if err != nil {
+		return nil, err
+	}
+	z := new(field.Element).One()
+	t := new(field.Element).Multiply(x, y)
+	value, err := edwards25519.NewIdentityPoint().SetExtendedCoordinates(x, y, z, t)
+	if err != nil {
+		return nil, err
+	}
+	return &PointEd25519{value}, nil
+}
+
+func (p *PointEd25519) CurveName() string {
+	return ED25519Name
+}
+
+func (p *PointEd25519) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nScalars := make([]*edwards25519.Scalar, len(scalars))
+	nPoints := make([]*edwards25519.Point, len(points))
+	for i, sc := range scalars {
+		s, err := edwards25519.NewScalar().SetCanonicalBytes(sc.Bytes())
+		if err != nil {
+			return nil
+		}
+		nScalars[i] = s
+	}
+	for i, pt := range points {
+		pp, ok := pt.(*PointEd25519)
+		if !ok {
+			return nil
+		}
+		nPoints[i] = pp.value
+	}
+	pt := edwards25519.NewIdentityPoint().MultiScalarMult(nScalars, nPoints)
+	return &PointEd25519{value: pt}
+}
+
+func (p *PointEd25519) VarTimeDoubleScalarBaseMult(a Scalar, A Point, b Scalar) Point {
+	AA, ok := A.(*PointEd25519)
+	if !ok {
+		return nil
+	}
+	aa, ok := a.(*ScalarEd25519)
+	if !ok {
+		return nil
+	}
+	bb, ok := b.(*ScalarEd25519)
+	if !ok {
+		return nil
+	}
+	value := edwards25519.NewIdentityPoint().VarTimeDoubleScalarBaseMult(aa.value, AA.value, bb.value)
+	return &PointEd25519{value}
+}
+
+func (p *PointEd25519) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointEd25519) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointEd25519)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointEd25519) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointEd25519) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointEd25519)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointEd25519) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointEd25519) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointEd25519)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.value = P.value
+	return nil
+}
+
+func (p *PointEd25519) GetEdwardsPoint() *edwards25519.Point {
+	return edwards25519.NewIdentityPoint().Set(p.value)
+}
+
+func (p *PointEd25519) SetEdwardsPoint(pt *edwards25519.Point) *PointEd25519 {
+	return &PointEd25519{value: edwards25519.NewIdentityPoint().Set(pt)}
+}
+
+// Attempt to convert to an `EdwardsPoint`, using the supplied
+// choice of sign for the `EdwardsPoint`.
+// * `sign`: a `u8` donating the desired sign of the resulting
+//   `EdwardsPoint`.  `0` denotes positive and `1` negative.
+func toEdwards(u *ed.FieldElement, sign byte) *PointEd25519 {
+	one := new(ed.FieldElement).SetOne()
+	// To decompress the Montgomery u coordinate to an
+	// `EdwardsPoint`, we apply the birational map to obtain the
+	// Edwards y coordinate, then do Edwards decompression.
+	//
+	// The birational map is y = (u-1)/(u+1).
+	//
+	// The exceptional points are the zeros of the denominator,
+	// i.e., u = -1.
+	//
+	// But when u = -1, v^2 = u*(u^2+486662*u+1) = 486660.
+	//
+	// Since this is nonsquare mod p, u = -1 corresponds to a point
+	// on the twist, not the curve, so we can reject it early.
+	if u.Equals(new(ed.FieldElement).Neg(one)) {
+		return nil
+	}
+
+	// y = (u-1)/(u+1)
+	yLhs := new(ed.FieldElement).Sub(u, one)
+	yRhs := new(ed.FieldElement).Add(u, one)
+	yInv := new(ed.FieldElement).Inverse(yRhs)
+	y := new(ed.FieldElement).Mul(yLhs, yInv)
+	yBytes := y.Bytes()
+	yBytes[31] ^= sign << 7
+
+	pt, err := edwards25519.NewIdentityPoint().SetBytes(yBytes[:])
+	if err != nil {
+		return nil
+	}
+	pt.MultByCofactor(pt)
+	return &PointEd25519{value: pt}
+}
+
+// Perform the Elligator2 mapping to a Montgomery point encoded as a 32 byte value
+//
+// See <https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-11#section-6.7.1>
+func elligatorEncode(r0 *ed.FieldElement) *ed.FieldElement {
+	montgomeryA := &ed.FieldElement{
+		486662, 0, 0, 0, 0,
+	}
+	// montgomeryANeg is equal to -486662.
+	montgomeryANeg := &ed.FieldElement{2251799813198567,
+		2251799813685247,
+		2251799813685247,
+		2251799813685247,
+		2251799813685247}
+	t := new(ed.FieldElement)
+	one := new(ed.FieldElement).SetOne()
+	// 2r^2
+	d1 := new(ed.FieldElement).Add(one, t.DoubledSquare(r0))
+	// A/(1+2r^2)
+	d := new(ed.FieldElement).Mul(montgomeryANeg, t.Inverse(d1))
+	dsq := new(ed.FieldElement).Square(d)
+	au := new(ed.FieldElement).Mul(montgomeryA, d)
+
+	inner := new(ed.FieldElement).Add(dsq, au)
+	inner.Add(inner, one)
+
+	// d^3 + Ad^2 + d
+	eps := new(ed.FieldElement).Mul(d, inner)
+	_, wasSquare := sqrtRatio(eps, one)
+
+	zero := new(ed.FieldElement).SetZero()
+	aTemp := new(ed.FieldElement).SetZero()
+	// 0 or A if non-square
+	cselect(aTemp, zero, montgomeryA, wasSquare)
+	// d, or d+A if non-square
+	u := new(ed.FieldElement).Add(d, aTemp)
+	// d or -d-A if non-square
+	cselect(u, u, new(ed.FieldElement).Neg(u), wasSquare)
+	return u
+}
diff --git a/pkg/core/curves/ed25519_curve_test.go b/pkg/core/curves/ed25519_curve_test.go
new file mode 100644
index 00000000..1b913976
--- /dev/null
+++ b/pkg/core/curves/ed25519_curve_test.go
@@ -0,0 +1,401 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	crand "crypto/rand"
+	"encoding/hex"
+	ed "filippo.io/edwards25519"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"testing"
+)
+
+func TestScalarEd25519Random(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Scalar.Random(testRng())
+	s, ok := sc.(*ScalarEd25519)
+	assert.True(t, ok)
+	expected := toRSc("feaa6a9d6dda758da6145f7d411a3af9f8a120698e0093faa97085b384c3f00e")
+	assert.Equal(t, s.value.Equal(expected), 1)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := ed25519.Scalar.Random(crand.Reader)
+		_, ok := sc.(*ScalarEd25519)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsZero())
+	}
+}
+
+func TestScalarEd25519Hash(t *testing.T) {
+	var b [32]byte
+	ed25519 := ED25519()
+	sc := ed25519.Scalar.Hash(b[:])
+	s, ok := sc.(*ScalarEd25519)
+	assert.True(t, ok)
+	expected := toRSc("9d574494a02d72f5ff311cf0fb844d0fdd6103b17255274e029bdeed7207d409")
+	assert.Equal(t, s.value.Equal(expected), 1)
+}
+
+func TestScalarEd25519Zero(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Scalar.Zero()
+	assert.True(t, sc.IsZero())
+	assert.True(t, sc.IsEven())
+}
+
+func TestScalarEd25519One(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Scalar.One()
+	assert.True(t, sc.IsOne())
+	assert.True(t, sc.IsOdd())
+}
+
+func TestScalarEd25519New(t *testing.T) {
+	ed25519 := ED25519()
+	three := ed25519.Scalar.New(3)
+	assert.True(t, three.IsOdd())
+	four := ed25519.Scalar.New(4)
+	assert.True(t, four.IsEven())
+	neg1 := ed25519.Scalar.New(-1)
+	assert.True(t, neg1.IsEven())
+	neg2 := ed25519.Scalar.New(-2)
+	assert.True(t, neg2.IsOdd())
+}
+
+func TestScalarEd25519Square(t *testing.T) {
+	ed25519 := ED25519()
+	three := ed25519.Scalar.New(3)
+	nine := ed25519.Scalar.New(9)
+	assert.Equal(t, three.Square().Cmp(nine), 0)
+}
+
+func TestScalarEd25519Cube(t *testing.T) {
+	ed25519 := ED25519()
+	three := ed25519.Scalar.New(3)
+	twentySeven := ed25519.Scalar.New(27)
+	assert.Equal(t, three.Cube().Cmp(twentySeven), 0)
+}
+
+func TestScalarEd25519Double(t *testing.T) {
+	ed25519 := ED25519()
+	three := ed25519.Scalar.New(3)
+	six := ed25519.Scalar.New(6)
+	assert.Equal(t, three.Double().Cmp(six), 0)
+}
+
+func TestScalarEd25519Neg(t *testing.T) {
+	ed25519 := ED25519()
+	one := ed25519.Scalar.One()
+	neg1 := ed25519.Scalar.New(-1)
+	assert.Equal(t, one.Neg().Cmp(neg1), 0)
+	lotsOfThrees := ed25519.Scalar.New(333333)
+	expected := ed25519.Scalar.New(-333333)
+	assert.Equal(t, lotsOfThrees.Neg().Cmp(expected), 0)
+}
+
+func TestScalarEd25519Invert(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	actual, _ := nine.Invert()
+	sa, _ := actual.(*ScalarEd25519)
+	expected := toRSc("c3d9c4db0516043013b1e1ce8637dc92e3388ee3388ee3388ee3388ee3388e03")
+	assert.Equal(t, sa.value.Equal(expected), 1)
+}
+
+func TestScalarEd25519Sqrt(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	actual, err := nine.Sqrt()
+	sa, _ := actual.(*ScalarEd25519)
+	expected := toRSc("03")
+	assert.NoError(t, err)
+	assert.Equal(t, sa.value.Equal(expected), 1)
+}
+
+func TestScalarEd25519Add(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	six := ed25519.Scalar.New(6)
+	fifteen := nine.Add(six)
+	assert.NotNil(t, fifteen)
+	expected := ed25519.Scalar.New(15)
+	assert.Equal(t, expected.Cmp(fifteen), 0)
+
+	upper := ed25519.Scalar.New(-3)
+	actual := upper.Add(nine)
+	assert.NotNil(t, actual)
+	assert.Equal(t, actual.Cmp(six), 0)
+}
+
+func TestScalarEd25519Sub(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	six := ed25519.Scalar.New(6)
+	expected := ed25519.Scalar.New(-3)
+
+	actual := six.Sub(nine)
+	assert.Equal(t, expected.Cmp(actual), 0)
+
+	actual = nine.Sub(six)
+	assert.Equal(t, actual.Cmp(ed25519.Scalar.New(3)), 0)
+}
+
+func TestScalarEd25519Mul(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	six := ed25519.Scalar.New(6)
+	actual := nine.Mul(six)
+	assert.Equal(t, actual.Cmp(ed25519.Scalar.New(54)), 0)
+
+	upper := ed25519.Scalar.New(-1)
+	assert.Equal(t, upper.Mul(upper).Cmp(ed25519.Scalar.New(1)), 0)
+}
+
+func TestScalarEd25519Div(t *testing.T) {
+	ed25519 := ED25519()
+	nine := ed25519.Scalar.New(9)
+	actual := nine.Div(nine)
+	assert.Equal(t, actual.Cmp(ed25519.Scalar.New(1)), 0)
+	assert.Equal(t, ed25519.Scalar.New(54).Div(nine).Cmp(ed25519.Scalar.New(6)), 0)
+}
+
+func TestScalarEd25519Serialize(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Scalar.New(255)
+	sequence := sc.Bytes()
+	assert.Equal(t, len(sequence), 32)
+	assert.Equal(t, sequence, []byte{0xff, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0})
+	ret, err := ed25519.Scalar.SetBytes(sequence)
+	assert.NoError(t, err)
+	assert.Equal(t, ret.Cmp(sc), 0)
+
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc = ed25519.Scalar.Random(crand.Reader)
+		sequence = sc.Bytes()
+		assert.Equal(t, len(sequence), 32)
+		ret, err = ed25519.Scalar.SetBytes(sequence)
+		assert.NoError(t, err)
+		assert.Equal(t, ret.Cmp(sc), 0)
+	}
+}
+
+func TestScalarEd25519Nil(t *testing.T) {
+	ed25519 := ED25519()
+	one := ed25519.Scalar.New(1)
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, one.Div(nil))
+	assert.Nil(t, ed25519.Scalar.Random(nil))
+	assert.Equal(t, one.Cmp(nil), -2)
+	_, err := ed25519.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointEd25519Random(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Point.Random(testRng())
+	s, ok := sc.(*PointEd25519)
+	assert.True(t, ok)
+	expected := toRPt("6011540c6231421a70ced5f577432531f198d318facfaad6e52cc42fba6e6fc5")
+	assert.True(t, s.Equal(&PointEd25519{expected}))
+	// Try 25 random values
+	for i := 0; i < 25; i++ {
+		sc := ed25519.Point.Random(crand.Reader)
+		_, ok := sc.(*PointEd25519)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+		pBytes := sc.ToAffineCompressed()
+		_, err := ed.NewIdentityPoint().SetBytes(pBytes)
+		assert.NoError(t, err)
+	}
+}
+
+func TestPointEd25519Hash(t *testing.T) {
+	var b [32]byte
+	ed25519 := ED25519()
+	sc := ed25519.Point.Hash(b[:])
+	s, ok := sc.(*PointEd25519)
+	assert.True(t, ok)
+	expected := toRPt("b4d75c3bb03ca644ab6c6d2a955c911003d8cfa719415de93a6b85eeb0c8dd97")
+	assert.True(t, s.Equal(&PointEd25519{expected}))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		_, _ = crand.Read(b[:])
+		sc = ed25519.Point.Hash(b[:])
+		assert.NotNil(t, sc)
+	}
+}
+
+func TestPointEd25519Identity(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+}
+
+func TestPointEd25519Generator(t *testing.T) {
+	ed25519 := ED25519()
+	sc := ed25519.Point.Generator()
+	s, ok := sc.(*PointEd25519)
+	assert.True(t, ok)
+	assert.Equal(t, s.ToAffineCompressed(), []byte{0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66})
+}
+
+func TestPointEd25519Set(t *testing.T) {
+	ed25519 := ED25519()
+	iden, err := ed25519.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	xBytes, _ := hex.DecodeString("1ad5258f602d56c9b2a7259560c72c695cdcd6fd31e2a4c0fe536ecdd3366921")
+	yBytes, _ := hex.DecodeString("5866666666666666666666666666666666666666666666666666666666666666")
+	x := new(big.Int).SetBytes(internal.ReverseScalarBytes(xBytes))
+	y := new(big.Int).SetBytes(internal.ReverseScalarBytes(yBytes))
+	newPoint, err := ed25519.Point.Set(x, y)
+	assert.NoError(t, err)
+	assert.NotEqualf(t, iden, newPoint, "after setting valid x and y, the point should NOT be identity point")
+
+	emptyX := new(big.Int).SetBytes(internal.ReverseScalarBytes([]byte{}))
+	identityPoint, err := ed25519.Point.Set(emptyX, y)
+	assert.NoError(t, err)
+	assert.Equalf(t, iden, identityPoint, "When x is empty, the point will be identity")
+}
+
+func TestPointEd25519Double(t *testing.T) {
+	ed25519 := ED25519()
+	g := ed25519.Point.Generator()
+	g2 := g.Double()
+	assert.True(t, g2.Equal(g.Mul(ed25519.Scalar.New(2))))
+	i := ed25519.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointEd25519Neg(t *testing.T) {
+	ed25519 := ED25519()
+	g := ed25519.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(ed25519.Point.Generator()))
+	assert.True(t, ed25519.Point.Identity().Neg().Equal(ed25519.Point.Identity()))
+}
+
+func TestPointEd25519Add(t *testing.T) {
+	ed25519 := ED25519()
+	pt := ed25519.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(ed25519.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointEd25519Sub(t *testing.T) {
+	ed25519 := ED25519()
+	g := ed25519.Point.Generator()
+	pt := ed25519.Point.Generator().Mul(ed25519.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointEd25519Mul(t *testing.T) {
+	ed25519 := ED25519()
+	g := ed25519.Point.Generator()
+	pt := ed25519.Point.Generator().Mul(ed25519.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointEd25519Serialize(t *testing.T) {
+	ed25519 := ED25519()
+	ss := ed25519.Scalar.Random(testRng())
+	g := ed25519.Point.Generator()
+
+	ppt := g.Mul(ss)
+	expectedC := []byte{0x7f, 0x5b, 0xa, 0xd9, 0xb8, 0xce, 0xb7, 0x7, 0x4c, 0x10, 0xc8, 0xb4, 0x27, 0xe8, 0xd2, 0x28, 0x50, 0x42, 0x6c, 0x0, 0x8a, 0x3, 0x72, 0x2b, 0x7c, 0x3c, 0x37, 0x6f, 0xf8, 0x8f, 0x42, 0x5d}
+	expectedU := []byte{0x70, 0xad, 0x4, 0xa1, 0x6, 0x8, 0x9f, 0x47, 0xe1, 0xe8, 0x9b, 0x9c, 0x81, 0x5a, 0xfb, 0xb9, 0x85, 0x6a, 0x2c, 0xa, 0xbc, 0xff, 0xe, 0xc6, 0xa0, 0xb0, 0xac, 0x75, 0xc, 0xd8, 0x59, 0x53, 0x7f, 0x5b, 0xa, 0xd9, 0xb8, 0xce, 0xb7, 0x7, 0x4c, 0x10, 0xc8, 0xb4, 0x27, 0xe8, 0xd2, 0x28, 0x50, 0x42, 0x6c, 0x0, 0x8a, 0x3, 0x72, 0x2b, 0x7c, 0x3c, 0x37, 0x6f, 0xf8, 0x8f, 0x42, 0x5d}
+	assert.Equal(t, ppt.ToAffineCompressed(), expectedC)
+	assert.Equal(t, ppt.ToAffineUncompressed(), expectedU)
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := ed25519.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 32)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 64)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointEd25519Nil(t *testing.T) {
+	ed25519 := ED25519()
+	one := ed25519.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, ed25519.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := ed25519.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointEd25519SumOfProducts(t *testing.T) {
+	lhs := new(PointEd25519).Generator().Mul(new(ScalarEd25519).New(50))
+	points := make([]Point, 5)
+	for i := range points {
+		points[i] = new(PointEd25519).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarEd25519).New(8),
+		new(ScalarEd25519).New(9),
+		new(ScalarEd25519).New(10),
+		new(ScalarEd25519).New(11),
+		new(ScalarEd25519).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
+
+func TestPointEd25519VarTimeDoubleScalarBaseMult(t *testing.T) {
+	curve := ED25519()
+	h := curve.Point.Hash([]byte("TestPointEd25519VarTimeDoubleScalarBaseMult"))
+	a := curve.Scalar.New(23)
+	b := curve.Scalar.New(77)
+	H, ok := h.(*PointEd25519)
+	assert.True(t, ok)
+	rhs := H.VarTimeDoubleScalarBaseMult(a, H, b)
+	lhs := h.Mul(a).Add(curve.Point.Generator().Mul(b))
+	assert.True(t, lhs.Equal(rhs))
+}
+
+func toRSc(hx string) *ed.Scalar {
+	e, _ := hex.DecodeString(hx)
+	var data [32]byte
+	copy(data[:], e)
+	value, _ := new(ed.Scalar).SetCanonicalBytes(data[:])
+	return value
+}
+
+func toRPt(hx string) *ed.Point {
+	e, _ := hex.DecodeString(hx)
+	var data [32]byte
+	copy(data[:], e)
+	pt, _ := new(PointEd25519).FromAffineCompressed(data[:])
+	return pt.(*PointEd25519).value
+}
diff --git a/pkg/core/curves/field.go b/pkg/core/curves/field.go
new file mode 100644
index 00000000..a0586d63
--- /dev/null
+++ b/pkg/core/curves/field.go
@@ -0,0 +1,280 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// This implementation IS NOT constant time as it leverages math/big for big number operations.
+package curves
+
+import (
+	"crypto/rand"
+	"encoding/json"
+	"fmt"
+	"io"
+	"math/big"
+	"sync"
+)
+
+var ed25519SubGroupOrderOnce sync.Once
+var ed25519SubGroupOrder *big.Int
+
+// Field is a finite field.
+type Field struct {
+	*big.Int
+}
+
+// Element is a group element within a finite field.
+type Element struct {
+	Modulus *Field   `json:"modulus"`
+	Value   *big.Int `json:"value"`
+}
+
+// ElementJSON is used in JSON<>Element conversions.
+// For years, big.Int hasn't properly supported JSON unmarshaling
+// https://github.com/golang/go/issues/28154
+type ElementJSON struct {
+	Modulus string `json:"modulus"`
+	Value   string `json:"value"`
+}
+
+// Marshal Element to JSON
+func (x *Element) MarshalJSON() ([]byte, error) {
+	return json.Marshal(ElementJSON{
+		Modulus: x.Modulus.String(),
+		Value:   x.Value.String(),
+	})
+}
+
+func (x *Element) UnmarshalJSON(bytes []byte) error {
+	var e ElementJSON
+	err := json.Unmarshal(bytes, &e)
+	if err != nil {
+		return err
+	}
+	// Convert the strings to big.Ints
+	modulus, ok := new(big.Int).SetString(e.Modulus, 10)
+	if !ok {
+		return fmt.Errorf("failed to unmarshal modulus string '%v' to big.Int", e.Modulus)
+	}
+	x.Modulus = &Field{modulus}
+	x.Value, ok = new(big.Int).SetString(e.Value, 10)
+	if !ok {
+		return fmt.Errorf("failed to unmarshal value string '%v' to big.Int", e.Value)
+	}
+	return nil
+}
+
+// The probability of returning true for a randomly chosen
+// non-prime is at most ¼ⁿ. 64 is a widely used standard
+// that is more than sufficient.
+const millerRabinRounds = 64
+
+// New is a constructor for a Field.
+func NewField(modulus *big.Int) *Field {
+	// For our purposes we never expect to be dealing with a non-prime field. This provides some protection against
+	// accidentally doing that.
+	if !modulus.ProbablyPrime(millerRabinRounds) {
+		panic(fmt.Sprintf("modulus: %x is not a prime", modulus))
+	}
+
+	return &Field{modulus}
+}
+
+func newElement(field *Field, value *big.Int) *Element {
+	if !field.IsValid(value) {
+		panic(fmt.Sprintf("value: %x is not within field: %x", value, field))
+	}
+
+	return &Element{field, value}
+}
+
+// IsValid returns whether or not the value is within [0, modulus)
+func (f Field) IsValid(value *big.Int) bool {
+	// value < modulus && value >= 0
+	return value.Cmp(f.Int) < 0 && value.Sign() >= 0
+}
+
+func (f Field) NewElement(value *big.Int) *Element {
+	return newElement(&f, value)
+}
+
+func (f Field) Zero() *Element {
+	return newElement(&f, big.NewInt(0))
+}
+
+func (f Field) One() *Element {
+	return newElement(&f, big.NewInt(1))
+}
+
+func (f Field) RandomElement(r io.Reader) (*Element, error) {
+	if r == nil {
+		r = rand.Reader
+	}
+	var randInt *big.Int
+	var err error
+	// Ed25519 needs to do special handling
+	// in case the value is used in
+	// Scalar multiplications with points
+	if f.Int.Cmp(Ed25519Order()) == 0 {
+		scalar := NewEd25519Scalar()
+		randInt, err = scalar.RandomWithReader(r)
+	} else {
+		// Read a random integer within the field. This is defined as [0, max) so we don't need to
+		// explicitly check it is within the field. If it is not, NewElement will panic anyways.
+		randInt, err = rand.Int(r, f.Int)
+	}
+	if err != nil {
+		return nil, err
+	}
+	return newElement(&f, randInt), nil
+}
+
+// ElementFromBytes initializes a new field element from big-endian bytes
+func (f Field) ElementFromBytes(bytes []byte) *Element {
+	return newElement(&f, new(big.Int).SetBytes(bytes))
+}
+
+// ReducedElementFromBytes initializes a new field element from big-endian bytes and reduces it by
+// the modulus of the field.
+//
+// WARNING: If this is used with cryptographic constructions which rely on a uniform distribution of
+// values, this may introduce a bias to the value of the returned field element. This happens when
+// the integer range of the provided bytes is not an integer multiple of the field order.
+//
+// Assume we are working in field which a modulus of 3 and the range of the uniform random bytes we
+// provide as input is 5. Thus, the set of field elements is {0, 1, 2} and the set of integer values
+// for the input bytes is: {0, 1, 2, 3, 4}. What is the distribution of the output values produced
+// by this function?
+//
+//   ReducedElementFromBytes(0) => 0
+//   ReducedElementFromBytes(1) => 1
+//   ReducedElementFromBytes(2) => 2
+//   ReducedElementFromBytes(3) => 0
+//   ReducedElementFromBytes(4) => 1
+//
+// For a value space V and random value v, a uniform distribution is defined as P[V = v] = 1/|V|
+// where |V| is to the order of the field. Using the results from above, we see that P[v = 0] = 2/5,
+// P[v = 1] = 2/5, and P[v = 2] = 1/5. For a uniform distribution we would expect these to each be
+// equal to 1/3. As they do not, this does not return uniform output for that example.
+//
+// To see why this is okay if the range is a multiple of the field order, change the input range to
+// 6 and notice that now each output has a probability of 2/6 = 1/3, and the output is uniform.
+func (f Field) ReducedElementFromBytes(bytes []byte) *Element {
+	value := new(big.Int).SetBytes(bytes)
+	value.Mod(value, f.Int)
+	return newElement(&f, value)
+}
+
+func (x Element) Field() *Field {
+	return x.Modulus
+}
+
+// Add returns the sum x+y
+func (x Element) Add(y *Element) *Element {
+	x.validateFields(y)
+
+	sum := new(big.Int).Add(x.Value, y.Value)
+	sum.Mod(sum, x.Modulus.Int)
+	return newElement(x.Modulus, sum)
+}
+
+// Sub returns the difference x-y
+func (x Element) Sub(y *Element) *Element {
+	x.validateFields(y)
+
+	difference := new(big.Int).Sub(x.Value, y.Value)
+	difference.Mod(difference, x.Modulus.Int)
+	return newElement(x.Modulus, difference)
+}
+
+// Neg returns the field negation
+func (x Element) Neg() *Element {
+	z := new(big.Int).Neg(x.Value)
+	z.Mod(z, x.Modulus.Int)
+	return newElement(x.Modulus, z)
+}
+
+// Mul returns the product x*y
+func (x Element) Mul(y *Element) *Element {
+	x.validateFields(y)
+
+	product := new(big.Int).Mul(x.Value, y.Value)
+	product.Mod(product, x.Modulus.Int)
+	return newElement(x.Modulus, product)
+}
+
+// Div returns the quotient x/y
+func (x Element) Div(y *Element) *Element {
+	x.validateFields(y)
+
+	yInv := new(big.Int).ModInverse(y.Value, x.Modulus.Int)
+	quotient := new(big.Int).Mul(x.Value, yInv)
+	quotient.Mod(quotient, x.Modulus.Int)
+	return newElement(x.Modulus, quotient)
+}
+
+// Pow computes x^y reduced by the modulus
+func (x Element) Pow(y *Element) *Element {
+	x.validateFields(y)
+
+	return newElement(x.Modulus, new(big.Int).Exp(x.Value, y.Value, x.Modulus.Int))
+}
+
+func (x Element) Invert() *Element {
+	return newElement(x.Modulus, new(big.Int).ModInverse(x.Value, x.Modulus.Int))
+}
+
+func (x Element) Sqrt() *Element {
+	return newElement(x.Modulus, new(big.Int).ModSqrt(x.Value, x.Modulus.Int))
+}
+
+// BigInt returns value as a big.Int
+func (x Element) BigInt() *big.Int {
+	return x.Value
+}
+
+// Bytes returns the value as bytes
+func (x Element) Bytes() []byte {
+	return x.BigInt().Bytes()
+}
+
+// IsEqual returns x == y
+func (x Element) IsEqual(y *Element) bool {
+	if !x.isEqualFields(y) {
+		return false
+	}
+
+	return x.Value.Cmp(y.Value) == 0
+}
+
+// Clone returns a new copy of the element
+func (x Element) Clone() *Element {
+	return x.Modulus.ElementFromBytes(x.Bytes())
+}
+
+func (x Element) isEqualFields(y *Element) bool {
+	return x.Modulus.Int.Cmp(y.Modulus.Int) == 0
+}
+
+func (x Element) validateFields(y *Element) {
+	if !x.isEqualFields(y) {
+		panic("fields must match for valid binary operation")
+	}
+}
+
+// SubgroupOrder returns the order of the Ed25519 base Point.
+func Ed25519Order() *big.Int {
+	ed25519SubGroupOrderOnce.Do(func() {
+		order, ok := new(big.Int).SetString(
+			"1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
+			16,
+		)
+		if !ok {
+			panic("invalid hex string provided. This should never happen as it is constant.")
+		}
+		ed25519SubGroupOrder = order
+	})
+
+	return ed25519SubGroupOrder
+}
diff --git a/pkg/core/curves/field_test.go b/pkg/core/curves/field_test.go
new file mode 100644
index 00000000..0b26f17d
--- /dev/null
+++ b/pkg/core/curves/field_test.go
@@ -0,0 +1,295 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"encoding/json"
+	"errors"
+	"fmt"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	one                = big.NewInt(1)
+	modulus, modulusOk = new(big.Int).SetString(
+		"1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
+		16,
+	)
+	oneBelowModulus = zero().Sub(modulus, one)
+	oneAboveModulus = zero().Add(modulus, one)
+	field25519      = NewField(modulus)
+)
+
+type buggedReader struct{}
+
+func (r buggedReader) Read(p []byte) (n int, err error) {
+	return 0, errors.New("EOF")
+}
+
+func zero() *big.Int {
+	return new(big.Int)
+}
+
+func assertElementZero(t *testing.T, e *Element) {
+	assert.Equal(t, zero().Bytes(), e.Bytes())
+}
+
+type binaryOperation func(*Element) *Element
+
+func assertUnequalFieldsPanic(t *testing.T, b binaryOperation) {
+	altField := NewField(big.NewInt(23))
+	altElement := altField.NewElement(one)
+
+	assert.PanicsWithValue(
+		t,
+		"fields must match for valid binary operation",
+		func() { b(altElement) },
+	)
+}
+
+func TestFieldModulus(t *testing.T) {
+	assert.True(t, modulusOk)
+}
+
+func TestNewField(t *testing.T) {
+	assert.PanicsWithValue(
+		t,
+		fmt.Sprintf("modulus: %x is not a prime", oneBelowModulus),
+		func() { NewField(oneBelowModulus) },
+	)
+	assert.NotPanics(
+		t,
+		func() { NewField(modulus) },
+	)
+}
+
+func TestNewElement(t *testing.T) {
+	assert.PanicsWithValue(
+		t,
+		fmt.Sprintf("value: %x is not within field: %x", modulus, field25519.Int),
+		func() { newElement(field25519, modulus) },
+	)
+	assert.NotPanics(
+		t,
+		func() { newElement(field25519, oneBelowModulus) },
+	)
+}
+
+func TestElementIsValid(t *testing.T) {
+	assert.False(t, field25519.IsValid(zero().Neg(one)))
+	assert.False(t, field25519.IsValid(modulus))
+	assert.False(t, field25519.IsValid(oneAboveModulus))
+	assert.True(t, field25519.IsValid(oneBelowModulus))
+}
+
+func TestFieldNewElement(t *testing.T) {
+	element := field25519.NewElement(oneBelowModulus)
+
+	assert.Equal(t, oneBelowModulus, element.Value)
+	assert.Equal(t, field25519, element.Field())
+}
+
+func TestZeroElement(t *testing.T) {
+	assert.Equal(t, zero(), field25519.Zero().Value)
+	assert.Equal(t, field25519, field25519.Zero().Field())
+}
+
+func TestOneElement(t *testing.T) {
+	assert.Equal(t, field25519.One().Value, one)
+	assert.Equal(t, field25519.One().Field(), field25519)
+}
+
+func TestRandomElement(t *testing.T) {
+	randomElement1, err := field25519.RandomElement(nil)
+	require.NoError(t, err)
+	randomElement2, err := field25519.RandomElement(nil)
+	require.NoError(t, err)
+	randomElement3, err := field25519.RandomElement(new(buggedReader))
+	require.Error(t, err)
+
+	assert.Equal(t, field25519, randomElement1.Field())
+	assert.Equal(t, field25519, randomElement2.Field())
+	assert.NotEqual(t, randomElement1.Value, randomElement2.Value)
+	assert.Nil(t, randomElement3)
+}
+
+func TestElementFromBytes(t *testing.T) {
+	element := field25519.ElementFromBytes(oneBelowModulus.Bytes())
+
+	assert.Equal(t, field25519, element.Field())
+	assert.Equal(t, oneBelowModulus, element.Value)
+}
+
+func TestReducedElementFromBytes(t *testing.T) {
+	element := field25519.ReducedElementFromBytes(oneBelowModulus.Bytes())
+
+	assert.Equal(t, field25519, element.Field())
+	assert.Equal(t, oneBelowModulus, element.Value)
+
+	element = field25519.ReducedElementFromBytes(oneAboveModulus.Bytes())
+
+	assert.Equal(t, field25519, element.Field())
+	assert.Equal(t, one, element.Value)
+}
+
+func TestAddElement(t *testing.T) {
+	element1 := field25519.NewElement(one)
+	element2 := field25519.NewElement(big.NewInt(2))
+	element3 := field25519.NewElement(oneBelowModulus)
+	element4 := &Element{field25519, modulus}
+
+	assert.Equal(t, element2, element1.Add(element1))
+	assert.Equal(t, big.NewInt(3), element1.Add(element2).Value)
+	assert.Equal(t, big.NewInt(3), element2.Add(element1).Value)
+	assert.Equal(t, one, element1.Add(element4).Value)
+	assert.Equal(t, one, element3.Add(element2).Value)
+	assertElementZero(t, element1.Add(element3))
+	assertUnequalFieldsPanic(t, element1.Add)
+}
+
+func TestSubElement(t *testing.T) {
+	element1 := field25519.NewElement(one)
+	element2 := field25519.NewElement(big.NewInt(2))
+	element3 := field25519.NewElement(oneBelowModulus)
+	element4 := &Element{field25519, modulus}
+
+	assertElementZero(t, element1.Sub(element1))
+	assert.Equal(t, element3, element1.Sub(element2))
+	assert.Equal(t, element1, element2.Sub(element1))
+	assert.Equal(t, element1, element1.Sub(element4))
+	assert.Equal(t, element3, element4.Sub(element1))
+	assert.Equal(t, element1, element4.Sub(element3))
+	assert.Equal(t, element3, element3.Sub(element4))
+	assertUnequalFieldsPanic(t, element1.Sub)
+}
+
+func TestMulElement(t *testing.T) {
+	element1 := field25519.NewElement(one)
+	element2 := field25519.NewElement(big.NewInt(2))
+	element3 := field25519.NewElement(oneBelowModulus)
+	element4 := field25519.NewElement(zero())
+	expectedProduct, ok := new(big.Int).SetString(
+		"1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3eb",
+		16,
+	)
+	require.True(t, ok)
+
+	assertElementZero(t, element1.Mul(element4))
+	assertElementZero(t, element4.Mul(element1))
+	assert.Equal(t, element3, element1.Mul(element3))
+	assert.Equal(t, element3, element3.Mul(element1))
+	assert.Equal(t, expectedProduct, element3.Mul(element2).Value)
+	assert.Equal(t, expectedProduct, element2.Mul(element3).Value)
+	assertUnequalFieldsPanic(t, element1.Mul)
+}
+
+func TestDivElement(t *testing.T) {
+	element1 := field25519.NewElement(one)
+	element2 := field25519.NewElement(big.NewInt(2))
+	element3 := field25519.NewElement(oneBelowModulus)
+	element4 := field25519.NewElement(zero())
+	expectedQuotient1, ok := new(big.Int).SetString(
+		"80000000000000000000000000000000a6f7cef517bce6b2c09318d2e7ae9f6",
+		16,
+	)
+	require.True(t, ok)
+	expectedQuotient2, ok := new(big.Int).SetString(
+		"1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3eb",
+		16,
+	)
+	require.True(t, ok)
+
+	assertElementZero(t, element4.Div(element3))
+	assert.Equal(t, element3, element3.Div(element1))
+	assert.Equal(t, expectedQuotient1, element3.Div(element2).Value)
+	assert.Equal(t, expectedQuotient2, element2.Div(element3).Value)
+	assert.Panics(t, func() { element3.Div(element4) })
+	assertUnequalFieldsPanic(t, element1.Div)
+}
+
+func TestIsEqualElement(t *testing.T) {
+	element1 := field25519.NewElement(oneBelowModulus)
+	element2 := field25519.NewElement(big.NewInt(23))
+	element3 := field25519.NewElement(oneBelowModulus)
+	altField := NewField(big.NewInt(23))
+	altElement1 := altField.NewElement(one)
+
+	assert.False(t, element1.IsEqual(element2))
+	assert.True(t, element1.IsEqual(element3))
+	assert.True(t, element1.IsEqual(element1))
+	assert.False(t, element1.IsEqual(altElement1))
+}
+
+func TestBigIntElement(t *testing.T) {
+	element := field25519.NewElement(oneBelowModulus)
+
+	assert.Equal(t, oneBelowModulus, element.BigInt())
+}
+
+func TestBytesElement(t *testing.T) {
+	element := field25519.NewElement(oneBelowModulus)
+
+	assert.Equal(
+		t,
+		[]byte{
+			0x10, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
+			0x0, 0x0, 0x0, 0x0, 0x0, 0x14, 0xde, 0xf9, 0xde, 0xa2,
+			0xf7, 0x9c, 0xd6, 0x58, 0x12, 0x63, 0x1a, 0x5c, 0xf5,
+			0xd3, 0xec,
+		},
+		element.Bytes(),
+	)
+}
+
+func TestCloneElement(t *testing.T) {
+	element := field25519.NewElement(oneBelowModulus)
+	clone := element.Clone()
+
+	assert.Equal(t, clone, element)
+
+	clone.Value.Add(one, one)
+
+	assert.NotEqual(t, clone, element)
+}
+
+// Tests un/marshaling Element
+func TestElementMarshalJsonRoundTrip(t *testing.T) {
+	// TODO: test really large numbers for field25519/value
+	ins := []*Element{
+		newElement(field25519, big.NewInt(300)),
+		newElement(field25519, big.NewInt(300000)),
+		newElement(field25519, big.NewInt(12812798)),
+		newElement(field25519, big.NewInt(17)),
+		newElement(field25519, big.NewInt(5066680)),
+		newElement(field25519, big.NewInt(3005)),
+		newElement(field25519, big.NewInt(317)),
+		newElement(field25519, big.NewInt(323)),
+		newElement(field25519, oneBelowModulus),
+	}
+
+	// Run all the tests!
+	for _, in := range ins {
+		bytes, err := json.Marshal(in)
+		require.NoError(t, err)
+		require.NotNil(t, bytes)
+
+		// Unmarshal and test
+		out := &Element{}
+		err = json.Unmarshal(bytes, &out)
+		require.NoError(t, err)
+		require.NotNil(t, out)
+		require.NotNil(t, out.Modulus)
+		require.NotNil(t, out.Value)
+
+		assert.Equal(t, in.Modulus.Bytes(), out.Modulus.Bytes())
+		assert.Equal(t, in.Value.Bytes(), out.Value.Bytes())
+	}
+}
diff --git a/pkg/core/curves/k256_curve.go b/pkg/core/curves/k256_curve.go
new file mode 100644
index 00000000..8001c57c
--- /dev/null
+++ b/pkg/core/curves/k256_curve.go
@@ -0,0 +1,636 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/btcsuite/btcd/btcec"
+	"io"
+	"math/big"
+)
+
+type ScalarK256 struct {
+	value *big.Int
+}
+
+type PointK256 struct {
+	x, y *big.Int
+}
+
+func (s *ScalarK256) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarK256) Hash(bytes []byte) Scalar {
+	xmd, err := expandMsgXmd(sha256.New(), bytes, []byte("secp256k1_XMD:SHA-256_SSWU_RO_"), 48)
+	if err != nil {
+		return nil
+	}
+	v := new(big.Int).SetBytes(xmd)
+	return &ScalarK256{
+		value: v.Mod(v, btcec.S256().N),
+	}
+}
+
+func (s *ScalarK256) Zero() Scalar {
+	return &ScalarK256{
+		value: big.NewInt(0),
+	}
+}
+
+func (s *ScalarK256) One() Scalar {
+	return &ScalarK256{
+		value: big.NewInt(1),
+	}
+}
+
+func (s *ScalarK256) IsZero() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{}) == 1
+}
+
+func (s *ScalarK256) IsOne() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{1}) == 1
+}
+
+func (s *ScalarK256) IsOdd() bool {
+	return s.value.Bit(0) == 1
+}
+
+func (s *ScalarK256) IsEven() bool {
+	return s.value.Bit(0) == 0
+}
+
+func (s *ScalarK256) New(value int) Scalar {
+	v := big.NewInt(int64(value))
+	if value < 0 {
+		v.Mod(v, btcec.S256().N)
+	}
+	return &ScalarK256{
+		value: v,
+	}
+}
+
+func (s *ScalarK256) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		return s.value.Cmp(r.value)
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarK256) Square() Scalar {
+	return &ScalarK256{
+		value: new(big.Int).Exp(s.value, big.NewInt(2), btcec.S256().N),
+	}
+}
+
+func (s *ScalarK256) Double() Scalar {
+	v := new(big.Int).Add(s.value, s.value)
+	return &ScalarK256{
+		value: v.Mod(v, btcec.S256().N),
+	}
+}
+
+func (s *ScalarK256) Invert() (Scalar, error) {
+	return &ScalarK256{
+		value: new(big.Int).ModInverse(s.value, btcec.S256().N),
+	}, nil
+}
+
+func (s *ScalarK256) Sqrt() (Scalar, error) {
+	return &ScalarK256{
+		value: new(big.Int).ModSqrt(s.value, btcec.S256().N),
+	}, nil
+}
+
+func (s *ScalarK256) Cube() Scalar {
+	return &ScalarK256{
+		value: new(big.Int).Exp(s.value, big.NewInt(3), btcec.S256().N),
+	}
+}
+
+func (s *ScalarK256) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		v := new(big.Int).Add(s.value, r.value)
+		return &ScalarK256{
+			value: v.Mod(v, btcec.S256().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarK256) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		v := new(big.Int).Sub(s.value, r.value)
+		return &ScalarK256{
+			value: v.Mod(v, btcec.S256().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarK256) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		v := new(big.Int).Mul(s.value, r.value)
+		return &ScalarK256{
+			value: v.Mod(v, btcec.S256().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarK256) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarK256) Div(rhs Scalar) Scalar {
+	n := btcec.S256().N
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		v := new(big.Int).ModInverse(r.value, n)
+		v.Mul(v, s.value)
+		return &ScalarK256{
+			value: v.Mod(v, n),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarK256) Neg() Scalar {
+	z := new(big.Int).Neg(s.value)
+	return &ScalarK256{
+		value: z.Mod(z, btcec.S256().N),
+	}
+}
+
+func (s *ScalarK256) SetBigInt(v *big.Int) (Scalar, error) {
+	if v == nil {
+		return nil, fmt.Errorf("invalid value")
+	}
+	t := new(big.Int).Mod(v, btcec.S256().N)
+	if t.Cmp(v) != 0 {
+		return nil, fmt.Errorf("invalid value")
+	}
+	return &ScalarK256{
+		value: t,
+	}, nil
+}
+
+func (s *ScalarK256) BigInt() *big.Int {
+	return new(big.Int).Set(s.value)
+}
+
+func (s *ScalarK256) Bytes() []byte {
+	var out [32]byte
+	return s.value.FillBytes(out[:])
+}
+
+func (s *ScalarK256) SetBytes(bytes []byte) (Scalar, error) {
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, btcec.S256().N)
+	if t.Cmp(value) != 0 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	return &ScalarK256{
+		value: t,
+	}, nil
+}
+
+func (s *ScalarK256) SetBytesWide(bytes []byte) (Scalar, error) {
+	if len(bytes) < 32 || len(bytes) > 128 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value := new(big.Int).SetBytes(bytes)
+	value.Mod(value, btcec.S256().N)
+	return &ScalarK256{
+		value,
+	}, nil
+}
+
+func (s *ScalarK256) Point() Point {
+	return new(PointK256).Identity()
+}
+
+func (s *ScalarK256) Clone() Scalar {
+	return &ScalarK256{
+		value: new(big.Int).Set(s.value),
+	}
+}
+
+func (s *ScalarK256) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarK256) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarK256)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarK256) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarK256) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarK256)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarK256) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarK256) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarK256)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+func (p *PointK256) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointK256) Hash(bytes []byte) Point {
+	curve := btcec.S256()
+
+	var domain = []byte("secp256k1_XMD:SHA-256_SSWU_RO_")
+	uniformBytes, _ := expandMsgXmd(sha256.New(), bytes, domain, 96)
+
+	u0 := new(big.Int).SetBytes(uniformBytes[:48])
+	u1 := new(big.Int).SetBytes(uniformBytes[48:])
+
+	u0.Mod(u0, curve.P)
+	u1.Mod(u1, curve.P)
+
+	ssParams := k256SswuParams()
+	r0x, r0y := osswu3mod4(u0, ssParams)
+	r1x, r1y := osswu3mod4(u1, ssParams)
+
+	isoParams := k256IsogenyParams()
+	q0x, q0y := isogenyMap(r0x, r0y, isoParams)
+	q1x, q1y := isogenyMap(r1x, r1y, isoParams)
+
+	x, y := curve.Add(q0x, q0y, q1x, q1y)
+	return &PointK256{
+		x, y,
+	}
+}
+
+func (p *PointK256) Identity() Point {
+	return &PointK256{
+		x: big.NewInt(0), y: big.NewInt(0),
+	}
+}
+
+func (p *PointK256) Generator() Point {
+	curve := btcec.S256()
+	return &PointK256{
+		x: new(big.Int).Set(curve.Gx),
+		y: new(big.Int).Set(curve.Gy),
+	}
+}
+
+func (p *PointK256) IsIdentity() bool {
+	x := core.ConstantTimeEqByte(p.x, core.Zero)
+	y := core.ConstantTimeEqByte(p.y, core.Zero)
+	return (x & y) == 1
+}
+
+func (p *PointK256) IsNegative() bool {
+	return p.y.Bit(0) == 1
+}
+
+func (p *PointK256) IsOnCurve() bool {
+	return btcec.S256().IsOnCurve(p.x, p.y)
+}
+
+func (p *PointK256) Double() Point {
+	x, y := btcec.S256().Double(p.x, p.y)
+	return &PointK256{x, y}
+}
+
+func (p *PointK256) Scalar() Scalar {
+	return new(ScalarK256).Zero()
+}
+
+func (p *PointK256) Neg() Point {
+	y := new(big.Int).Sub(btcec.S256().P, p.y)
+	y.Mod(y, btcec.S256().P)
+	return &PointK256{x: p.x, y: y}
+}
+
+func (p *PointK256) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointK256)
+	if ok {
+		x, y := btcec.S256().Add(p.x, p.y, r.x, r.y)
+		return &PointK256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointK256) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.Neg().(*PointK256)
+	if ok {
+		x, y := btcec.S256().Add(p.x, p.y, r.x, r.y)
+		return &PointK256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointK256) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarK256)
+	if ok {
+		x, y := btcec.S256().ScalarMult(p.x, p.y, r.value.Bytes())
+		return &PointK256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointK256) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointK256)
+	if ok {
+		x := core.ConstantTimeEqByte(p.x, r.x)
+		y := core.ConstantTimeEqByte(p.y, r.y)
+		return (x & y) == 1
+	} else {
+		return false
+	}
+}
+
+func (p *PointK256) Set(x, y *big.Int) (Point, error) {
+	// check is identity or on curve
+	xx := subtle.ConstantTimeCompare(x.Bytes(), []byte{})
+	yy := subtle.ConstantTimeCompare(y.Bytes(), []byte{})
+	// Checks are constant time
+	onCurve := btcec.S256().IsOnCurve(x, y)
+	if !onCurve && (xx&yy) != 1 {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	x = new(big.Int).Set(x)
+	y = new(big.Int).Set(y)
+	return &PointK256{x, y}, nil
+}
+
+func (p *PointK256) ToAffineCompressed() []byte {
+	var x [33]byte
+	x[0] = byte(2)
+	x[0] |= byte(p.y.Bit(0))
+	p.x.FillBytes(x[1:])
+	return x[:]
+}
+
+func (p *PointK256) ToAffineUncompressed() []byte {
+	var out [65]byte
+	out[0] = byte(4)
+	p.x.FillBytes(out[1:33])
+	p.y.FillBytes(out[33:])
+	return out[:]
+}
+
+func (p *PointK256) FromAffineCompressed(bytes []byte) (Point, error) {
+	if len(bytes) != 33 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	sign := int(bytes[0])
+	if sign != 2 && sign != 3 {
+		return nil, fmt.Errorf("invalid sign byte")
+	}
+	sign &= 0x1
+
+	x := new(big.Int).SetBytes(bytes[1:])
+	rhs := rhsK256(x, btcec.S256().Params())
+	// test that rhs is quadratic residue
+	// if not, then this Point is at infinity
+	y := new(big.Int).ModSqrt(rhs, btcec.S256().P)
+	if y != nil {
+		// fix the sign
+		if int(y.Bit(0)) != sign {
+			y.Neg(y)
+			y.Mod(y, btcec.S256().P)
+		}
+	} else {
+		x = new(big.Int)
+		y = new(big.Int)
+	}
+	return &PointK256{
+		x, y,
+	}, nil
+}
+
+func (p *PointK256) FromAffineUncompressed(bytes []byte) (Point, error) {
+	if len(bytes) != 65 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	if bytes[0] != 4 {
+		return nil, fmt.Errorf("invalid sign byte")
+	}
+	x := new(big.Int).SetBytes(bytes[1:33])
+	y := new(big.Int).SetBytes(bytes[33:])
+	return &PointK256{x, y}, nil
+}
+
+func (p *PointK256) CurveName() string {
+	return btcec.S256().Name
+}
+
+func (p *PointK256) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nScalars := make([]*big.Int, len(scalars))
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarK256)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.value
+	}
+	return sumOfProductsPippenger(points, nScalars)
+}
+
+func (p *PointK256) X() *big.Int {
+	return new(big.Int).Set(p.x)
+}
+
+func (p *PointK256) Y() *big.Int {
+	return new(big.Int).Set(p.y)
+}
+
+func (p *PointK256) Params() *elliptic.CurveParams {
+	return btcec.S256().Params()
+}
+
+func (p *PointK256) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointK256) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointK256)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.x = ppt.x
+	p.y = ppt.y
+	return nil
+}
+
+func (p *PointK256) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointK256) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointK256)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.x = ppt.x
+	p.y = ppt.y
+	return nil
+}
+
+func (p *PointK256) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointK256) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointK256)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.x = P.x
+	p.y = P.y
+	return nil
+}
+
+// rhs of the curve equation
+func rhsK256(x *big.Int, params *elliptic.CurveParams) *big.Int {
+	f := NewField(params.P)
+	r := f.NewElement(x)
+	r2 := r.Mul(r)
+
+	// x^3+Ax+B
+	// A = 0 for secp256k1
+	// Just add B
+	r = r2.Mul(r)
+	return r.Add(f.NewElement(params.B)).Value
+}
+
+// Taken from https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-E.1
+func k256IsogenyParams() *isogenyParams {
+	return &isogenyParams{
+		P: btcec.S256().P,
+		Xnum: []*big.Int{
+			bhex("8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7"),
+			bhex("07d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581"),
+			bhex("534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262"),
+			bhex("8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c"),
+		},
+		Xden: []*big.Int{
+			bhex("d35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b"),
+			bhex("edadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14"),
+			bhex("0000000000000000000000000000000000000000000000000000000000000001"),
+		},
+		Ynum: []*big.Int{
+			bhex("4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c"),
+			bhex("c75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3"),
+			bhex("29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931"),
+			bhex("2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84"),
+		},
+		Yden: []*big.Int{
+			bhex("fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b"),
+			bhex("7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573"),
+			bhex("6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f"),
+			bhex("0000000000000000000000000000000000000000000000000000000000000001"),
+		},
+	}
+}
+
+// Take from https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-8.7
+func k256SswuParams() *sswuParams {
+	params := btcec.S256().Params()
+
+	// c1 = (q - 3) / 4
+	c1 := new(big.Int).Set(params.P)
+	c1.Sub(c1, big.NewInt(3))
+	c1.Rsh(c1, 2)
+
+	a, _ := new(big.Int).SetString("3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533", 16)
+	b := big.NewInt(1771)
+	z := big.NewInt(-11)
+	z.Mod(z, params.P)
+	// sqrt(-Z^3)
+	zTmp := new(big.Int).Exp(z, big.NewInt(3), nil)
+	zTmp = zTmp.Neg(zTmp)
+	zTmp.Mod(zTmp, params.P)
+	c2 := new(big.Int).ModSqrt(zTmp, params.P)
+
+	return &sswuParams{
+		params, c1, c2, a, b, z,
+	}
+}
diff --git a/pkg/core/curves/k256_curve_test.go b/pkg/core/curves/k256_curve_test.go
new file mode 100644
index 00000000..01ce38b0
--- /dev/null
+++ b/pkg/core/curves/k256_curve_test.go
@@ -0,0 +1,398 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	crand "crypto/rand"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"sync"
+	"testing"
+)
+
+type mockReader struct {
+	index int
+	seed  []byte
+}
+
+var mockRngInitonce sync.Once
+var mockRng mockReader
+
+func newMockReader() {
+	mockRng.index = 0
+	mockRng.seed = make([]byte, 32)
+	for i := range mockRng.seed {
+		mockRng.seed[i] = 1
+	}
+}
+
+func testRng() *mockReader {
+	mockRngInitonce.Do(newMockReader)
+	return &mockRng
+}
+
+func (m *mockReader) Read(p []byte) (n int, err error) {
+	limit := len(m.seed)
+	for i := range p {
+		p[i] = m.seed[m.index]
+		m.index += 1
+		m.index %= limit
+	}
+	n = len(p)
+	err = nil
+	return
+}
+
+func TestScalarK256Random(t *testing.T) {
+	k256 := K256()
+	sc := k256.Scalar.Random(testRng())
+	s, ok := sc.(*ScalarK256)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("2f71aaec5e14d747c72e46cdcaffffe6f542f38b3f0925469ceb24ac1c65885d", 16)
+	assert.Equal(t, s.value, expected)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := k256.Scalar.Random(crand.Reader)
+		_, ok := sc.(*ScalarK256)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsZero())
+	}
+}
+
+func TestScalarK256Hash(t *testing.T) {
+	var b [32]byte
+	k256 := K256()
+	sc := k256.Scalar.Hash(b[:])
+	s, ok := sc.(*ScalarK256)
+	assert.True(t, ok)
+	expected, _ := new(big.Int).SetString("e5cb3500b809a8202de0834a805068bc21bde09bd6367815e7523a37adf8f52e", 16)
+	assert.Equal(t, s.value, expected)
+}
+
+func TestScalarK256Zero(t *testing.T) {
+	k256 := K256()
+	sc := k256.Scalar.Zero()
+	assert.True(t, sc.IsZero())
+	assert.True(t, sc.IsEven())
+}
+
+func TestScalarK256One(t *testing.T) {
+	k256 := K256()
+	sc := k256.Scalar.One()
+	assert.True(t, sc.IsOne())
+	assert.True(t, sc.IsOdd())
+}
+
+func TestScalarK256New(t *testing.T) {
+	k256 := K256()
+	three := k256.Scalar.New(3)
+	assert.True(t, three.IsOdd())
+	four := k256.Scalar.New(4)
+	assert.True(t, four.IsEven())
+	neg1 := k256.Scalar.New(-1)
+	assert.True(t, neg1.IsEven())
+	neg2 := k256.Scalar.New(-2)
+	assert.True(t, neg2.IsOdd())
+}
+
+func TestScalarK256Square(t *testing.T) {
+	k256 := K256()
+	three := k256.Scalar.New(3)
+	nine := k256.Scalar.New(9)
+	assert.Equal(t, three.Square().Cmp(nine), 0)
+}
+
+func TestScalarK256Cube(t *testing.T) {
+	k256 := K256()
+	three := k256.Scalar.New(3)
+	twentySeven := k256.Scalar.New(27)
+	assert.Equal(t, three.Cube().Cmp(twentySeven), 0)
+}
+
+func TestScalarK256Double(t *testing.T) {
+	k256 := K256()
+	three := k256.Scalar.New(3)
+	six := k256.Scalar.New(6)
+	assert.Equal(t, three.Double().Cmp(six), 0)
+}
+
+func TestScalarK256Neg(t *testing.T) {
+	k256 := K256()
+	one := k256.Scalar.One()
+	neg1 := k256.Scalar.New(-1)
+	assert.Equal(t, one.Neg().Cmp(neg1), 0)
+	lotsOfThrees := k256.Scalar.New(333333)
+	expected := k256.Scalar.New(-333333)
+	assert.Equal(t, lotsOfThrees.Neg().Cmp(expected), 0)
+}
+
+func TestScalarK256Invert(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	actual, _ := nine.Invert()
+	sa, _ := actual.(*ScalarK256)
+	bn, _ := new(big.Int).SetString("8e38e38e38e38e38e38e38e38e38e38d842841d57dd303af6a9150f8e5737996", 16)
+	expected, err := k256.Scalar.SetBigInt(bn)
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarK256Sqrt(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	actual, err := nine.Sqrt()
+	sa, _ := actual.(*ScalarK256)
+	expected := k256.Scalar.New(3)
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarK256Add(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	six := k256.Scalar.New(6)
+	fifteen := nine.Add(six)
+	assert.NotNil(t, fifteen)
+	expected := k256.Scalar.New(15)
+	assert.Equal(t, expected.Cmp(fifteen), 0)
+	n := new(big.Int).Set(btcec.S256().N)
+	n.Sub(n, big.NewInt(3))
+
+	upper, err := k256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := upper.Add(nine)
+	assert.NotNil(t, actual)
+	assert.Equal(t, actual.Cmp(six), 0)
+}
+
+func TestScalarK256Sub(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	six := k256.Scalar.New(6)
+	n := new(big.Int).Set(btcec.S256().N)
+	n.Sub(n, big.NewInt(3))
+
+	expected, err := k256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := six.Sub(nine)
+	assert.Equal(t, expected.Cmp(actual), 0)
+
+	actual = nine.Sub(six)
+	assert.Equal(t, actual.Cmp(k256.Scalar.New(3)), 0)
+}
+
+func TestScalarK256Mul(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	six := k256.Scalar.New(6)
+	actual := nine.Mul(six)
+	assert.Equal(t, actual.Cmp(k256.Scalar.New(54)), 0)
+	n := new(big.Int).Set(btcec.S256().N)
+	n.Sub(n, big.NewInt(1))
+	upper, err := k256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	assert.Equal(t, upper.Mul(upper).Cmp(k256.Scalar.New(1)), 0)
+}
+
+func TestScalarK256Div(t *testing.T) {
+	k256 := K256()
+	nine := k256.Scalar.New(9)
+	actual := nine.Div(nine)
+	assert.Equal(t, actual.Cmp(k256.Scalar.New(1)), 0)
+	assert.Equal(t, k256.Scalar.New(54).Div(nine).Cmp(k256.Scalar.New(6)), 0)
+}
+
+func TestScalarK256Serialize(t *testing.T) {
+	k256 := K256()
+	sc := k256.Scalar.New(255)
+	sequence := sc.Bytes()
+	assert.Equal(t, len(sequence), 32)
+	assert.Equal(t, sequence, []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0xff})
+	ret, err := k256.Scalar.SetBytes(sequence)
+	assert.NoError(t, err)
+	assert.Equal(t, ret.Cmp(sc), 0)
+
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc = k256.Scalar.Random(crand.Reader)
+		sequence = sc.Bytes()
+		assert.Equal(t, len(sequence), 32)
+		ret, err = k256.Scalar.SetBytes(sequence)
+		assert.NoError(t, err)
+		assert.Equal(t, ret.Cmp(sc), 0)
+	}
+}
+
+func TestScalarK256Nil(t *testing.T) {
+	k256 := K256()
+	one := k256.Scalar.New(1)
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, one.Div(nil))
+	assert.Nil(t, k256.Scalar.Random(nil))
+	assert.Equal(t, one.Cmp(nil), -2)
+	_, err := k256.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointK256Random(t *testing.T) {
+	k256 := K256()
+	sc := k256.Point.Random(testRng())
+	s, ok := sc.(*PointK256)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("c6e18a1d7cf834462675b31581639a18e14fd0f73f8dfd5fe2993f88f6fbe008", 16)
+	expectedY, _ := new(big.Int).SetString("b65fab3243c5d07cef005d7fb335ebe8019efd954e95e68c86ef9b3bd7bccd36", 16)
+	assert.Equal(t, s.x, expectedX)
+	assert.Equal(t, s.y, expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := k256.Point.Random(crand.Reader)
+		_, ok := sc.(*PointK256)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointK256Hash(t *testing.T) {
+	var b [32]byte
+	k256 := K256()
+	sc := k256.Point.Hash(b[:])
+	s, ok := sc.(*PointK256)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("95d0ad42f68ddb5a808469dd75fa866890dcc7d039844e0e2d58a6d25bd9a66b", 16)
+	expectedY, _ := new(big.Int).SetString("f37c564d05168dab4413caacdb8e3426143fc5fb24a470ccd8a51856c11d163c", 16)
+	assert.Equal(t, s.x, expectedX)
+	assert.Equal(t, s.y, expectedY)
+}
+
+func TestPointK256Identity(t *testing.T) {
+	k256 := K256()
+	sc := k256.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+}
+
+func TestPointK256Generator(t *testing.T) {
+	k256 := K256()
+	sc := k256.Point.Generator()
+	s, ok := sc.(*PointK256)
+	assert.True(t, ok)
+	assert.Equal(t, s.x.Cmp(btcec.S256().Gx), 0)
+	assert.Equal(t, s.y.Cmp(btcec.S256().Gy), 0)
+}
+
+func TestPointK256Set(t *testing.T) {
+	k256 := K256()
+	iden, err := k256.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	_, err = k256.Point.Set(btcec.S256().Gx, btcec.S256().Gy)
+	assert.NoError(t, err)
+}
+
+func TestPointK256Double(t *testing.T) {
+	k256 := K256()
+	g := k256.Point.Generator()
+	g2 := g.Double()
+	assert.True(t, g2.Equal(g.Mul(k256.Scalar.New(2))))
+	i := k256.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointK256Neg(t *testing.T) {
+	k256 := K256()
+	g := k256.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(k256.Point.Generator()))
+	assert.True(t, k256.Point.Identity().Neg().Equal(k256.Point.Identity()))
+}
+
+func TestPointK256Add(t *testing.T) {
+	k256 := K256()
+	pt := k256.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(k256.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointK256Sub(t *testing.T) {
+	k256 := K256()
+	g := k256.Point.Generator()
+	pt := k256.Point.Generator().Mul(k256.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointK256Mul(t *testing.T) {
+	k256 := K256()
+	g := k256.Point.Generator()
+	pt := k256.Point.Generator().Mul(k256.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointK256Serialize(t *testing.T) {
+	k256 := K256()
+	ss := k256.Scalar.Random(testRng())
+	g := k256.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0x2, 0x1b, 0xa7, 0x7e, 0x98, 0xd6, 0xd8, 0x49, 0x45, 0xa4, 0x75, 0xd8, 0x6, 0xc0, 0x94, 0x5b, 0x8c, 0xf0, 0x5b, 0x8a, 0xb2, 0x76, 0xbb, 0x9f, 0x6e, 0x52, 0x9a, 0x11, 0x9c, 0x79, 0xdd, 0xf6, 0x5a})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x4, 0x1b, 0xa7, 0x7e, 0x98, 0xd6, 0xd8, 0x49, 0x45, 0xa4, 0x75, 0xd8, 0x6, 0xc0, 0x94, 0x5b, 0x8c, 0xf0, 0x5b, 0x8a, 0xb2, 0x76, 0xbb, 0x9f, 0x6e, 0x52, 0x9a, 0x11, 0x9c, 0x79, 0xdd, 0xf6, 0x5a, 0xb2, 0x96, 0x7c, 0x59, 0x4, 0xeb, 0x9a, 0xaa, 0xa9, 0x1d, 0x4d, 0xd0, 0x2d, 0xc6, 0x37, 0xee, 0x4a, 0x95, 0x51, 0x60, 0xab, 0xab, 0xf7, 0xdb, 0x30, 0x7d, 0x7d, 0x0, 0x68, 0x6c, 0xcf, 0xf6})
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := k256.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 33)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 65)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointK256Nil(t *testing.T) {
+	k256 := K256()
+	one := k256.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, k256.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := k256.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointK256SumOfProducts(t *testing.T) {
+	lhs := new(PointK256).Generator().Mul(new(ScalarK256).New(50))
+	points := make([]Point, 5)
+	for i := range points {
+		points[i] = new(PointK256).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarK256).New(8),
+		new(ScalarK256).New(9),
+		new(ScalarK256).New(10),
+		new(ScalarK256).New(11),
+		new(ScalarK256).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
diff --git a/pkg/core/curves/native/bls12-381/LICENSE b/pkg/core/curves/native/bls12-381/LICENSE
new file mode 100644
index 00000000..7a4a3ea2
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/LICENSE
@@ -0,0 +1,202 @@
+
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
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diff --git a/pkg/core/curves/native/bls12-381/README.md b/pkg/core/curves/native/bls12-381/README.md
new file mode 100644
index 00000000..cd993a91
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/README.md
@@ -0,0 +1,828 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# bls12381
+
+```go
+import "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+```
+
+## Index
+
+- [Variables](<#variables>)
+- [type E](<#type-e>)
+  - [func (g *E) Equal(g2 *E) bool](<#func-e-equal>)
+  - [func (e *E) IsOne() bool](<#func-e-isone>)
+  - [func (e *E) One() *E](<#func-e-one>)
+  - [func (e *E) Set(e2 *E) *E](<#func-e-set>)
+- [type Engine](<#type-engine>)
+  - [func NewEngine() *Engine](<#func-newengine>)
+  - [func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine](<#func-engine-addpair>)
+  - [func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine](<#func-engine-addpairinv>)
+  - [func (e *Engine) Check() (bool, error)](<#func-engine-check>)
+  - [func (e *Engine) GT() *GT](<#func-engine-gt>)
+  - [func (e *Engine) Reset() *Engine](<#func-engine-reset>)
+  - [func (e *Engine) Result() (*E, error)](<#func-engine-result>)
+- [type G1](<#type-g1>)
+  - [func NewG1() *G1](<#func-newg1>)
+  - [func (g *G1) Add(r, p1, p2 *PointG1) *PointG1](<#func-g1-add>)
+  - [func (g *G1) Affine(p *PointG1) *PointG1](<#func-g1-affine>)
+  - [func (g *G1) ClearCofactor(p *PointG1)](<#func-g1-clearcofactor>)
+  - [func (g *G1) Double(r, p *PointG1) *PointG1](<#func-g1-double>)
+  - [func (g *G1) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)](<#func-g1-encodetocurve>)
+  - [func (g *G1) Equal(p1, p2 *PointG1) bool](<#func-g1-equal>)
+  - [func (g *G1) FromBytes(in []byte) (*PointG1, error)](<#func-g1-frombytes>)
+  - [func (g *G1) FromCompressed(compressed []byte) (*PointG1, error)](<#func-g1-fromcompressed>)
+  - [func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error)](<#func-g1-fromuncompressed>)
+  - [func (g *G1) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)](<#func-g1-hashtocurve>)
+  - [func (g *G1) InCorrectSubgroup(p *PointG1) bool](<#func-g1-incorrectsubgroup>)
+  - [func (g *G1) IsAffine(p *PointG1) bool](<#func-g1-isaffine>)
+  - [func (g *G1) IsOnCurve(p *PointG1) bool](<#func-g1-isoncurve>)
+  - [func (g *G1) IsZero(p *PointG1) bool](<#func-g1-iszero>)
+  - [func (g *G1) MapToCurve(in []byte) (*PointG1, error)](<#func-g1-maptocurve>)
+  - [func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1](<#func-g1-mulscalar>)
+  - [func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error)](<#func-g1-multiexp>)
+  - [func (g *G1) Neg(r, p *PointG1) *PointG1](<#func-g1-neg>)
+  - [func (g *G1) New() *PointG1](<#func-g1-new>)
+  - [func (g *G1) One() *PointG1](<#func-g1-one>)
+  - [func (g *G1) Q() *big.Int](<#func-g1-q>)
+  - [func (g *G1) Sub(c, a, b *PointG1) *PointG1](<#func-g1-sub>)
+  - [func (g *G1) ToBytes(p *PointG1) []byte](<#func-g1-tobytes>)
+  - [func (g *G1) ToCompressed(p *PointG1) []byte](<#func-g1-tocompressed>)
+  - [func (g *G1) ToUncompressed(p *PointG1) ([]byte, error)](<#func-g1-touncompressed>)
+  - [func (g *G1) Zero() *PointG1](<#func-g1-zero>)
+- [type G2](<#type-g2>)
+  - [func NewG2() *G2](<#func-newg2>)
+  - [func (g *G2) Add(r, p1, p2 *PointG2) *PointG2](<#func-g2-add>)
+  - [func (g *G2) Affine(p *PointG2) *PointG2](<#func-g2-affine>)
+  - [func (g *G2) ClearCofactor(p *PointG2) *PointG2](<#func-g2-clearcofactor>)
+  - [func (g *G2) Double(r, p *PointG2) *PointG2](<#func-g2-double>)
+  - [func (g *G2) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)](<#func-g2-encodetocurve>)
+  - [func (g *G2) Equal(p1, p2 *PointG2) bool](<#func-g2-equal>)
+  - [func (g *G2) FromBytes(in []byte) (*PointG2, error)](<#func-g2-frombytes>)
+  - [func (g *G2) FromCompressed(compressed []byte) (*PointG2, error)](<#func-g2-fromcompressed>)
+  - [func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error)](<#func-g2-fromuncompressed>)
+  - [func (g *G2) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)](<#func-g2-hashtocurve>)
+  - [func (g *G2) InCorrectSubgroup(p *PointG2) bool](<#func-g2-incorrectsubgroup>)
+  - [func (g *G2) IsAffine(p *PointG2) bool](<#func-g2-isaffine>)
+  - [func (g *G2) IsOnCurve(p *PointG2) bool](<#func-g2-isoncurve>)
+  - [func (g *G2) IsZero(p *PointG2) bool](<#func-g2-iszero>)
+  - [func (g *G2) MapToCurve(in []byte) (*PointG2, error)](<#func-g2-maptocurve>)
+  - [func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2](<#func-g2-mulscalar>)
+  - [func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error)](<#func-g2-multiexp>)
+  - [func (g *G2) Neg(r, p *PointG2) *PointG2](<#func-g2-neg>)
+  - [func (g *G2) New() *PointG2](<#func-g2-new>)
+  - [func (g *G2) One() *PointG2](<#func-g2-one>)
+  - [func (g *G2) Q() *big.Int](<#func-g2-q>)
+  - [func (g *G2) Sub(c, a, b *PointG2) *PointG2](<#func-g2-sub>)
+  - [func (g *G2) ToBytes(p *PointG2) []byte](<#func-g2-tobytes>)
+  - [func (g *G2) ToCompressed(p *PointG2) []byte](<#func-g2-tocompressed>)
+  - [func (g *G2) ToUncompressed(p *PointG2) ([]byte, error)](<#func-g2-touncompressed>)
+  - [func (g *G2) Zero() *PointG2](<#func-g2-zero>)
+- [type GT](<#type-gt>)
+  - [func NewGT() *GT](<#func-newgt>)
+  - [func (g *GT) Add(c, a, b *E)](<#func-gt-add>)
+  - [func (g *GT) Exp(c, a *E, s *big.Int)](<#func-gt-exp>)
+  - [func (g *GT) FromBytes(in []byte) (*E, error)](<#func-gt-frombytes>)
+  - [func (g *GT) Inverse(c, a *E)](<#func-gt-inverse>)
+  - [func (g *GT) IsValid(e *E) bool](<#func-gt-isvalid>)
+  - [func (g *GT) Mul(c, a, b *E)](<#func-gt-mul>)
+  - [func (g *GT) New() *E](<#func-gt-new>)
+  - [func (g *GT) Q() *big.Int](<#func-gt-q>)
+  - [func (g *GT) Square(c, a *E)](<#func-gt-square>)
+  - [func (g *GT) Sub(c, a, b *E)](<#func-gt-sub>)
+  - [func (g *GT) ToBytes(e *E) []byte](<#func-gt-tobytes>)
+- [type PointG1](<#type-pointg1>)
+  - [func (p *PointG1) Set(p2 *PointG1) *PointG1](<#func-pointg1-set>)
+  - [func (p *PointG1) Zero() *PointG1](<#func-pointg1-zero>)
+- [type PointG2](<#type-pointg2>)
+  - [func (p *PointG2) Set(p2 *PointG2) *PointG2](<#func-pointg2-set>)
+  - [func (p *PointG2) Zero() *PointG2](<#func-pointg2-zero>)
+
+
+## Variables
+
+```go
+var G1One = g1One
+```
+
+```go
+var G2One = g2One
+```
+
+Inp = \-p^\(\-1\) mod 2^64
+
+```go
+var Inp uint64 = 0x89f3fffcfffcfffd
+```
+
+## type [E](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L15>)
+
+E is type for target group element
+
+```go
+type E = fe12
+```
+
+### func \(\*E\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L39>)
+
+```go
+func (g *E) Equal(g2 *E) bool
+```
+
+Equal returns true if given two element is equal\, otherwise returns false
+
+### func \(\*E\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L34>)
+
+```go
+func (e *E) IsOne() bool
+```
+
+IsOne returns true if given element equals to one
+
+### func \(\*E\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L28>)
+
+```go
+func (e *E) One() *E
+```
+
+One sets a new target group element to one
+
+### func \(\*E\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L23>)
+
+```go
+func (e *E) Set(e2 *E) *E
+```
+
+Set copies given value into the destination
+
+## type [Engine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L21-L28>)
+
+Engine is BLS12\-381 elliptic curve pairing engine
+
+```go
+type Engine struct {
+    G1  *G1
+    G2  *G2
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewEngine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L31>)
+
+```go
+func NewEngine() *Engine
+```
+
+NewEngine creates new pairing engine insteace\.
+
+### func \(\*Engine\) [AddPair](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L62>)
+
+```go
+func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine
+```
+
+AddPair adds a g1\, g2 point pair to pairing engine returns nil if no more pairs can be added
+
+### func \(\*Engine\) [AddPairInv](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L76>)
+
+```go
+func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine
+```
+
+AddPairInv adds a G1\, G2 point pair to pairing engine\. G1 point is negated\. returns nil if no more pairs can be added
+
+### func \(\*Engine\) [Check](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L282>)
+
+```go
+func (e *Engine) Check() (bool, error)
+```
+
+Check computes pairing and checks if result is equal to one
+
+### func \(\*Engine\) [GT](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L301>)
+
+```go
+func (e *Engine) GT() *GT
+```
+
+GT returns target group instance\.
+
+### func \(\*Engine\) [Reset](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L86>)
+
+```go
+func (e *Engine) Reset() *Engine
+```
+
+Reset deletes added pairs\.
+
+### func \(\*Engine\) [Result](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/pairing.go#L291>)
+
+```go
+func (e *Engine) Result() (*E, error)
+```
+
+Result computes pairing and returns target group element as result\.
+
+## type [G1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L41-L43>)
+
+G1 is struct for G1 group\.
+
+```go
+type G1 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewG1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L46>)
+
+```go
+func NewG1() *G1
+```
+
+NewG1 constructs a new G1 instance\.
+
+### func \(\*G1\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L392>)
+
+```go
+func (g *G1) Add(r, p1, p2 *PointG1) *PointG1
+```
+
+Add adds two G1 points p1\, p2 and assigns the result to point at first argument\.
+
+### func \(\*G1\) [Affine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L375>)
+
+```go
+func (g *G1) Affine(p *PointG1) *PointG1
+```
+
+Add adds two G1 points p1\, p2 and assigns the result to point at first argument\.
+
+### func \(\*G1\) [ClearCofactor](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L506>)
+
+```go
+func (g *G1) ClearCofactor(p *PointG1)
+```
+
+ClearCofactor maps given a G1 point to correct subgroup
+
+### func \(\*G1\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L441>)
+
+```go
+func (g *G1) Double(r, p *PointG1) *PointG1
+```
+
+Double doubles a G1 point p and assigns the result to the point at first argument\.
+
+### func \(\*G1\) [EncodeToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L585>)
+
+```go
+func (g *G1) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)
+```
+
+EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point\. Implementation follows BLS12381G1\_XMD:SHA\-256\_SSWU\_NU\_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+
+### func \(\*G1\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L326>)
+
+```go
+func (g *G1) Equal(p1, p2 *PointG1) bool
+```
+
+Equal checks if given two G1 point is equal in their affine form\.
+
+### func \(\*G1\) [FromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L221>)
+
+```go
+func (g *G1) FromBytes(in []byte) (*PointG1, error)
+```
+
+FromBytes constructs a new point given uncompressed byte input\. FromBytes does not take zcash flags into account\. Byte input expected to be larger than 96 bytes\. First 96 bytes should be concatenation of x and y values\. Point \(0\, 0\) is considered as infinity\.
+
+### func \(\*G1\) [FromCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L131>)
+
+```go
+func (g *G1) FromCompressed(compressed []byte) (*PointG1, error)
+```
+
+FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G1\) [FromUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L68>)
+
+```go
+func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error)
+```
+
+FromUncompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G1\) [HashToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L611>)
+
+```go
+func (g *G1) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error)
+```
+
+HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point\. Implementation follows BLS12381G1\_XMD:SHA\-256\_SSWU\_RO\_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+
+### func \(\*G1\) [InCorrectSubgroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L346>)
+
+```go
+func (g *G1) InCorrectSubgroup(p *PointG1) bool
+```
+
+InCorrectSubgroup checks whether given point is in correct subgroup\.
+
+### func \(\*G1\) [IsAffine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L370>)
+
+```go
+func (g *G1) IsAffine(p *PointG1) bool
+```
+
+IsAffine checks a G1 point whether it is in affine form\.
+
+### func \(\*G1\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L353>)
+
+```go
+func (g *G1) IsOnCurve(p *PointG1) bool
+```
+
+IsOnCurve checks a G1 point is on curve\.
+
+### func \(\*G1\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L316>)
+
+```go
+func (g *G1) IsZero(p *PointG1) bool
+```
+
+IsZero returns true if given point is equal to zero\.
+
+### func \(\*G1\) [MapToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L568>)
+
+```go
+func (g *G1) MapToCurve(in []byte) (*PointG1, error)
+```
+
+MapToCurve given a byte slice returns a valid G1 point\. This mapping function implements the Simplified Shallue\-van de Woestijne\-Ulas method\. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08 Input byte slice should be a valid field element\, otherwise an error is returned\.
+
+### func \(\*G1\) [MulScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L489>)
+
+```go
+func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1
+```
+
+MulScalar multiplies a point by given scalar value in big\.Int and assigns the result to point at first argument\.
+
+### func \(\*G1\) [MultiExp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L514>)
+
+```go
+func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error)
+```
+
+MultiExp calculates multi exponentiation\. Given pairs of G1 point and scalar values \(P\_0\, e\_0\)\, \(P\_1\, e\_1\)\, \.\.\. \(P\_n\, e\_n\) calculates r = e\_0 \* P\_0 \+ e\_1 \* P\_1 \+ \.\.\. \+ e\_n \* P\_n Length of points and scalars are expected to be equal\, otherwise an error is returned\. Result is assigned to point at first argument\.
+
+### func \(\*G1\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L473>)
+
+```go
+func (g *G1) Neg(r, p *PointG1) *PointG1
+```
+
+Neg negates a G1 point p and assigns the result to the point at first argument\.
+
+### func \(\*G1\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L300>)
+
+```go
+func (g *G1) New() *PointG1
+```
+
+New creates a new G1 Point which is equal to zero in other words point at infinity\.
+
+### func \(\*G1\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L310>)
+
+```go
+func (g *G1) One() *PointG1
+```
+
+One returns a new G1 Point which is equal to generator point\.
+
+### func \(\*G1\) [Q](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L60>)
+
+```go
+func (g *G1) Q() *big.Int
+```
+
+Q returns group order in big\.Int\.
+
+### func \(\*G1\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L481>)
+
+```go
+func (g *G1) Sub(c, a, b *PointG1) *PointG1
+```
+
+Sub subtracts two G1 points p1\, p2 and assigns the result to point at first argument\.
+
+### func \(\*G1\) [ToBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L251>)
+
+```go
+func (g *G1) ToBytes(p *PointG1) []byte
+```
+
+ToBytes serializes a point into bytes in uncompressed form\. ToBytes does not take zcash flags into account\. ToBytes returns \(0\, 0\) if point is infinity\.
+
+### func \(\*G1\) [ToCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L181>)
+
+```go
+func (g *G1) ToCompressed(p *PointG1) []byte
+```
+
+ToCompressed given a G1 point returns bytes in compressed form of the point\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G1\) [ToUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L112>)
+
+```go
+func (g *G1) ToUncompressed(p *PointG1) ([]byte, error)
+```
+
+ToUncompressed given a G1 point returns bytes in uncompressed \(x\, y\) form of the point\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G1\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L305>)
+
+```go
+func (g *G1) Zero() *PointG1
+```
+
+Zero returns a new G1 Point which is equal to point at infinity\.
+
+## type [G2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L43-L46>)
+
+G2 is struct for G2 group\.
+
+```go
+type G2 struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewG2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L49>)
+
+```go
+func NewG2() *G2
+```
+
+NewG2 constructs a new G2 instance\.
+
+### func \(\*G2\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L399>)
+
+```go
+func (g *G2) Add(r, p1, p2 *PointG2) *PointG2
+```
+
+Add adds two G2 points p1\, p2 and assigns the result to point at first argument\.
+
+### func \(\*G2\) [Affine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L382>)
+
+```go
+func (g *G2) Affine(p *PointG2) *PointG2
+```
+
+Affine calculates affine form of given G2 point\.
+
+### func \(\*G2\) [ClearCofactor](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L513>)
+
+```go
+func (g *G2) ClearCofactor(p *PointG2) *PointG2
+```
+
+ClearCofactor maps given a G2 point to correct subgroup
+
+### func \(\*G2\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L448>)
+
+```go
+func (g *G2) Double(r, p *PointG2) *PointG2
+```
+
+Double doubles a G2 point p and assigns the result to the point at first argument\.
+
+### func \(\*G2\) [EncodeToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L632>)
+
+```go
+func (g *G2) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)
+```
+
+EncodeToCurve given a message and domain seperator tag returns the hash result which is a valid curve point\. Implementation follows BLS12381G1\_XMD:SHA\-256\_SSWU\_NU\_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+
+### func \(\*G2\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L333>)
+
+```go
+func (g *G2) Equal(p1, p2 *PointG2) bool
+```
+
+Equal checks if given two G2 point is equal in their affine form\.
+
+### func \(\*G2\) [FromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L231>)
+
+```go
+func (g *G2) FromBytes(in []byte) (*PointG2, error)
+```
+
+FromBytes constructs a new point given uncompressed byte input\. FromBytes does not take zcash flags into account\. Byte input expected to be larger than 96 bytes\. First 192 bytes should be concatenation of x and y values Point \(0\, 0\) is considered as infinity\.
+
+### func \(\*G2\) [FromCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L141>)
+
+```go
+func (g *G2) FromCompressed(compressed []byte) (*PointG2, error)
+```
+
+FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G2\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G2\) [FromUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L78>)
+
+```go
+func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error)
+```
+
+FromUncompressed expects byte slice larger than 192 bytes and given bytes returns a new point in G2\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G2\) [HashToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L659>)
+
+```go
+func (g *G2) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error)
+```
+
+HashToCurve given a message and domain seperator tag returns the hash result which is a valid curve point\. Implementation follows BLS12381G1\_XMD:SHA\-256\_SSWU\_RO\_ suite at https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+
+### func \(\*G2\) [InCorrectSubgroup](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L353>)
+
+```go
+func (g *G2) InCorrectSubgroup(p *PointG2) bool
+```
+
+InCorrectSubgroup checks whether given point is in correct subgroup\.
+
+### func \(\*G2\) [IsAffine](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L377>)
+
+```go
+func (g *G2) IsAffine(p *PointG2) bool
+```
+
+IsAffine checks a G2 point whether it is in affine form\.
+
+### func \(\*G2\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L360>)
+
+```go
+func (g *G2) IsOnCurve(p *PointG2) bool
+```
+
+IsOnCurve checks a G2 point is on curve\.
+
+### func \(\*G2\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L323>)
+
+```go
+func (g *G2) IsZero(p *PointG2) bool
+```
+
+IsZero returns true if given point is equal to zero\.
+
+### func \(\*G2\) [MapToCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L614>)
+
+```go
+func (g *G2) MapToCurve(in []byte) (*PointG2, error)
+```
+
+MapToCurve given a byte slice returns a valid G2 point\. This mapping function implements the Simplified Shallue\-van de Woestijne\-Ulas method\. https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2 Input byte slice should be a valid field element\, otherwise an error is returned\.
+
+### func \(\*G2\) [MulScalar](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L496>)
+
+```go
+func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2
+```
+
+MulScalar multiplies a point by given scalar value in big\.Int and assigns the result to point at first argument\.
+
+### func \(\*G2\) [MultiExp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L521>)
+
+```go
+func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error)
+```
+
+MultiExp calculates multi exponentiation\. Given pairs of G2 point and scalar values \(P\_0\, e\_0\)\, \(P\_1\, e\_1\)\, \.\.\. \(P\_n\, e\_n\) calculates r = e\_0 \* P\_0 \+ e\_1 \* P\_1 \+ \.\.\. \+ e\_n \* P\_n Length of points and scalars are expected to be equal\, otherwise an error is returned\. Result is assigned to point at first argument\.
+
+### func \(\*G2\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L480>)
+
+```go
+func (g *G2) Neg(r, p *PointG2) *PointG2
+```
+
+Neg negates a G2 point p and assigns the result to the point at first argument\.
+
+### func \(\*G2\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L307>)
+
+```go
+func (g *G2) New() *PointG2
+```
+
+New creates a new G2 Point which is equal to zero in other words point at infinity\.
+
+### func \(\*G2\) [One](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L317>)
+
+```go
+func (g *G2) One() *PointG2
+```
+
+One returns a new G2 Point which is equal to generator point\.
+
+### func \(\*G2\) [Q](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L70>)
+
+```go
+func (g *G2) Q() *big.Int
+```
+
+Q returns group order in big\.Int\.
+
+### func \(\*G2\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L488>)
+
+```go
+func (g *G2) Sub(c, a, b *PointG2) *PointG2
+```
+
+Sub subtracts two G2 points p1\, p2 and assigns the result to point at first argument\.
+
+### func \(\*G2\) [ToBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L261>)
+
+```go
+func (g *G2) ToBytes(p *PointG2) []byte
+```
+
+ToBytes serializes a point into bytes in uncompressed form\, does not take zcash flags into account\, returns \(0\, 0\) if point is infinity\.
+
+### func \(\*G2\) [ToCompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L191>)
+
+```go
+func (g *G2) ToCompressed(p *PointG2) []byte
+```
+
+ToCompressed given a G2 point returns bytes in compressed form of the point\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G2\) [ToUncompressed](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L122>)
+
+```go
+func (g *G2) ToUncompressed(p *PointG2) ([]byte, error)
+```
+
+ToUncompressed given a G2 point returns bytes in uncompressed \(x\, y\) form of the point\. Serialization rules are in line with zcash library\. See below for details\. https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+
+### func \(\*G2\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L312>)
+
+```go
+func (g *G2) Zero() *PointG2
+```
+
+Zero returns a new G2 Point which is equal to point at infinity\.
+
+## type [GT](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L18-L20>)
+
+GT is type for target multiplicative group GT\.
+
+```go
+type GT struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewGT](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L44>)
+
+```go
+func NewGT() *GT
+```
+
+NewGT constructs new target group instance\.
+
+### func \(\*GT\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L85>)
+
+```go
+func (g *GT) Add(c, a, b *E)
+```
+
+Add adds two field element \`a\` and \`b\` and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [Exp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L105>)
+
+```go
+func (g *GT) Exp(c, a *E, s *big.Int)
+```
+
+Exp exponents an element \`a\` by a scalar \`s\` and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [FromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L56>)
+
+```go
+func (g *GT) FromBytes(in []byte) (*E, error)
+```
+
+FromBytes expects 576 byte input and returns target group element FromBytes returns error if given element is not on correct subgroup\.
+
+### func \(\*GT\) [Inverse](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L110>)
+
+```go
+func (g *GT) Inverse(c, a *E)
+```
+
+Inverse inverses an element \`a\` and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [IsValid](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L73>)
+
+```go
+func (g *GT) IsValid(e *E) bool
+```
+
+IsValid checks whether given target group element is in correct subgroup\.
+
+### func \(\*GT\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L95>)
+
+```go
+func (g *GT) Mul(c, a, b *E)
+```
+
+Mul multiplies two field element \`a\` and \`b\` and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [New](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L80>)
+
+```go
+func (g *GT) New() *E
+```
+
+New initializes a new target group element which is equal to one
+
+### func \(\*GT\) [Q](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L50>)
+
+```go
+func (g *GT) Q() *big.Int
+```
+
+Q returns group order in big\.Int\.
+
+### func \(\*GT\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L100>)
+
+```go
+func (g *GT) Square(c, a *E)
+```
+
+Square squares an element \`a\` and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L90>)
+
+```go
+func (g *GT) Sub(c, a, b *E)
+```
+
+Sub subtracts two field element \`a\` and \`b\`\, and assigns the result to the element in first argument\.
+
+### func \(\*GT\) [ToBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/gt.go#L68>)
+
+```go
+func (g *GT) ToBytes(e *E) []byte
+```
+
+ToBytes serializes target group element\.
+
+## type [PointG1](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L20>)
+
+PointG1 is type for point in G1\. PointG1 is both used for Affine and Jacobian point representation\. If z is equal to one the point is accounted as in affine form\.
+
+```go
+type PointG1 [3]fe
+```
+
+### func \(\*PointG1\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L22>)
+
+```go
+func (p *PointG1) Set(p2 *PointG1) *PointG1
+```
+
+### func \(\*PointG1\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g1.go#L29>)
+
+```go
+func (p *PointG1) Zero() *PointG1
+```
+
+## type [PointG2](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L20>)
+
+PointG2 is type for point in G2\. PointG2 is both used for Affine and Jacobian point representation\. If z is equal to one the point is accounted as in affine form\.
+
+```go
+type PointG2 [3]fe2
+```
+
+### func \(\*PointG2\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L23>)
+
+```go
+func (p *PointG2) Set(p2 *PointG2) *PointG2
+```
+
+Set copies valeus of one point to another\.
+
+### func \(\*PointG2\) [Zero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/bls12-381/g2.go#L30>)
+
+```go
+func (p *PointG2) Zero() *PointG2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/curves/native/bls12-381/arithmetic_decl.go b/pkg/core/curves/native/bls12-381/arithmetic_decl.go
new file mode 100644
index 00000000..c1d839de
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/arithmetic_decl.go
@@ -0,0 +1,72 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// +build amd64,!generic
+
+package bls12381
+
+import (
+	"golang.org/x/sys/cpu"
+)
+
+func init() {
+	if !cpu.X86.HasADX || !cpu.X86.HasBMI2 {
+		mul = mulNoADX
+	}
+}
+
+var mul func(c, a, b *fe) = mulADX
+
+func square(c, a *fe) {
+	mul(c, a, a)
+}
+
+func neg(c, a *fe) {
+	if a.isZero() {
+		c.set(a)
+	} else {
+		_neg(c, a)
+	}
+}
+
+//go:noescape
+func add(c, a, b *fe)
+
+//go:noescape
+func addAssign(a, b *fe)
+
+//go:noescape
+func ladd(c, a, b *fe)
+
+//go:noescape
+func laddAssign(a, b *fe)
+
+//go:noescape
+func double(c, a *fe)
+
+//go:noescape
+func doubleAssign(a *fe)
+
+//go:noescape
+func ldouble(c, a *fe)
+
+//go:noescape
+func sub(c, a, b *fe)
+
+//go:noescape
+func subAssign(a, b *fe)
+
+//go:noescape
+func lsubAssign(a, b *fe)
+
+//go:noescape
+func _neg(c, a *fe)
+
+//go:noescape
+func mulNoADX(c, a, b *fe)
+
+//go:noescape
+func mulADX(c, a, b *fe)
diff --git a/pkg/core/curves/native/bls12-381/arithmetic_fallback.go b/pkg/core/curves/native/bls12-381/arithmetic_fallback.go
new file mode 100644
index 00000000..73e931fd
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/arithmetic_fallback.go
@@ -0,0 +1,565 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// +build !amd64 generic
+
+// Native go field arithmetic code is generated with 'goff'
+// https://github.com/ConsenSys/goff
+// Many function signature of field operations are renamed.
+
+// Copyright 2020 ConsenSys AG
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// field modulus q =
+//
+// 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
+// Code generated by goff DO NOT EDIT
+// goff version: v0.1.0 - build: 790f1f56eac432441e043abff8819eacddd1d668
+// fe are assumed to be in Montgomery form in all methods
+
+// /!\ WARNING /!\
+// this code has not been audited and is provided as-is. In particular,
+// there is no security guarantees such as constant time implementation
+// or side-channel attack resistance
+// /!\ WARNING /!\
+
+// Package bls (generated by goff) contains field arithmetics operations
+
+package bls12381
+
+import (
+	"math/bits"
+)
+
+func add(z, x, y *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	z[1], carry = bits.Add64(x[1], y[1], carry)
+	z[2], carry = bits.Add64(x[2], y[2], carry)
+	z[3], carry = bits.Add64(x[3], y[3], carry)
+	z[4], carry = bits.Add64(x[4], y[4], carry)
+	z[5], _ = bits.Add64(x[5], y[5], carry)
+
+	// if z > q --> z -= q
+	zMinusQConstantTime(z)
+}
+
+func addAssign(x, y *fe) {
+	var carry uint64
+
+	x[0], carry = bits.Add64(x[0], y[0], 0)
+	x[1], carry = bits.Add64(x[1], y[1], carry)
+	x[2], carry = bits.Add64(x[2], y[2], carry)
+	x[3], carry = bits.Add64(x[3], y[3], carry)
+	x[4], carry = bits.Add64(x[4], y[4], carry)
+	x[5], _ = bits.Add64(x[5], y[5], carry)
+
+	// if x > q --> x -= q
+	zMinusQConstantTime(x)
+}
+
+func ladd(z, x, y *fe) {
+	var carry uint64
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	z[1], carry = bits.Add64(x[1], y[1], carry)
+	z[2], carry = bits.Add64(x[2], y[2], carry)
+	z[3], carry = bits.Add64(x[3], y[3], carry)
+	z[4], carry = bits.Add64(x[4], y[4], carry)
+	z[5], _ = bits.Add64(x[5], y[5], carry)
+}
+
+func laddAssign(x, y *fe) {
+	var carry uint64
+	x[0], carry = bits.Add64(x[0], y[0], 0)
+	x[1], carry = bits.Add64(x[1], y[1], carry)
+	x[2], carry = bits.Add64(x[2], y[2], carry)
+	x[3], carry = bits.Add64(x[3], y[3], carry)
+	x[4], carry = bits.Add64(x[4], y[4], carry)
+	x[5], _ = bits.Add64(x[5], y[5], carry)
+}
+
+func double(z, x *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], x[0], 0)
+	z[1], carry = bits.Add64(x[1], x[1], carry)
+	z[2], carry = bits.Add64(x[2], x[2], carry)
+	z[3], carry = bits.Add64(x[3], x[3], carry)
+	z[4], carry = bits.Add64(x[4], x[4], carry)
+	z[5], _ = bits.Add64(x[5], x[5], carry)
+
+	// if z > q --> z -= q
+	zMinusQConstantTime(z)
+}
+
+func doubleAssign(z *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(z[0], z[0], 0)
+	z[1], carry = bits.Add64(z[1], z[1], carry)
+	z[2], carry = bits.Add64(z[2], z[2], carry)
+	z[3], carry = bits.Add64(z[3], z[3], carry)
+	z[4], carry = bits.Add64(z[4], z[4], carry)
+	z[5], _ = bits.Add64(z[5], z[5], carry)
+
+	// if z > q --> z -= q
+	zMinusQConstantTime(z)
+}
+
+func ldouble(z, x *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], x[0], 0)
+	z[1], carry = bits.Add64(x[1], x[1], carry)
+	z[2], carry = bits.Add64(x[2], x[2], carry)
+	z[3], carry = bits.Add64(x[3], x[3], carry)
+	z[4], carry = bits.Add64(x[4], x[4], carry)
+	z[5], _ = bits.Add64(x[5], x[5], carry)
+}
+
+func sub(z, x, y *fe) {
+	var b uint64
+	z[0], b = bits.Sub64(x[0], y[0], 0)
+	z[1], b = bits.Sub64(x[1], y[1], b)
+	z[2], b = bits.Sub64(x[2], y[2], b)
+	z[3], b = bits.Sub64(x[3], y[3], b)
+	z[4], b = bits.Sub64(x[4], y[4], b)
+	z[5], b = bits.Sub64(x[5], y[5], b)
+
+	updateIfBNotZero(z, b)
+}
+
+func subAssign(z, x *fe) {
+	var b uint64
+	z[0], b = bits.Sub64(z[0], x[0], 0)
+	z[1], b = bits.Sub64(z[1], x[1], b)
+	z[2], b = bits.Sub64(z[2], x[2], b)
+	z[3], b = bits.Sub64(z[3], x[3], b)
+	z[4], b = bits.Sub64(z[4], x[4], b)
+	z[5], b = bits.Sub64(z[5], x[5], b)
+
+	updateIfBNotZero(z, b)
+}
+
+func updateIfBNotZero(z *fe, b uint64) {
+	// Get cmove flag based off of b
+	bIsZero := b == 0
+	isZeroToMap := make(map[bool]uint)
+	isZeroToMap[true] = 0
+	isZeroToMap[false] = 1
+
+	flag := isZeroToMap[bIsZero]
+
+	// To set if B is not Zero
+	zPrime := &fe{}
+	var c uint64
+	zPrime[0], c = bits.Add64(z[0], 13402431016077863595, 0)
+	zPrime[1], c = bits.Add64(z[1], 2210141511517208575, c)
+	zPrime[2], c = bits.Add64(z[2], 7435674573564081700, c)
+	zPrime[3], c = bits.Add64(z[3], 7239337960414712511, c)
+	zPrime[4], c = bits.Add64(z[4], 5412103778470702295, c)
+	zPrime[5], _ = bits.Add64(z[5], 1873798617647539866, c)
+
+	// Move zPrime into z if flag
+	z.cmove(flag, zPrime)
+}
+
+func lsubAssign(z, x *fe) {
+	var b uint64
+	z[0], b = bits.Sub64(z[0], x[0], 0)
+	z[1], b = bits.Sub64(z[1], x[1], b)
+	z[2], b = bits.Sub64(z[2], x[2], b)
+	z[3], b = bits.Sub64(z[3], x[3], b)
+	z[4], b = bits.Sub64(z[4], x[4], b)
+	z[5], _ = bits.Sub64(z[5], x[5], b)
+}
+
+func neg(z *fe, x *fe) {
+	var borrow uint64
+	z[0], borrow = bits.Sub64(13402431016077863595, x[0], 0)
+	z[1], borrow = bits.Sub64(2210141511517208575, x[1], borrow)
+	z[2], borrow = bits.Sub64(7435674573564081700, x[2], borrow)
+	z[3], borrow = bits.Sub64(7239337960414712511, x[3], borrow)
+	z[4], borrow = bits.Sub64(5412103778470702295, x[4], borrow)
+	z[5], _ = bits.Sub64(1873798617647539866, x[5], borrow)
+
+	isZeroToMap := make(map[bool]uint)
+	isZeroToMap[true] = 1
+	isZeroToMap[false] = 0
+
+	flag := isZeroToMap[x.isZero()]
+	zPrime := &fe{}
+	zPrime.zero()
+
+	z.cmove(flag, zPrime)
+}
+
+func mul(z, x, y *fe) {
+	var t [6]uint64
+	var c [3]uint64
+	{
+		// round 0
+		v := x[0]
+		c[1], c[0] = bits.Mul64(v, y[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd1(v, y[1], c[1])
+		c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd1(v, y[2], c[1])
+		c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd1(v, y[3], c[1])
+		c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd1(v, y[4], c[1])
+		c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd1(v, y[5], c[1])
+		t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+	{
+		// round 1
+		v := x[1]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd2(v, y[4], c[1], t[4])
+		c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd2(v, y[5], c[1], t[5])
+		t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+	{
+		// round 2
+		v := x[2]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd2(v, y[4], c[1], t[4])
+		c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd2(v, y[5], c[1], t[5])
+		t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+	{
+		// round 3
+		v := x[3]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd2(v, y[4], c[1], t[4])
+		c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd2(v, y[5], c[1], t[5])
+		t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+	{
+		// round 4
+		v := x[4]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], t[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], t[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		c[2], t[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd2(v, y[4], c[1], t[4])
+		c[2], t[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd2(v, y[5], c[1], t[5])
+		t[5], t[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+	{
+		// round 5
+		v := x[5]
+		c[1], c[0] = madd1(v, y[0], t[0])
+		m := c[0] * 9940570264628428797
+		c[2] = madd0(m, 13402431016077863595, c[0])
+		c[1], c[0] = madd2(v, y[1], c[1], t[1])
+		c[2], z[0] = madd2(m, 2210141511517208575, c[2], c[0])
+		c[1], c[0] = madd2(v, y[2], c[1], t[2])
+		c[2], z[1] = madd2(m, 7435674573564081700, c[2], c[0])
+		c[1], c[0] = madd2(v, y[3], c[1], t[3])
+		c[2], z[2] = madd2(m, 7239337960414712511, c[2], c[0])
+		c[1], c[0] = madd2(v, y[4], c[1], t[4])
+		c[2], z[3] = madd2(m, 5412103778470702295, c[2], c[0])
+		c[1], c[0] = madd2(v, y[5], c[1], t[5])
+		z[5], z[4] = madd3(m, 1873798617647539866, c[0], c[2], c[1])
+	}
+
+	// if z > q --> z -= q
+	zMinusQConstantTime(z)
+}
+
+func square(z, x *fe) {
+
+	var p [6]uint64
+
+	var u, v uint64
+	{
+		// round 0
+		u, p[0] = bits.Mul64(x[0], x[0])
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		var t uint64
+		t, u, v = madd1sb(x[0], x[1], u)
+		C, p[0] = madd2(m, 2210141511517208575, v, C)
+		t, u, v = madd1s(x[0], x[2], t, u)
+		C, p[1] = madd2(m, 7435674573564081700, v, C)
+		t, u, v = madd1s(x[0], x[3], t, u)
+		C, p[2] = madd2(m, 7239337960414712511, v, C)
+		t, u, v = madd1s(x[0], x[4], t, u)
+		C, p[3] = madd2(m, 5412103778470702295, v, C)
+		_, u, v = madd1s(x[0], x[5], t, u)
+		p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+	{
+		// round 1
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		u, v = madd1(x[1], x[1], p[1])
+		C, p[0] = madd2(m, 2210141511517208575, v, C)
+		var t uint64
+		t, u, v = madd2sb(x[1], x[2], p[2], u)
+		C, p[1] = madd2(m, 7435674573564081700, v, C)
+		t, u, v = madd2s(x[1], x[3], p[3], t, u)
+		C, p[2] = madd2(m, 7239337960414712511, v, C)
+		t, u, v = madd2s(x[1], x[4], p[4], t, u)
+		C, p[3] = madd2(m, 5412103778470702295, v, C)
+		_, u, v = madd2s(x[1], x[5], p[5], t, u)
+		p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+	{
+		// round 2
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		C, p[0] = madd2(m, 2210141511517208575, p[1], C)
+		u, v = madd1(x[2], x[2], p[2])
+		C, p[1] = madd2(m, 7435674573564081700, v, C)
+		var t uint64
+		t, u, v = madd2sb(x[2], x[3], p[3], u)
+		C, p[2] = madd2(m, 7239337960414712511, v, C)
+		t, u, v = madd2s(x[2], x[4], p[4], t, u)
+		C, p[3] = madd2(m, 5412103778470702295, v, C)
+		_, u, v = madd2s(x[2], x[5], p[5], t, u)
+		p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+	{
+		// round 3
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		C, p[0] = madd2(m, 2210141511517208575, p[1], C)
+		C, p[1] = madd2(m, 7435674573564081700, p[2], C)
+		u, v = madd1(x[3], x[3], p[3])
+		C, p[2] = madd2(m, 7239337960414712511, v, C)
+		var t uint64
+		t, u, v = madd2sb(x[3], x[4], p[4], u)
+		C, p[3] = madd2(m, 5412103778470702295, v, C)
+		_, u, v = madd2s(x[3], x[5], p[5], t, u)
+		p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+	{
+		// round 4
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		C, p[0] = madd2(m, 2210141511517208575, p[1], C)
+		C, p[1] = madd2(m, 7435674573564081700, p[2], C)
+		C, p[2] = madd2(m, 7239337960414712511, p[3], C)
+		u, v = madd1(x[4], x[4], p[4])
+		C, p[3] = madd2(m, 5412103778470702295, v, C)
+		_, u, v = madd2sb(x[4], x[5], p[5], u)
+		p[5], p[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+	{
+		// round 5
+		m := p[0] * 9940570264628428797
+		C := madd0(m, 13402431016077863595, p[0])
+		C, z[0] = madd2(m, 2210141511517208575, p[1], C)
+		C, z[1] = madd2(m, 7435674573564081700, p[2], C)
+		C, z[2] = madd2(m, 7239337960414712511, p[3], C)
+		C, z[3] = madd2(m, 5412103778470702295, p[4], C)
+		u, v = madd1(x[5], x[5], p[5])
+		z[5], z[4] = madd3(m, 1873798617647539866, v, C, u)
+	}
+
+	// if z > q --> z -= q
+	zMinusQConstantTime(z)
+}
+
+// zminusq
+func zMinusQConstantTime(z *fe) {
+	// Get q as fe
+	q := &fe{
+		13402431016077863595,
+		2210141511517208575,
+		7435674573564081700,
+		7239337960414712511,
+		5412103778470702295,
+		1873798617647539866,
+	}
+
+	// if z > q -> 1
+	// if z < q -> -1
+	// if z == q -> 0
+	cmpZQ := z.cmp(q)
+	// twiddle cmpZQ st 1 --> 1, {-1,0} --> 0
+	flag := ^((cmpZQ - 1) >> 31) & 1
+
+	// z-q
+	zPrime := &fe{}
+	var b uint64
+	zPrime[0], b = bits.Sub64(z[0], q[0], 0)
+	zPrime[1], b = bits.Sub64(z[1], q[1], b)
+	zPrime[2], b = bits.Sub64(z[2], q[2], b)
+	zPrime[3], b = bits.Sub64(z[3], q[3], b)
+	zPrime[4], b = bits.Sub64(z[4], q[4], b)
+	zPrime[5], _ = bits.Sub64(z[5], q[5], b)
+
+	z.cmove(uint(flag), zPrime)
+}
+
+// arith.go
+// Copyright 2020 ConsenSys AG
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// Code generated by goff DO NOT EDIT
+
+func madd(a, b, t, u, v uint64) (uint64, uint64, uint64) {
+	var carry uint64
+	hi, lo := bits.Mul64(a, b)
+	v, carry = bits.Add64(lo, v, 0)
+	u, carry = bits.Add64(hi, u, carry)
+	t, _ = bits.Add64(t, 0, carry)
+	return t, u, v
+}
+
+// madd0 hi = a*b + c (discards lo bits)
+func madd0(a, b, c uint64) (hi uint64) {
+	var carry, lo uint64
+	hi, lo = bits.Mul64(a, b)
+	_, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd1 hi, lo = a*b + c
+func madd1(a, b, c uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2 hi, lo = a*b + c + d
+func madd2(a, b, c, d uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+// madd2s superhi, hi, lo = 2*a*b + c + d + e
+func madd2s(a, b, c, d, e uint64) (superhi, hi, lo uint64) {
+	var carry, sum uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+
+	sum, carry = bits.Add64(c, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, sum, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	hi, _ = bits.Add64(hi, 0, d)
+	return
+}
+
+func madd1s(a, b, d, e uint64) (superhi, hi, lo uint64) {
+	var carry uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+	lo, carry = bits.Add64(lo, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	hi, _ = bits.Add64(hi, 0, d)
+	return
+}
+
+func madd2sb(a, b, c, e uint64) (superhi, hi, lo uint64) {
+	var carry, sum uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+
+	sum, carry = bits.Add64(c, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, sum, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd1sb(a, b, e uint64) (superhi, hi, lo uint64) {
+	var carry uint64
+
+	hi, lo = bits.Mul64(a, b)
+	lo, carry = bits.Add64(lo, lo, 0)
+	hi, superhi = bits.Add64(hi, hi, carry)
+	lo, carry = bits.Add64(lo, e, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	return
+}
+
+func madd3(a, b, c, d, e uint64) (hi uint64, lo uint64) {
+	var carry uint64
+	hi, lo = bits.Mul64(a, b)
+	c, carry = bits.Add64(c, d, 0)
+	hi, _ = bits.Add64(hi, 0, carry)
+	lo, carry = bits.Add64(lo, c, 0)
+	hi, _ = bits.Add64(hi, e, carry)
+	return
+}
diff --git a/pkg/core/curves/native/bls12-381/arithmetic_fallback_test.go b/pkg/core/curves/native/bls12-381/arithmetic_fallback_test.go
new file mode 100644
index 00000000..98a01c37
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/arithmetic_fallback_test.go
@@ -0,0 +1,230 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"github.com/stretchr/testify/assert"
+	"math/bits"
+	mrand "math/rand"
+	"testing"
+)
+
+func TestFieldElementAdd(t *testing.T) {
+	for i := 0; i < 25; i++ {
+		a := new(fe)
+		z := new(fe)
+		x := new(fe)
+		y := new(fe)
+
+		x[0] = mrand.Uint64()
+		x[1] = mrand.Uint64()
+		x[2] = mrand.Uint64()
+		x[3] = mrand.Uint64()
+
+		y[0] = mrand.Uint64()
+		y[1] = mrand.Uint64()
+		y[2] = mrand.Uint64()
+		y[3] = mrand.Uint64()
+		newAdd(z, x, y)
+		oldAdd(a, x, y)
+		assert.Equal(t, z, a)
+	}
+}
+
+func newAdd(z, x, y *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	z[1], carry = bits.Add64(x[1], y[1], carry)
+	z[2], carry = bits.Add64(x[2], y[2], carry)
+	z[3], carry = bits.Add64(x[3], y[3], carry)
+	z[4], carry = bits.Add64(x[4], y[4], carry)
+	z[5], _ = bits.Add64(x[5], y[5], carry)
+
+	setZConstantTime(z)
+}
+
+func setZConstantTime(z *fe) {
+	// Get q as fe
+	q := &fe{
+		13402431016077863595,
+		2210141511517208575,
+		7435674573564081700,
+		7239337960414712511,
+		5412103778470702295,
+		1873798617647539866,
+	}
+
+	// if z > q -> 1
+	// if z < q -> -1
+	// if z == q -> 0
+	cmpZQ := z.cmp(q)
+	// twiddle cmpZQ st 1 --> 1, {-1,0} --> 0
+	flag := ^((cmpZQ - 1) >> 31) & 1
+
+	// z-q
+	zPrime := &fe{}
+	var b uint64
+	zPrime[0], b = bits.Sub64(z[0], q[0], 0)
+	zPrime[1], b = bits.Sub64(z[1], q[1], b)
+	zPrime[2], b = bits.Sub64(z[2], q[2], b)
+	zPrime[3], b = bits.Sub64(z[3], q[3], b)
+	zPrime[4], b = bits.Sub64(z[4], q[4], b)
+	zPrime[5], _ = bits.Sub64(z[5], q[5], b)
+
+	z.cmove(uint(flag), zPrime)
+}
+
+func oldAdd(z, x, y *fe) {
+	var carry uint64
+
+	z[0], carry = bits.Add64(x[0], y[0], 0)
+	z[1], carry = bits.Add64(x[1], y[1], carry)
+	z[2], carry = bits.Add64(x[2], y[2], carry)
+	z[3], carry = bits.Add64(x[3], y[3], carry)
+	z[4], carry = bits.Add64(x[4], y[4], carry)
+	z[5], _ = bits.Add64(x[5], y[5], carry)
+
+	// if z > q --> z -= q
+	// note: this is NOT constant time
+	if !(z[5] < 1873798617647539866 || (z[5] == 1873798617647539866 && (z[4] < 5412103778470702295 || (z[4] == 5412103778470702295 && (z[3] < 7239337960414712511 || (z[3] == 7239337960414712511 && (z[2] < 7435674573564081700 || (z[2] == 7435674573564081700 && (z[1] < 2210141511517208575 || (z[1] == 2210141511517208575 && (z[0] < 13402431016077863595))))))))))) {
+		var b uint64
+		z[0], b = bits.Sub64(z[0], 13402431016077863595, 0)
+		z[1], b = bits.Sub64(z[1], 2210141511517208575, b)
+		z[2], b = bits.Sub64(z[2], 7435674573564081700, b)
+		z[3], b = bits.Sub64(z[3], 7239337960414712511, b)
+		z[4], b = bits.Sub64(z[4], 5412103778470702295, b)
+		z[5], _ = bits.Sub64(z[5], 1873798617647539866, b)
+	}
+}
+
+func TestFieldElementSub(t *testing.T) {
+	for i := 0; i < 25; i++ {
+		a := new(fe)
+		z := new(fe)
+		x := new(fe)
+		y := new(fe)
+
+		x[0] = mrand.Uint64()
+		x[1] = mrand.Uint64()
+		x[2] = mrand.Uint64()
+		x[3] = mrand.Uint64()
+
+		y[0] = mrand.Uint64()
+		y[1] = mrand.Uint64()
+		y[2] = mrand.Uint64()
+		y[3] = mrand.Uint64()
+		newSub(z, x, y)
+		oldSub(a, x, y)
+		assert.Equal(t, z, a)
+	}
+}
+
+func oldSub(z, x, y *fe) {
+	var b uint64
+	z[0], b = bits.Sub64(x[0], y[0], 0)
+	z[1], b = bits.Sub64(x[1], y[1], b)
+	z[2], b = bits.Sub64(x[2], y[2], b)
+	z[3], b = bits.Sub64(x[3], y[3], b)
+	z[4], b = bits.Sub64(x[4], y[4], b)
+	z[5], b = bits.Sub64(x[5], y[5], b)
+	if b != 0 {
+		var c uint64
+		z[0], c = bits.Add64(z[0], 13402431016077863595, 0)
+		z[1], c = bits.Add64(z[1], 2210141511517208575, c)
+		z[2], c = bits.Add64(z[2], 7435674573564081700, c)
+		z[3], c = bits.Add64(z[3], 7239337960414712511, c)
+		z[4], c = bits.Add64(z[4], 5412103778470702295, c)
+		z[5], _ = bits.Add64(z[5], 1873798617647539866, c)
+	}
+}
+
+func newSub(z, x, y *fe) {
+	var b uint64
+	z[0], b = bits.Sub64(x[0], y[0], 0)
+	z[1], b = bits.Sub64(x[1], y[1], b)
+	z[2], b = bits.Sub64(x[2], y[2], b)
+	z[3], b = bits.Sub64(x[3], y[3], b)
+	z[4], b = bits.Sub64(x[4], y[4], b)
+	z[5], b = bits.Sub64(x[5], y[5], b)
+
+	setZConstantTimeSub(z, b)
+}
+
+func setZConstantTimeSub(z *fe, b uint64) {
+	// Get cmove flag based off of b
+	bIsZero := b == 0
+	isZeroToMap := make(map[bool]uint)
+	isZeroToMap[true] = 0
+	isZeroToMap[false] = 1
+
+	flag := isZeroToMap[bIsZero]
+
+	// To set if B is not Zero
+	zPrime := &fe{}
+	var c uint64
+	zPrime[0], c = bits.Add64(z[0], 13402431016077863595, 0)
+	zPrime[1], c = bits.Add64(z[1], 2210141511517208575, c)
+	zPrime[2], c = bits.Add64(z[2], 7435674573564081700, c)
+	zPrime[3], c = bits.Add64(z[3], 7239337960414712511, c)
+	zPrime[4], c = bits.Add64(z[4], 5412103778470702295, c)
+	zPrime[5], _ = bits.Add64(z[5], 1873798617647539866, c)
+
+	// Move zPrime into z if flag
+	z.cmove(flag, zPrime)
+}
+
+func TestFieldElementNeg(t *testing.T) {
+	for i := 0; i < 25; i++ {
+		a := new(fe)
+		z := new(fe)
+		x := new(fe)
+
+		x[0] = mrand.Uint64()
+		x[1] = mrand.Uint64()
+		x[2] = mrand.Uint64()
+		x[3] = mrand.Uint64()
+
+		newNeg(z, x)
+		oldNeg(a, x)
+		assert.Equal(t, z, a)
+	}
+}
+
+func oldNeg(z *fe, x *fe) {
+	if x.isZero() {
+		z.zero()
+		return
+	}
+	var borrow uint64
+	z[0], borrow = bits.Sub64(13402431016077863595, x[0], 0)
+	z[1], borrow = bits.Sub64(2210141511517208575, x[1], borrow)
+	z[2], borrow = bits.Sub64(7435674573564081700, x[2], borrow)
+	z[3], borrow = bits.Sub64(7239337960414712511, x[3], borrow)
+	z[4], borrow = bits.Sub64(5412103778470702295, x[4], borrow)
+	z[5], _ = bits.Sub64(1873798617647539866, x[5], borrow)
+}
+
+func newNeg(z *fe, x *fe) {
+	var borrow uint64
+	z[0], borrow = bits.Sub64(13402431016077863595, x[0], 0)
+	z[1], borrow = bits.Sub64(2210141511517208575, x[1], borrow)
+	z[2], borrow = bits.Sub64(7435674573564081700, x[2], borrow)
+	z[3], borrow = bits.Sub64(7239337960414712511, x[3], borrow)
+	z[4], borrow = bits.Sub64(5412103778470702295, x[4], borrow)
+	z[5], _ = bits.Sub64(1873798617647539866, x[5], borrow)
+
+	isZeroToMap := make(map[bool]uint)
+	isZeroToMap[true] = 1
+	isZeroToMap[false] = 0
+
+	flag := isZeroToMap[x.isZero()]
+	zPrime := &fe{}
+	zPrime.zero()
+
+	z.cmove(flag, zPrime)
+}
diff --git a/pkg/core/curves/native/bls12-381/arithmetic_x86.s b/pkg/core/curves/native/bls12-381/arithmetic_x86.s
new file mode 100644
index 00000000..9dd5a90f
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/arithmetic_x86.s
@@ -0,0 +1,2151 @@
+// +build amd64,!generic
+
+#include "textflag.h"
+
+// single-precision addition w/ modular reduction
+// a' = (a + b) % p
+TEXT ·addAssign(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ b+8(FP), SI
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+
+	// |
+	ADDQ (SI), R8
+	ADCQ 8(SI), R9
+	ADCQ 16(SI), R10
+	ADCQ 24(SI), R11
+	ADCQ 32(SI), R12
+	ADCQ 40(SI), R13
+
+	// |
+	MOVQ R8, R14
+	MOVQ R9, R15
+	MOVQ R10, CX
+	MOVQ R11, DX
+	MOVQ R12, SI
+	MOVQ R13, BX
+	MOVQ $0xb9feffffffffaaab, AX
+	SUBQ AX, R14
+	MOVQ $0x1eabfffeb153ffff, AX
+	SBBQ AX, R15
+	MOVQ $0x6730d2a0f6b0f624, AX
+	SBBQ AX, CX
+	MOVQ $0x64774b84f38512bf, AX
+	SBBQ AX, DX
+	MOVQ $0x4b1ba7b6434bacd7, AX
+	SBBQ AX, SI
+	MOVQ $0x1a0111ea397fe69a, AX
+	SBBQ AX, BX
+	CMOVQCC R14, R8
+	CMOVQCC R15, R9
+	CMOVQCC CX, R10
+	CMOVQCC DX, R11
+	CMOVQCC SI, R12
+	CMOVQCC BX, R13
+
+	// |
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+
+/*	 | end											*/
+
+
+// single-precision addition w/ modular reduction
+// c = (a + b) % p
+TEXT ·add(SB), NOSPLIT, $0-24
+	// |
+	MOVQ a+8(FP), DI
+	MOVQ b+16(FP), SI
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+
+	// |
+	ADDQ (SI), R8
+	ADCQ 8(SI), R9
+	ADCQ 16(SI), R10
+	ADCQ 24(SI), R11
+	ADCQ 32(SI), R12
+	ADCQ 40(SI), R13
+
+	// |
+	MOVQ R8, R14
+	MOVQ R9, R15
+	MOVQ R10, CX
+	MOVQ R11, DX
+	MOVQ R12, SI
+	MOVQ R13, BX
+	MOVQ $0xb9feffffffffaaab, DI
+	SUBQ DI, R14
+	MOVQ $0x1eabfffeb153ffff, DI
+	SBBQ DI, R15
+	MOVQ $0x6730d2a0f6b0f624, DI
+	SBBQ DI, CX
+	MOVQ $0x64774b84f38512bf, DI
+	SBBQ DI, DX
+	MOVQ $0x4b1ba7b6434bacd7, DI
+	SBBQ DI, SI
+	MOVQ $0x1a0111ea397fe69a, DI
+	SBBQ DI, BX
+	CMOVQCC R14, R8
+	CMOVQCC R15, R9
+	CMOVQCC CX, R10
+	CMOVQCC DX, R11
+	CMOVQCC SI, R12
+	CMOVQCC BX, R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision addition w/o reduction check
+// c = (a + b)
+TEXT ·ladd(SB), NOSPLIT, $0-24
+	// |
+	MOVQ a+8(FP), DI
+	MOVQ b+16(FP), SI
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+
+	// |
+	ADDQ (SI), R8
+	ADCQ 8(SI), R9
+	ADCQ 16(SI), R10
+	ADCQ 24(SI), R11
+	ADCQ 32(SI), R12
+	ADCQ 40(SI), R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision addition w/o check
+// a' = a + b
+TEXT ·laddAssign(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ b+8(FP), SI
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+
+	// |
+	ADDQ (SI), R8
+	ADCQ 8(SI), R9
+	ADCQ 16(SI), R10
+	ADCQ 24(SI), R11
+	ADCQ 32(SI), R12
+	ADCQ 40(SI), R13
+
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision subtraction with modular reduction
+// c = (a - b) % p
+TEXT ·sub(SB), NOSPLIT, $0-24
+	// |
+	MOVQ a+8(FP), DI
+	MOVQ b+16(FP), SI
+	XORQ AX, AX
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+	SUBQ (SI), R8
+	SBBQ 8(SI), R9
+	SBBQ 16(SI), R10
+	SBBQ 24(SI), R11
+	SBBQ 32(SI), R12
+	SBBQ 40(SI), R13
+
+	// |
+	MOVQ $0xb9feffffffffaaab, R14
+	MOVQ $0x1eabfffeb153ffff, R15
+	MOVQ $0x6730d2a0f6b0f624, CX
+	MOVQ $0x64774b84f38512bf, DX
+	MOVQ $0x4b1ba7b6434bacd7, SI
+	MOVQ $0x1a0111ea397fe69a, BX
+	CMOVQCC AX, R14
+	CMOVQCC AX, R15
+	CMOVQCC AX, CX
+	CMOVQCC AX, DX
+	CMOVQCC AX, SI
+	CMOVQCC AX, BX
+	ADDQ R14, R8
+	ADCQ R15, R9
+	ADCQ CX, R10
+	ADCQ DX, R11
+	ADCQ SI, R12
+	ADCQ BX, R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision subtraction with modular reduction
+// a' = (a - b) % p
+TEXT ·subAssign(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ b+8(FP), SI
+	XORQ AX, AX
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+	SUBQ (SI), R8
+	SBBQ 8(SI), R9
+	SBBQ 16(SI), R10
+	SBBQ 24(SI), R11
+	SBBQ 32(SI), R12
+	SBBQ 40(SI), R13
+
+	// |
+	MOVQ $0xb9feffffffffaaab, R14
+	MOVQ $0x1eabfffeb153ffff, R15
+	MOVQ $0x6730d2a0f6b0f624, CX
+	MOVQ $0x64774b84f38512bf, DX
+	MOVQ $0x4b1ba7b6434bacd7, SI
+	MOVQ $0x1a0111ea397fe69a, BX
+	CMOVQCC AX, R14
+	CMOVQCC AX, R15
+	CMOVQCC AX, CX
+	CMOVQCC AX, DX
+	CMOVQCC AX, SI
+	CMOVQCC AX, BX
+	ADDQ R14, R8
+	ADCQ R15, R9
+	ADCQ CX, R10
+	ADCQ DX, R11
+	ADCQ SI, R12
+	ADCQ BX, R13
+
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision subtraction no modular red check
+// a' = (a - b)
+TEXT ·lsubAssign(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ b+8(FP), SI
+
+	// |
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+	SUBQ (SI), R8
+	SBBQ 8(SI), R9
+	SBBQ 16(SI), R10
+	SBBQ 24(SI), R11
+	SBBQ 32(SI), R12
+	SBBQ 40(SI), R13
+	
+	// |
+	MOVQ a+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+// single-precision doubling
+// c = (2 * a) % p
+TEXT ·double(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+8(FP), DI
+
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+	ADDQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+
+	// |
+	MOVQ R8, R14
+	MOVQ R9, R15
+	MOVQ R10, CX
+	MOVQ R11, DX
+	MOVQ R12, SI
+	MOVQ R13, BX
+	MOVQ $0xb9feffffffffaaab, DI
+	SUBQ DI, R14
+	MOVQ $0x1eabfffeb153ffff, DI
+	SBBQ DI, R15
+	MOVQ $0x6730d2a0f6b0f624, DI
+	SBBQ DI, CX
+	MOVQ $0x64774b84f38512bf, DI
+	SBBQ DI, DX
+	MOVQ $0x4b1ba7b6434bacd7, DI
+	SBBQ DI, SI
+	MOVQ $0x1a0111ea397fe69a, DI
+	SBBQ DI, BX
+	CMOVQCC R14, R8
+	CMOVQCC R15, R9
+	CMOVQCC CX, R10
+	CMOVQCC DX, R11
+	CMOVQCC SI, R12
+	CMOVQCC BX, R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision doubling
+// a' = (2 * a) % p
+TEXT ·doubleAssign(SB), NOSPLIT, $0-8
+	// |
+	MOVQ a+0(FP), DI
+
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+	ADDQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+
+	// |
+	MOVQ R8, R14
+	MOVQ R9, R15
+	MOVQ R10, CX
+	MOVQ R11, DX
+	MOVQ R12, SI
+	MOVQ R13, BX
+	MOVQ $0xb9feffffffffaaab, AX
+	SUBQ AX, R14
+	MOVQ $0x1eabfffeb153ffff, AX
+	SBBQ AX, R15
+	MOVQ $0x6730d2a0f6b0f624, AX
+	SBBQ AX, CX
+	MOVQ $0x64774b84f38512bf, AX
+	SBBQ AX, DX
+	MOVQ $0x4b1ba7b6434bacd7, AX
+	SBBQ AX, SI
+	MOVQ $0x1a0111ea397fe69a, AX
+	SBBQ AX, BX
+	CMOVQCC R14, R8
+	CMOVQCC R15, R9
+	CMOVQCC CX, R10
+	CMOVQCC DX, R11
+	CMOVQCC SI, R12
+	CMOVQCC BX, R13
+
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+// single-precision doubling w/o carry check
+// c = 2 * a
+TEXT ·ldouble(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+8(FP), DI
+
+	MOVQ (DI), R8
+	MOVQ 8(DI), R9
+	MOVQ 16(DI), R10
+	MOVQ 24(DI), R11
+	MOVQ 32(DI), R12
+	MOVQ 40(DI), R13
+
+	// |
+	ADDQ R8, R8
+	ADCQ R9, R9
+	ADCQ R10, R10
+	ADCQ R11, R11
+	ADCQ R12, R12
+	ADCQ R13, R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+
+	RET
+/*	 | end													*/
+
+
+TEXT ·_neg(SB), NOSPLIT, $0-16
+	// |
+	MOVQ a+8(FP), DI
+
+	// |
+	MOVQ $0xb9feffffffffaaab, R8
+	MOVQ $0x1eabfffeb153ffff, R9
+	MOVQ $0x6730d2a0f6b0f624, R10
+	MOVQ $0x64774b84f38512bf, R11
+	MOVQ $0x4b1ba7b6434bacd7, R12
+	MOVQ $0x1a0111ea397fe69a, R13
+	SUBQ (DI), R8
+	SBBQ 8(DI), R9
+	SBBQ 16(DI), R10
+	SBBQ 24(DI), R11
+	SBBQ 32(DI), R12
+	SBBQ 40(DI), R13
+
+	// |
+	MOVQ c+0(FP), DI
+	MOVQ R8, (DI)
+	MOVQ R9, 8(DI)
+	MOVQ R10, 16(DI)
+	MOVQ R11, 24(DI)
+	MOVQ R12, 32(DI)
+	MOVQ R13, 40(DI)
+	RET
+/*	 | end													*/
+
+
+
+// multiplication without using MULX/ADX
+// c = a * b % p
+TEXT ·mulNoADX(SB), NOSPLIT, $24-24
+	// |
+
+/* inputs                                  */
+
+	MOVQ a+8(FP), DI
+	MOVQ b+16(FP), SI
+	MOVQ $0x00, R9
+	MOVQ $0x00, R10
+	MOVQ $0x00, R11
+	MOVQ $0x00, R12
+	MOVQ $0x00, R13
+	MOVQ $0x00, R14
+	MOVQ $0x00, R15
+
+	// |
+
+/* i0                                   */
+
+	// | a0 @ CX
+	MOVQ (DI), CX
+
+	// | a0 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	MOVQ AX, (SP)
+	MOVQ DX, R8
+
+	// | a0 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R8
+	ADCQ DX, R9
+
+	// | a0 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R9
+	ADCQ DX, R10
+
+	// | a0 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R10
+	ADCQ DX, R11
+
+	// | a0 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R11
+	ADCQ DX, R12
+
+	// | a0 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+
+	// |
+
+/* i1                                   */
+
+	// | a1 @ CX
+	MOVQ 8(DI), CX
+	MOVQ $0x00, BX
+
+	// | a1 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	ADDQ AX, R8
+	ADCQ DX, R9
+	ADCQ $0x00, R10
+	ADCQ $0x00, BX
+	MOVQ R8, 8(SP)
+	MOVQ $0x00, R8
+
+	// | a1 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R9
+	ADCQ DX, R10
+	ADCQ BX, R11
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a1 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R10
+	ADCQ DX, R11
+	ADCQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a1 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R11
+	ADCQ DX, R12
+	ADCQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a1 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+	ADCQ BX, R14
+
+	// | a1 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R13
+	ADCQ DX, R14
+
+	// |
+
+/* i2                                   */
+
+	// | a2 @ CX
+	MOVQ 16(DI), CX
+	MOVQ $0x00, BX
+
+	// | a2 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	ADDQ AX, R9
+	ADCQ DX, R10
+	ADCQ $0x00, R11
+	ADCQ $0x00, BX
+	MOVQ R9, 16(SP)
+	MOVQ $0x00, R9
+
+	// | a2 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R10
+	ADCQ DX, R11
+	ADCQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a2 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R11
+	ADCQ DX, R12
+	ADCQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a2 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+	ADCQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a2 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R13
+	ADCQ DX, R14
+	ADCQ BX, R15
+
+	// | a2 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R14
+	ADCQ DX, R15
+
+	// |
+
+/* i3                                   */
+
+	// | a3 @ CX
+	MOVQ 24(DI), CX
+	MOVQ $0x00, BX
+
+	// | a3 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	ADDQ AX, R10
+	ADCQ DX, R11
+	ADCQ $0x00, R12
+	ADCQ $0x00, BX
+
+	// | a3 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R11
+	ADCQ DX, R12
+	ADCQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a3 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+	ADCQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a3 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R13
+	ADCQ DX, R14
+	ADCQ BX, R15
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a3 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R14
+	ADCQ DX, R15
+	ADCQ BX, R8
+
+	// | a3 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R15
+	ADCQ DX, R8
+
+	// |
+
+/* i4                                   */
+
+	// | a4 @ CX
+	MOVQ 32(DI), CX
+	MOVQ $0x00, BX
+
+	// | a4 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	ADDQ AX, R11
+	ADCQ DX, R12
+	ADCQ $0x00, R13
+	ADCQ $0x00, BX
+
+	// | a4 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+	ADCQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a4 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R13
+	ADCQ DX, R14
+	ADCQ BX, R15
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a4 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R14
+	ADCQ DX, R15
+	ADCQ BX, R8
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a4 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R15
+	ADCQ DX, R8
+	ADCQ BX, R9
+
+	// | a4 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R8
+	ADCQ DX, R9
+
+	// |
+
+/* i5                                   */
+
+	// | a5 @ CX
+	MOVQ 40(DI), CX
+	MOVQ $0x00, BX
+
+	// | a5 * b0
+	MOVQ (SI), AX
+	MULQ CX
+	ADDQ AX, R12
+	ADCQ DX, R13
+	ADCQ $0x00, R14
+	ADCQ $0x00, BX
+
+	// | a5 * b1
+	MOVQ 8(SI), AX
+	MULQ CX
+	ADDQ AX, R13
+	ADCQ DX, R14
+	ADCQ BX, R15
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a5 * b2
+	MOVQ 16(SI), AX
+	MULQ CX
+	ADDQ AX, R14
+	ADCQ DX, R15
+	ADCQ BX, R8
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a5 * b3
+	MOVQ 24(SI), AX
+	MULQ CX
+	ADDQ AX, R15
+	ADCQ DX, R8
+	ADCQ BX, R9
+	MOVQ $0x00, BX
+	ADCQ $0x00, BX
+
+	// | a5 * b4
+	MOVQ 32(SI), AX
+	MULQ CX
+	ADDQ AX, R8
+	ADCQ DX, R9
+	ADCQ $0x00, BX
+
+	// | a5 * b5
+	MOVQ 40(SI), AX
+	MULQ CX
+	ADDQ AX, R9
+	ADCQ DX, BX
+
+	// |
+
+/* 			                                     */
+
+	// |
+	// | W
+	// | 0   (SP)      | 1   8(SP)     | 2   16(SP)    | 3   R10       | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  R9        | 11  BX
+
+
+	MOVQ (SP), CX
+	MOVQ 8(SP), DI
+	MOVQ 16(SP), SI
+	MOVQ BX, (SP)
+	MOVQ R9, 8(SP)
+
+	// |
+
+/* montgomery reduction                    */
+
+	// |
+
+/* i0                                   */
+
+	// |
+	// | W
+	// | 0   CX        | 1   DI        | 2   SI        | 3   R10       | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  8(SP)     | 11  (SP)
+
+
+	// | | u0 = w0 * inp
+	MOVQ CX, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w0 @ CX
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, CX
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w1 @ DI
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, DI
+	ADCQ $0x00, DX
+	ADDQ BX, DI
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w2 @ SI
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, SI
+	ADCQ $0x00, DX
+	ADDQ BX, SI
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w3 @ R10
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R10
+	ADCQ $0x00, DX
+	ADDQ BX, R10
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w4 @ R11
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R11
+	ADCQ $0x00, DX
+	ADDQ BX, R11
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w5 @ R12
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ $0x00, DX
+	ADDQ BX, R12
+
+	// | w6 @ R13
+	ADCQ DX, R13
+	ADCQ $0x00, CX
+
+	// |
+
+/* i1                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   DI        | 2   SI        | 3   R10       | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  8(SP)     | 11  (SP)
+
+
+	// | | u1 = w1 * inp
+	MOVQ DI, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w1 @ DI
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, DI
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w2 @ SI
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, SI
+	ADCQ $0x00, DX
+	ADDQ BX, SI
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w3 @ R10
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, R10
+	ADCQ $0x00, DX
+	ADDQ BX, R10
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w4 @ R11
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R11
+	ADCQ $0x00, DX
+	ADDQ BX, R11
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w5 @ R12
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ $0x00, DX
+	ADDQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w6 @ R13
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, R13
+	ADCQ DX, CX
+	ADDQ BX, R13
+
+	// | w7 @ R14
+	ADCQ CX, R14
+	MOVQ $0x00, CX
+	ADCQ $0x00, CX
+
+	// |
+
+/* i2                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   SI        | 3   R10       | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  8(SP)     | 11  (SP)
+
+
+	// | | u2 = w2 * inp
+	MOVQ SI, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w2 @ SI
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, SI
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w3 @ R10
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, R10
+	ADCQ $0x00, DX
+	ADDQ BX, R10
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w4 @ R11
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, R11
+	ADCQ $0x00, DX
+	ADDQ BX, R11
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w5 @ R12
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ $0x00, DX
+	ADDQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w6 @ R13
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R13
+	ADCQ $0x00, DX
+	ADDQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w7 @ R14
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, R14
+	ADCQ DX, CX
+	ADDQ BX, R14
+
+	// | w8 @ R15
+	ADCQ CX, R15
+	MOVQ $0x00, CX
+	ADCQ $0x00, CX
+
+	// |
+
+/* i3                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   R10       | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  8(SP)     | 11  (SP)
+
+
+	// | | u3 = w3 * inp
+	MOVQ R10, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w3 @ R10
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, R10
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w4 @ R11
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, R11
+	ADCQ $0x00, DX
+	ADDQ BX, R11
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w5 @ R12
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ $0x00, DX
+	ADDQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w6 @ R13
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R13
+	ADCQ $0x00, DX
+	ADDQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w7 @ R14
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R14
+	ADCQ $0x00, DX
+	ADDQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w8 @ R15
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, R15
+	ADCQ DX, CX
+	ADDQ BX, R15
+
+	// | w9 @ R8
+	ADCQ CX, R8
+	MOVQ $0x00, CX
+	ADCQ $0x00, CX
+
+	// |
+
+/* i4                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   R11       | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  8(SP)     | 11  (SP)
+
+
+	// | | u4 = w4 * inp
+	MOVQ R11, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w4 @ R11
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, R11
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w5 @ R12
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ $0x00, DX
+	ADDQ BX, R12
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w6 @ R13
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, R13
+	ADCQ $0x00, DX
+	ADDQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w7 @ R14
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R14
+	ADCQ $0x00, DX
+	ADDQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w8 @ R15
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R15
+	ADCQ $0x00, DX
+	ADDQ BX, R15
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w9 @ R8
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, R8
+	ADCQ DX, CX
+	ADDQ BX, R8
+
+	// | move to idle register
+	MOVQ 8(SP), DI
+
+	// | w10 @ DI
+	ADCQ CX, DI
+	MOVQ $0x00, CX
+	ADCQ $0x00, CX
+
+	// |
+
+/* i5                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   -         | 5   R12
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  DI        | 11  (SP)
+
+
+	// | | u5 = w5 * inp
+	MOVQ R12, AX
+	MULQ ·Inp+0(SB)
+	MOVQ AX, R9
+	MOVQ $0x00, BX
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w5 @ R12
+	MOVQ ·modulus+0(SB), AX
+	MULQ R9
+	ADDQ AX, R12
+	ADCQ DX, BX
+
+	// | j1
+
+	// | w6 @ R13
+	MOVQ ·modulus+8(SB), AX
+	MULQ R9
+	ADDQ AX, R13
+	ADCQ $0x00, DX
+	ADDQ BX, R13
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j2
+
+	// | w7 @ R14
+	MOVQ ·modulus+16(SB), AX
+	MULQ R9
+	ADDQ AX, R14
+	ADCQ $0x00, DX
+	ADDQ BX, R14
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j3
+
+	// | w8 @ R15
+	MOVQ ·modulus+24(SB), AX
+	MULQ R9
+	ADDQ AX, R15
+	ADCQ $0x00, DX
+	ADDQ BX, R15
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j4
+
+	// | w9 @ R8
+	MOVQ ·modulus+32(SB), AX
+	MULQ R9
+	ADDQ AX, R8
+	ADCQ $0x00, DX
+	ADDQ BX, R8
+	MOVQ $0x00, BX
+	ADCQ DX, BX
+
+	// | j5
+
+	// | w10 @ DI
+	MOVQ ·modulus+40(SB), AX
+	MULQ R9
+	ADDQ AX, DI
+	ADCQ DX, CX
+	ADDQ BX, DI
+
+	// | w11 @ CX
+	ADCQ (SP), CX
+
+	// |
+	// | W montgomerry reduction ends
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   -         | 5   -
+	// | 6   R13       | 7   R14       | 8   R15       | 9   R8        | 10  DI        | 11  CX
+
+
+	// |
+
+
+/* modular reduction                       */
+
+	MOVQ R13, R10
+	SUBQ ·modulus+0(SB), R10
+	MOVQ R14, R11
+	SBBQ ·modulus+8(SB), R11
+	MOVQ R15, R12
+	SBBQ ·modulus+16(SB), R12
+	MOVQ R8, AX
+	SBBQ ·modulus+24(SB), AX
+	MOVQ DI, BX
+	SBBQ ·modulus+32(SB), BX
+	MOVQ CX, R9
+	SBBQ ·modulus+40(SB), R9
+	// |
+
+/* out                                     */
+
+	MOVQ    c+0(FP), SI
+	CMOVQCC R10, R13
+	MOVQ    R13, (SI)
+	CMOVQCC R11, R14
+	MOVQ    R14, 8(SI)
+	CMOVQCC R12, R15
+	MOVQ    R15, 16(SI)
+	CMOVQCC AX, R8
+	MOVQ    R8, 24(SI)
+	CMOVQCC BX, DI
+	MOVQ    DI, 32(SI)
+	CMOVQCC R9, CX
+	MOVQ    CX, 40(SI)
+	RET
+
+	// |
+
+/* end                                     */
+
+
+// multiplication
+// c = a * b % p
+TEXT ·mulADX(SB), NOSPLIT, $16-24
+	// |
+
+/* inputs                                  */
+
+	MOVQ a+8(FP), DI
+	MOVQ b+16(FP), SI
+	XORQ AX, AX
+
+	// |
+
+/* i0                                   */
+
+	// | a0 @ DX
+	MOVQ (DI), DX
+
+	// | a0 * b0
+	MULXQ (SI), AX, CX
+	MOVQ  AX, (SP)
+
+	// | a0 * b1
+	MULXQ 8(SI), AX, R8
+	ADCXQ AX, CX
+
+	// | a0 * b2
+	MULXQ 16(SI), AX, R9
+	ADCXQ AX, R8
+
+	// | a0 * b3
+	MULXQ 24(SI), AX, R10
+	ADCXQ AX, R9
+
+	// | a0 * b4
+	MULXQ 32(SI), AX, R11
+	ADCXQ AX, R10
+
+	// | a0 * b5
+	MULXQ 40(SI), AX, R12
+	ADCXQ AX, R11
+	ADCQ  $0x00, R12
+
+	// |
+
+/* i1                                   */
+
+	// | a1 @ DX
+	MOVQ 8(DI), DX
+	XORQ R13, R13
+
+	// | a1 * b0
+	MULXQ (SI), AX, BX
+	ADOXQ AX, CX
+	ADCXQ BX, R8
+	MOVQ  CX, 8(SP)
+
+	// | a1 * b1
+	MULXQ 8(SI), AX, BX
+	ADOXQ AX, R8
+	ADCXQ BX, R9
+
+	// | a1 * b2
+	MULXQ 16(SI), AX, BX
+	ADOXQ AX, R9
+	ADCXQ BX, R10
+
+	// | a1 * b3
+	MULXQ 24(SI), AX, BX
+	ADOXQ AX, R10
+	ADCXQ BX, R11
+
+	// | a1 * b4
+	MULXQ 32(SI), AX, BX
+	ADOXQ AX, R11
+	ADCXQ BX, R12
+
+	// | a1 * b5
+	MULXQ 40(SI), AX, BX
+	ADOXQ AX, R12
+	ADOXQ R13, R13
+	ADCXQ BX, R13
+
+	// |
+
+/* i2                                   */
+
+	// | a2 @ DX
+	MOVQ 16(DI), DX
+	XORQ R14, R14
+
+	// | a2 * b0
+	MULXQ (SI), AX, BX
+	ADOXQ AX, R8
+	ADCXQ BX, R9
+
+	// | a2 * b1
+	MULXQ 8(SI), AX, BX
+	ADOXQ AX, R9
+	ADCXQ BX, R10
+
+	// | a2 * b2
+	MULXQ 16(SI), AX, BX
+	ADOXQ AX, R10
+	ADCXQ BX, R11
+
+	// | a2 * b3
+	MULXQ 24(SI), AX, BX
+	ADOXQ AX, R11
+	ADCXQ BX, R12
+
+	// | a2 * b4
+	MULXQ 32(SI), AX, BX
+	ADOXQ AX, R12
+	ADCXQ BX, R13
+
+	// | a2 * b5
+	MULXQ 40(SI), AX, BX
+	ADOXQ AX, R13
+	ADOXQ R14, R14
+	ADCXQ BX, R14
+
+	// |
+
+/* i3                                   */
+
+	// | a3 @ DX
+	MOVQ 24(DI), DX
+	XORQ R15, R15
+
+	// | a3 * b0
+	MULXQ (SI), AX, BX
+	ADOXQ AX, R9
+	ADCXQ BX, R10
+
+	// | a3 * b1
+	MULXQ 8(SI), AX, BX
+	ADOXQ AX, R10
+	ADCXQ BX, R11
+
+	// | a3 * b2
+	MULXQ 16(SI), AX, BX
+	ADOXQ AX, R11
+	ADCXQ BX, R12
+
+	// | a3 * b3
+	MULXQ 24(SI), AX, BX
+	ADOXQ AX, R12
+	ADCXQ BX, R13
+
+	// | a3 * b4
+	MULXQ 32(SI), AX, BX
+	ADOXQ AX, R13
+	ADCXQ BX, R14
+
+	// | a3 * b5
+	MULXQ 40(SI), AX, BX
+	ADOXQ AX, R14
+	ADOXQ R15, R15
+	ADCXQ BX, R15
+
+	// |
+
+/* i4                                   */
+
+	// | a4 @ DX
+	MOVQ 32(DI), DX
+	XORQ CX, CX
+
+	// | a4 * b0
+	MULXQ (SI), AX, BX
+	ADOXQ AX, R10
+	ADCXQ BX, R11
+
+	// | a4 * b1
+	MULXQ 8(SI), AX, BX
+	ADOXQ AX, R11
+	ADCXQ BX, R12
+
+	// | a4 * b2
+	MULXQ 16(SI), AX, BX
+	ADOXQ AX, R12
+	ADCXQ BX, R13
+
+	// | a4 * b3
+	MULXQ 24(SI), AX, BX
+	ADOXQ AX, R13
+	ADCXQ BX, R14
+
+	// | a4 * b4
+	MULXQ 32(SI), AX, BX
+	ADOXQ AX, R14
+	ADCXQ BX, R15
+
+	// | a4 * b5
+	MULXQ 40(SI), AX, BX
+	ADOXQ AX, R15
+	ADOXQ CX, CX
+	ADCXQ BX, CX
+
+	// |
+
+/* i5                                   */
+
+	// | a5 @ DX
+	MOVQ 40(DI), DX
+	XORQ DI, DI
+
+	// | a5 * b0
+	MULXQ (SI), AX, BX
+	ADOXQ AX, R11
+	ADCXQ BX, R12
+
+	// | a5 * b1
+	MULXQ 8(SI), AX, BX
+	ADOXQ AX, R12
+	ADCXQ BX, R13
+
+	// | a5 * b2
+	MULXQ 16(SI), AX, BX
+	ADOXQ AX, R13
+	ADCXQ BX, R14
+
+	// | a5 * b3
+	MULXQ 24(SI), AX, BX
+	ADOXQ AX, R14
+	ADCXQ BX, R15
+
+	// | a5 * b4
+	MULXQ 32(SI), AX, BX
+	ADOXQ AX, R15
+	ADCXQ BX, CX
+
+	// | a5 * b5
+	MULXQ 40(SI), AX, BX
+	ADOXQ AX, CX
+	ADOXQ BX, DI
+	ADCQ  $0x00, DI
+
+	// |
+
+/* 			                                     */
+
+	// |
+	// | W
+	// | 0   (SP)      | 1   8(SP)     | 2   R8        | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  DI
+
+
+	MOVQ (SP), BX
+	MOVQ 8(SP), SI
+	MOVQ DI, (SP)
+
+	// |
+	// | W ready to mont
+	// | 0   BX        | 1   SI        | 2   R8        | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// |
+
+/* montgomery reduction                    */
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i0                                   */
+
+	// |
+	// | W
+	// | 0   BX        | 1   SI        | 2   R8        | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u0 = w0 * inp
+	MOVQ  BX, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w0 @ BX
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, BX
+	ADCXQ DI, SI
+
+	// | j1
+
+	// | w1 @ SI
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, SI
+	ADCXQ DI, R8
+
+	// | j2
+
+	// | w2 @ R8
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R8
+	ADCXQ DI, R9
+
+	// | j3
+
+	// | w3 @ R9
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R9
+	ADCXQ DI, R10
+
+	// | j4
+
+	// | w4 @ R10
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R10
+	ADCXQ DI, R11
+
+	// | j5
+
+	// | w5 @ R11
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+	ADOXQ BX, R12
+	ADCXQ BX, BX
+	MOVQ  $0x00, AX
+	ADOXQ AX, BX
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i1                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   SI        | 2   R8        | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u1 = w1 * inp
+	MOVQ  SI, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w1 @ SI
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, SI
+	ADCXQ DI, R8
+
+	// | j1
+
+	// | w2 @ R8
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, R8
+	ADCXQ DI, R9
+
+	// | j2
+
+	// | w3 @ R9
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R9
+	ADCXQ DI, R10
+
+	// | j3
+
+	// | w4 @ R10
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R10
+	ADCXQ DI, R11
+
+	// | j4
+
+	// | w5 @ R11
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+
+	// | j5
+
+	// | w6 @ R12
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, R12
+	ADCXQ DI, R13
+	ADOXQ BX, R13
+	ADCXQ SI, SI
+	MOVQ  $0x00, AX
+	ADOXQ AX, SI
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i2                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   R8        | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u2 = w2 * inp
+	MOVQ  R8, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w2 @ R8
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, R8
+	ADCXQ DI, R9
+
+	// | j1
+
+	// | w3 @ R9
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, R9
+	ADCXQ DI, R10
+
+	// | j2
+
+	// | w4 @ R10
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R10
+	ADCXQ DI, R11
+
+	// | j3
+
+	// | w5 @ R11
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+
+	// | j4
+
+	// | w6 @ R12
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R12
+	ADCXQ DI, R13
+
+	// | j5
+
+	// | w7 @ R13
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, R13
+	ADCXQ DI, R14
+	ADOXQ SI, R14
+	ADCXQ R8, R8
+	MOVQ  $0x00, AX
+	ADOXQ AX, R8
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i3                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   R9        | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u3 = w3 * inp
+	MOVQ  R9, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w3 @ R9
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, R9
+	ADCXQ DI, R10
+
+	// | j1
+
+	// | w4 @ R10
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, R10
+	ADCXQ DI, R11
+
+	// | j2
+
+	// | w5 @ R11
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+
+	// | j3
+
+	// | w6 @ R12
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R12
+	ADCXQ DI, R13
+
+	// | j4
+
+	// | w7 @ R13
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R13
+	ADCXQ DI, R14
+
+	// | j5
+
+	// | w8 @ R14
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, R14
+	ADCXQ DI, R15
+	ADOXQ R8, R15
+	ADCXQ R9, R9
+	MOVQ  $0x00, AX
+	ADOXQ AX, R9
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i4                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   R10       | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u4 = w4 * inp
+	MOVQ  R10, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w4 @ R10
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, R10
+	ADCXQ DI, R11
+
+	// | j1
+
+	// | w5 @ R11
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+
+	// | j2
+
+	// | w6 @ R12
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R12
+	ADCXQ DI, R13
+
+	// | j3
+
+	// | w7 @ R13
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R13
+	ADCXQ DI, R14
+
+	// | j4
+
+	// | w8 @ R14
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R14
+	ADCXQ DI, R15
+
+	// | j5
+
+	// | w9 @ R15
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, R15
+	ADCXQ DI, CX
+	ADOXQ R9, CX
+	ADCXQ R10, R10
+	MOVQ  $0x00, AX
+	ADOXQ AX, R10
+
+	// | clear flags
+	XORQ AX, AX
+
+	// |
+
+/* i5                                   */
+
+	// |
+	// | W
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   -         | 5   R11
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  (SP)
+
+
+	// | | u5 = w5 * inp
+	MOVQ  R11, DX
+	MULXQ ·Inp+0(SB), DX, DI
+
+	// |
+
+/*                                         */
+
+	// | j0
+
+	// | w5 @ R11
+	MULXQ ·modulus+0(SB), AX, DI
+	ADOXQ AX, R11
+	ADCXQ DI, R12
+
+	// | j1
+
+	// | w6 @ R12
+	MULXQ ·modulus+8(SB), AX, DI
+	ADOXQ AX, R12
+	ADCXQ DI, R13
+
+	// | j2
+
+	// | w7 @ R13
+	MULXQ ·modulus+16(SB), AX, DI
+	ADOXQ AX, R13
+	ADCXQ DI, R14
+
+	// | j3
+
+	// | w8 @ R14
+	MULXQ ·modulus+24(SB), AX, DI
+	ADOXQ AX, R14
+	ADCXQ DI, R15
+
+	// | j4
+
+	// | w9 @ R15
+	MULXQ ·modulus+32(SB), AX, DI
+	ADOXQ AX, R15
+	ADCXQ DI, CX
+
+	// | j5
+
+	// | w10 @ CX
+	MULXQ ·modulus+40(SB), AX, DI
+	ADOXQ AX, CX
+
+	// | w11 @ (SP)
+	// | move to an idle register
+	MOVQ  (SP), BX
+	ADCXQ DI, BX
+	ADOXQ R10, BX
+
+	// |
+	// | W montgomery reduction ends
+	// | 0   -         | 1   -         | 2   -         | 3   -         | 4   -         | 5   -
+	// | 6   R12       | 7   R13       | 8   R14       | 9   R15       | 10  CX        | 11  BX
+
+
+	// |
+
+/* modular reduction                       */
+
+	MOVQ R12, AX
+	SUBQ ·modulus+0(SB), AX
+	MOVQ R13, DI
+	SBBQ ·modulus+8(SB), DI
+	MOVQ R14, SI
+	SBBQ ·modulus+16(SB), SI
+	MOVQ R15, R8
+	SBBQ ·modulus+24(SB), R8
+	MOVQ CX, R9
+	SBBQ ·modulus+32(SB), R9
+	MOVQ BX, R10
+	SBBQ ·modulus+40(SB), R10
+
+	// |
+
+/* out                                     */
+
+	MOVQ    c+0(FP), R11
+	CMOVQCC AX, R12
+	MOVQ    R12, (R11)
+	CMOVQCC DI, R13
+	MOVQ    R13, 8(R11)
+	CMOVQCC SI, R14
+	MOVQ    R14, 16(R11)
+	CMOVQCC R8, R15
+	MOVQ    R15, 24(R11)
+	CMOVQCC R9, CX
+	MOVQ    CX, 32(R11)
+	CMOVQCC R10, BX
+	MOVQ    BX, 40(R11)
+	RET
+
+	// |
+
+/* end 																			*/
diff --git a/pkg/core/curves/native/bls12-381/bls12_381.go b/pkg/core/curves/native/bls12-381/bls12_381.go
new file mode 100644
index 00000000..31d0ee1e
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/bls12_381.go
@@ -0,0 +1,255 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import "fmt"
+
+/*
+	Field Constants
+*/
+
+// Base field modulus
+// p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab
+
+// Size of six words
+// r = 2 ^ 384
+
+// modulus = p
+var modulus = fe{0xb9feffffffffaaab, 0x1eabfffeb153ffff, 0x6730d2a0f6b0f624, 0x64774b84f38512bf, 0x4b1ba7b6434bacd7, 0x1a0111ea397fe69a}
+
+// Inp = -p^(-1) mod 2^64
+var Inp uint64 = 0x89f3fffcfffcfffd
+
+// r mod p
+var r1 = &fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493}
+
+// r^2 mod p
+var r2 = &fe{
+	0xf4df1f341c341746, 0x0a76e6a609d104f1, 0x8de5476c4c95b6d5, 0x67eb88a9939d83c0, 0x9a793e85b519952d, 0x11988fe592cae3aa,
+}
+
+// -1 + 0 * u
+var negativeOne2 = &fe2{
+	fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
+	fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+}
+
+// 2 ^ (-1)
+var twoInv = &fe{0x1804000000015554, 0x855000053ab00001, 0x633cb57c253c276f, 0x6e22d1ec31ebb502, 0xd3916126f2d14ca2, 0x17fbb8571a006596}
+
+// (p - 3) / 4
+var pMinus3Over4 = bigFromHex("0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaaa")
+
+// (p + 1) / 4
+var pPlus1Over4 = bigFromHex("0x680447a8e5ff9a692c6e9ed90d2eb35d91dd2e13ce144afd9cc34a83dac3d8907aaffffac54ffffee7fbfffffffeaab")
+
+// (p - 1) / 2
+var pMinus1Over2 = bigFromHex("0xd0088f51cbff34d258dd3db21a5d66bb23ba5c279c2895fb39869507b587b120f55ffff58a9ffffdcff7fffffffd555")
+
+var pMinus2 = bigFromHex("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9")
+
+// -1
+var nonResidue1 = &fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206}
+
+// (1 + 1 * u)
+var nonResidue2 = &fe2{
+	fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+	fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+}
+
+/*
+	Curve Constants
+*/
+
+// b coefficient for G1
+var b = &fe{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x09d645513d83de7e}
+
+// b coefficient for G2
+var b2 = &fe2{
+	fe{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x09d645513d83de7e},
+	fe{0xaa270000000cfff3, 0x53cc0032fc34000a, 0x478fe97a6b0a807f, 0xb1d37ebee6ba24d7, 0x8ec9733bbf78ab2f, 0x09d645513d83de7e},
+}
+
+// Group order
+var q = bigFromHex("0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001")
+
+// G1 cofactor
+//var cofactorG1 = bigFromHex("0x396c8c005555e1568c00aaab0000aaab")
+
+// G2 cofactor
+//var cofactorG2 = bigFromHex("5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5")
+
+// Efficient G1 cofactor
+var cofactorEFFG1 = bigFromHex("0xd201000000010001")
+
+// Efficient G2 cofactor
+var cofactorEFFG2 = bigFromHex("0x0bc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551")
+
+// G1 generator
+var g1One = PointG1{
+	fe{0x5cb38790fd530c16, 0x7817fc679976fff5, 0x154f95c7143ba1c1, 0xf0ae6acdf3d0e747, 0xedce6ecc21dbf440, 0x120177419e0bfb75},
+	fe{0xbaac93d50ce72271, 0x8c22631a7918fd8e, 0xdd595f13570725ce, 0x51ac582950405194, 0x0e1c8c3fad0059c0, 0x0bbc3efc5008a26a},
+	fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+}
+
+var G1One = g1One
+
+// Negated G1 generator
+//var g1NegativeOne = PointG1{
+//	fe{0x5cb38790fd530c16, 0x7817fc679976fff5, 0x154f95c7143ba1c1, 0xf0ae6acdf3d0e747, 0xedce6ecc21dbf440, 0x120177419e0bfb75},
+//	fe{0xff526c2af318883a, 0x92899ce4383b0270, 0x89d7738d9fa9d055, 0x12caf35ba344c12a, 0x3cff1b76964b5317, 0x0e44d2ede9774430},
+//	fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+//}
+
+// G2 generator
+var g2One = PointG2{
+	fe2{
+		fe{0xf5f28fa202940a10, 0xb3f5fb2687b4961a, 0xa1a893b53e2ae580, 0x9894999d1a3caee9, 0x6f67b7631863366b, 0x058191924350bcd7},
+		fe{0xa5a9c0759e23f606, 0xaaa0c59dbccd60c3, 0x3bb17e18e2867806, 0x1b1ab6cc8541b367, 0xc2b6ed0ef2158547, 0x11922a097360edf3},
+	},
+	fe2{
+		fe{0x4c730af860494c4a, 0x597cfa1f5e369c5a, 0xe7e6856caa0a635a, 0xbbefb5e96e0d495f, 0x07d3a975f0ef25a2, 0x083fd8e7e80dae5},
+		fe{0xadc0fc92df64b05d, 0x18aa270a2b1461dc, 0x86adac6a3be4eba0, 0x79495c4ec93da33a, 0xe7175850a43ccaed, 0xb2bc2a163de1bf2},
+	},
+	fe2{
+		fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+}
+
+var G2One = g2One
+
+/*
+	Frobenious Coeffs
+*/
+
+//var frobeniusCoeffs2 = [2]fe{
+//	fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+//	fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
+//}
+
+var frobeniusCoeffs61 = [6]fe2{
+	fe2{
+		fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+		fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
+	},
+	fe2{
+		fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+		fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+	},
+	fe2{
+		fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+		fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
+	},
+}
+
+var frobeniusCoeffs62 = [6]fe2{
+	fe2{
+		fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+}
+
+var frobeniusCoeffs12 = [12]fe2{
+	fe2{
+		fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
+		fe{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
+	},
+	fe2{
+		fe{0xecfb361b798dba3a, 0xc100ddb891865a2c, 0x0ec08ff1232bda8e, 0xd5c13cc6f1ca4721, 0x47222a47bf7b5c04, 0x0110f184e51c5f59},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
+		fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
+	},
+	fe2{
+		fe{0x30f1361b798a64e8, 0xf3b8ddab7ece5a2a, 0x16a8ca3ac61577f7, 0xc26a2ff874fd029b, 0x3636b76660701c6e, 0x051ba4ab241b6160},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
+		fe{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
+	},
+	fe2{
+		fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0xb2f66aad4ce5d646, 0x5842a06bfc497cec, 0xcf4895d42599d394, 0xc11b9cba40a8e8d0, 0x2e3813cbe5a0de89, 0x110eefda88847faf},
+		fe{0x07089552b319d465, 0xc6695f92b50a8313, 0x97e83cccd117228f, 0xa35baecab2dc29ee, 0x1ce393ea5daace4d, 0x08f2220fb0fb66eb},
+	},
+	fe2{
+		fe{0xcd03c9e48671f071, 0x5dab22461fcda5d2, 0x587042afd3851b95, 0x8eb60ebe01bacb9e, 0x03f97d6e83d050d2, 0x18f0206554638741},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x7bcfa7a25aa30fda, 0xdc17dec12a927e7c, 0x2f088dd86b4ebef1, 0xd1ca2087da74d4a7, 0x2da2596696cebc1d, 0x0e2b7eedbbfd87d2},
+		fe{0x3e2f585da55c9ad1, 0x4294213d86c18183, 0x382844c88b623732, 0x92ad2afd19103e18, 0x1d794e4fac7cf0b9, 0x0bd592fc7d825ec8},
+	},
+	fe2{
+		fe{0x890dc9e4867545c3, 0x2af322533285a5d5, 0x50880866309b7e2c, 0xa20d1b8c7e881024, 0x14e4f04fe2db9068, 0x14e56d3f1564853a},
+		fe{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000},
+	},
+	fe2{
+		fe{0x82d83cf50dbce43f, 0xa2813e53df9d018f, 0xc6f0caa53c65e181, 0x7525cf528d50fe95, 0x4a85ed50f4798a6b, 0x171da0fd6cf8eebd},
+		fe{0x3726c30af242c66c, 0x7c2ac1aad1b6fe70, 0xa04007fbba4b14a2, 0xef517c3266341429, 0x0095ba654ed2226b, 0x02e370eccc86f7dd},
+	},
+}
+
+/*
+	x
+*/
+
+var x = bigFromHex("0xd201000000010000")
+
+// maxInputLength is the total number of arbitrary length bytes that can be passed
+// to some function like EncodeToCurve and HashToCurve
+const maxInputLength = 134217728
+
+func longerThanLimit(in []byte) error {
+	if len(in) > maxInputLength {
+		return fmt.Errorf("input length too long")
+	}
+	return nil
+}
diff --git a/pkg/core/curves/native/bls12-381/bls12_381_test.go b/pkg/core/curves/native/bls12-381/bls12_381_test.go
new file mode 100644
index 00000000..9331478f
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/bls12_381_test.go
@@ -0,0 +1,77 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"crypto/rand"
+	"encoding/hex"
+	"errors"
+	"flag"
+	"math/big"
+	"os"
+	"testing"
+)
+
+var fuz int
+
+func TestMain(m *testing.M) {
+	_fuz := flag.Int("fuzz", 10, "# of iterations")
+	flag.Parse()
+	fuz = *_fuz
+	m.Run()
+	os.Exit(0)
+}
+
+func randScalar(max *big.Int) *big.Int {
+	a, err := rand.Int(rand.Reader, max)
+	if err != nil {
+		panic(errors.New(""))
+	}
+	return a
+}
+
+//func randScalars(max *big.Int, size int) []*big.Int {
+//	var scalars []*big.Int
+//	for i := 0; i < size; i++ {
+//		a, err := rand.Int(rand.Reader, max)
+//		if err != nil {
+//			panic(errors.New(""))
+//		}
+//		scalars = append(scalars, a)
+//	}
+//	return scalars
+//}
+
+func fromHex(size int, hexStrs ...string) []byte {
+	var out []byte
+	if size > 0 {
+		out = make([]byte, size*len(hexStrs))
+	}
+	for i := 0; i < len(hexStrs); i++ {
+		hexStr := hexStrs[i]
+		if hexStr[:2] == "0x" {
+			hexStr = hexStr[2:]
+		}
+		if len(hexStr)%2 == 1 {
+			hexStr = "0" + hexStr
+		}
+		bytes, err := hex.DecodeString(hexStr)
+		if err != nil {
+			return nil
+		}
+		if size <= 0 {
+			out = append(out, bytes...)
+		} else {
+			if len(bytes) > size {
+				return nil
+			}
+			offset := i*size + (size - len(bytes))
+			copy(out[offset:], bytes)
+		}
+	}
+	return out
+}
diff --git a/pkg/core/curves/native/bls12-381/field_element.go b/pkg/core/curves/native/bls12-381/field_element.go
new file mode 100644
index 00000000..1ca38971
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/field_element.go
@@ -0,0 +1,394 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"crypto/rand"
+	"encoding/hex"
+	"fmt"
+	"io"
+	"math/big"
+)
+
+// fe is base field element representation
+type fe /***			***/ [6]uint64
+
+// fe2 is element representation of 'fp2' which is quadratic extention of base field 'fp'
+// Representation follows c[0] + c[1] * u encoding order.
+type fe2 /**			***/ [2]fe
+
+// fe6 is element representation of 'fp6' field which is cubic extention of 'fp2'
+// Representation follows c[0] + c[1] * v + c[2] * v^2 encoding order.
+type fe6 /**			***/ [3]fe2
+
+// fe12 is element representation of 'fp12' field which is quadratic extention of 'fp6'
+// Representation follows c[0] + c[1] * w encoding order.
+type fe12 /**			***/ [2]fe6
+
+func (fe *fe) setBytes(in []byte) *fe {
+	size := 48
+	l := len(in)
+	if l >= size {
+		l = size
+	}
+	padded := make([]byte, size)
+	copy(padded[size-l:], in[:])
+	var a int
+	for i := 0; i < 6; i++ {
+		a = size - i*8
+		fe[i] = uint64(padded[a-1]) | uint64(padded[a-2])<<8 |
+			uint64(padded[a-3])<<16 | uint64(padded[a-4])<<24 |
+			uint64(padded[a-5])<<32 | uint64(padded[a-6])<<40 |
+			uint64(padded[a-7])<<48 | uint64(padded[a-8])<<56
+	}
+	return fe
+}
+
+func (fe *fe) setBig(a *big.Int) *fe {
+	if a.Sign() == -1 {
+		a.Neg(a)
+	}
+	return fe.setBytes(a.Bytes())
+}
+
+func (fe *fe) setString(s string) (*fe, error) {
+	if s[:2] == "0x" {
+		s = s[2:]
+	}
+	bytes, err := hex.DecodeString(s)
+	if err != nil {
+		return nil, err
+	}
+	return fe.setBytes(bytes), nil
+}
+
+func (fe *fe) set(fe2 *fe) *fe {
+	fe[0] = fe2[0]
+	fe[1] = fe2[1]
+	fe[2] = fe2[2]
+	fe[3] = fe2[3]
+	fe[4] = fe2[4]
+	fe[5] = fe2[5]
+	return fe
+}
+
+func (fe *fe) bytes() []byte {
+	out := make([]byte, 48)
+	var a int
+	for i := 0; i < 6; i++ {
+		a = 48 - i*8
+		out[a-1] = byte(fe[i])
+		out[a-2] = byte(fe[i] >> 8)
+		out[a-3] = byte(fe[i] >> 16)
+		out[a-4] = byte(fe[i] >> 24)
+		out[a-5] = byte(fe[i] >> 32)
+		out[a-6] = byte(fe[i] >> 40)
+		out[a-7] = byte(fe[i] >> 48)
+		out[a-8] = byte(fe[i] >> 56)
+	}
+	return out
+}
+
+func (fe *fe) big() *big.Int {
+	return new(big.Int).SetBytes(fe.bytes())
+}
+
+func (fe *fe) string() (s string) {
+	for i := 5; i >= 0; i-- {
+		s = fmt.Sprintf("%s%16.16x", s, fe[i])
+	}
+	return "0x" + s
+}
+
+func (fe *fe) zero() *fe {
+	fe[0] = 0
+	fe[1] = 0
+	fe[2] = 0
+	fe[3] = 0
+	fe[4] = 0
+	fe[5] = 0
+	return fe
+}
+
+func (fe *fe) one() *fe {
+	return fe.set(r1)
+}
+
+func (fe *fe) rand(r io.Reader) (*fe, error) {
+	bi, err := rand.Int(r, modulus.big())
+	if err != nil {
+		return nil, err
+	}
+	return fe.setBig(bi), nil
+}
+
+func (fe *fe) isValid() bool {
+	return fe.cmp(&modulus) == -1
+}
+
+func (fe *fe) isOdd() bool {
+	var mask uint64 = 1
+	return fe[0]&mask != 0
+}
+
+func (fe *fe) isEven() bool {
+	var mask uint64 = 1
+	return fe[0]&mask == 0
+}
+
+func (fe *fe) isZero() bool {
+	return (fe[5] | fe[4] | fe[3] | fe[2] | fe[1] | fe[0]) == 0
+}
+
+func (fe *fe) isOne() bool {
+	return fe.equal(r1)
+}
+
+func (fe *fe) cmp(fe2 *fe) int {
+	gt := 0
+	lt := 0
+	for i := 5; i > -1; i-- {
+		//if fe[i] > fe2[i] {
+		//	return 1
+		gt |= int(((fe2[i]-fe[i])>>63)&1) & ^lt
+		//} else if fe[i] < fe2[i] {
+		//	return -1
+		//}
+		lt |= int(((fe[i]-fe2[i])>>63)&1) & ^gt
+	}
+	//return 0
+	return gt - lt
+}
+
+func (fe *fe) equal(fe2 *fe) bool {
+	res := fe2[0] == fe[0]
+	res = res && fe2[1] == fe[1]
+	res = res && fe2[2] == fe[2]
+	res = res && fe2[3] == fe[3]
+	res = res && fe2[4] == fe[4]
+	res = res && fe2[5] == fe[5]
+	return res
+}
+
+func (e *fe) signBE() bool {
+	negZ, z := new(fe), new(fe)
+	fromMont(z, e)
+	neg(negZ, z)
+	return negZ.cmp(z) > -1
+}
+
+func (e *fe) sign() bool {
+	r := new(fe)
+	fromMont(r, e)
+	return r[0]&1 == 0
+}
+
+//func (fe *fe) div2(e uint64) {
+//	fe[0] = fe[0]>>1 | fe[1]<<63
+//	fe[1] = fe[1]>>1 | fe[2]<<63
+//	fe[2] = fe[2]>>1 | fe[3]<<63
+//	fe[3] = fe[3]>>1 | fe[4]<<63
+//	fe[4] = fe[4]>>1 | fe[5]<<63
+//	fe[5] = fe[5]>>1 | e<<63
+//}
+
+//func (fe *fe) mul2() uint64 {
+//	e := fe[5] >> 63
+//	fe[5] = fe[5]<<1 | fe[4]>>63
+//	fe[4] = fe[4]<<1 | fe[3]>>63
+//	fe[3] = fe[3]<<1 | fe[2]>>63
+//	fe[2] = fe[2]<<1 | fe[1]>>63
+//	fe[1] = fe[1]<<1 | fe[0]>>63
+//	fe[0] = fe[0] << 1
+//	return e
+//}
+
+// cmove sets self to y if v == 1 and does nothing if v == 0
+// no branches
+// Its behavior is undefined if v takes any other value.
+func (fe *fe) cmove(v uint, y *fe) {
+	b := -uint64(v)
+	fe[0] ^= (fe[0] ^ y[0]) & b
+	fe[1] ^= (fe[1] ^ y[1]) & b
+	fe[2] ^= (fe[2] ^ y[2]) & b
+	fe[3] ^= (fe[3] ^ y[3]) & b
+	fe[4] ^= (fe[4] ^ y[4]) & b
+	fe[5] ^= (fe[5] ^ y[5]) & b
+}
+
+func (e *fe2) zero() *fe2 {
+	e[0].zero()
+	e[1].zero()
+	return e
+}
+
+func (e *fe2) one() *fe2 {
+	e[0].one()
+	e[1].zero()
+	return e
+}
+
+func (e *fe2) set(e2 *fe2) *fe2 {
+	e[0].set(&e2[0])
+	e[1].set(&e2[1])
+	return e
+}
+
+func (e *fe2) rand(r io.Reader) (*fe2, error) {
+	a0, err := new(fe).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	a1, err := new(fe).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	return &fe2{*a0, *a1}, nil
+}
+
+func (e *fe2) isOne() bool {
+	return e[0].isOne() && e[1].isZero()
+}
+
+func (e *fe2) isZero() bool {
+	return e[0].isZero() && e[1].isZero()
+}
+
+func (e *fe2) equal(e2 *fe2) bool {
+	one := e[0].equal(&e2[0])
+	two := e[1].equal(&e2[1])
+	return one && two
+}
+
+func (e *fe2) signBE() bool {
+	if !e[1].isZero() {
+		return e[1].signBE()
+	}
+	return e[0].signBE()
+}
+
+func (e *fe2) sign() bool {
+	r := new(fe)
+	if !e[0].isZero() {
+		fromMont(r, &e[0])
+		return r[0]&1 == 0
+	}
+	fromMont(r, &e[1])
+	return r[0]&1 == 0
+}
+
+func (e *fe2) cmove(v uint, y *fe2) {
+	e[0].cmove(v, &y[0])
+	e[1].cmove(v, &y[1])
+}
+
+func (e *fe6) zero() *fe6 {
+	e[0].zero()
+	e[1].zero()
+	e[2].zero()
+	return e
+}
+
+func (e *fe6) one() *fe6 {
+	e[0].one()
+	e[1].zero()
+	e[2].zero()
+	return e
+}
+
+func (e *fe6) set(e2 *fe6) *fe6 {
+	e[0].set(&e2[0])
+	e[1].set(&e2[1])
+	e[2].set(&e2[2])
+	return e
+}
+
+func (e *fe6) rand(r io.Reader) (*fe6, error) {
+	a0, err := new(fe2).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	a1, err := new(fe2).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	a2, err := new(fe2).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	return &fe6{*a0, *a1, *a2}, nil
+}
+
+func (e *fe6) isOne() bool {
+	return e[0].isOne() && e[1].isZero() && e[2].isZero()
+}
+
+func (e *fe6) isZero() bool {
+	return e[0].isZero() && e[1].isZero() && e[2].isZero()
+}
+
+func (e *fe6) equal(e2 *fe6) bool {
+	res := e[0].equal(&e2[0])
+	res = res && e[1].equal(&e2[1])
+	res = res && e[2].equal(&e2[2])
+	return res
+}
+
+func (e *fe6) cmove(v uint, y *fe6) {
+	e[0].cmove(v, &y[0])
+	e[1].cmove(v, &y[1])
+	e[2].cmove(v, &y[2])
+}
+
+func (e *fe12) zero() *fe12 {
+	e[0].zero()
+	e[1].zero()
+	return e
+}
+
+func (e *fe12) one() *fe12 {
+	e[0].one()
+	e[1].zero()
+	return e
+}
+
+func (e *fe12) set(e2 *fe12) *fe12 {
+	e[0].set(&e2[0])
+	e[1].set(&e2[1])
+	return e
+}
+
+func (e *fe12) rand(r io.Reader) (*fe12, error) {
+	a0, err := new(fe6).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	a1, err := new(fe6).rand(r)
+	if err != nil {
+		return nil, err
+	}
+	return &fe12{*a0, *a1}, nil
+}
+
+func (e *fe12) isOne() bool {
+	return e[0].isOne() && e[1].isZero()
+}
+
+func (e *fe12) isZero() bool {
+	return e[0].isZero() && e[1].isZero()
+}
+
+func (e *fe12) equal(e2 *fe12) bool {
+	one := e[0].equal(&e2[0])
+	two := e[1].equal(&e2[1])
+	return one && two
+}
+
+func (e *fe12) cmove(v uint, y *fe12) {
+	e[0].cmove(v, &y[0])
+	e[1].cmove(v, &y[1])
+}
diff --git a/pkg/core/curves/native/bls12-381/field_element_test.go b/pkg/core/curves/native/bls12-381/field_element_test.go
new file mode 100644
index 00000000..5f699050
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/field_element_test.go
@@ -0,0 +1,258 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"bytes"
+	"crypto/rand"
+	"math/big"
+	"testing"
+)
+
+func TestFieldElementValidation(t *testing.T) {
+	// fe
+	zero := new(fe).zero()
+	if !zero.isValid() {
+		t.Fatal("zero must be valid")
+	}
+	one := new(fe).one()
+	if !one.isValid() {
+		t.Fatal("one must be valid")
+	}
+	if modulus.isValid() {
+		t.Fatal("modulus must be invalid")
+	}
+	n := modulus.big()
+	n.Add(n, big.NewInt(1))
+	if new(fe).setBig(n).isValid() {
+		t.Fatal("number greater than modulus must be invalid")
+	}
+}
+
+func TestFieldElementEquality(t *testing.T) {
+	// fe
+	zero := new(fe).zero()
+	if !zero.equal(zero) {
+		t.Fatal("0 == 0")
+	}
+	one := new(fe).one()
+	if !one.equal(one) {
+		t.Fatal("1 == 1")
+	}
+	a, _ := new(fe).rand(rand.Reader)
+	if !a.equal(a) {
+		t.Fatal("a == a")
+	}
+	b := new(fe)
+	add(b, a, one)
+	if a.equal(b) {
+		t.Fatal("a != a + 1")
+	}
+	// fe2
+	zero2 := new(fe2).zero()
+	if !zero2.equal(zero2) {
+		t.Fatal("0 == 0")
+	}
+	one2 := new(fe2).one()
+	if !one2.equal(one2) {
+		t.Fatal("1 == 1")
+	}
+	a2, _ := new(fe2).rand(rand.Reader)
+	if !a2.equal(a2) {
+		t.Fatal("a == a")
+	}
+	b2 := new(fe2)
+	fp2 := newFp2()
+	fp2.add(b2, a2, one2)
+	if a2.equal(b2) {
+		t.Fatal("a != a + 1")
+	}
+	// fe6
+	zero6 := new(fe6).zero()
+	if !zero6.equal(zero6) {
+		t.Fatal("0 == 0")
+	}
+	one6 := new(fe6).one()
+	if !one6.equal(one6) {
+		t.Fatal("1 == 1")
+	}
+	a6, _ := new(fe6).rand(rand.Reader)
+	if !a6.equal(a6) {
+		t.Fatal("a == a")
+	}
+	b6 := new(fe6)
+	fp6 := newFp6(fp2)
+	fp6.add(b6, a6, one6)
+	if a6.equal(b6) {
+		t.Fatal("a != a + 1")
+	}
+	// fe12
+	zero12 := new(fe12).zero()
+	if !zero12.equal(zero12) {
+		t.Fatal("0 == 0")
+	}
+	one12 := new(fe12).one()
+	if !one12.equal(one12) {
+		t.Fatal("1 == 1")
+	}
+	a12, _ := new(fe12).rand(rand.Reader)
+	if !a12.equal(a12) {
+		t.Fatal("a == a")
+	}
+	b12 := new(fe12)
+	fp12 := newFp12(fp6)
+	fp12.add(b12, a12, one12)
+	if a12.equal(b12) {
+		t.Fatal("a != a + 1")
+	}
+
+}
+
+func TestFieldElementHelpers(t *testing.T) {
+	// fe
+	zero := new(fe).zero()
+	if !zero.isZero() {
+		t.Fatal("'zero' is not zero")
+	}
+	one := new(fe).one()
+	if !one.isOne() {
+		t.Fatal("'one' is not one")
+	}
+	odd := new(fe).setBig(big.NewInt(1))
+	if !odd.isOdd() {
+		t.Fatal("1 must be odd")
+	}
+	if odd.isEven() {
+		t.Fatal("1 must not be even")
+	}
+	even := new(fe).setBig(big.NewInt(2))
+	if !even.isEven() {
+		t.Fatal("2 must be even")
+	}
+	if even.isOdd() {
+		t.Fatal("2 must not be odd")
+	}
+	// fe2
+	zero2 := new(fe2).zero()
+	if !zero2.isZero() {
+		t.Fatal("'zero' is not zero, 2")
+	}
+	one2 := new(fe2).one()
+	if !one2.isOne() {
+		t.Fatal("'one' is not one, 2")
+	}
+	// fe6
+	zero6 := new(fe6).zero()
+	if !zero6.isZero() {
+		t.Fatal("'zero' is not zero, 6")
+	}
+	one6 := new(fe6).one()
+	if !one6.isOne() {
+		t.Fatal("'one' is not one, 6")
+	}
+	// fe12
+	zero12 := new(fe12).zero()
+	if !zero12.isZero() {
+		t.Fatal("'zero' is not zero, 12")
+	}
+	one12 := new(fe12).one()
+	if !one12.isOne() {
+		t.Fatal("'one' is not one, 12")
+	}
+}
+
+func TestFieldElementSerialization(t *testing.T) {
+	t.Run("zero", func(t *testing.T) {
+		in := make([]byte, 48)
+		fe := new(fe).setBytes(in)
+		if !fe.isZero() {
+			t.Fatal("bad serialization")
+		}
+		if !bytes.Equal(in, fe.bytes()) {
+			t.Fatal("bad serialization")
+		}
+	})
+	t.Run("bytes", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b := new(fe).setBytes(a.bytes())
+			if !a.equal(b) {
+				t.Fatal("bad serialization")
+			}
+		}
+	})
+	t.Run("big", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b := new(fe).setBig(a.big())
+			if !a.equal(b) {
+				t.Fatal("bad encoding or decoding")
+			}
+		}
+	})
+	t.Run("string", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b, err := new(fe).setString(a.string())
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !a.equal(b) {
+				t.Fatal("bad encoding or decoding")
+			}
+		}
+	})
+}
+
+func TestFieldElementByteInputs(t *testing.T) {
+	zero := new(fe).zero()
+	in := make([]byte, 0)
+	a := new(fe).setBytes(in)
+	if !a.equal(zero) {
+		t.Fatal("bad serialization")
+	}
+	in = make([]byte, 48)
+	a = new(fe).setBytes(in)
+	if !a.equal(zero) {
+		t.Fatal("bad serialization")
+	}
+	in = make([]byte, 64)
+	a = new(fe).setBytes(in)
+	if !a.equal(zero) {
+		t.Fatal("bad serialization")
+	}
+	in = make([]byte, 49)
+	in[47] = 1
+	normalOne := &fe{1, 0, 0, 0, 0, 0}
+	a = new(fe).setBytes(in)
+	if !a.equal(normalOne) {
+		t.Fatal("bad serialization")
+	}
+}
+
+func TestFieldElementCopy(t *testing.T) {
+	a, _ := new(fe).rand(rand.Reader)
+	b := new(fe).set(a)
+	if !a.equal(b) {
+		t.Fatal("bad copy, 1")
+	}
+	a2, _ := new(fe2).rand(rand.Reader)
+	b2 := new(fe2).set(a2)
+	if !a2.equal(b2) {
+		t.Fatal("bad copy, 2")
+	}
+	a6, _ := new(fe6).rand(rand.Reader)
+	b6 := new(fe6).set(a6)
+	if !a6.equal(b6) {
+		t.Fatal("bad copy, 6")
+	}
+	a12, _ := new(fe12).rand(rand.Reader)
+	b12 := new(fe12).set(a12)
+	if !a12.equal(b12) {
+		t.Fatal("bad copy, 12")
+	}
+}
diff --git a/pkg/core/curves/native/bls12-381/fp.go b/pkg/core/curves/native/bls12-381/fp.go
new file mode 100644
index 00000000..a9f2f264
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/fp.go
@@ -0,0 +1,131 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"errors"
+	"math/big"
+)
+
+func fromBytes(in []byte) (*fe, error) {
+	fe := &fe{}
+	if len(in) != 48 {
+		return nil, errors.New("input string should be equal 48 bytes")
+	}
+	fe.setBytes(in)
+	if !fe.isValid() {
+		return nil, errors.New("must be less than modulus")
+	}
+	toMont(fe, fe)
+	return fe, nil
+}
+
+func from64Bytes(in []byte) (*fe, error) {
+	if len(in) != 64 {
+		return nil, errors.New("input string should be equal 64 bytes")
+	}
+	a0 := make([]byte, 48)
+	copy(a0[16:48], in[:32])
+	a1 := make([]byte, 48)
+	copy(a1[16:48], in[32:])
+	e0, err := fromBytes(a0)
+	if err != nil {
+		return nil, err
+	}
+	e1, err := fromBytes(a1)
+	if err != nil {
+		return nil, err
+	}
+	// F = 2 ^ 256 * R
+	F := fe{
+		0x75b3cd7c5ce820f,
+		0x3ec6ba621c3edb0b,
+		0x168a13d82bff6bce,
+		0x87663c4bf8c449d2,
+		0x15f34c83ddc8d830,
+		0xf9628b49caa2e85,
+	}
+
+	mul(e0, e0, &F)
+	add(e1, e1, e0)
+	return e1, nil
+}
+
+func fromBig(in *big.Int) (*fe, error) {
+	fe := new(fe).setBig(in)
+	if !fe.isValid() {
+		return nil, errors.New("invalid input string")
+	}
+	toMont(fe, fe)
+	return fe, nil
+}
+
+func fromString(in string) (*fe, error) {
+	fe, err := new(fe).setString(in)
+	if err != nil {
+		return nil, err
+	}
+	if !fe.isValid() {
+		return nil, errors.New("invalid input string")
+	}
+	toMont(fe, fe)
+	return fe, nil
+}
+
+func toBytes(e *fe) []byte {
+	e2 := new(fe)
+	fromMont(e2, e)
+	return e2.bytes()
+}
+
+func toBig(e *fe) *big.Int {
+	e2 := new(fe)
+	fromMont(e2, e)
+	return e2.big()
+}
+
+func toString(e *fe) (s string) {
+	e2 := new(fe)
+	fromMont(e2, e)
+	return e2.string()
+}
+
+func toMont(c, a *fe) {
+	mul(c, a, r2)
+}
+
+func fromMont(c, a *fe) {
+	mul(c, a, &fe{1})
+}
+
+func exp(c, a *fe, e *big.Int) {
+	z := new(fe).set(r1)
+	t := new(fe)
+	for i := e.BitLen(); i >= 0; i-- {
+		mul(z, z, z)
+		mul(t, z, a)
+		z.cmove(e.Bit(i), t)
+	}
+	c.set(z)
+}
+
+func inverse(inv, e *fe) {
+	exp(inv, e, pMinus2)
+}
+
+func sqrt(c, a *fe) bool {
+	u, v := new(fe).set(a), new(fe)
+	exp(c, a, pPlus1Over4)
+	square(v, c)
+	return u.equal(v)
+}
+
+func isQuadraticNonResidue(elem *fe) bool {
+	result := new(fe)
+	exp(result, elem, pMinus1Over2)
+	return !result.isOne()
+}
diff --git a/pkg/core/curves/native/bls12-381/fp12.go b/pkg/core/curves/native/bls12-381/fp12.go
new file mode 100644
index 00000000..c4aa8fb4
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/fp12.go
@@ -0,0 +1,270 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"errors"
+	"math/big"
+)
+
+type fp12 struct {
+	fp12temp
+	fp6 *fp6
+}
+
+type fp12temp struct {
+	t2  [9]*fe2
+	t6  [5]*fe6
+	t12 *fe12
+}
+
+func newFp12Temp() fp12temp {
+	t2 := [9]*fe2{}
+	t6 := [5]*fe6{}
+	for i := 0; i < len(t2); i++ {
+		t2[i] = &fe2{}
+	}
+	for i := 0; i < len(t6); i++ {
+		t6[i] = &fe6{}
+	}
+	return fp12temp{t2, t6, &fe12{}}
+}
+
+func newFp12(fp6 *fp6) *fp12 {
+	t := newFp12Temp()
+	if fp6 == nil {
+		return &fp12{t, newFp6(nil)}
+	}
+	return &fp12{t, fp6}
+}
+
+func (e *fp12) fp2() *fp2 {
+	return e.fp6.fp2
+}
+
+func (e *fp12) fromBytes(in []byte) (*fe12, error) {
+	if len(in) != 576 {
+		return nil, errors.New("input string should be larger than 96 bytes")
+	}
+	fp6 := e.fp6
+	c1, err := fp6.fromBytes(in[:288])
+	if err != nil {
+		return nil, err
+	}
+	c0, err := fp6.fromBytes(in[288:])
+	if err != nil {
+		return nil, err
+	}
+	return &fe12{*c0, *c1}, nil
+}
+
+func (e *fp12) toBytes(a *fe12) []byte {
+	fp6 := e.fp6
+	out := make([]byte, 576)
+	copy(out[:288], fp6.toBytes(&a[1]))
+	copy(out[288:], fp6.toBytes(&a[0]))
+	return out
+}
+
+func (e *fp12) new() *fe12 {
+	return new(fe12)
+}
+
+func (e *fp12) zero() *fe12 {
+	return new(fe12)
+}
+
+func (e *fp12) one() *fe12 {
+	return new(fe12).one()
+}
+
+func (e *fp12) add(c, a, b *fe12) {
+	fp6 := e.fp6
+	fp6.add(&c[0], &a[0], &b[0])
+	fp6.add(&c[1], &a[1], &b[1])
+
+}
+
+func (e *fp12) double(c, a *fe12) {
+	fp6 := e.fp6
+	fp6.double(&c[0], &a[0])
+	fp6.double(&c[1], &a[1])
+}
+
+func (e *fp12) sub(c, a, b *fe12) {
+	fp6 := e.fp6
+	fp6.sub(&c[0], &a[0], &b[0])
+	fp6.sub(&c[1], &a[1], &b[1])
+
+}
+
+func (e *fp12) neg(c, a *fe12) {
+	fp6 := e.fp6
+	fp6.neg(&c[0], &a[0])
+	fp6.neg(&c[1], &a[1])
+}
+
+func (e *fp12) conjugate(c, a *fe12) {
+	fp6 := e.fp6
+	c[0].set(&a[0])
+	fp6.neg(&c[1], &a[1])
+}
+
+func (e *fp12) square(c, a *fe12) {
+	fp6, t := e.fp6, e.t6
+	fp6.add(t[0], &a[0], &a[1])
+	fp6.mul(t[2], &a[0], &a[1])
+	fp6.mulByNonResidue(t[1], &a[1])
+	fp6.addAssign(t[1], &a[0])
+	fp6.mulByNonResidue(t[3], t[2])
+	fp6.mulAssign(t[0], t[1])
+	fp6.subAssign(t[0], t[2])
+	fp6.sub(&c[0], t[0], t[3])
+	fp6.double(&c[1], t[2])
+}
+
+func (e *fp12) cyclotomicSquare(c, a *fe12) {
+	t, fp2 := e.t2, e.fp2()
+	e.fp4Square(t[3], t[4], &a[0][0], &a[1][1])
+	fp2.sub(t[2], t[3], &a[0][0])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[0][0], t[2], t[3])
+	fp2.add(t[2], t[4], &a[1][1])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[1][1], t[2], t[4])
+	e.fp4Square(t[3], t[4], &a[1][0], &a[0][2])
+	e.fp4Square(t[5], t[6], &a[0][1], &a[1][2])
+	fp2.sub(t[2], t[3], &a[0][1])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[0][1], t[2], t[3])
+	fp2.add(t[2], t[4], &a[1][2])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[1][2], t[2], t[4])
+	fp2.mulByNonResidue(t[3], t[6])
+	fp2.add(t[2], t[3], &a[1][0])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[1][0], t[2], t[3])
+	fp2.sub(t[2], t[5], &a[0][2])
+	fp2.doubleAssign(t[2])
+	fp2.add(&c[0][2], t[2], t[5])
+}
+
+func (e *fp12) mul(c, a, b *fe12) {
+	t, fp6 := e.t6, e.fp6
+	fp6.mul(t[1], &a[0], &b[0])
+	fp6.mul(t[2], &a[1], &b[1])
+	fp6.add(t[0], t[1], t[2])
+	fp6.mulByNonResidue(t[2], t[2])
+	fp6.add(t[3], t[1], t[2])
+	fp6.add(t[1], &a[0], &a[1])
+	fp6.add(t[2], &b[0], &b[1])
+	fp6.mulAssign(t[1], t[2])
+	c[0].set(t[3])
+	fp6.sub(&c[1], t[1], t[0])
+}
+
+func (e *fp12) mulAssign(a, b *fe12) {
+	t, fp6 := e.t6, e.fp6
+	fp6.mul(t[1], &a[0], &b[0])
+	fp6.mul(t[2], &a[1], &b[1])
+	fp6.add(t[0], t[1], t[2])
+	fp6.mulByNonResidue(t[2], t[2])
+	fp6.add(t[3], t[1], t[2])
+	fp6.add(t[1], &a[0], &a[1])
+	fp6.add(t[2], &b[0], &b[1])
+	fp6.mulAssign(t[1], t[2])
+	a[0].set(t[3])
+	fp6.sub(&a[1], t[1], t[0])
+}
+
+func (e *fp12) fp4Square(c0, c1, a0, a1 *fe2) {
+	t, fp2 := e.t2, e.fp2()
+	fp2.square(t[0], a0)
+	fp2.square(t[1], a1)
+	fp2.mulByNonResidue(t[2], t[1])
+	fp2.add(c0, t[2], t[0])
+	fp2.add(t[2], a0, a1)
+	fp2.squareAssign(t[2])
+	fp2.subAssign(t[2], t[0])
+	fp2.sub(c1, t[2], t[1])
+}
+
+func (e *fp12) inverse(c, a *fe12) {
+	fp6, t := e.fp6, e.t6
+	fp6.square(t[0], &a[0])
+	fp6.square(t[1], &a[1])
+	fp6.mulByNonResidue(t[1], t[1])
+	fp6.sub(t[1], t[0], t[1])
+	fp6.inverse(t[0], t[1])
+	fp6.mul(&c[0], &a[0], t[0])
+	fp6.mulAssign(t[0], &a[1])
+	fp6.neg(&c[1], t[0])
+}
+
+func (e *fp12) mulBy014Assign(a *fe12, c0, c1, c4 *fe2) {
+	fp2, fp6, t, t2 := e.fp2(), e.fp6, e.t6, e.t2[0]
+	fp6.mulBy01(t[0], &a[0], c0, c1)
+	fp6.mulBy1(t[1], &a[1], c4)
+	fp2.add(t2, c1, c4)
+	fp6.add(t[2], &a[1], &a[0])
+	fp6.mulBy01Assign(t[2], c0, t2)
+	fp6.subAssign(t[2], t[0])
+	fp6.sub(&a[1], t[2], t[1])
+	fp6.mulByNonResidue(t[1], t[1])
+	fp6.add(&a[0], t[1], t[0])
+}
+
+func (e *fp12) exp(c, a *fe12, s *big.Int) {
+	z := e.one()
+	t := e.one()
+	for i := s.BitLen() - 1; i >= 0; i-- {
+		e.square(z, z)
+		e.mul(t, z, a)
+		z.cmove(s.Bit(i), t)
+	}
+	c.set(z)
+}
+
+func (e *fp12) cyclotomicExp(c, a *fe12, s *big.Int) {
+	ss := new(big.Int).Mod(s, q)
+	z := e.one()
+	for i := s.BitLen() - 1; i >= 0; i-- {
+		e.cyclotomicSquare(z, z)
+		t := e.one()
+		e.mul(t, z, a)
+		z.cmove(ss.Bit(i), t)
+	}
+	c.set(z)
+}
+
+func (e *fp12) frobeniusMap(c, a *fe12, power uint) {
+	fp6 := e.fp6
+	fp6.frobeniusMap(&c[0], &a[0], power)
+	fp6.frobeniusMap(&c[1], &a[1], power)
+	switch power {
+	case 0:
+		return
+	case 6:
+		fp6.neg(&c[1], &c[1])
+	default:
+		fp6.mulByBaseField(&c[1], &c[1], &frobeniusCoeffs12[power])
+	}
+}
+
+func (e *fp12) frobeniusMapAssign(a *fe12, power uint) {
+	fp6 := e.fp6
+	fp6.frobeniusMapAssign(&a[0], power)
+	fp6.frobeniusMapAssign(&a[1], power)
+	switch power {
+	case 0:
+		return
+	case 6:
+		fp6.neg(&a[1], &a[1])
+	default:
+		fp6.mulByBaseField(&a[1], &a[1], &frobeniusCoeffs12[power])
+	}
+}
diff --git a/pkg/core/curves/native/bls12-381/fp2.go b/pkg/core/curves/native/bls12-381/fp2.go
new file mode 100644
index 00000000..01b5c6f7
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/fp2.go
@@ -0,0 +1,251 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"errors"
+	"math/big"
+)
+
+type fp2Temp struct {
+	t [4]*fe
+}
+
+type fp2 struct {
+	fp2Temp
+}
+
+func newFp2Temp() fp2Temp {
+	t := [4]*fe{}
+	for i := 0; i < len(t); i++ {
+		t[i] = &fe{}
+	}
+	return fp2Temp{t}
+}
+
+func newFp2() *fp2 {
+	t := newFp2Temp()
+	return &fp2{t}
+}
+
+func (e *fp2) fromBytes(in []byte) (*fe2, error) {
+	if len(in) != 96 {
+		return nil, errors.New("input string should be larger than 96 bytes")
+	}
+	c1, err := fromBytes(in[:48])
+	if err != nil {
+		return nil, err
+	}
+	c0, err := fromBytes(in[48:])
+	if err != nil {
+		return nil, err
+	}
+	return &fe2{*c0, *c1}, nil
+}
+
+func (e *fp2) toBytes(a *fe2) []byte {
+	out := make([]byte, 96)
+	copy(out[:48], toBytes(&a[1]))
+	copy(out[48:], toBytes(&a[0]))
+	return out
+}
+
+func (e *fp2) new() *fe2 {
+	return new(fe2).zero()
+}
+
+func (e *fp2) zero() *fe2 {
+	return new(fe2).zero()
+}
+
+func (e *fp2) one() *fe2 {
+	return new(fe2).one()
+}
+
+//func (e *fp2) fromMont(c, a *fe2) {
+//	fromMont(&c[0], &a[0])
+//	fromMont(&c[1], &a[1])
+//}
+
+func (e *fp2) add(c, a, b *fe2) {
+	add(&c[0], &a[0], &b[0])
+	add(&c[1], &a[1], &b[1])
+}
+
+func (e *fp2) addAssign(a, b *fe2) {
+	addAssign(&a[0], &b[0])
+	addAssign(&a[1], &b[1])
+}
+
+func (e *fp2) ladd(c, a, b *fe2) {
+	ladd(&c[0], &a[0], &b[0])
+	ladd(&c[1], &a[1], &b[1])
+}
+
+func (e *fp2) double(c, a *fe2) {
+	double(&c[0], &a[0])
+	double(&c[1], &a[1])
+}
+
+func (e *fp2) doubleAssign(a *fe2) {
+	doubleAssign(&a[0])
+	doubleAssign(&a[1])
+}
+
+func (e *fp2) ldouble(c, a *fe2) {
+	ldouble(&c[0], &a[0])
+	ldouble(&c[1], &a[1])
+}
+
+func (e *fp2) sub(c, a, b *fe2) {
+	sub(&c[0], &a[0], &b[0])
+	sub(&c[1], &a[1], &b[1])
+}
+
+func (e *fp2) subAssign(c, a *fe2) {
+	subAssign(&c[0], &a[0])
+	subAssign(&c[1], &a[1])
+}
+
+func (e *fp2) neg(c, a *fe2) {
+	neg(&c[0], &a[0])
+	neg(&c[1], &a[1])
+}
+
+//func (e *fp2) conjugate(c, a *fe2) {
+//	c[0].set(&a[0])
+//	neg(&c[1], &a[1])
+//}
+
+func (e *fp2) mul(c, a, b *fe2) {
+	t := e.t
+	mul(t[1], &a[0], &b[0])
+	mul(t[2], &a[1], &b[1])
+	add(t[0], &a[0], &a[1])
+	add(t[3], &b[0], &b[1])
+	sub(&c[0], t[1], t[2])
+	addAssign(t[1], t[2])
+	mul(t[0], t[0], t[3])
+	sub(&c[1], t[0], t[1])
+}
+
+func (e *fp2) mulAssign(a, b *fe2) {
+	t := e.t
+	mul(t[1], &a[0], &b[0])
+	mul(t[2], &a[1], &b[1])
+	add(t[0], &a[0], &a[1])
+	add(t[3], &b[0], &b[1])
+	sub(&a[0], t[1], t[2])
+	addAssign(t[1], t[2])
+	mul(t[0], t[0], t[3])
+	sub(&a[1], t[0], t[1])
+}
+
+func (e *fp2) square(c, a *fe2) {
+	t := e.t
+	ladd(t[0], &a[0], &a[1])
+	sub(t[1], &a[0], &a[1])
+	ldouble(t[2], &a[0])
+	mul(&c[0], t[0], t[1])
+	mul(&c[1], t[2], &a[1])
+}
+
+func (e *fp2) squareAssign(a *fe2) {
+	t := e.t
+	ladd(t[0], &a[0], &a[1])
+	sub(t[1], &a[0], &a[1])
+	ldouble(t[2], &a[0])
+	mul(&a[0], t[0], t[1])
+	mul(&a[1], t[2], &a[1])
+}
+
+func (e *fp2) mulByNonResidue(c, a *fe2) {
+	t := e.t
+	sub(t[0], &a[0], &a[1])
+	add(&c[1], &a[0], &a[1])
+	c[0].set(t[0])
+}
+
+func (e *fp2) mulByB(c, a *fe2) {
+	t := e.t
+	double(t[0], &a[0])
+	double(t[1], &a[1])
+	doubleAssign(t[0])
+	doubleAssign(t[1])
+	sub(&c[0], t[0], t[1])
+	add(&c[1], t[0], t[1])
+}
+
+func (e *fp2) inverse(c, a *fe2) {
+	t := e.t
+	square(t[0], &a[0])
+	square(t[1], &a[1])
+	addAssign(t[0], t[1])
+	inverse(t[0], t[0])
+	mul(&c[0], &a[0], t[0])
+	mul(t[0], t[0], &a[1])
+	neg(&c[1], t[0])
+}
+
+func (e *fp2) mulByFq(c, a *fe2, b *fe) {
+	mul(&c[0], &a[0], b)
+	mul(&c[1], &a[1], b)
+}
+
+func (e *fp2) exp(c, a *fe2, s *big.Int) {
+	z := e.one()
+	t := e.one()
+	for i := s.BitLen() - 1; i >= 0; i-- {
+		e.square(z, z)
+		e.mul(t, z, a)
+		z.cmove(s.Bit(i), t)
+	}
+	c.set(z)
+}
+
+func (e *fp2) frobeniusMap(c, a *fe2, power uint) {
+	c[0].set(&a[0])
+	if power%2 == 1 {
+		neg(&c[1], &a[1])
+		return
+	}
+	c[1].set(&a[1])
+}
+
+func (e *fp2) frobeniusMapAssign(a *fe2, power uint) {
+	if power%2 == 1 {
+		neg(&a[1], &a[1])
+		return
+	}
+}
+
+func (e *fp2) sqrt(c, a *fe2) bool {
+	u, x0, a1, alpha := &fe2{}, &fe2{}, &fe2{}, &fe2{}
+	u.set(a)
+	e.exp(a1, a, pMinus3Over4)
+	e.square(alpha, a1)
+	e.mul(alpha, alpha, a)
+	e.mul(x0, a1, a)
+	if alpha.equal(negativeOne2) {
+		neg(&c[0], &x0[1])
+		c[1].set(&x0[0])
+		return true
+	}
+	e.add(alpha, alpha, e.one())
+	e.exp(alpha, alpha, pMinus1Over2)
+	e.mul(c, alpha, x0)
+	e.square(alpha, c)
+	return alpha.equal(u)
+}
+
+func (e *fp2) isQuadraticNonResidue(a *fe2) bool {
+	c0, c1 := new(fe), new(fe)
+	square(c0, &a[0])
+	square(c1, &a[1])
+	add(c1, c1, c0)
+	return isQuadraticNonResidue(c1)
+}
diff --git a/pkg/core/curves/native/bls12-381/fp6.go b/pkg/core/curves/native/bls12-381/fp6.go
new file mode 100644
index 00000000..43c11b20
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/fp6.go
@@ -0,0 +1,348 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"errors"
+	"math/big"
+)
+
+type fp6Temp struct {
+	t [6]*fe2
+}
+
+type fp6 struct {
+	fp2 *fp2
+	fp6Temp
+}
+
+func newFp6Temp() fp6Temp {
+	t := [6]*fe2{}
+	for i := 0; i < len(t); i++ {
+		t[i] = &fe2{}
+	}
+	return fp6Temp{t}
+}
+
+func newFp6(f *fp2) *fp6 {
+	t := newFp6Temp()
+	if f == nil {
+		return &fp6{newFp2(), t}
+	}
+	return &fp6{f, t}
+}
+
+func (e *fp6) fromBytes(b []byte) (*fe6, error) {
+	if len(b) < 288 {
+		return nil, errors.New("input string should be larger than 288 bytes")
+	}
+	fp2 := e.fp2
+	u2, err := fp2.fromBytes(b[:96])
+	if err != nil {
+		return nil, err
+	}
+	u1, err := fp2.fromBytes(b[96:192])
+	if err != nil {
+		return nil, err
+	}
+	u0, err := fp2.fromBytes(b[192:])
+	if err != nil {
+		return nil, err
+	}
+	return &fe6{*u0, *u1, *u2}, nil
+}
+
+func (e *fp6) toBytes(a *fe6) []byte {
+	fp2 := e.fp2
+	out := make([]byte, 288)
+	copy(out[:96], fp2.toBytes(&a[2]))
+	copy(out[96:192], fp2.toBytes(&a[1]))
+	copy(out[192:], fp2.toBytes(&a[0]))
+	return out
+}
+
+func (e *fp6) new() *fe6 {
+	return new(fe6)
+}
+
+func (e *fp6) zero() *fe6 {
+	return new(fe6)
+}
+
+func (e *fp6) one() *fe6 {
+	return new(fe6).one()
+}
+
+func (e *fp6) add(c, a, b *fe6) {
+	fp2 := e.fp2
+	fp2.add(&c[0], &a[0], &b[0])
+	fp2.add(&c[1], &a[1], &b[1])
+	fp2.add(&c[2], &a[2], &b[2])
+}
+
+func (e *fp6) addAssign(a, b *fe6) {
+	fp2 := e.fp2
+	fp2.addAssign(&a[0], &b[0])
+	fp2.addAssign(&a[1], &b[1])
+	fp2.addAssign(&a[2], &b[2])
+}
+
+func (e *fp6) double(c, a *fe6) {
+	fp2 := e.fp2
+	fp2.double(&c[0], &a[0])
+	fp2.double(&c[1], &a[1])
+	fp2.double(&c[2], &a[2])
+}
+
+func (e *fp6) doubleAssign(a *fe6) {
+	fp2 := e.fp2
+	fp2.doubleAssign(&a[0])
+	fp2.doubleAssign(&a[1])
+	fp2.doubleAssign(&a[2])
+}
+
+func (e *fp6) sub(c, a, b *fe6) {
+	fp2 := e.fp2
+	fp2.sub(&c[0], &a[0], &b[0])
+	fp2.sub(&c[1], &a[1], &b[1])
+	fp2.sub(&c[2], &a[2], &b[2])
+}
+
+func (e *fp6) subAssign(a, b *fe6) {
+	fp2 := e.fp2
+	fp2.subAssign(&a[0], &b[0])
+	fp2.subAssign(&a[1], &b[1])
+	fp2.subAssign(&a[2], &b[2])
+}
+
+func (e *fp6) neg(c, a *fe6) {
+	fp2 := e.fp2
+	fp2.neg(&c[0], &a[0])
+	fp2.neg(&c[1], &a[1])
+	fp2.neg(&c[2], &a[2])
+}
+
+//func (e *fp6) conjugate(c, a *fe6) {
+//	fp2 := e.fp2
+//	c[0].set(&a[0])
+//	fp2.neg(&c[1], &a[1])
+//	c[0].set(&a[2])
+//}
+
+func (e *fp6) mul(c, a, b *fe6) {
+	fp2, t := e.fp2, e.t
+	fp2.mul(t[0], &a[0], &b[0])
+	fp2.mul(t[1], &a[1], &b[1])
+	fp2.mul(t[2], &a[2], &b[2])
+	fp2.add(t[3], &a[1], &a[2])
+	fp2.add(t[4], &b[1], &b[2])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[1], t[2])
+	fp2.subAssign(t[3], t[4])
+	fp2.mulByNonResidue(t[3], t[3])
+	fp2.add(t[5], t[0], t[3])
+	fp2.add(t[3], &a[0], &a[1])
+	fp2.add(t[4], &b[0], &b[1])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[0], t[1])
+	fp2.subAssign(t[3], t[4])
+	fp2.mulByNonResidue(t[4], t[2])
+	fp2.add(&c[1], t[3], t[4])
+	fp2.add(t[3], &a[0], &a[2])
+	fp2.add(t[4], &b[0], &b[2])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[0], t[2])
+	fp2.subAssign(t[3], t[4])
+	fp2.add(&c[2], t[1], t[3])
+	c[0].set(t[5])
+}
+
+func (e *fp6) mulAssign(a, b *fe6) {
+	fp2, t := e.fp2, e.t
+	fp2.mul(t[0], &a[0], &b[0])
+	fp2.mul(t[1], &a[1], &b[1])
+	fp2.mul(t[2], &a[2], &b[2])
+	fp2.add(t[3], &a[1], &a[2])
+	fp2.add(t[4], &b[1], &b[2])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[1], t[2])
+	fp2.subAssign(t[3], t[4])
+	fp2.mulByNonResidue(t[3], t[3])
+	fp2.add(t[5], t[0], t[3])
+	fp2.add(t[3], &a[0], &a[1])
+	fp2.add(t[4], &b[0], &b[1])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[0], t[1])
+	fp2.subAssign(t[3], t[4])
+	fp2.mulByNonResidue(t[4], t[2])
+	fp2.add(&a[1], t[3], t[4])
+	fp2.add(t[3], &a[0], &a[2])
+	fp2.add(t[4], &b[0], &b[2])
+	fp2.mulAssign(t[3], t[4])
+	fp2.add(t[4], t[0], t[2])
+	fp2.subAssign(t[3], t[4])
+	fp2.add(&a[2], t[1], t[3])
+	a[0].set(t[5])
+}
+
+func (e *fp6) square(c, a *fe6) {
+	fp2, t := e.fp2, e.t
+	fp2.square(t[0], &a[0])
+	fp2.mul(t[1], &a[0], &a[1])
+	fp2.doubleAssign(t[1])
+	fp2.sub(t[2], &a[0], &a[1])
+	fp2.addAssign(t[2], &a[2])
+	fp2.squareAssign(t[2])
+	fp2.mul(t[3], &a[1], &a[2])
+	fp2.doubleAssign(t[3])
+	fp2.square(t[4], &a[2])
+	fp2.mulByNonResidue(t[5], t[3])
+	fp2.add(&c[0], t[0], t[5])
+	fp2.mulByNonResidue(t[5], t[4])
+	fp2.add(&c[1], t[1], t[5])
+	fp2.addAssign(t[1], t[2])
+	fp2.addAssign(t[1], t[3])
+	fp2.addAssign(t[0], t[4])
+	fp2.sub(&c[2], t[1], t[0])
+}
+
+func (e *fp6) mulBy01Assign(a *fe6, b0, b1 *fe2) {
+	fp2, t := e.fp2, e.t
+	fp2.mul(t[0], &a[0], b0)
+	fp2.mul(t[1], &a[1], b1)
+	fp2.add(t[5], &a[1], &a[2])
+	fp2.mul(t[2], b1, t[5])
+	fp2.subAssign(t[2], t[1])
+	fp2.mulByNonResidue(t[2], t[2])
+	fp2.add(t[5], &a[0], &a[2])
+	fp2.mul(t[3], b0, t[5])
+	fp2.subAssign(t[3], t[0])
+	fp2.add(&a[2], t[3], t[1])
+	fp2.add(t[4], b0, b1)
+	fp2.add(t[5], &a[0], &a[1])
+	fp2.mulAssign(t[4], t[5])
+	fp2.subAssign(t[4], t[0])
+	fp2.sub(&a[1], t[4], t[1])
+	fp2.add(&a[0], t[2], t[0])
+}
+
+func (e *fp6) mulBy01(c, a *fe6, b0, b1 *fe2) {
+	fp2, t := e.fp2, e.t
+	fp2.mul(t[0], &a[0], b0)
+	fp2.mul(t[1], &a[1], b1)
+	fp2.add(t[2], &a[1], &a[2])
+	fp2.mulAssign(t[2], b1)
+	fp2.subAssign(t[2], t[1])
+	fp2.mulByNonResidue(t[2], t[2])
+	fp2.add(t[3], &a[0], &a[2])
+	fp2.mulAssign(t[3], b0)
+	fp2.subAssign(t[3], t[0])
+	fp2.add(&c[2], t[3], t[1])
+	fp2.add(t[4], b0, b1)
+	fp2.add(t[3], &a[0], &a[1])
+	fp2.mulAssign(t[4], t[3])
+	fp2.subAssign(t[4], t[0])
+	fp2.sub(&c[1], t[4], t[1])
+	fp2.add(&c[0], t[2], t[0])
+}
+
+func (e *fp6) mulBy1(c, a *fe6, b1 *fe2) {
+	fp2, t := e.fp2, e.t
+	fp2.mul(t[0], &a[2], b1)
+	fp2.mul(&c[2], &a[1], b1)
+	fp2.mul(&c[1], &a[0], b1)
+	fp2.mulByNonResidue(&c[0], t[0])
+}
+
+func (e *fp6) mulByNonResidue(c, a *fe6) {
+	fp2, t := e.fp2, e.t
+	t[0].set(&a[0])
+	fp2.mulByNonResidue(&c[0], &a[2])
+	c[2].set(&a[1])
+	c[1].set(t[0])
+}
+
+func (e *fp6) mulByBaseField(c, a *fe6, b *fe2) {
+	fp2 := e.fp2
+	fp2.mul(&c[0], &a[0], b)
+	fp2.mul(&c[1], &a[1], b)
+	fp2.mul(&c[2], &a[2], b)
+}
+
+func (e *fp6) exp(c, a *fe6, s *big.Int) {
+	z := e.one()
+	t := e.one()
+	for i := s.BitLen() - 1; i >= 0; i-- {
+		e.square(z, z)
+		e.mul(t, z, a)
+		z.cmove(s.Bit(i), t)
+	}
+	c.set(z)
+}
+
+func (e *fp6) inverse(c, a *fe6) {
+	fp2, t := e.fp2, e.t
+	fp2.square(t[0], &a[0])
+	fp2.mul(t[1], &a[1], &a[2])
+	fp2.mulByNonResidue(t[1], t[1])
+	fp2.subAssign(t[0], t[1])
+	fp2.square(t[1], &a[1])
+	fp2.mul(t[2], &a[0], &a[2])
+	fp2.subAssign(t[1], t[2])
+	fp2.square(t[2], &a[2])
+	fp2.mulByNonResidue(t[2], t[2])
+	fp2.mul(t[3], &a[0], &a[1])
+	fp2.subAssign(t[2], t[3])
+	fp2.mul(t[3], &a[2], t[2])
+	fp2.mul(t[4], &a[1], t[1])
+	fp2.addAssign(t[3], t[4])
+	fp2.mulByNonResidue(t[3], t[3])
+	fp2.mul(t[4], &a[0], t[0])
+	fp2.addAssign(t[3], t[4])
+	fp2.inverse(t[3], t[3])
+	fp2.mul(&c[0], t[0], t[3])
+	fp2.mul(&c[1], t[2], t[3])
+	fp2.mul(&c[2], t[1], t[3])
+}
+
+func (e *fp6) frobeniusMap(c, a *fe6, power uint) {
+	fp2 := e.fp2
+	fp2.frobeniusMap(&c[0], &a[0], power)
+	fp2.frobeniusMap(&c[1], &a[1], power)
+	fp2.frobeniusMap(&c[2], &a[2], power)
+	switch power % 6 {
+	case 0:
+		return
+	case 3:
+		neg(&c[0][0], &a[1][1])
+		c[1][1].set(&a[1][0])
+		fp2.neg(&a[2], &a[2])
+	default:
+		fp2.mul(&c[1], &c[1], &frobeniusCoeffs61[power%6])
+		fp2.mul(&c[2], &c[2], &frobeniusCoeffs62[power%6])
+	}
+}
+
+func (e *fp6) frobeniusMapAssign(a *fe6, power uint) {
+	fp2 := e.fp2
+	fp2.frobeniusMapAssign(&a[0], power)
+	fp2.frobeniusMapAssign(&a[1], power)
+	fp2.frobeniusMapAssign(&a[2], power)
+	t := e.t
+	switch power % 6 {
+	case 0:
+		return
+	case 3:
+		neg(&t[0][0], &a[1][1])
+		a[1][1].set(&a[1][0])
+		a[1][0].set(&t[0][0])
+		fp2.neg(&a[2], &a[2])
+	default:
+		fp2.mulAssign(&a[1], &frobeniusCoeffs61[power%6])
+		fp2.mulAssign(&a[2], &frobeniusCoeffs62[power%6])
+	}
+}
diff --git a/pkg/core/curves/native/bls12-381/fp_test.go b/pkg/core/curves/native/bls12-381/fp_test.go
new file mode 100644
index 00000000..9048c0ce
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/fp_test.go
@@ -0,0 +1,1411 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"bytes"
+	"crypto/rand"
+	"math/big"
+	"testing"
+)
+
+func TestFpSerialization(t *testing.T) {
+	t.Run("zero", func(t *testing.T) {
+		in := make([]byte, 48)
+		fe, err := fromBytes(in)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !fe.isZero() {
+			t.Fatal("bad serialization")
+		}
+		if !bytes.Equal(in, toBytes(fe)) {
+			t.Fatal("bad serialization")
+		}
+	})
+	t.Run("bytes", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b, err := fromBytes(toBytes(a))
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !a.equal(b) {
+				t.Fatal("bad serialization")
+			}
+		}
+	})
+	t.Run("string", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b, err := fromString(toString(a))
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !a.equal(b) {
+				t.Fatal("bad encoding or decoding")
+			}
+		}
+	})
+	t.Run("big", func(t *testing.T) {
+		for i := 0; i < fuz; i++ {
+			a, _ := new(fe).rand(rand.Reader)
+			b, err := fromBig(toBig(a))
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !a.equal(b) {
+				t.Fatal("bad encoding or decoding")
+			}
+		}
+	})
+}
+
+func TestFpAdditionCrossAgainstBigInt(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		c := new(fe)
+		big_a := toBig(a)
+		big_b := toBig(b)
+		big_c := new(big.Int)
+		add(c, a, b)
+		out_1 := toBytes(c)
+		out_2 := padBytes(big_c.Add(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied A")
+		}
+		double(c, a)
+		out_1 = toBytes(c)
+		out_2 = padBytes(big_c.Add(big_a, big_a).Mod(big_c, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied B")
+		}
+		sub(c, a, b)
+		out_1 = toBytes(c)
+		out_2 = padBytes(big_c.Sub(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied C")
+		}
+		neg(c, a)
+		out_1 = toBytes(c)
+		out_2 = padBytes(big_c.Neg(big_a).Mod(big_c, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied D")
+		}
+	}
+}
+
+func TestFpAdditionCrossAgainstBigIntAssigned(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		big_a, big_b := toBig(a), toBig(b)
+		addAssign(a, b)
+		out_1 := toBytes(a)
+		out_2 := padBytes(big_a.Add(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied A")
+		}
+		a, _ = new(fe).rand(rand.Reader)
+		big_a = toBig(a)
+		doubleAssign(a)
+		out_1 = toBytes(a)
+		out_2 = padBytes(big_a.Add(big_a, big_a).Mod(big_a, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied B")
+		}
+		a, _ = new(fe).rand(rand.Reader)
+		b, _ = new(fe).rand(rand.Reader)
+		big_a, big_b = toBig(a), toBig(b)
+		subAssign(a, b)
+		out_1 = toBytes(a)
+		out_2 = padBytes(big_a.Sub(big_a, big_b).Mod(big_a, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied A")
+		}
+	}
+}
+
+func TestFpAdditionProperties(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+
+		zero := new(fe).zero()
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		c_1, c_2 := new(fe), new(fe)
+		add(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a + 0 == a")
+		}
+		sub(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a - 0 == a")
+		}
+		double(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		neg(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("-0 == 0")
+		}
+		sub(c_1, zero, a)
+		neg(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("0-a == -a")
+		}
+		double(c_1, a)
+		add(c_2, a, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("2 * a == a + a")
+		}
+		add(c_1, a, b)
+		add(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		sub(c_1, a, b)
+		sub(c_2, b, a)
+		neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		c_x, _ := new(fe).rand(rand.Reader)
+		add(c_1, a, b)
+		add(c_1, c_1, c_x)
+		add(c_2, a, c_x)
+		add(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		sub(c_1, a, b)
+		sub(c_1, c_1, c_x)
+		sub(c_2, a, c_x)
+		sub(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a - b) - c == (a - c ) -b")
+		}
+	}
+}
+
+func TestFpAdditionPropertiesAssigned(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		zero := new(fe).zero()
+		a, b := new(fe), new(fe)
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		addAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a + 0 == a")
+		}
+		subAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a - 0 == a")
+		}
+		a.set(zero)
+		doubleAssign(a)
+		if !a.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		a.set(zero)
+		subAssign(a, b)
+		neg(b, b)
+		if !a.equal(b) {
+			t.Fatal("0-a == -a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		doubleAssign(a)
+		addAssign(b, b)
+		if !a.equal(b) {
+			t.Fatal("2 * a == a + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1, c_2 := new(fe).set(a), new(fe).set(b)
+		addAssign(c_1, b)
+		addAssign(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1.set(a)
+		c_2.set(b)
+		subAssign(c_1, b)
+		subAssign(c_2, a)
+		neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c, _ := new(fe).rand(rand.Reader)
+		a0 := new(fe).set(a)
+		addAssign(a, b)
+		addAssign(a, c)
+		addAssign(b, c)
+		addAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("(a + b) + c == (b + c) + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		_, _ = c.rand(rand.Reader)
+		a0.set(a)
+		subAssign(a, b)
+		subAssign(a, c)
+		subAssign(a0, c)
+		subAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a - b) - c == (a - c) -b")
+		}
+	}
+}
+
+func TestFpLazyOperations(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		c, _ := new(fe).rand(rand.Reader)
+		c0 := new(fe)
+		c1 := new(fe)
+		ladd(c0, a, b)
+		add(c1, a, b)
+		mul(c0, c0, c)
+		mul(c1, c1, c)
+		if !c0.equal(c1) {
+			// l+ operator stands for lazy addition
+			t.Fatal("(a + b) * c == (a l+ b) * c")
+		}
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		ldouble(a, a)
+		ladd(b, b, b)
+		if !a.equal(b) {
+			t.Fatal("2 l* a = a l+ a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		_, _ = c.rand(rand.Reader)
+		a0 := new(fe).set(a)
+		lsubAssign(a, b)
+		laddAssign(a, &modulus)
+		mul(a, a, c)
+		subAssign(a0, b)
+		mul(a0, a0, c)
+		if !a.equal(a0) {
+			t.Fatal("((a l- b) + p) * c = (a-b) * c")
+		}
+	}
+}
+
+func TestFpMultiplicationCrossAgainstBigInt(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		c := new(fe)
+		big_a := toBig(a)
+		big_b := toBig(b)
+		big_c := new(big.Int)
+		mul(c, a, b)
+		out_1 := toBytes(c)
+		out_2 := padBytes(big_c.Mul(big_a, big_b).Mod(big_c, modulus.big()).Bytes(), 48)
+		if !bytes.Equal(out_1, out_2) {
+			t.Fatal("cross test against big.Int is not satisfied")
+		}
+	}
+}
+
+func TestFpMultiplicationProperties(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		b, _ := new(fe).rand(rand.Reader)
+		zero, one := new(fe).zero(), new(fe).one()
+		c_1, c_2 := new(fe), new(fe)
+		mul(c_1, a, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		mul(c_1, a, one)
+		if !c_1.equal(a) {
+			t.Fatal("a * 1 == a")
+		}
+		mul(c_1, a, b)
+		mul(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a * b == b * a")
+		}
+		c_x, _ := new(fe).rand(rand.Reader)
+		mul(c_1, a, b)
+		mul(c_1, c_1, c_x)
+		mul(c_2, c_x, b)
+		mul(c_2, c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+		square(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("0^2 == 0")
+		}
+		square(a, one)
+		if !a.equal(one) {
+			t.Fatal("1^2 == 1")
+		}
+		_, _ = a.rand(rand.Reader)
+		square(c_1, a)
+		mul(c_2, a, a)
+		if !c_1.equal(c_1) {
+			t.Fatal("a^2 == a*a")
+		}
+	}
+}
+
+func TestFpExponentiation(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		u := new(fe)
+		exp(u, a, big.NewInt(0))
+		if !u.isOne() {
+			t.Fatal("a^0 == 1")
+		}
+		exp(u, a, big.NewInt(1))
+		if !u.equal(a) {
+			t.Fatal("a^1 == a")
+		}
+		v := new(fe)
+		mul(u, a, a)
+		mul(u, u, u)
+		mul(u, u, u)
+		exp(v, a, big.NewInt(8))
+		if !u.equal(v) {
+			t.Fatal("((a^2)^2)^2 == a^8")
+		}
+		p := modulus.big()
+		exp(u, a, p)
+		if !u.equal(a) {
+			t.Fatal("a^p == a")
+		}
+		exp(u, a, p.Sub(p, big.NewInt(1)))
+		if !u.isOne() {
+			t.Fatal("a^(p-1) == 1")
+		}
+	}
+}
+
+func TestFpInversion(t *testing.T) {
+	for i := 0; i < fuz; i++ {
+		u := new(fe)
+		zero, one := new(fe).zero(), new(fe).one()
+		inverse(u, zero)
+		if !u.equal(zero) {
+			t.Fatal("(0^-1) == 0)")
+		}
+		inverse(u, one)
+		if !u.equal(one) {
+			t.Fatal("(1^-1) == 1)")
+		}
+		a, _ := new(fe).rand(rand.Reader)
+		inverse(u, a)
+		mul(u, u, a)
+		if !u.equal(one) {
+			t.Fatal("(r*a) * r*(a^-1) == r)")
+		}
+		v := new(fe)
+		p := modulus.big()
+		exp(u, a, p.Sub(p, big.NewInt(2)))
+		inverse(v, a)
+		if !v.equal(u) {
+			t.Fatal("a^(p-2) == a^-1")
+		}
+	}
+}
+
+func TestFpSquareRoot(t *testing.T) {
+	r := new(fe)
+	if sqrt(r, nonResidue1) {
+		t.Fatal("non residue cannot have a sqrt")
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		aa, rr, r := &fe{}, &fe{}, &fe{}
+		square(aa, a)
+		if !sqrt(r, aa) {
+			t.Fatal("bad sqrt 1")
+		}
+		square(rr, r)
+		if !rr.equal(aa) {
+			t.Fatal("bad sqrt 2")
+		}
+	}
+}
+
+func TestFpNonResidue(t *testing.T) {
+
+	if !isQuadraticNonResidue(nonResidue1) {
+		t.Fatal("element is quadratic non residue, 1")
+	}
+	if isQuadraticNonResidue(new(fe).one()) {
+		t.Fatal("one is not quadratic non residue")
+	}
+	if !isQuadraticNonResidue(new(fe).zero()) {
+		t.Fatal("should accept zero as quadratic non residue")
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		square(a, a)
+		if isQuadraticNonResidue(new(fe).one()) {
+			t.Fatal("element is not quadratic non residue")
+		}
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe).rand(rand.Reader)
+		if !sqrt(new(fe), a) {
+			if !isQuadraticNonResidue(a) {
+				t.Fatal("element is quadratic non residue, 2", i)
+			}
+		} else {
+			i -= 1
+		}
+	}
+
+}
+
+func TestFp2Serialization(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		b, err := field.fromBytes(field.toBytes(a))
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !a.equal(b) {
+			t.Fatal("bad serialization")
+		}
+	}
+}
+
+func TestFp2AdditionProperties(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		zero := field.zero()
+		a, _ := new(fe2).rand(rand.Reader)
+		b, _ := new(fe2).rand(rand.Reader)
+		c_1 := field.new()
+		c_2 := field.new()
+		field.add(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a + 0 == a")
+		}
+		field.sub(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a - 0 == a")
+		}
+		field.double(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		field.neg(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("-0 == 0")
+		}
+		field.sub(c_1, zero, a)
+		field.neg(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("0-a == -a")
+		}
+		field.double(c_1, a)
+		field.add(c_2, a, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("2 * a == a + a")
+		}
+		field.add(c_1, a, b)
+		field.add(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_2, b, a)
+		field.neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		c_x, _ := new(fe2).rand(rand.Reader)
+		field.add(c_1, a, b)
+		field.add(c_1, c_1, c_x)
+		field.add(c_2, a, c_x)
+		field.add(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_1, c_1, c_x)
+		field.sub(c_2, a, c_x)
+		field.sub(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a - b) - c == (a - c ) -b")
+		}
+	}
+}
+
+func TestFp2AdditionPropertiesAssigned(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		zero := new(fe2).zero()
+		a, b := new(fe2), new(fe2)
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		field.addAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a + 0 == a")
+		}
+		field.subAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a - 0 == a")
+		}
+		a.set(zero)
+		field.doubleAssign(a)
+		if !a.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		a.set(zero)
+		field.subAssign(a, b)
+		field.neg(b, b)
+		if !a.equal(b) {
+			t.Fatal("0-a == -a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		field.doubleAssign(a)
+		field.addAssign(b, b)
+		if !a.equal(b) {
+			t.Fatal("2 * a == a + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1, c_2 := new(fe2).set(a), new(fe2).set(b)
+		field.addAssign(c_1, b)
+		field.addAssign(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1.set(a)
+		c_2.set(b)
+		field.subAssign(c_1, b)
+		field.subAssign(c_2, a)
+		field.neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c, _ := new(fe2).rand(rand.Reader)
+		a0 := new(fe2).set(a)
+		field.addAssign(a, b)
+		field.addAssign(a, c)
+		field.addAssign(b, c)
+		field.addAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("(a + b) + c == (b + c) + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		_, _ = c.rand(rand.Reader)
+		a0.set(a)
+		field.subAssign(a, b)
+		field.subAssign(a, c)
+		field.subAssign(a0, c)
+		field.subAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a - b) - c == (a - c) -b")
+		}
+	}
+}
+
+func TestFp2LazyOperations(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		b, _ := new(fe2).rand(rand.Reader)
+		c, _ := new(fe2).rand(rand.Reader)
+		c0 := new(fe2)
+		c1 := new(fe2)
+		field.ladd(c0, a, b)
+		field.add(c1, a, b)
+		field.mulAssign(c0, c)
+		field.mulAssign(c1, c)
+		if !c0.equal(c1) {
+			// l+ operator stands for lazy addition
+			t.Fatal("(a + b) * c == (a l+ b) * c")
+		}
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		field.ldouble(a, a)
+		field.ladd(b, b, b)
+		if !a.equal(b) {
+			t.Fatal("2 l* a = a l+ a")
+		}
+	}
+}
+
+func TestFp2MultiplicationProperties(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		b, _ := new(fe2).rand(rand.Reader)
+		zero := field.zero()
+		one := field.one()
+		c_1, c_2 := field.new(), field.new()
+		field.mul(c_1, a, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		field.mul(c_1, a, one)
+		if !c_1.equal(a) {
+			t.Fatal("a * 1 == a")
+		}
+		field.mul(c_1, a, b)
+		field.mul(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a * b == b * a")
+		}
+		c_x, _ := new(fe2).rand(rand.Reader)
+		field.mul(c_1, a, b)
+		field.mul(c_1, c_1, c_x)
+		field.mul(c_2, c_x, b)
+		field.mul(c_2, c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+		field.square(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("0^2 == 0")
+		}
+		field.square(a, one)
+		if !a.equal(one) {
+			t.Fatal("1^2 == 1")
+		}
+		_, _ = a.rand(rand.Reader)
+		field.square(c_1, a)
+		field.mul(c_2, a, a)
+		if !c_2.equal(c_1) {
+			t.Fatal("a^2 == a*a")
+		}
+	}
+}
+
+func TestFp2MultiplicationPropertiesAssigned(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		zero, one := new(fe2).zero(), new(fe2).one()
+		field.mulAssign(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		_, _ = a.rand(rand.Reader)
+		a0 := new(fe2).set(a)
+		field.mulAssign(a, one)
+		if !a.equal(a0) {
+			t.Fatal("a * 1 == a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b, _ := new(fe2).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("a * b == b * a")
+		}
+		c, _ := new(fe2).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(a, c)
+		field.mulAssign(a0, c)
+		field.mulAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+		a0.set(a)
+		field.squareAssign(a)
+		field.mulAssign(a0, a0)
+		if !a.equal(a0) {
+			t.Fatal("a^2 == a*a")
+		}
+	}
+}
+
+func TestFp2Exponentiation(t *testing.T) {
+	field := newFp2()
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		u := field.new()
+		field.exp(u, a, big.NewInt(0))
+		if !u.equal(field.one()) {
+			t.Fatal("a^0 == 1")
+		}
+		field.exp(u, a, big.NewInt(1))
+		if !u.equal(a) {
+			t.Fatal("a^1 == a")
+		}
+		v := field.new()
+		field.mul(u, a, a)
+		field.mul(u, u, u)
+		field.mul(u, u, u)
+		field.exp(v, a, big.NewInt(8))
+		if !u.equal(v) {
+			t.Fatal("((a^2)^2)^2 == a^8")
+		}
+	}
+}
+
+func TestFp2Inversion(t *testing.T) {
+	field := newFp2()
+	u := field.new()
+	zero := field.zero()
+	one := field.one()
+	field.inverse(u, zero)
+	if !u.equal(zero) {
+		t.Fatal("(0 ^ -1) == 0)")
+	}
+	field.inverse(u, one)
+	if !u.equal(one) {
+		t.Fatal("(1 ^ -1) == 1)")
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		field.inverse(u, a)
+		field.mul(u, u, a)
+		if !u.equal(one) {
+			t.Fatal("(r * a) * r * (a ^ -1) == r)")
+		}
+	}
+}
+
+func TestFp2SquareRoot(t *testing.T) {
+	field := newFp2()
+	for z := 0; z < fuz; z++ {
+		zi := new(fe)
+		sub(zi, &modulus, &fe{uint64(z * z)})
+		// r = (-z*z, 0)
+		r := &fe2{*zi, fe{0}}
+		toMont(&r[0], &r[0])
+		toMont(&r[1], &r[1])
+		c := field.new()
+		// sqrt((-z*z, 0)) = (0, z)
+		if !field.sqrt(c, r) {
+			t.Fatal("z*z does have a square root")
+		}
+		e := &fe2{fe{uint64(0)}, fe{uint64(z)}}
+		toMont(&e[0], &e[0])
+		toMont(&e[1], &e[1])
+		field.square(e, e)
+		field.square(c, c)
+		if !e.equal(c) {
+			t.Fatal("square root failed")
+		}
+	}
+	if field.sqrt(field.new(), nonResidue2) {
+		t.Fatal("non residue cannot have a sqrt")
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		aa, rr, r := field.new(), field.new(), field.new()
+		field.square(aa, a)
+		if !field.sqrt(r, aa) {
+			t.Fatal("bad sqrt 1")
+		}
+		field.square(rr, r)
+		if !rr.equal(aa) {
+			t.Fatal("bad sqrt 2")
+		}
+	}
+}
+
+func TestFp2NonResidue(t *testing.T) {
+	field := newFp2()
+	if !field.isQuadraticNonResidue(nonResidue2) {
+		t.Fatal("element is quadratic non residue, 1")
+	}
+	if field.isQuadraticNonResidue(new(fe2).one()) {
+		t.Fatal("one is not quadratic non residue")
+	}
+	if !field.isQuadraticNonResidue(new(fe2).zero()) {
+		t.Fatal("should accept zero as quadratic non residue")
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		field.squareAssign(a)
+		if field.isQuadraticNonResidue(new(fe2).one()) {
+			t.Fatal("element is not quadratic non residue")
+		}
+	}
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe2).rand(rand.Reader)
+		if !field.sqrt(new(fe2), a) {
+			if !field.isQuadraticNonResidue(a) {
+				t.Fatal("element is quadratic non residue, 2", i)
+			}
+		} else {
+			i -= 1
+		}
+	}
+}
+
+func TestFp6Serialization(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe6).rand(rand.Reader)
+		b, err := field.fromBytes(field.toBytes(a))
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !a.equal(b) {
+			t.Fatal("bad serialization")
+		}
+	}
+}
+
+func TestFp6AdditionProperties(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		zero := field.zero()
+		a, _ := new(fe6).rand(rand.Reader)
+		b, _ := new(fe6).rand(rand.Reader)
+		c_1 := field.new()
+		c_2 := field.new()
+		field.add(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a + 0 == a")
+		}
+		field.sub(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a - 0 == a")
+		}
+		field.double(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		field.neg(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("-0 == 0")
+		}
+		field.sub(c_1, zero, a)
+		field.neg(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("0-a == -a")
+		}
+		field.double(c_1, a)
+		field.add(c_2, a, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("2 * a == a + a")
+		}
+		field.add(c_1, a, b)
+		field.add(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_2, b, a)
+		field.neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		c_x, _ := new(fe6).rand(rand.Reader)
+		field.add(c_1, a, b)
+		field.add(c_1, c_1, c_x)
+		field.add(c_2, a, c_x)
+		field.add(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_1, c_1, c_x)
+		field.sub(c_2, a, c_x)
+		field.sub(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a - b) - c == (a - c ) -b")
+		}
+	}
+}
+
+func TestFp6AdditionPropertiesAssigned(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		zero := new(fe6).zero()
+		a, b := new(fe6), new(fe6)
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		field.addAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a + 0 == a")
+		}
+		field.subAssign(a, zero)
+		if !a.equal(b) {
+			t.Fatal("a - 0 == a")
+		}
+		a.set(zero)
+		field.doubleAssign(a)
+		if !a.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		a.set(zero)
+		field.subAssign(a, b)
+		field.neg(b, b)
+		if !a.equal(b) {
+			t.Fatal("0-a == -a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b.set(a)
+		field.doubleAssign(a)
+		field.addAssign(b, b)
+		if !a.equal(b) {
+			t.Fatal("2 * a == a + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1, c_2 := new(fe6).set(a), new(fe6).set(b)
+		field.addAssign(c_1, b)
+		field.addAssign(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c_1.set(a)
+		c_2.set(b)
+		field.subAssign(c_1, b)
+		field.subAssign(c_2, a)
+		field.neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		c, _ := new(fe6).rand(rand.Reader)
+		a0 := new(fe6).set(a)
+		field.addAssign(a, b)
+		field.addAssign(a, c)
+		field.addAssign(b, c)
+		field.addAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("(a + b) + c == (b + c) + a")
+		}
+		_, _ = a.rand(rand.Reader)
+		_, _ = b.rand(rand.Reader)
+		_, _ = c.rand(rand.Reader)
+		a0.set(a)
+		field.subAssign(a, b)
+		field.subAssign(a, c)
+		field.subAssign(a0, c)
+		field.subAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a - b) - c == (a - c) -b")
+		}
+	}
+}
+
+func TestFp6SparseMultiplication(t *testing.T) {
+	fp6 := newFp6(nil)
+	var a, b, u *fe6
+	for j := 0; j < fuz; j++ {
+		a, _ = new(fe6).rand(rand.Reader)
+		b, _ = new(fe6).rand(rand.Reader)
+		u, _ = new(fe6).rand(rand.Reader)
+		b[2].zero()
+		fp6.mul(u, a, b)
+		fp6.mulBy01(a, a, &b[0], &b[1])
+		if !a.equal(u) {
+			t.Fatal("bad mul by 01")
+		}
+	}
+	for j := 0; j < fuz; j++ {
+		a, _ = new(fe6).rand(rand.Reader)
+		b, _ = new(fe6).rand(rand.Reader)
+		u, _ = new(fe6).rand(rand.Reader)
+		b[2].zero()
+		b[0].zero()
+		fp6.mul(u, a, b)
+		fp6.mulBy1(a, a, &b[1])
+		if !a.equal(u) {
+			t.Fatal("bad mul by 1")
+		}
+	}
+}
+
+func TestFp6MultiplicationProperties(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe6).rand(rand.Reader)
+		b, _ := new(fe6).rand(rand.Reader)
+		zero := field.zero()
+		one := field.one()
+		c_1, c_2 := field.new(), field.new()
+		field.mul(c_1, a, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		field.mul(c_1, a, one)
+		if !c_1.equal(a) {
+			t.Fatal("a * 1 == a")
+		}
+		field.mul(c_1, a, b)
+		field.mul(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a * b == b * a")
+		}
+		c_x, _ := new(fe6).rand(rand.Reader)
+		field.mul(c_1, a, b)
+		field.mul(c_1, c_1, c_x)
+		field.mul(c_2, c_x, b)
+		field.mul(c_2, c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+		field.square(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("0^2 == 0")
+		}
+		field.square(a, one)
+		if !a.equal(one) {
+			t.Fatal("1^2 == 1")
+		}
+		_, _ = a.rand(rand.Reader)
+		field.square(c_1, a)
+		field.mul(c_2, a, a)
+		if !c_2.equal(c_1) {
+			t.Fatal("a^2 == a*a")
+		}
+	}
+}
+
+func TestFp6MultiplicationPropertiesAssigned(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe6).rand(rand.Reader)
+		zero, one := new(fe6).zero(), new(fe6).one()
+		field.mulAssign(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		_, _ = a.rand(rand.Reader)
+		a0 := new(fe6).set(a)
+		field.mulAssign(a, one)
+		if !a.equal(a0) {
+			t.Fatal("a * 1 == a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b, _ := new(fe6).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("a * b == b * a")
+		}
+		c, _ := new(fe6).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(a, c)
+		field.mulAssign(a0, c)
+		field.mulAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+	}
+}
+
+func TestFp6Exponentiation(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe6).rand(rand.Reader)
+		u := field.new()
+		field.exp(u, a, big.NewInt(0))
+		if !u.equal(field.one()) {
+			t.Fatal("a^0 == 1")
+		}
+		field.exp(u, a, big.NewInt(1))
+		if !u.equal(a) {
+			t.Fatal("a^1 == a")
+		}
+		v := field.new()
+		field.mul(u, a, a)
+		field.mul(u, u, u)
+		field.mul(u, u, u)
+		field.exp(v, a, big.NewInt(8))
+		if !u.equal(v) {
+			t.Fatal("((a^2)^2)^2 == a^8")
+		}
+	}
+}
+
+func TestFp6Inversion(t *testing.T) {
+	field := newFp6(nil)
+	for i := 0; i < fuz; i++ {
+		u := field.new()
+		zero := field.zero()
+		one := field.one()
+		field.inverse(u, zero)
+		if !u.equal(zero) {
+			t.Fatal("(0^-1) == 0)")
+		}
+		field.inverse(u, one)
+		if !u.equal(one) {
+			t.Fatal("(1^-1) == 1)")
+		}
+		a, _ := new(fe6).rand(rand.Reader)
+		field.inverse(u, a)
+		field.mul(u, u, a)
+		if !u.equal(one) {
+			t.Fatal("(r*a) * r*(a^-1) == r)")
+		}
+	}
+}
+
+func TestFp12Serialization(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe12).rand(rand.Reader)
+		b, err := field.fromBytes(field.toBytes(a))
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !a.equal(b) {
+			t.Fatal("bad serialization")
+		}
+	}
+}
+
+func TestFp12AdditionProperties(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		zero := field.zero()
+		a, _ := new(fe12).rand(rand.Reader)
+		b, _ := new(fe12).rand(rand.Reader)
+		c_1 := field.new()
+		c_2 := field.new()
+		field.add(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a + 0 == a")
+		}
+		field.sub(c_1, a, zero)
+		if !c_1.equal(a) {
+			t.Fatal("a - 0 == a")
+		}
+		field.double(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		field.neg(c_1, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("-0 == 0")
+		}
+		field.sub(c_1, zero, a)
+		field.neg(c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("0-a == -a")
+		}
+		field.double(c_1, a)
+		field.add(c_2, a, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("2 * a == a + a")
+		}
+		field.add(c_1, a, b)
+		field.add(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a + b = b + a")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_2, b, a)
+		field.neg(c_2, c_2)
+		if !c_1.equal(c_2) {
+			t.Fatal("a - b = - ( b - a )")
+		}
+		c_x, _ := new(fe12).rand(rand.Reader)
+		field.add(c_1, a, b)
+		field.add(c_1, c_1, c_x)
+		field.add(c_2, a, c_x)
+		field.add(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		field.sub(c_1, a, b)
+		field.sub(c_1, c_1, c_x)
+		field.sub(c_2, a, c_x)
+		field.sub(c_2, c_2, b)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a - b) - c == (a - c ) -b")
+		}
+	}
+}
+
+func TestFp12MultiplicationProperties(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe12).rand(rand.Reader)
+		b, _ := new(fe12).rand(rand.Reader)
+		zero := field.zero()
+		one := field.one()
+		c_1, c_2 := field.new(), field.new()
+		field.mul(c_1, a, zero)
+		if !c_1.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		field.mul(c_1, a, one)
+		if !c_1.equal(a) {
+			t.Fatal("a * 1 == a")
+		}
+		field.mul(c_1, a, b)
+		field.mul(c_2, b, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("a * b == b * a")
+		}
+		c_x, _ := new(fe12).rand(rand.Reader)
+		field.mul(c_1, a, b)
+		field.mul(c_1, c_1, c_x)
+		field.mul(c_2, c_x, b)
+		field.mul(c_2, c_2, a)
+		if !c_1.equal(c_2) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+		field.square(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("0^2 == 0")
+		}
+		field.square(a, one)
+		if !a.equal(one) {
+			t.Fatal("1^2 == 1")
+		}
+		_, _ = a.rand(rand.Reader)
+		field.square(c_1, a)
+		field.mul(c_2, a, a)
+		if !c_2.equal(c_1) {
+			t.Fatal("a^2 == a*a")
+		}
+	}
+}
+
+func TestFp12MultiplicationPropertiesAssigned(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe12).rand(rand.Reader)
+		zero, one := new(fe12).zero(), new(fe12).one()
+		field.mulAssign(a, zero)
+		if !a.equal(zero) {
+			t.Fatal("a * 0 == 0")
+		}
+		_, _ = a.rand(rand.Reader)
+		a0 := new(fe12).set(a)
+		field.mulAssign(a, one)
+		if !a.equal(a0) {
+			t.Fatal("a * 1 == a")
+		}
+		_, _ = a.rand(rand.Reader)
+		b, _ := new(fe12).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(b, a0)
+		if !a.equal(b) {
+			t.Fatal("a * b == b * a")
+		}
+		c, _ := new(fe12).rand(rand.Reader)
+		a0.set(a)
+		field.mulAssign(a, b)
+		field.mulAssign(a, c)
+		field.mulAssign(a0, c)
+		field.mulAssign(a0, b)
+		if !a.equal(a0) {
+			t.Fatal("(a * b) * c == (a * c) * b")
+		}
+	}
+}
+
+func TestFp12SparseMultiplication(t *testing.T) {
+	fp12 := newFp12(nil)
+	var a, b, u *fe12
+	for j := 0; j < fuz; j++ {
+		a, _ = new(fe12).rand(rand.Reader)
+		b, _ = new(fe12).rand(rand.Reader)
+		u, _ = new(fe12).rand(rand.Reader)
+		b[0][2].zero()
+		b[1][0].zero()
+		b[1][2].zero()
+		fp12.mul(u, a, b)
+		fp12.mulBy014Assign(a, &b[0][0], &b[0][1], &b[1][1])
+		if !a.equal(u) {
+			t.Fatal("bad mul by 01")
+		}
+	}
+}
+
+func TestFp12Exponentiation(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		a, _ := new(fe12).rand(rand.Reader)
+		u := field.new()
+		field.exp(u, a, big.NewInt(0))
+		if !u.equal(field.one()) {
+			t.Fatal("a^0 == 1")
+		}
+		field.exp(u, a, big.NewInt(1))
+		if !u.equal(a) {
+			t.Fatal("a^1 == a")
+		}
+		v := field.new()
+		field.mul(u, a, a)
+		field.mul(u, u, u)
+		field.mul(u, u, u)
+		field.exp(v, a, big.NewInt(8))
+		if !u.equal(v) {
+			t.Fatal("((a^2)^2)^2 == a^8")
+		}
+	}
+}
+
+func TestFp12Inversion(t *testing.T) {
+	field := newFp12(nil)
+	for i := 0; i < fuz; i++ {
+		u := field.new()
+		zero := field.zero()
+		one := field.one()
+		field.inverse(u, zero)
+		if !u.equal(zero) {
+			t.Fatal("(0^-1) == 0)")
+		}
+		field.inverse(u, one)
+		if !u.equal(one) {
+			t.Fatal("(1^-1) == 1)")
+		}
+		a, _ := new(fe12).rand(rand.Reader)
+		field.inverse(u, a)
+		field.mul(u, u, a)
+		if !u.equal(one) {
+			t.Fatal("(r*a) * r*(a^-1) == r)")
+		}
+	}
+}
+
+func BenchmarkMultiplication(t *testing.B) {
+	a, _ := new(fe).rand(rand.Reader)
+	b, _ := new(fe).rand(rand.Reader)
+	c, _ := new(fe).rand(rand.Reader)
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		mul(c, a, b)
+	}
+}
+
+func padBytes(in []byte, size int) []byte {
+	out := make([]byte, size)
+	if len(in) > size {
+		panic("bad input for padding")
+	}
+	copy(out[size-len(in):], in)
+	return out
+}
diff --git a/pkg/core/curves/native/bls12-381/g1.go b/pkg/core/curves/native/bls12-381/g1.go
new file mode 100644
index 00000000..f4483f77
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/g1.go
@@ -0,0 +1,634 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"crypto/subtle"
+	"errors"
+	"hash"
+	"math"
+	"math/big"
+)
+
+// PointG1 is type for point in G1.
+// PointG1 is both used for Affine and Jacobian point representation.
+// If z is equal to one the point is accounted as in affine form.
+type PointG1 [3]fe
+
+func (p *PointG1) Set(p2 *PointG1) *PointG1 {
+	p[0].set(&p2[0])
+	p[1].set(&p2[1])
+	p[2].set(&p2[2])
+	return p
+}
+
+func (p *PointG1) Zero() *PointG1 {
+	p[0].zero()
+	p[1].one()
+	p[2].zero()
+	return p
+}
+
+type tempG1 struct {
+	t [9]*fe
+}
+
+// G1 is struct for G1 group.
+type G1 struct {
+	tempG1
+}
+
+// NewG1 constructs a new G1 instance.
+func NewG1() *G1 {
+	t := newTempG1()
+	return &G1{t}
+}
+
+func newTempG1() tempG1 {
+	t := [9]*fe{}
+	for i := 0; i < 9; i++ {
+		t[i] = &fe{}
+	}
+	return tempG1{t}
+}
+
+// Q returns group order in big.Int.
+func (g *G1) Q() *big.Int {
+	return new(big.Int).Set(q)
+}
+
+// FromUncompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G1) FromUncompressed(uncompressed []byte) (*PointG1, error) {
+	if len(uncompressed) < 96 {
+		return nil, errors.New("input string should be equal or larger than 96")
+	}
+	var in [96]byte
+	copy(in[:], uncompressed[:96])
+	if in[0]&(1<<7) != 0 {
+		return nil, errors.New("input string should be equal or larger than 96")
+	}
+	if in[0]&(1<<5) != 0 {
+		return nil, errors.New("input string should be equal or larger than 96")
+	}
+	if in[0]&(1<<6) != 0 {
+		for i, v := range in {
+			if (i == 0 && v != 0x40) || (i != 0 && v != 0x00) {
+				return nil, errors.New("input string should be equal or larger than 96")
+			}
+		}
+		return g.Zero(), nil
+	}
+	in[0] &= 0x1f
+	x, err := fromBytes(in[:48])
+	if err != nil {
+		return nil, err
+	}
+	y, err := fromBytes(in[48:])
+	if err != nil {
+		return nil, err
+	}
+	z := new(fe).one()
+	p := &PointG1{*x, *y, *z}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToUncompressed given a G1 point returns bytes in uncompressed (x, y) form of the point.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G1) ToUncompressed(p *PointG1) ([]byte, error) {
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("to uncompressed: input point is not in group")
+	}
+	out := make([]byte, 96)
+	if g.IsZero(p) {
+		out[0] |= 1 << 6
+		return out, nil
+	}
+	g.Affine(p)
+	copy(out[:48], toBytes(&p[0]))
+	copy(out[48:], toBytes(&p[1]))
+	return out, nil
+}
+
+// FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G1.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G1) FromCompressed(compressed []byte) (*PointG1, error) {
+	if len(compressed) != 48 {
+		return nil, errors.New("input string should be exactly 48 bytes")
+	}
+	var in [48]byte
+	copy(in[:], compressed[:])
+	if in[0]&(1<<7) == 0 {
+		return nil, errors.New("compression flag should be set")
+	}
+	if in[0]&(1<<6) != 0 {
+		// in[0] == (1 << 6) + (1 << 7)
+		for i, v := range in {
+			if (i == 0 && v != 0xc0) || (i != 0 && v != 0x00) {
+				return nil, errors.New("input string should be zero when infinity flag is set")
+			}
+		}
+		return g.Zero(), nil
+	}
+	a := in[0]&(1<<5) != 0
+	in[0] &= 0x1f
+	x, err := fromBytes(in[:])
+	if err != nil {
+		return nil, err
+	}
+	// solve curve equation
+	y := &fe{}
+	square(y, x)
+	mul(y, y, x)
+	add(y, y, b)
+	if ok := sqrt(y, y); !ok {
+		return nil, errors.New("point is not on curve")
+	}
+	if y.signBE() == a {
+		neg(y, y)
+	}
+	z := new(fe).one()
+	p := &PointG1{*x, *y, *z}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToCompressed given a G1 point returns bytes in compressed form of the point.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G1) ToCompressed(p *PointG1) []byte {
+	out := make([]byte, 48)
+	g.Affine(p)
+	if g.IsZero(p) {
+		out[0] |= 1 << 6
+	} else {
+		copy(out[:], toBytes(&p[0]))
+		if !p[1].signBE() {
+			out[0] |= 1 << 5
+		}
+	}
+	out[0] |= 1 << 7
+	return out
+}
+
+func (g *G1) fromBytesUnchecked(in []byte) (*PointG1, error) {
+	p0, err := fromBytes(in[:48])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := fromBytes(in[48:])
+	if err != nil {
+		return nil, err
+	}
+	p2 := new(fe).one()
+	p := &PointG1{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// FromBytes constructs a new point given uncompressed byte input.
+// FromBytes does not take zcash flags into account.
+// Byte input expected to be larger than 96 bytes.
+// First 96 bytes should be concatenation of x and y values.
+// Point (0, 0) is considered as infinity.
+func (g *G1) FromBytes(in []byte) (*PointG1, error) {
+	if len(in) < 96 {
+		return nil, errors.New("input string should be equal or larger than 96")
+	}
+	p0, err := fromBytes(in[:48])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := fromBytes(in[48:])
+	if err != nil {
+		return nil, err
+	}
+	// check if given input points to infinity
+	if p0.isZero() && p1.isZero() {
+		return g.Zero(), nil
+	}
+	p2 := new(fe).one()
+	p := &PointG1{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToBytes serializes a point into bytes in uncompressed form.
+// ToBytes does not take zcash flags into account.
+// ToBytes returns (0, 0) if point is infinity.
+func (g *G1) ToBytes(p *PointG1) []byte {
+	out := make([]byte, 96)
+	if g.IsZero(p) {
+		return out
+	}
+	g.Affine(p)
+	copy(out[:48], toBytes(&p[0]))
+	copy(out[48:], toBytes(&p[1]))
+	return out
+}
+
+func (g *G1) toBytesJacobi(p *PointG1) []byte {
+	out := make([]byte, 144)
+	if g.IsZero(p) {
+		return out
+	}
+	copy(out[:48], toBytes(&p[0]))   // x
+	copy(out[48:96], toBytes(&p[1])) // y
+	copy(out[96:], toBytes(&p[2]))   // z
+	return out
+}
+
+func (g *G1) fromBytesJacobi(in []byte) (*PointG1, error) {
+	if len(in) < 144 {
+		return nil, errors.New("input string should be equal or larger than toBytesJacobi")
+	}
+	p0, err := fromBytes(in[:48])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := fromBytes(in[48:96])
+	if err != nil {
+		return nil, err
+	}
+	p2, err := fromBytes(in[96:])
+	if err != nil {
+		return nil, err
+	}
+	p := &PointG1{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// New creates a new G1 Point which is equal to zero in other words point at infinity.
+func (g *G1) New() *PointG1 {
+	return g.Zero()
+}
+
+// Zero returns a new G1 Point which is equal to point at infinity.
+func (g *G1) Zero() *PointG1 {
+	return new(PointG1).Zero()
+}
+
+// One returns a new G1 Point which is equal to generator point.
+func (g *G1) One() *PointG1 {
+	p := &PointG1{}
+	return p.Set(&g1One)
+}
+
+// IsZero returns true if given point is equal to zero.
+func (g *G1) IsZero(p *PointG1) bool {
+	// uninitialized usually means a bug
+	// return false
+	if p == nil {
+		return false
+	}
+	return p[2].isZero()
+}
+
+// Equal checks if given two G1 point is equal in their affine form.
+func (g *G1) Equal(p1, p2 *PointG1) bool {
+	if g.IsZero(p1) {
+		return g.IsZero(p2)
+	}
+	if g.IsZero(p2) {
+		return g.IsZero(p1)
+	}
+	t := g.t
+	square(t[0], &p1[2])
+	square(t[1], &p2[2])
+	mul(t[2], t[0], &p2[0])
+	mul(t[3], t[1], &p1[0])
+	mul(t[0], t[0], &p1[2])
+	mul(t[1], t[1], &p2[2])
+	mul(t[1], t[1], &p1[1])
+	mul(t[0], t[0], &p2[1])
+	return t[0].equal(t[1]) && t[2].equal(t[3])
+}
+
+// InCorrectSubgroup checks whether given point is in correct subgroup.
+func (g *G1) InCorrectSubgroup(p *PointG1) bool {
+	tmp := &PointG1{}
+	g.MulScalar(tmp, p, q)
+	return g.IsZero(tmp)
+}
+
+// IsOnCurve checks a G1 point is on curve.
+func (g *G1) IsOnCurve(p *PointG1) bool {
+	if g.IsZero(p) {
+		return true
+	}
+	t := g.t
+	square(t[0], &p[1])
+	square(t[1], &p[0])
+	mul(t[1], t[1], &p[0])
+	square(t[2], &p[2])
+	square(t[3], t[2])
+	mul(t[2], t[2], t[3])
+	mul(t[2], b, t[2])
+	add(t[1], t[1], t[2])
+	return t[0].equal(t[1])
+}
+
+// IsAffine checks a G1 point whether it is in affine form.
+func (g *G1) IsAffine(p *PointG1) bool {
+	return p[2].isOne()
+}
+
+// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
+func (g *G1) Affine(p *PointG1) *PointG1 {
+	if g.IsZero(p) {
+		return p
+	}
+	if !g.IsAffine(p) {
+		t := g.t
+		inverse(t[0], &p[2])
+		square(t[1], t[0])
+		mul(&p[0], &p[0], t[1])
+		mul(t[0], t[0], t[1])
+		mul(&p[1], &p[1], t[0])
+		p[2].one()
+	}
+	return p
+}
+
+// Add adds two G1 points p1, p2 and assigns the result to point at first argument.
+func (g *G1) Add(r, p1, p2 *PointG1) *PointG1 {
+	// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#addition-add-2007-bl
+	if g.IsZero(p1) {
+		return r.Set(p2)
+	}
+	if g.IsZero(p2) {
+		return r.Set(p1)
+	}
+	t := g.t
+	square(t[7], &p1[2])
+	mul(t[1], &p2[0], t[7])
+	mul(t[2], &p1[2], t[7])
+	mul(t[0], &p2[1], t[2])
+	square(t[8], &p2[2])
+	mul(t[3], &p1[0], t[8])
+	mul(t[4], &p2[2], t[8])
+	mul(t[2], &p1[1], t[4])
+	if t[1].equal(t[3]) {
+		if t[0].equal(t[2]) {
+			return g.Double(r, p1)
+		} else {
+			return r.Zero()
+		}
+	}
+	sub(t[1], t[1], t[3])
+	double(t[4], t[1])
+	square(t[4], t[4])
+	mul(t[5], t[1], t[4])
+	sub(t[0], t[0], t[2])
+	double(t[0], t[0])
+	square(t[6], t[0])
+	sub(t[6], t[6], t[5])
+	mul(t[3], t[3], t[4])
+	double(t[4], t[3])
+	sub(&r[0], t[6], t[4])
+	sub(t[4], t[3], &r[0])
+	mul(t[6], t[2], t[5])
+	double(t[6], t[6])
+	mul(t[0], t[0], t[4])
+	sub(&r[1], t[0], t[6])
+	add(t[0], &p1[2], &p2[2])
+	square(t[0], t[0])
+	sub(t[0], t[0], t[7])
+	sub(t[0], t[0], t[8])
+	mul(&r[2], t[0], t[1])
+	return r
+}
+
+// Double doubles a G1 point p and assigns the result to the point at first argument.
+func (g *G1) Double(r, p *PointG1) *PointG1 {
+	// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+	if g.IsZero(p) {
+		return r.Set(p)
+	}
+	t := g.t
+	square(t[0], &p[0])
+	square(t[1], &p[1])
+	square(t[2], t[1])
+	add(t[1], &p[0], t[1])
+	square(t[1], t[1])
+	sub(t[1], t[1], t[0])
+	sub(t[1], t[1], t[2])
+	double(t[1], t[1])
+	double(t[3], t[0])
+	add(t[0], t[3], t[0])
+	square(t[4], t[0])
+	double(t[3], t[1])
+	sub(&r[0], t[4], t[3])
+	sub(t[1], t[1], &r[0])
+	double(t[2], t[2])
+	double(t[2], t[2])
+	double(t[2], t[2])
+	mul(t[0], t[0], t[1])
+	sub(t[1], t[0], t[2])
+	mul(t[0], &p[1], &p[2])
+	r[1].set(t[1])
+	double(&r[2], t[0])
+	return r
+}
+
+// Neg negates a G1 point p and assigns the result to the point at first argument.
+func (g *G1) Neg(r, p *PointG1) *PointG1 {
+	r[0].set(&p[0])
+	r[2].set(&p[2])
+	neg(&r[1], &p[1])
+	return r
+}
+
+// Sub subtracts two G1 points p1, p2 and assigns the result to point at first argument.
+func (g *G1) Sub(c, a, b *PointG1) *PointG1 {
+	d := &PointG1{}
+	g.Neg(d, b)
+	g.Add(c, a, d)
+	return c
+}
+
+// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
+func (g *G1) MulScalar(c, p *PointG1, e *big.Int) *PointG1 {
+	ee := new(big.Int).Mod(e, q)
+	q, n := &PointG1{}, &PointG1{}
+	n.Set(p)
+	l := ee.BitLen()
+	for i := 0; i < l; i++ {
+		bytes := g.toBytesJacobi(q)
+		r := &PointG1{}
+		g.Add(r, q, n)
+		subtle.ConstantTimeCopy(int(ee.Bit(i)), bytes, g.toBytesJacobi(r))
+		q, _ = g.fromBytesJacobi(bytes)
+		g.Double(n, n)
+	}
+	return c.Set(q)
+}
+
+// ClearCofactor maps given a G1 point to correct subgroup
+func (g *G1) ClearCofactor(p *PointG1) {
+	g.MulScalar(p, p, cofactorEFFG1)
+}
+
+// MultiExp calculates multi exponentiation. Given pairs of G1 point and scalar values
+// (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n
+// Length of points and scalars are expected to be equal, otherwise an error is returned.
+// Result is assigned to point at first argument.
+func (g *G1) MultiExp(r *PointG1, points []*PointG1, powers []*big.Int) (*PointG1, error) {
+	if len(points) != len(powers) {
+		return nil, errors.New("point and scalar vectors should be in same length")
+	}
+	var c uint32 = 3
+	if len(powers) >= 32 {
+		c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
+	}
+	fPowers := make([]*big.Int, len(powers))
+	for i, p := range powers {
+		fPowers[i] = new(big.Int).Mod(p, q)
+	}
+	numBits := uint32(q.BitLen())
+	windows := make([]*PointG1, (numBits+c-1)/c)
+	acc, sum := g.New(), g.New()
+	mask := (uint64(1) << c) - 1
+	j := 0
+	var cur uint32
+	for cur < numBits {
+		acc.Zero()
+		bucket := make([]*PointG1, 1<<c)
+		for i := 0; i < len(bucket); i++ {
+			bucket[i] = g.New()
+		}
+		for i := 0; i < len(fPowers); i++ {
+			s0 := fPowers[i].Uint64()
+			index := uint(s0 & mask)
+			g.Add(bucket[index], bucket[index], points[i])
+			fPowers[i] = new(big.Int).Rsh(fPowers[i], uint(c))
+		}
+		sum.Zero()
+		for i := len(bucket) - 1; i > 0; i-- {
+			g.Add(sum, sum, bucket[i])
+			g.Add(acc, acc, sum)
+		}
+		windows[j] = g.New()
+		windows[j].Set(acc)
+		j++
+		cur += c
+	}
+	acc.Zero()
+	for i := len(windows) - 1; i >= 0; i-- {
+		for j := uint32(0); j < c; j++ {
+			g.Double(acc, acc)
+		}
+		g.Add(acc, acc, windows[i])
+	}
+	return r.Set(acc), nil
+}
+
+// MapToCurve given a byte slice returns a valid G1 point.
+// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+// Input byte slice should be a valid field element, otherwise an error is returned.
+func (g *G1) MapToCurve(in []byte) (*PointG1, error) {
+	u, err := fromBytes(in)
+	if err != nil {
+		return nil, err
+	}
+	x, y := swuMapG1(u)
+	isogenyMapG1(x, y)
+	one := new(fe).one()
+	p := &PointG1{*x, *y, *one}
+	g.ClearCofactor(p)
+	return g.Affine(p), nil
+}
+
+// EncodeToCurve given a message and domain seperator tag returns the hash result
+// which is a valid curve point.
+// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+func (g *G1) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error) {
+	err := longerThanLimit(msg)
+	if err != nil {
+		return nil, err
+	}
+	err = longerThanLimit(domain)
+	if err != nil {
+		return nil, err
+	}
+	hashRes, err := hashToFpXMD(f, msg, domain, 1)
+	if err != nil {
+		return nil, err
+	}
+	u := hashRes[0]
+	x, y := swuMapG1(u)
+	isogenyMapG1(x, y)
+	one := new(fe).one()
+	p := &PointG1{*x, *y, *one}
+	g.ClearCofactor(p)
+	return g.Affine(p), nil
+}
+
+// HashToCurve given a message and domain seperator tag returns the hash result
+// which is a valid curve point.
+// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+func (g *G1) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG1, error) {
+	err := longerThanLimit(msg)
+	if err != nil {
+		return nil, err
+	}
+	err = longerThanLimit(domain)
+	if err != nil {
+		return nil, err
+	}
+	hashRes, err := hashToFpXMD(f, msg, domain, 2)
+	if err != nil {
+		return nil, err
+	}
+	u0, u1 := hashRes[0], hashRes[1]
+	x0, y0 := swuMapG1(u0)
+	x1, y1 := swuMapG1(u1)
+	one := new(fe).one()
+	p0, p1 := &PointG1{*x0, *y0, *one}, &PointG1{*x1, *y1, *one}
+	g.Add(p0, p0, p1)
+	g.Affine(p0)
+	isogenyMapG1(&p0[0], &p0[1])
+	g.ClearCofactor(p0)
+	return g.Affine(p0), nil
+}
diff --git a/pkg/core/curves/native/bls12-381/g1_test.go b/pkg/core/curves/native/bls12-381/g1_test.go
new file mode 100644
index 00000000..5372828b
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/g1_test.go
@@ -0,0 +1,537 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"bytes"
+	"crypto/rand"
+	"crypto/sha256"
+	"encoding/hex"
+	"io/ioutil"
+	"math/big"
+	"testing"
+)
+
+func (g *G1) one() *PointG1 {
+	one, _ := g.fromBytesUnchecked(fromHex(48,
+		"0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb",
+		"0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1",
+	))
+	return one
+}
+
+func (g *G1) rand() *PointG1 {
+	k, err := rand.Int(rand.Reader, q)
+	if err != nil {
+		panic(err)
+	}
+	return g.MulScalar(&PointG1{}, g.one(), k)
+}
+
+func TestG1Serialization(t *testing.T) {
+	var err error
+	g1 := NewG1()
+	zero := g1.Zero()
+	b0, err := g1.ToUncompressed(zero)
+	if err != nil {
+		t.Fatal(err)
+	}
+	p0, err := g1.FromUncompressed(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g1.IsZero(p0) {
+		t.Fatal("bad infinity serialization 1")
+	}
+	b0 = g1.ToCompressed(zero)
+	p0, err = g1.FromCompressed(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g1.IsZero(p0) {
+		t.Fatal("bad infinity serialization 2")
+	}
+	b0 = g1.ToBytes(zero)
+	p0, err = g1.FromBytes(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g1.IsZero(p0) {
+		t.Fatal("bad infinity serialization 3")
+	}
+	for i := 0; i < fuz; i++ {
+		a := g1.rand()
+		uncompressed, err := g1.ToUncompressed(a)
+		if err != nil {
+			t.Fatal(err)
+		}
+		b, err := g1.FromUncompressed(uncompressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g1.Equal(a, b) {
+			t.Fatal("bad serialization 1")
+		}
+		compressed := g1.ToCompressed(b)
+		a, err = g1.FromCompressed(compressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g1.Equal(a, b) {
+			t.Fatal("bad serialization 2")
+		}
+	}
+	for i := 0; i < fuz; i++ {
+		a := g1.rand()
+		uncompressed := g1.ToBytes(a)
+		b, err := g1.FromBytes(uncompressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g1.Equal(a, b) {
+			t.Fatal("bad serialization 3")
+		}
+	}
+}
+
+func TestG1IsOnCurve(t *testing.T) {
+	g := NewG1()
+	zero := g.Zero()
+	if !g.IsOnCurve(zero) {
+		t.Fatal("zero must be on curve")
+	}
+	one := new(fe).one()
+	p := &PointG1{*one, *one, *one}
+	if g.IsOnCurve(p) {
+		t.Fatal("(1, 1) is not on curve")
+	}
+}
+
+func TestG1AdditiveProperties(t *testing.T) {
+	g := NewG1()
+	t0, t1 := g.New(), g.New()
+	zero := g.Zero()
+	for i := 0; i < fuz; i++ {
+		a, b := g.rand(), g.rand()
+		g.Add(t0, a, zero)
+		if !g.Equal(t0, a) {
+			t.Fatal("a + 0 == a")
+		}
+		g.Add(t0, zero, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("0 + 0 == 0")
+		}
+		g.Sub(t0, a, zero)
+		if !g.Equal(t0, a) {
+			t.Fatal("a - 0 == a")
+		}
+		g.Sub(t0, zero, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("0 - 0 == 0")
+		}
+		g.Neg(t0, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("- 0 == 0")
+		}
+		g.Sub(t0, zero, a)
+		g.Neg(t0, t0)
+		if !g.Equal(t0, a) {
+			t.Fatal(" - (0 - a) == a")
+		}
+		g.Double(t0, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		g.Double(t0, a)
+		g.Sub(t0, t0, a)
+		if !g.Equal(t0, a) || !g.IsOnCurve(t0) {
+			t.Fatal(" (2 * a) - a == a")
+		}
+		g.Add(t0, a, b)
+		g.Add(t1, b, a)
+		if !g.Equal(t0, t1) {
+			t.Fatal("a + b == b + a")
+		}
+		g.Sub(t0, a, b)
+		g.Sub(t1, b, a)
+		g.Neg(t1, t1)
+		if !g.Equal(t0, t1) {
+			t.Fatal("a - b == - ( b - a )")
+		}
+		c := g.rand()
+		g.Add(t0, a, b)
+		g.Add(t0, t0, c)
+		g.Add(t1, a, c)
+		g.Add(t1, t1, b)
+		if !g.Equal(t0, t1) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		g.Sub(t0, a, b)
+		g.Sub(t0, t0, c)
+		g.Sub(t1, a, c)
+		g.Sub(t1, t1, b)
+		if !g.Equal(t0, t1) {
+			t.Fatal("(a - b) - c == (a - c) -b")
+		}
+	}
+}
+
+func TestG1MultiplicativeProperties(t *testing.T) {
+	g := NewG1()
+	t0, t1 := g.New(), g.New()
+	zero := g.Zero()
+	for i := 0; i < fuz; i++ {
+		a := g.rand()
+		s1, s2, s3 := randScalar(q), randScalar(q), randScalar(q)
+		sone := big.NewInt(1)
+		g.MulScalar(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatal(" 0 ^ s == 0")
+		}
+		g.MulScalar(t0, a, sone)
+		if !g.Equal(t0, a) {
+			t.Fatal(" a ^ 1 == a")
+		}
+		g.MulScalar(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatal(" 0 ^ s == a")
+		}
+		g.MulScalar(t0, a, s1)
+		g.MulScalar(t0, t0, s2)
+		s3.Mul(s1, s2)
+		g.MulScalar(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
+		}
+		g.MulScalar(t0, a, s1)
+		g.MulScalar(t1, a, s2)
+		g.Add(t0, t0, t1)
+		s3.Add(s1, s2)
+		g.MulScalar(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
+		}
+	}
+}
+
+func TestZKCryptoVectorsG1UncompressedValid(t *testing.T) {
+	data, err := ioutil.ReadFile("tests/g1_uncompressed_valid_test_vectors.dat")
+	if err != nil {
+		panic(err)
+	}
+	g := NewG1()
+	p1 := g.Zero()
+	for i := 0; i < 1000; i++ {
+		vector := data[i*96 : (i+1)*96]
+		p2, err := g.FromUncompressed(vector)
+		if err != nil {
+			t.Fatal("decoing fails", err, i)
+		}
+		uncompressed, err := g.ToUncompressed(p2)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !bytes.Equal(vector, uncompressed) || !g.Equal(p1, p2) {
+			t.Fatal("bad serialization")
+		}
+
+		g.Add(p1, p1, &g1One)
+	}
+}
+
+func TestZKCryptoVectorsG1CompressedValid(t *testing.T) {
+	data, err := ioutil.ReadFile("tests/g1_compressed_valid_test_vectors.dat")
+	if err != nil {
+		panic(err)
+	}
+	g := NewG1()
+	p1 := g.Zero()
+	for i := 0; i < 1000; i++ {
+		vector := data[i*48 : (i+1)*48]
+		p2, err := g.FromCompressed(vector)
+		if err != nil {
+			t.Fatal("decoing fails", err, i)
+		}
+		compressed := g.ToCompressed(p2)
+		if !bytes.Equal(vector, compressed) || !g.Equal(p1, p2) {
+			t.Fatal("bad serialization")
+		}
+		g.Add(p1, p1, &g1One)
+	}
+}
+
+func TestG1MultiExpExpected(t *testing.T) {
+	g := NewG1()
+	one := g.one()
+	var scalars [2]*big.Int
+	var bases [2]*PointG1
+	scalars[0] = big.NewInt(2)
+	scalars[1] = big.NewInt(3)
+	bases[0], bases[1] = new(PointG1).Set(one), new(PointG1).Set(one)
+	expected, result := g.New(), g.New()
+	g.MulScalar(expected, one, big.NewInt(5))
+	_, _ = g.MultiExp(result, bases[:], scalars[:])
+	if !g.Equal(expected, result) {
+		t.Fatal("bad multi-exponentiation")
+	}
+}
+
+func TestG1MultiExpBatch(t *testing.T) {
+	g := NewG1()
+	n := 1000
+	bases := make([]*PointG1, n)
+	scalars := make([]*big.Int, n)
+	for i := 0; i < n; i++ {
+		bases[i] = g.rand()
+		scalars[i], _ = rand.Int(rand.Reader, g.Q())
+	}
+	expected, tmp := g.New(), g.New()
+	for i := 0; i < n; i++ {
+		g.MulScalar(tmp, bases[i], scalars[i])
+		g.Add(expected, expected, tmp)
+	}
+	result := g.New()
+	_, _ = g.MultiExp(result, bases, scalars)
+	if !g.Equal(expected, result) {
+		t.Fatal("bad multi-exponentiation")
+	}
+}
+
+func TestG1MapToCurve(t *testing.T) {
+	for i, v := range []struct {
+		u        []byte
+		expected []byte
+	}{
+		{
+			u: make([]byte, 48),
+			expected: fromHex(-1,
+				"11a9a0372b8f332d5c30de9ad14e50372a73fa4c45d5f2fa5097f2d6fb93bcac592f2e1711ac43db0519870c7d0ea415",
+				"092c0f994164a0719f51c24ba3788de240ff926b55f58c445116e8bc6a47cd63392fd4e8e22bdf9feaa96ee773222133",
+			),
+		},
+		{
+			u: fromHex(-1, "07fdf49ea58e96015d61f6b5c9d1c8f277146a533ae7fbca2a8ef4c41055cd961fbc6e26979b5554e4b4f22330c0e16d"),
+			expected: fromHex(-1,
+				"1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c",
+				"0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5",
+			),
+		},
+		{
+			u: fromHex(-1, "1275ab3adbf824a169ed4b1fd669b49cf406d822f7fe90d6b2f8c601b5348436f89761bb1ad89a6fb1137cd91810e5d2"),
+			expected: fromHex(-1,
+				"179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6",
+				"0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4",
+			),
+		},
+		{
+			u: fromHex(-1, "0e93d11d30de6d84b8578827856f5c05feef36083eef0b7b263e35ecb9b56e86299614a042e57d467fa20948e8564909"),
+			expected: fromHex(-1,
+				"15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af",
+				"0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788",
+			),
+		},
+		{
+			u: fromHex(-1, "015a41481155d17074d20be6d8ec4d46632a51521cd9c916e265bd9b47343b3689979b50708c8546cbc2916b86cb1a3a"),
+			expected: fromHex(-1,
+				"06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee",
+				"094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca",
+			),
+		},
+	} {
+		g := NewG1()
+		p0, err := g.MapToCurve(v.u)
+		if err != nil {
+			t.Fatal("map to curve fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("map to curve fails", i)
+		}
+	}
+}
+
+func TestG1EncodeToCurve(t *testing.T) {
+	domain := []byte("BLS12381G1_XMD:SHA-256_SSWU_NU_TESTGEN")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c",
+				"0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6",
+				"0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af",
+				"0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee",
+				"094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca",
+			),
+		},
+	} {
+		g := NewG1()
+		p0, err := g.EncodeToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("encode to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("encode to point fails", i)
+		}
+	}
+}
+
+func TestG1HashToCurve(t *testing.T) {
+	domain := []byte("BLS12381G1_XMD:SHA-256_SSWU_RO_TESTGEN")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"0576730ab036cbac1d95b38dca905586f28d0a59048db4e8778782d89bff856ddef89277ead5a21e2975c4a6e3d8c79e",
+				"1273e568bebf1864393c517f999b87c1eaa1b8432f95aea8160cd981b5b05d8cd4a7cf00103b6ef87f728e4b547dd7ae",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"061daf0cc00d8912dac1d4cf5a7c32fca97f8b3bf3f805121888e5eb89f77f9a9f406569027ac6d0e61b1229f42c43d6",
+				"0de1601e5ba02cb637c1d35266f5700acee9850796dc88e860d022d7b9e7e3dce5950952e97861e5bb16d215c87f030d",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"0fb3455436843e76079c7cf3dfef75e5a104dfe257a29a850c145568d500ad31ccfe79be9ae0ea31a722548070cf98cd",
+				"177989f7e2c751658df1b26943ee829d3ebcf131d8f805571712f3a7527ee5334ecff8a97fc2a50cea86f5e6212e9a57",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"0514af2137c1ae1d78d5cb97ee606ea142824c199f0f25ac463a0c78200de57640d34686521d3e9cf6b3721834f8a038",
+				"047a85d6898416a0899e26219bca7c4f0fa682717199de196b02b95eaf9fb55456ac3b810e78571a1b7f5692b7c58ab6",
+			),
+		},
+	} {
+		g := NewG1()
+		p0, err := g.HashToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("hash to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("hash to point fails", i)
+		}
+	}
+
+	domain = []byte("QUUX-V01-CS02-with-expander")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"140c7a6dbfff5ece70b651e951964551296f70efd3a72d64bd2c145f4469ba54840a4495f8ca4ee7a86dc25b83a54fde13871e80c7eaeb5af63ecf7e95ffa24b326ddab44cf1837ac3ba00bd7772c2b88e2f7d61271abdf84cd30deae9c0c798",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"10122323a3260d856bde2fc1662dc0fa863fda1abcd081fd932fb8cd01ff24b21af3900bd32d4e34558289b4c5d0cfc5129d3715ac3bb90229ec09e7649d2442f2991082d137072adfc664e185d879763f5c490cb261f8484c23872857bd16ce",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"00d6baa7c082c3bb02531bc329cfc6c00e04d32a0225faad568e081e5b761c1c9bc080020f88775e4eef90494f7f6b1719a8098791b3a8fa318a309bf84984bc32d435161df73c184c98a32351d39eb4c3a7236ad51ad28ef0151bcfcad66911",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"1386c705ca91cefd5feb2cacb337c6beaaa2161937ebfbb2bf1838adfaac0c4922d674f0ed394f247c0d1b9befc8964d08fa7f130bd73137226438335797a20ebcf6d3699ac520aa0db1f9268865db330f36108fed71e6cf2c2f3651acb3e48a",
+			),
+		},
+	} {
+		g := NewG1()
+		p0, err := g.HashToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("hash to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatalf("hash to point fails %d: expected: %v, got: %v", i, hex.EncodeToString(v.expected), hex.EncodeToString(g.ToBytes(p0)))
+		}
+	}
+}
+
+func TestCheckG1InfinityPoint(t *testing.T) {
+	g1 := NewG1()
+	// Zero is considered infinity point
+	inf := g1.Zero()
+	if !g1.InCorrectSubgroup(inf) {
+		t.Fatal("infinity point not considered in subgroup")
+	}
+	if !g1.IsOnCurve(inf) {
+		t.Fatal("infinity point not considered on curve")
+	}
+
+	zeroBytes := make([]byte, 96)
+	infPoint, err := g1.FromBytes(zeroBytes)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g1.IsZero(infPoint) {
+		t.Fatal("created point not inf point")
+	}
+}
+
+func BenchmarkG1Add(t *testing.B) {
+	g1 := NewG1()
+	a, b, c := g1.rand(), g1.rand(), PointG1{}
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		g1.Add(&c, a, b)
+	}
+}
+
+func BenchmarkG1Mul(t *testing.B) {
+	g1 := NewG1()
+	a, e, c := g1.rand(), q, PointG1{}
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		g1.MulScalar(&c, a, e)
+	}
+}
+
+func BenchmarkG1MapToCurve(t *testing.B) {
+	a := fromHex(48, "0x1234")
+	g1 := NewG1()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		_, err := g1.MapToCurve(a)
+		if err != nil {
+			t.Fatal(err)
+		}
+	}
+}
diff --git a/pkg/core/curves/native/bls12-381/g2.go b/pkg/core/curves/native/bls12-381/g2.go
new file mode 100644
index 00000000..4ed6c59d
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/g2.go
@@ -0,0 +1,684 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"crypto/subtle"
+	"errors"
+	"hash"
+	"math"
+	"math/big"
+)
+
+// PointG2 is type for point in G2.
+// PointG2 is both used for Affine and Jacobian point representation.
+// If z is equal to one the point is accounted as in affine form.
+type PointG2 [3]fe2
+
+// Set copies valeus of one point to another.
+func (p *PointG2) Set(p2 *PointG2) *PointG2 {
+	p[0].set(&p2[0])
+	p[1].set(&p2[1])
+	p[2].set(&p2[2])
+	return p
+}
+
+func (p *PointG2) Zero() *PointG2 {
+	p[0].zero()
+	p[1].one()
+	p[2].zero()
+	return p
+
+}
+
+type tempG2 struct {
+	t [9]*fe2
+}
+
+// G2 is struct for G2 group.
+type G2 struct {
+	f *fp2
+	tempG2
+}
+
+// NewG2 constructs a new G2 instance.
+func NewG2() *G2 {
+	return newG2(nil)
+}
+
+func newG2(f *fp2) *G2 {
+	if f == nil {
+		f = newFp2()
+	}
+	t := newTempG2()
+	return &G2{f, t}
+}
+
+func newTempG2() tempG2 {
+	t := [9]*fe2{}
+	for i := 0; i < 9; i++ {
+		t[i] = &fe2{}
+	}
+	return tempG2{t}
+}
+
+// Q returns group order in big.Int.
+func (g *G2) Q() *big.Int {
+	return new(big.Int).Set(q)
+}
+
+// FromUncompressed expects byte slice larger than 192 bytes and given bytes returns a new point in G2.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G2) FromUncompressed(uncompressed []byte) (*PointG2, error) {
+	if len(uncompressed) < 192 {
+		return nil, errors.New("input string should be equal or larger than 192")
+	}
+	var in [192]byte
+	copy(in[:], uncompressed[:192])
+	if in[0]&(1<<7) != 0 {
+		return nil, errors.New("compression flag should be zero")
+	}
+	if in[0]&(1<<5) != 0 {
+		return nil, errors.New("sort flag should be zero")
+	}
+	if in[0]&(1<<6) != 0 {
+		for i, v := range in {
+			if (i == 0 && v != 0x40) || (i != 0 && v != 0x00) {
+				return nil, errors.New("input string should be zero when infinity flag is set")
+			}
+		}
+		return g.Zero(), nil
+	}
+	in[0] &= 0x1f
+	x, err := g.f.fromBytes(in[:96])
+	if err != nil {
+		return nil, err
+	}
+	y, err := g.f.fromBytes(in[96:])
+	if err != nil {
+		return nil, err
+	}
+	z := new(fe2).one()
+	p := &PointG2{*x, *y, *z}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToUncompressed given a G2 point returns bytes in uncompressed (x, y) form of the point.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G2) ToUncompressed(p *PointG2) ([]byte, error) {
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("to uncompressed: input point is not in group")
+	}
+	out := make([]byte, 192)
+	g.Affine(p)
+	if g.IsZero(p) {
+		out[0] |= 1 << 6
+		return out, nil
+	}
+	copy(out[:96], g.f.toBytes(&p[0]))
+	copy(out[96:], g.f.toBytes(&p[1]))
+	return out, nil
+}
+
+// FromCompressed expects byte slice larger than 96 bytes and given bytes returns a new point in G2.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G2) FromCompressed(compressed []byte) (*PointG2, error) {
+	if len(compressed) != 96 {
+		return nil, errors.New("input string should be exactly 96 bytes")
+	}
+	var in [96]byte
+	copy(in[:], compressed[:])
+	if in[0]&(1<<7) == 0 {
+		return nil, errors.New("bad compression")
+	}
+	if in[0]&(1<<6) != 0 {
+		// in[0] == (1 << 6) + (1 << 7)
+		for i, v := range in {
+			if (i == 0 && v != 0xc0) || (i != 0 && v != 0x00) {
+				return nil, errors.New("input string should be zero when infinity flag is set")
+			}
+		}
+		return g.Zero(), nil
+	}
+	a := in[0]&(1<<5) != 0
+	in[0] &= 0x1f
+	x, err := g.f.fromBytes(in[:])
+	if err != nil {
+		return nil, err
+	}
+	// solve curve equation
+	y := &fe2{}
+	g.f.square(y, x)
+	g.f.mul(y, y, x)
+	g.f.add(y, y, b2)
+	if ok := g.f.sqrt(y, y); !ok {
+		return nil, errors.New("point is not on curve")
+	}
+	if y.signBE() == a {
+		g.f.neg(y, y)
+	}
+	z := new(fe2).one()
+	p := &PointG2{*x, *y, *z}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToCompressed given a G2 point returns bytes in compressed form of the point.
+// Serialization rules are in line with zcash library. See below for details.
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (g *G2) ToCompressed(p *PointG2) []byte {
+	out := make([]byte, 96)
+	g.Affine(p)
+	if g.IsZero(p) {
+		out[0] |= 1 << 6
+	} else {
+		copy(out[:], g.f.toBytes(&p[0]))
+		if !p[1].signBE() {
+			out[0] |= 1 << 5
+		}
+	}
+	out[0] |= 1 << 7
+	return out
+}
+
+func (g *G2) fromBytesUnchecked(in []byte) (*PointG2, error) {
+	p0, err := g.f.fromBytes(in[:96])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := g.f.fromBytes(in[96:])
+	if err != nil {
+		return nil, err
+	}
+	p2 := new(fe2).one()
+	p := &PointG2{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// FromBytes constructs a new point given uncompressed byte input.
+// FromBytes does not take zcash flags into account.
+// Byte input expected to be larger than 96 bytes.
+// First 192 bytes should be concatenation of x and y values
+// Point (0, 0) is considered as infinity.
+func (g *G2) FromBytes(in []byte) (*PointG2, error) {
+	if len(in) < 192 {
+		return nil, errors.New("input string should be equal or larger than 192")
+	}
+	p0, err := g.f.fromBytes(in[:96])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := g.f.fromBytes(in[96:])
+	if err != nil {
+		return nil, err
+	}
+	// check if given input points to infinity
+	if p0.isZero() && p1.isZero() {
+		return g.Zero(), nil
+	}
+	p2 := new(fe2).one()
+	p := &PointG2{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// ToBytes serializes a point into bytes in uncompressed form,
+// does not take zcash flags into account,
+// returns (0, 0) if point is infinity.
+func (g *G2) ToBytes(p *PointG2) []byte {
+	out := make([]byte, 192)
+	if g.IsZero(p) {
+		return out
+	}
+	g.Affine(p)
+	copy(out[:96], g.f.toBytes(&p[0]))
+	copy(out[96:], g.f.toBytes(&p[1]))
+	return out
+}
+
+func (g *G2) toBytesJacobi(p *PointG2) []byte {
+	out := make([]byte, 288)
+	copy(out[:96], g.f.toBytes(&p[0]))    // x
+	copy(out[96:192], g.f.toBytes(&p[1])) // y
+	copy(out[192:], g.f.toBytes(&p[2]))   // z
+	return out
+}
+
+func (g *G2) fromBytesJacobi(in []byte) (*PointG2, error) {
+	if len(in) < 288 {
+		return nil, errors.New("input string should be equal or larger than toBytesJacobi")
+	}
+	p0, err := g.f.fromBytes(in[:96])
+	if err != nil {
+		return nil, err
+	}
+	p1, err := g.f.fromBytes(in[96:192])
+	if err != nil {
+		return nil, err
+	}
+	p2, err := g.f.fromBytes(in[192:])
+	if err != nil {
+		return nil, err
+	}
+	p := &PointG2{*p0, *p1, *p2}
+	if !g.IsOnCurve(p) {
+		return nil, errors.New("point not on curve")
+	}
+	if !g.InCorrectSubgroup(p) {
+		return nil, errors.New("point not in correct subgroup")
+	}
+	return p, nil
+}
+
+// New creates a new G2 Point which is equal to zero in other words point at infinity.
+func (g *G2) New() *PointG2 {
+	return new(PointG2).Zero()
+}
+
+// Zero returns a new G2 Point which is equal to point at infinity.
+func (g *G2) Zero() *PointG2 {
+	return new(PointG2).Zero()
+}
+
+// One returns a new G2 Point which is equal to generator point.
+func (g *G2) One() *PointG2 {
+	p := &PointG2{}
+	return p.Set(&g2One)
+}
+
+// IsZero returns true if given point is equal to zero.
+func (g *G2) IsZero(p *PointG2) bool {
+	// uninitialized usually means a bug
+	// return false
+	if p == nil {
+		return false
+	}
+	return p[2].isZero()
+}
+
+// Equal checks if given two G2 point is equal in their affine form.
+func (g *G2) Equal(p1, p2 *PointG2) bool {
+	if g.IsZero(p1) {
+		return g.IsZero(p2)
+	}
+	if g.IsZero(p2) {
+		return g.IsZero(p1)
+	}
+	t := g.t
+	g.f.square(t[0], &p1[2])
+	g.f.square(t[1], &p2[2])
+	g.f.mul(t[2], t[0], &p2[0])
+	g.f.mul(t[3], t[1], &p1[0])
+	g.f.mul(t[0], t[0], &p1[2])
+	g.f.mul(t[1], t[1], &p2[2])
+	g.f.mul(t[1], t[1], &p1[1])
+	g.f.mul(t[0], t[0], &p2[1])
+	return t[0].equal(t[1]) && t[2].equal(t[3])
+}
+
+// InCorrectSubgroup checks whether given point is in correct subgroup.
+func (g *G2) InCorrectSubgroup(p *PointG2) bool {
+	tmp := &PointG2{}
+	g.MulScalar(tmp, p, q)
+	return g.IsZero(tmp)
+}
+
+// IsOnCurve checks a G2 point is on curve.
+func (g *G2) IsOnCurve(p *PointG2) bool {
+	if g.IsZero(p) {
+		return true
+	}
+	t := g.t
+	g.f.square(t[0], &p[1])
+	g.f.square(t[1], &p[0])
+	g.f.mul(t[1], t[1], &p[0])
+	g.f.square(t[2], &p[2])
+	g.f.square(t[3], t[2])
+	g.f.mul(t[2], t[2], t[3])
+	g.f.mul(t[2], b2, t[2])
+	g.f.add(t[1], t[1], t[2])
+	return t[0].equal(t[1])
+}
+
+// IsAffine checks a G2 point whether it is in affine form.
+func (g *G2) IsAffine(p *PointG2) bool {
+	return p[2].isOne()
+}
+
+// Affine calculates affine form of given G2 point.
+func (g *G2) Affine(p *PointG2) *PointG2 {
+	if g.IsZero(p) {
+		return p
+	}
+	if !g.IsAffine(p) {
+		t := g.t
+		g.f.inverse(t[0], &p[2])
+		g.f.square(t[1], t[0])
+		g.f.mul(&p[0], &p[0], t[1])
+		g.f.mul(t[0], t[0], t[1])
+		g.f.mul(&p[1], &p[1], t[0])
+		p[2].one()
+	}
+	return p
+}
+
+// Add adds two G2 points p1, p2 and assigns the result to point at first argument.
+func (g *G2) Add(r, p1, p2 *PointG2) *PointG2 {
+	// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#addition-add-2007-bl
+	if g.IsZero(p1) {
+		return r.Set(p2)
+	}
+	if g.IsZero(p2) {
+		return r.Set(p1)
+	}
+	t := g.t
+	g.f.square(t[7], &p1[2])
+	g.f.mul(t[1], &p2[0], t[7])
+	g.f.mul(t[2], &p1[2], t[7])
+	g.f.mul(t[0], &p2[1], t[2])
+	g.f.square(t[8], &p2[2])
+	g.f.mul(t[3], &p1[0], t[8])
+	g.f.mul(t[4], &p2[2], t[8])
+	g.f.mul(t[2], &p1[1], t[4])
+	if t[1].equal(t[3]) {
+		if t[0].equal(t[2]) {
+			return g.Double(r, p1)
+		} else {
+			return r.Zero()
+		}
+	}
+	g.f.sub(t[1], t[1], t[3])
+	g.f.double(t[4], t[1])
+	g.f.square(t[4], t[4])
+	g.f.mul(t[5], t[1], t[4])
+	g.f.sub(t[0], t[0], t[2])
+	g.f.double(t[0], t[0])
+	g.f.square(t[6], t[0])
+	g.f.sub(t[6], t[6], t[5])
+	g.f.mul(t[3], t[3], t[4])
+	g.f.double(t[4], t[3])
+	g.f.sub(&r[0], t[6], t[4])
+	g.f.sub(t[4], t[3], &r[0])
+	g.f.mul(t[6], t[2], t[5])
+	g.f.double(t[6], t[6])
+	g.f.mul(t[0], t[0], t[4])
+	g.f.sub(&r[1], t[0], t[6])
+	g.f.add(t[0], &p1[2], &p2[2])
+	g.f.square(t[0], t[0])
+	g.f.sub(t[0], t[0], t[7])
+	g.f.sub(t[0], t[0], t[8])
+	g.f.mul(&r[2], t[0], t[1])
+	return r
+}
+
+// Double doubles a G2 point p and assigns the result to the point at first argument.
+func (g *G2) Double(r, p *PointG2) *PointG2 {
+	// http://www.hyperelliptic.org/EFD/gp/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+	if g.IsZero(p) {
+		return r.Set(p)
+	}
+	t := g.t
+	g.f.square(t[0], &p[0])
+	g.f.square(t[1], &p[1])
+	g.f.square(t[2], t[1])
+	g.f.add(t[1], &p[0], t[1])
+	g.f.square(t[1], t[1])
+	g.f.sub(t[1], t[1], t[0])
+	g.f.sub(t[1], t[1], t[2])
+	g.f.double(t[1], t[1])
+	g.f.double(t[3], t[0])
+	g.f.add(t[0], t[3], t[0])
+	g.f.square(t[4], t[0])
+	g.f.double(t[3], t[1])
+	g.f.sub(&r[0], t[4], t[3])
+	g.f.sub(t[1], t[1], &r[0])
+	g.f.double(t[2], t[2])
+	g.f.double(t[2], t[2])
+	g.f.double(t[2], t[2])
+	g.f.mul(t[0], t[0], t[1])
+	g.f.sub(t[1], t[0], t[2])
+	g.f.mul(t[0], &p[1], &p[2])
+	r[1].set(t[1])
+	g.f.double(&r[2], t[0])
+	return r
+}
+
+// Neg negates a G2 point p and assigns the result to the point at first argument.
+func (g *G2) Neg(r, p *PointG2) *PointG2 {
+	r[0].set(&p[0])
+	g.f.neg(&r[1], &p[1])
+	r[2].set(&p[2])
+	return r
+}
+
+// Sub subtracts two G2 points p1, p2 and assigns the result to point at first argument.
+func (g *G2) Sub(c, a, b *PointG2) *PointG2 {
+	d := &PointG2{}
+	g.Neg(d, b)
+	g.Add(c, a, d)
+	return c
+}
+
+// MulScalar multiplies a point by given scalar value in big.Int and assigns the result to point at first argument.
+func (g *G2) MulScalar(c, p *PointG2, e *big.Int) *PointG2 {
+	ee := new(big.Int).Mod(e, q)
+	q, n := &PointG2{}, &PointG2{}
+	n.Set(p)
+	l := ee.BitLen()
+	for i := 0; i < l; i++ {
+		bytes := g.toBytesJacobi(q)
+		r := &PointG2{}
+		g.Add(r, q, n)
+		subtle.ConstantTimeCopy(int(ee.Bit(i)), bytes, g.toBytesJacobi(r))
+		q, _ = g.fromBytesJacobi(bytes)
+		g.Double(n, n)
+	}
+	return c.Set(q)
+}
+
+// ClearCofactor maps given a G2 point to correct subgroup
+func (g *G2) ClearCofactor(p *PointG2) *PointG2 {
+	return g.wnafMul(p, p, cofactorEFFG2)
+}
+
+// MultiExp calculates multi exponentiation. Given pairs of G2 point and scalar values
+// (P_0, e_0), (P_1, e_1), ... (P_n, e_n) calculates r = e_0 * P_0 + e_1 * P_1 + ... + e_n * P_n
+// Length of points and scalars are expected to be equal, otherwise an error is returned.
+// Result is assigned to point at first argument.
+func (g *G2) MultiExp(r *PointG2, points []*PointG2, powers []*big.Int) (*PointG2, error) {
+	if len(points) != len(powers) {
+		return nil, errors.New("point and scalar vectors should be in same length")
+	}
+	var c uint32 = 3
+	if len(powers) >= 32 {
+		c = uint32(math.Ceil(math.Log10(float64(len(powers)))))
+	}
+	fPowers := make([]*big.Int, len(powers))
+	for i, p := range powers {
+		fPowers[i] = new(big.Int).Mod(p, q)
+	}
+	numBits := uint32(g.Q().BitLen())
+	windows := make([]*PointG2, (numBits+c-1)/c)
+	acc, sum := g.New(), g.New()
+	mask := (uint64(1) << c) - 1
+	j := 0
+	var cur uint32
+	for cur < numBits {
+		acc.Zero()
+		bucket := make([]*PointG2, 1<<c)
+		for i := 0; i < len(bucket); i++ {
+			bucket[i] = g.New()
+		}
+		for i := 0; i < len(fPowers); i++ {
+			s0 := fPowers[i].Uint64()
+			index := uint(s0 & mask)
+			g.Add(bucket[index], bucket[index], points[i])
+			fPowers[i] = new(big.Int).Rsh(fPowers[i], uint(c))
+		}
+		sum.Zero()
+		for i := len(bucket) - 1; i > 0; i-- {
+			g.Add(sum, sum, bucket[i])
+			g.Add(acc, acc, sum)
+		}
+		windows[j] = g.New()
+		windows[j].Set(acc)
+		j++
+		cur += c
+	}
+	acc.Zero()
+	for i := len(windows) - 1; i >= 0; i-- {
+		for j := uint32(0); j < c; j++ {
+			g.Double(acc, acc)
+		}
+		g.Add(acc, acc, windows[i])
+	}
+	return r.Set(acc), nil
+}
+
+func (g *G2) wnafMul(c, p *PointG2, e *big.Int) *PointG2 {
+	windowSize := uint(6)
+	precompTable := make([]*PointG2, (1 << (windowSize - 1)))
+	for i := 0; i < len(precompTable); i++ {
+		precompTable[i] = g.New()
+	}
+	var indexForPositive uint64 = (1 << (windowSize - 2))
+	precompTable[indexForPositive].Set(p)
+	g.Neg(precompTable[indexForPositive-1], p)
+	doubled, precomp := g.New(), g.New()
+	g.Double(doubled, p)
+	precomp.Set(p)
+	for i := uint64(1); i < indexForPositive; i++ {
+		g.Add(precomp, precomp, doubled)
+		precompTable[indexForPositive+i].Set(precomp)
+		g.Neg(precompTable[indexForPositive-1-i], precomp)
+	}
+	wnaf := wnaf(e, windowSize)
+	q := g.Zero()
+	found := false
+	var idx uint64
+	for i := len(wnaf) - 1; i >= 0; i-- {
+		if found {
+			g.Double(q, q)
+		}
+		if wnaf[i] != 0 {
+			found = true
+			if wnaf[i] > 0 {
+				idx = uint64(wnaf[i] >> 1)
+				g.Add(q, q, precompTable[indexForPositive+idx])
+			} else {
+				idx = uint64(((0 - wnaf[i]) >> 1))
+				g.Add(q, q, precompTable[indexForPositive-1-idx])
+			}
+		}
+	}
+	return c.Set(q)
+}
+
+// MapToCurve given a byte slice returns a valid G2 point.
+// This mapping function implements the Simplified Shallue-van de Woestijne-Ulas method.
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-05#section-6.6.2
+// Input byte slice should be a valid field element, otherwise an error is returned.
+func (g *G2) MapToCurve(in []byte) (*PointG2, error) {
+	fp2 := g.f
+	u, err := fp2.fromBytes(in)
+	if err != nil {
+		return nil, err
+	}
+	x, y := swuMapG2(fp2, u)
+	isogenyMapG2(fp2, x, y)
+	z := new(fe2).one()
+	q := &PointG2{*x, *y, *z}
+	g.ClearCofactor(q)
+	return g.Affine(q), nil
+}
+
+// EncodeToCurve given a message and domain seperator tag returns the hash result
+// which is a valid curve point.
+// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_NU_ suite at
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+func (g *G2) EncodeToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error) {
+	err := longerThanLimit(msg)
+	if err != nil {
+		return nil, err
+	}
+	err = longerThanLimit(domain)
+	if err != nil {
+		return nil, err
+	}
+	hashRes, err := hashToFpXMD(f, msg, domain, 2)
+	if err != nil {
+		return nil, err
+	}
+	fp2 := g.f
+	u := &fe2{*hashRes[0], *hashRes[1]}
+	x, y := swuMapG2(fp2, u)
+	isogenyMapG2(fp2, x, y)
+	z := new(fe2).one()
+	q := &PointG2{*x, *y, *z}
+	g.ClearCofactor(q)
+	return g.Affine(q), nil
+}
+
+// HashToCurve given a message and domain seperator tag returns the hash result
+// which is a valid curve point.
+// Implementation follows BLS12381G1_XMD:SHA-256_SSWU_RO_ suite at
+// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08
+func (g *G2) HashToCurve(f func() hash.Hash, msg, domain []byte) (*PointG2, error) {
+	err := longerThanLimit(msg)
+	if err != nil {
+		return nil, err
+	}
+	err = longerThanLimit(domain)
+	if err != nil {
+		return nil, err
+	}
+	hashRes, err := hashToFpXMD(f, msg, domain, 4)
+	if err != nil {
+		return nil, err
+	}
+	fp2 := g.f
+	u0, u1 := &fe2{*hashRes[0], *hashRes[1]}, &fe2{*hashRes[2], *hashRes[3]}
+	x0, y0 := swuMapG2(fp2, u0)
+	x1, y1 := swuMapG2(fp2, u1)
+	z0 := new(fe2).one()
+	z1 := new(fe2).one()
+	p0, p1 := &PointG2{*x0, *y0, *z0}, &PointG2{*x1, *y1, *z1}
+	g.Add(p0, p0, p1)
+	g.Affine(p0)
+	isogenyMapG2(fp2, &p0[0], &p0[1])
+	g.ClearCofactor(p0)
+	return g.Affine(p0), nil
+}
diff --git a/pkg/core/curves/native/bls12-381/g2_test.go b/pkg/core/curves/native/bls12-381/g2_test.go
new file mode 100644
index 00000000..0fce7787
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/g2_test.go
@@ -0,0 +1,669 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"bytes"
+	"crypto/rand"
+	"crypto/sha256"
+	"encoding/hex"
+	"io/ioutil"
+	"math/big"
+	"testing"
+)
+
+func (g *G2) one() *PointG2 {
+	one, err := g.fromBytesUnchecked(fromHex(48,
+		"0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e",
+		"0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8",
+		"0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be",
+		"0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801",
+	))
+	if err != nil {
+		panic(err)
+	}
+	return one
+}
+
+func (g *G2) rand() *PointG2 {
+	k, err := rand.Int(rand.Reader, q)
+	if err != nil {
+		panic(err)
+	}
+	return g.MulScalar(&PointG2{}, g.one(), k)
+}
+
+func (g *G2) randCorrect() *PointG2 {
+	k, err := rand.Int(rand.Reader, q)
+	if err != nil {
+		panic(err)
+	}
+	a := g.new()
+	g.MulScalar(a, g.one(), k)
+	return g.ClearCofactor(a)
+}
+
+//func (g *G2) randAffine() *PointG2 {
+//	return g.Affine(g.rand())
+//}
+
+func (g *G2) new() *PointG2 {
+	return g.Zero()
+}
+
+func TestG2Serialization(t *testing.T) {
+	var err error
+	g2 := NewG2()
+	zero := g2.Zero()
+	b0, err := g2.ToUncompressed(zero)
+	if err != nil {
+		t.Fatal(err)
+	}
+	p0, err := g2.FromUncompressed(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g2.IsZero(p0) {
+		t.Fatal("bad infinity serialization 1")
+	}
+	b0 = g2.ToCompressed(zero)
+	p0, err = g2.FromCompressed(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g2.IsZero(p0) {
+		t.Fatal("bad infinity serialization 2")
+	}
+	b0 = g2.ToBytes(zero)
+	p0, err = g2.FromBytes(b0)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g2.IsZero(p0) {
+		t.Fatal("bad infinity serialization 3")
+	}
+	for i := 0; i < fuz; i++ {
+		a := g2.rand()
+		uncompressed, err := g2.ToUncompressed(a)
+		if err != nil {
+			t.Fatal(err)
+		}
+		b, err := g2.FromUncompressed(uncompressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g2.Equal(a, b) {
+			t.Fatal("bad serialization 1")
+		}
+		compressed := g2.ToCompressed(b)
+		a, err = g2.FromCompressed(compressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g2.Equal(a, b) {
+			t.Fatal("bad serialization 2")
+		}
+	}
+	for i := 0; i < fuz; i++ {
+		a := g2.rand()
+		uncompressed := g2.ToBytes(a)
+		b, err := g2.FromBytes(uncompressed)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !g2.Equal(a, b) {
+			t.Fatal("bad serialization 3")
+		}
+	}
+}
+
+func TestG2IsOnCurve(t *testing.T) {
+	g := NewG2()
+	zero := g.Zero()
+	if !g.IsOnCurve(zero) {
+		t.Fatal("zero must be on curve")
+	}
+	one := new(fe2).one()
+	p := &PointG2{*one, *one, *one}
+	if g.IsOnCurve(p) {
+		t.Fatal("(1, 1) is not on curve")
+	}
+}
+
+func TestG2AdditiveProperties(t *testing.T) {
+	g := NewG2()
+	t0, t1 := g.New(), g.New()
+	zero := g.Zero()
+	for i := 0; i < fuz; i++ {
+		a, b := g.rand(), g.rand()
+		_, _, _ = b, t1, zero
+		g.Add(t0, a, zero)
+		if !g.Equal(t0, a) {
+			t.Fatal("a + 0 == a")
+		}
+		g.Add(t0, zero, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("0 + 0 == 0")
+		}
+		g.Sub(t0, a, zero)
+		if !g.Equal(t0, a) {
+			t.Fatal("a - 0 == a")
+		}
+		g.Sub(t0, zero, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("0 - 0 == 0")
+		}
+		g.Neg(t0, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("- 0 == 0")
+		}
+		g.Sub(t0, zero, a)
+		g.Neg(t0, t0)
+		if !g.Equal(t0, a) {
+			t.Fatal(" - (0 - a) == a")
+		}
+		g.Double(t0, zero)
+		if !g.Equal(t0, zero) {
+			t.Fatal("2 * 0 == 0")
+		}
+		g.Double(t0, a)
+		g.Sub(t0, t0, a)
+		if !g.Equal(t0, a) || !g.IsOnCurve(t0) {
+			t.Fatal(" (2 * a) - a == a")
+		}
+		g.Add(t0, a, b)
+		g.Add(t1, b, a)
+		if !g.Equal(t0, t1) {
+			t.Fatal("a + b == b + a")
+		}
+		g.Sub(t0, a, b)
+		g.Sub(t1, b, a)
+		g.Neg(t1, t1)
+		if !g.Equal(t0, t1) {
+			t.Fatal("a - b == - ( b - a )")
+		}
+		c := g.rand()
+		g.Add(t0, a, b)
+		g.Add(t0, t0, c)
+		g.Add(t1, a, c)
+		g.Add(t1, t1, b)
+		if !g.Equal(t0, t1) {
+			t.Fatal("(a + b) + c == (a + c ) + b")
+		}
+		g.Sub(t0, a, b)
+		g.Sub(t0, t0, c)
+		g.Sub(t1, a, c)
+		g.Sub(t1, t1, b)
+		if !g.Equal(t0, t1) {
+			t.Fatal("(a - b) - c == (a - c) -b")
+		}
+	}
+}
+
+func TestG2MultiplicativeProperties(t *testing.T) {
+	g := NewG2()
+	t0, t1 := g.New(), g.New()
+	zero := g.Zero()
+	for i := 0; i < fuz; i++ {
+		a := g.rand()
+		s1, s2, s3 := randScalar(q), randScalar(q), randScalar(q)
+		sone := big.NewInt(1)
+		g.MulScalar(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatal(" 0 ^ s == 0")
+		}
+		g.MulScalar(t0, a, sone)
+		if !g.Equal(t0, a) {
+			t.Fatal(" a ^ 1 == a")
+		}
+		g.MulScalar(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatal(" 0 ^ s == a")
+		}
+		g.MulScalar(t0, a, s1)
+		g.MulScalar(t0, t0, s2)
+		s3.Mul(s1, s2)
+		g.MulScalar(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
+		}
+		g.MulScalar(t0, a, s1)
+		g.MulScalar(t1, a, s2)
+		g.Add(t0, t0, t1)
+		s3.Add(s1, s2)
+		g.MulScalar(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
+		}
+	}
+}
+
+func TestWNAFMulAgainstNaive(t *testing.T) {
+	g2 := NewG2()
+	for i := 0; i < fuz; i++ {
+		a := g2.randCorrect()
+		c0, c1 := g2.new(), g2.new()
+		e := randScalar(g2.Q())
+		g2.MulScalar(c0, a, e)
+		g2.wnafMul(c1, a, e)
+		if !g2.Equal(c0, c1) {
+			t.Fatal("wnaf against naive failed")
+		}
+	}
+}
+
+func TestG2MultiplicativePropertiesWNAF(t *testing.T) {
+	g := NewG2()
+	t0, t1 := g.new(), g.new()
+	zero := g.Zero()
+	for i := 0; i < fuz; i++ {
+		a := g.randCorrect()
+		s1, s2, s3 := randScalar(q), randScalar(q), randScalar(q)
+		sone := big.NewInt(1)
+		g.wnafMul(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatalf(" 0 ^ s == 0")
+		}
+		g.wnafMul(t0, a, sone)
+		if !g.Equal(t0, a) {
+			t.Fatalf(" a ^ 1 == a")
+		}
+		g.wnafMul(t0, zero, s1)
+		if !g.Equal(t0, zero) {
+			t.Fatalf(" 0 ^ s == a")
+		}
+		g.wnafMul(t0, a, s1)
+		g.wnafMul(t0, t0, s2)
+		s3.Mul(s1, s2)
+		g.wnafMul(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) ^ s2 == a ^ (s1 * s2)")
+		}
+		g.wnafMul(t0, a, s1)
+		g.wnafMul(t1, a, s2)
+		g.Add(t0, t0, t1)
+		s3.Add(s1, s2)
+		g.wnafMul(t1, a, s3)
+		if !g.Equal(t0, t1) {
+			t.Errorf(" (a ^ s1) + (a ^ s2) == a ^ (s1 + s2)")
+		}
+	}
+}
+
+func TestZKCryptoVectorsG2UncompressedValid(t *testing.T) {
+	data, err := ioutil.ReadFile("tests/g2_uncompressed_valid_test_vectors.dat")
+	if err != nil {
+		panic(err)
+	}
+	g := NewG2()
+	p1 := g.Zero()
+	for i := 0; i < 1000; i++ {
+		vector := data[i*192 : (i+1)*192]
+		p2, err := g.FromUncompressed(vector)
+		if err != nil {
+			t.Fatal("decoing fails", err, i)
+		}
+		uncompressed, err := g.ToUncompressed(p2)
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !bytes.Equal(vector, uncompressed) || !g.Equal(p1, p2) {
+			t.Fatal("bad serialization")
+		}
+		g.Add(p1, p1, &g2One)
+	}
+}
+
+func TestZKCryptoVectorsG2CompressedValid(t *testing.T) {
+	data, err := ioutil.ReadFile("tests/g2_compressed_valid_test_vectors.dat")
+	if err != nil {
+		panic(err)
+	}
+	g := NewG2()
+	p1 := g.Zero()
+	for i := 0; i < 1000; i++ {
+		vector := data[i*96 : (i+1)*96]
+		p2, err := g.FromCompressed(vector)
+		if err != nil {
+			t.Fatal("decoing fails", err, i)
+		}
+		compressed := g.ToCompressed(p2)
+		if !bytes.Equal(vector, compressed) || !g.Equal(p1, p2) {
+			t.Fatal("bad serialization")
+		}
+
+		g.Add(p1, p1, &g2One)
+	}
+}
+
+func TestG2MultiExpExpected(t *testing.T) {
+	g := NewG2()
+	one := g.one()
+	var scalars [2]*big.Int
+	var bases [2]*PointG2
+	scalars[0] = big.NewInt(2)
+	scalars[1] = big.NewInt(3)
+	bases[0], bases[1] = new(PointG2).Set(one), new(PointG2).Set(one)
+	expected, result := g.New(), g.New()
+	g.MulScalar(expected, one, big.NewInt(5))
+	_, _ = g.MultiExp(result, bases[:], scalars[:])
+	if !g.Equal(expected, result) {
+		t.Fatal("bad multi-exponentiation")
+	}
+}
+
+func TestG2MultiExpBatch(t *testing.T) {
+	g := NewG2()
+	n := 1000
+	bases := make([]*PointG2, n)
+	scalars := make([]*big.Int, n)
+	for i := 0; i < n; i++ {
+		bases[i] = g.rand()
+		scalars[i], _ = rand.Int(rand.Reader, g.Q())
+	}
+	expected, tmp := g.New(), g.New()
+	for i := 0; i < n; i++ {
+		g.MulScalar(tmp, bases[i], scalars[i])
+		g.Add(expected, expected, tmp)
+	}
+	result := g.New()
+	_, _ = g.MultiExp(result, bases, scalars)
+	if !g.Equal(expected, result) {
+		t.Fatal("bad multi-exponentiation")
+	}
+}
+
+func TestClearCofactor(t *testing.T) {
+	g2 := NewG2()
+	for i := 0; i < fuz; i++ {
+		a := g2.rand()
+		g2.ClearCofactor(a)
+		if !g2.InCorrectSubgroup(a) {
+			t.Fatal("clear cofactor failed")
+		}
+	}
+}
+
+func TestG2MapToCurve(t *testing.T) {
+	for i, v := range []struct {
+		u        []byte
+		expected []byte
+	}{
+		{
+			u: make([]byte, 96),
+			expected: fromHex(-1, "0a67d12118b5a35bb02d2e86b3ebfa7e23410db93de39fb06d7025fa95e96ffa428a7a27c3ae4dd4b40bd251ac658892",
+				"018320896ec9eef9d5e619848dc29ce266f413d02dd31d9b9d44ec0c79cd61f18b075ddba6d7bd20b7ff27a4b324bfce",
+				"04c69777a43f0bda07679d5805e63f18cf4e0e7c6112ac7f70266d199b4f76ae27c6269a3ceebdae30806e9a76aadf5c",
+				"0260e03644d1a2c321256b3246bad2b895cad13890cbe6f85df55106a0d334604fb143c7a042d878006271865bc35941",
+			),
+		},
+		{
+			u: fromHex(-1,
+				"025fbc07711ba267b7e70c82caa70a16fbb1d470ae24ceef307f5e2000751677820b7013ad4e25492dcf30052d3e5eca",
+				"0e775d7827adf385b83e20e4445bd3fab21d7b4498426daf3c1d608b9d41e9edb5eda0df022e753b8bb4bc3bb7db4914",
+			),
+			expected: fromHex(-1,
+				"0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8",
+				"027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d",
+				"0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db",
+				"053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7",
+			),
+		},
+		{
+			u: fromHex(-1,
+				"1870a7dbfd2a1deb74015a3546b20f598041bf5d5202997956a94a368d30d3f70f18cdaa1d33ce970a4e16af961cbdcb",
+				"045ab31ce4b5a8ba7c4b2851b64f063a66cd1223d3c85005b78e1beee65e33c90ceef0244e45fc45a5e1d6eab6644fdb",
+			),
+			expected: fromHex(-1,
+				"18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778",
+				"09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b",
+				"10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0",
+				"02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811",
+			),
+		},
+		{
+			u: fromHex(-1,
+				"088fe329b054db8a6474f21a7fbfdf17b4c18044db299d9007af582c3d5f17d00e56d99921d4b5640fce44b05219b5de",
+				"0b6e6135a4cd31ba980ddbd115ac48abef7ec60e226f264d7befe002c165f3a496f36f76dd524efd75d17422558d10b4",
+			),
+			expected: fromHex(-1,
+				"19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163",
+				"149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7",
+				"04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33",
+				"04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551",
+			),
+		},
+		{
+			u: fromHex(-1,
+				"03df16a66a05e4c1188c234788f43896e0565bfb64ac49b9639e6b284cc47dad73c47bb4ea7e677db8d496beb907fbb6",
+				"0f45b50647d67485295aa9eb2d91a877b44813677c67c8d35b2173ff3ba95f7bd0806f9ca8a1436b8b9d14ee81da4d7e",
+			),
+			expected: fromHex(-1,
+				"0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a",
+				"0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552",
+				"14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449",
+				"09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a",
+			),
+		},
+	} {
+		g := NewG2()
+		p0, err := g.MapToCurve(v.u)
+		if err != nil {
+			t.Fatal("map to curve fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("map to curve fails", i)
+		}
+	}
+}
+
+func TestG2EncodeToCurve(t *testing.T) {
+	domain := []byte("BLS12381G2_XMD:SHA-256_SSWU_NU_TESTGEN")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8",
+				"027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d",
+				"0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db",
+				"053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778",
+				"09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b",
+				"10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0",
+				"02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163",
+				"149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7",
+				"04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33",
+				"04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a",
+				"0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552",
+				"14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449",
+				"09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a",
+			),
+		},
+	} {
+		g := NewG2()
+		p0, err := g.EncodeToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("encode to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("encode to point fails x", i)
+		}
+	}
+}
+
+func TestG2HashToCurve(t *testing.T) {
+	domain := []byte("BLS12381G2_XMD:SHA-256_SSWU_RO_TESTGEN")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"0fbdae26f9f9586a46d4b0b70390d09064ef2afe5c99348438a3c7d9756471e015cb534204c1b6824617a85024c772dc",
+				"0a650bd36ae7455cb3fe5d8bb1310594551456f5c6593aec9ee0c03d2f6cb693bd2c5e99d4e23cbaec767609314f51d3",
+				"02e5cf8f9b7348428cc9e66b9a9b36fe45ba0b0a146290c3a68d92895b1af0e1f2d9f889fb412670ae8478d8abd4c5aa",
+				"0d8d49e7737d8f9fc5cef7c4b8817633103faf2613016cb86a1f3fc29968fe2413e232d9208d2d74a89bf7a48ac36f83",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"03578447618463deb106b60e609c6f7cc446dc6035f84a72801ba17c94cd800583b493b948eff0033f09086fdd7f6175",
+				"1953ce6d4267939c7360756d9cca8eb34aac4633ef35369a7dc249445069888e7d1b3f9d2e75fbd468fbcbba7110ea02",
+				"0184d26779ae9d4670aca9b267dbd4d3b30443ad05b8546d36a195686e1ccc3a59194aea05ed5bce7c3144a29ec047c4",
+				"0882ab045b8fe4d7d557ebb59a63a35ac9f3d312581b509af0f8eaa2960cbc5e1e36bb969b6e22980b5cbdd0787fcf4e",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"195fad48982e186ce3c5c82133aefc9b26d55979b6f530992a8849d4263ec5d57f7a181553c8799bcc83da44847bdc8d",
+				"17b461fc3b96a30c2408958cbfa5f5927b6063a8ad199d5ebf2d7cdeffa9c20c85487204804fab53f950b2f87db365aa",
+				"005cdf3d984e3391e7e969276fb4bc02323c5924a4449af167030d855acc2600cf3d4fab025432c6d868c79571a95bef",
+				"174a3473a3af2d0302b9065e895ca4adba4ece6ce0b41148ba597001abb152f852dd9a96fb45c9de0a43d944746f833e",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"123b6bd9feeba26dd4ad00f8bfda2718c9700dc093ea5287d7711844644eb981848316d3f3f57d5d3a652c6cdc816aca",
+				"0a162306f3b0f2bb326f0c4fb0e1fea020019c3af796dcd1d7264f50ddae94cacf3cade74603834d44b9ab3d5d0a6c98",
+				"05483f3b96d9252dd4fc0868344dfaf3c9d145e3387db23fa8e449304fab6a7b6ec9c15f05c0a1ea66ff0efcc03e001a",
+				"15c1d4f1a685bb63ee67ca1fd96155e3d091e852a684b78d085fd34f6091e5249ddddbdcf2e7ec82ce6c04c63647eeb7",
+			),
+		},
+	} {
+		g := NewG2()
+		p0, err := g.HashToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("encode to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatal("encode to point fails x", i)
+		}
+	}
+	domain = []byte("QUUX-V01-CS02-with-expander")
+	for i, v := range []struct {
+		msg      []byte
+		expected []byte
+	}{
+		{
+			msg: []byte(""),
+			expected: fromHex(-1,
+				"11476980d59511379345dddd759c97c2a799bf21ee991e977439d73ff24dfedb468e5b8a1fd99e1e79eb80b5b17e32f900d83d21bd763b2b783e2e420de8813998556464624a9f328d9f5993efcacfd35b5ebc2bbdcd50a9f82393ae769a165c1250d29a557c960255447cd524b24f48f158048383f8e956562a54564c468d3c40e77b434f7382a6c67078c59800ac7b0048f91e5ec8bbaa5cdb8993243a8bb255fcf2d6aaabf785e9129bff0ebfff8ac9e2cdb5919ccdf8e4a05b940c281b42",
+			),
+		},
+		{
+			msg: []byte("abc"),
+			expected: fromHex(-1,
+				"158715ddabfc01a58b21bf7590b36aeaf0af7b7f336d4b9a18ec2952801be51ff81e092f8d465ebe8433576acaf1970e0c5b94d02b027927c94ca7520ebc5e0b8ada1b778df99c2390f0a485b2939aa8c4aefd4100a81b4071a218689b890d230fc5edda32abcf705239d2ba7a67c08ec90de872765cab945b02449e44a3d8e933fb2982cdb286cd3e38e688ee736ce10f1b39c3fec1de32245b6bdba9848f9d3a93adbf1c69280f4e20c961885251227e798445947eff1038f8dfe93a713bf0",
+			),
+		},
+		{
+			msg: []byte("abcdef0123456789"),
+			expected: fromHex(-1,
+				"0b78c6db53a98aa4c600524cc8c24cabaf3f695645fd3f3c58e5a7c105737cf8dbccf4ef14517210bb200bda2f82374b029dfd5cfa8735a372aa5f5edd1449be549c76f611c859b7fbbbbb85c821be209685caae39c4f80c8fd10b6140309795146c6ffc2ee10da5379c237ef43e4c24f71e32ffc3d3949a0f07c6b177406ee90fef3059cd3a860bc74cc945bf3335360a7e5f4221f2e0f29589feab7d7ac6f7a17a50324881071a14a49556f2a8de47d164b317d480fb47ec0f082d44b7b641",
+			),
+		},
+		{
+			msg: []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"),
+			expected: fromHex(-1,
+				"164da56a56881558025526ddba71c1a25a5650ae44ff47ce78d784c03c1c523b85acd73fecca9beb7142df1852ecaccf0222289d1ebdac5c2cf336f6f5bb9880ee58efbeac543dcb5317222224052d3d1ada9aa26c74ccda6c90a7a0484080ed16b9cf44913ea3a924f762fdfa8061ca88cff73aa6f40e01eeb7eed75b7d45cc3163644ee8d00c9a00a750f56f6d492e0d39e2c0234380e8bf1503d754c3998e54460a4b9dc135f7f9b08b6a6d86dcc2bc1de0ec601b09970646ddf1c9f9c71c",
+			),
+		},
+	} {
+		g := NewG2()
+		p0, err := g.HashToCurve(sha256.New, v.msg, domain)
+		if err != nil {
+			t.Fatal("hash to point fails", i, err)
+		}
+		if !bytes.Equal(g.ToBytes(p0), v.expected) {
+			t.Fatalf("hash to point fails %d: expected: %v, got: %v", i, hex.EncodeToString(v.expected), hex.EncodeToString(g.ToBytes(p0)))
+		}
+	}
+}
+
+func TestCheckG2InfinityPoint(t *testing.T) {
+	g2 := NewG2()
+	// Zero is considered infinity point
+	inf := g2.Zero()
+	if !g2.InCorrectSubgroup(inf) {
+		t.Fatal("infinity point not considered in subgroup")
+	}
+	if !g2.IsOnCurve(inf) {
+		t.Fatal("infinity point not considered on curve")
+	}
+
+	zeroBytes := make([]byte, 192)
+	infPoint, err := g2.FromBytes(zeroBytes)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !g2.IsZero(infPoint) {
+		t.Fatal("created point not inf point")
+	}
+}
+
+func BenchmarkG2Add(t *testing.B) {
+	g2 := NewG2()
+	a, b, c := g2.rand(), g2.rand(), PointG2{}
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		g2.Add(&c, a, b)
+	}
+}
+
+func BenchmarkG2Mul(t *testing.B) {
+	g2 := NewG2()
+	a, e, c := g2.rand(), q, PointG2{}
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		g2.MulScalar(&c, a, e)
+	}
+}
+
+func BenchmarkG2ClearCofactor(t *testing.B) {
+	g2 := NewG2()
+	a := g2.rand()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		g2.ClearCofactor(a)
+	}
+}
+
+func BenchmarkG2SWUMap(t *testing.B) {
+	a := fromHex(96, "0x1234")
+	g2 := NewG2()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		_, err := g2.MapToCurve(a)
+		if err != nil {
+			t.Fatal(err)
+		}
+	}
+}
diff --git a/pkg/core/curves/native/bls12-381/gt.go b/pkg/core/curves/native/bls12-381/gt.go
new file mode 100644
index 00000000..1d23c6c0
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/gt.go
@@ -0,0 +1,112 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"errors"
+	"math/big"
+)
+
+// E is type for target group element
+type E = fe12
+
+// GT is type for target multiplicative group GT.
+type GT struct {
+	fp12 *fp12
+}
+
+// Set copies given value into the destination
+func (e *E) Set(e2 *E) *E {
+	return e.set(e2)
+}
+
+// One sets a new target group element to one
+func (e *E) One() *E {
+	e = new(fe12).one()
+	return e
+}
+
+// IsOne returns true if given element equals to one
+func (e *E) IsOne() bool {
+	return e.isOne()
+}
+
+// Equal returns true if given two element is equal, otherwise returns false
+func (g *E) Equal(g2 *E) bool {
+	return g.equal(g2)
+}
+
+// NewGT constructs new target group instance.
+func NewGT() *GT {
+	fp12 := newFp12(nil)
+	return &GT{fp12}
+}
+
+// Q returns group order in big.Int.
+func (g *GT) Q() *big.Int {
+	return new(big.Int).Set(q)
+}
+
+// FromBytes expects 576 byte input and returns target group element
+// FromBytes returns error if given element is not on correct subgroup.
+func (g *GT) FromBytes(in []byte) (*E, error) {
+	e, err := g.fp12.fromBytes(in)
+	if err != nil {
+		return nil, err
+	}
+	if !g.IsValid(e) {
+		return e, errors.New("invalid element")
+	}
+	return e, nil
+}
+
+// ToBytes serializes target group element.
+func (g *GT) ToBytes(e *E) []byte {
+	return g.fp12.toBytes(e)
+}
+
+// IsValid checks whether given target group element is in correct subgroup.
+func (g *GT) IsValid(e *E) bool {
+	r := g.New()
+	g.fp12.exp(r, e, q)
+	return r.isOne()
+}
+
+// New initializes a new target group element which is equal to one
+func (g *GT) New() *E {
+	return new(E).One()
+}
+
+// Add adds two field element `a` and `b` and assigns the result to the element in first argument.
+func (g *GT) Add(c, a, b *E) {
+	g.fp12.add(c, a, b)
+}
+
+// Sub subtracts two field element `a` and `b`, and assigns the result to the element in first argument.
+func (g *GT) Sub(c, a, b *E) {
+	g.fp12.sub(c, a, b)
+}
+
+// Mul multiplies two field element `a` and `b` and assigns the result to the element in first argument.
+func (g *GT) Mul(c, a, b *E) {
+	g.fp12.mul(c, a, b)
+}
+
+// Square squares an element `a` and assigns the result to the element in first argument.
+func (g *GT) Square(c, a *E) {
+	g.fp12.cyclotomicSquare(c, a)
+}
+
+// Exp exponents an element `a` by a scalar `s` and assigns the result to the element in first argument.
+func (g *GT) Exp(c, a *E, s *big.Int) {
+	g.fp12.cyclotomicExp(c, a, s)
+}
+
+// Inverse inverses an element `a` and assigns the result to the element in first argument.
+func (g *GT) Inverse(c, a *E) {
+	g.fp12.inverse(c, a)
+}
diff --git a/pkg/core/curves/native/bls12-381/hash_to_field.go b/pkg/core/curves/native/bls12-381/hash_to_field.go
new file mode 100644
index 00000000..6f859d4d
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/hash_to_field.go
@@ -0,0 +1,82 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"hash"
+)
+
+func hashToFpXMD(f func() hash.Hash, msg []byte, domain []byte, count int) ([]*fe, error) {
+	lenPerElm := 64
+	lenInBytes := count * lenPerElm
+	randBytes := expandMsgXMD(f, msg, domain, lenInBytes)
+	els := make([]*fe, count)
+	var err error
+	for i := 0; i < count; i++ {
+		els[i], err = from64Bytes(randBytes[i*64 : (i+1)*64])
+		if err != nil {
+			return nil, err
+		}
+	}
+	return els, nil
+}
+
+func expandMsgXMD(f func() hash.Hash, msg []byte, domain []byte, outLen int) []byte {
+	h := f()
+	domainLen := uint8(len(domain))
+	if len(domain) > 255 {
+		// See https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/?include_text=1
+		// Section 5.3.3
+		_, _ = h.Write([]byte("H2C-OVERSIZE-DST-"))
+		_, _ = h.Write(domain)
+		domain = h.Sum(nil)
+		h.Reset()
+		domainLen = uint8(len(domain))
+	}
+	// DST_prime = DST || I2OSP(len(DST), 1)
+	// b_0 = H(Z_pad || msg || l_i_b_str || I2OSP(0, 1) || DST_prime)
+	_, _ = h.Write(make([]byte, h.BlockSize()))
+	_, _ = h.Write(msg)
+	_, _ = h.Write([]byte{uint8(outLen >> 8), uint8(outLen)})
+	_, _ = h.Write([]byte{0})
+	_, _ = h.Write(domain)
+	_, _ = h.Write([]byte{domainLen})
+	b0 := h.Sum(nil)
+
+	// b_1 = H(b_0 || I2OSP(1, 1) || DST_prime)
+	h.Reset()
+	_, _ = h.Write(b0)
+	_, _ = h.Write([]byte{1})
+	_, _ = h.Write(domain)
+	_, _ = h.Write([]byte{domainLen})
+	b1 := h.Sum(nil)
+
+	// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
+	ell := (outLen + h.Size() - 1) / h.Size()
+	bi := b1
+	out := make([]byte, outLen)
+	for i := 1; i < ell; i++ {
+		h.Reset()
+		// b_i = H(strxor(b_0, b_(i - 1)) || I2OSP(i, 1) || DST_prime)
+		tmp := make([]byte, h.Size())
+		for j := 0; j < h.Size(); j++ {
+			tmp[j] = b0[j] ^ bi[j]
+		}
+		_, _ = h.Write(tmp)
+		_, _ = h.Write([]byte{1 + uint8(i)})
+		_, _ = h.Write(domain)
+		_, _ = h.Write([]byte{domainLen})
+
+		// b_1 || ... || b_(ell - 1)
+		copy(out[(i-1)*h.Size():i*h.Size()], bi[:])
+		bi = h.Sum(nil)
+	}
+	// b_ell
+	copy(out[(ell-1)*h.Size():], bi[:])
+	return out[:outLen]
+
+}
diff --git a/pkg/core/curves/native/bls12-381/isogeny.go b/pkg/core/curves/native/bls12-381/isogeny.go
new file mode 100644
index 00000000..d3cebcd3
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/isogeny.go
@@ -0,0 +1,217 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+// isogenyMapG1 applies 11-isogeny map for BLS12-381 G1 defined at draft-irtf-cfrg-hash-to-curve-06.
+func isogenyMapG1(x, y *fe) {
+	// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08#appendix-C.2
+	params := isogenyConstansG1
+	degree := 15
+	xNum, xDen, yNum, yDen := new(fe), new(fe), new(fe), new(fe)
+	xNum.set(params[0][degree])
+	xDen.set(params[1][degree])
+	yNum.set(params[2][degree])
+	yDen.set(params[3][degree])
+	for i := degree - 1; i >= 0; i-- {
+		mul(xNum, xNum, x)
+		mul(xDen, xDen, x)
+		mul(yNum, yNum, x)
+		mul(yDen, yDen, x)
+		add(xNum, xNum, params[0][i])
+		add(xDen, xDen, params[1][i])
+		add(yNum, yNum, params[2][i])
+		add(yDen, yDen, params[3][i])
+	}
+	inverse(xDen, xDen)
+	inverse(yDen, yDen)
+	mul(xNum, xNum, xDen)
+	mul(yNum, yNum, yDen)
+	mul(yNum, yNum, y)
+	x.set(xNum)
+	y.set(yNum)
+}
+
+// isogenyMapG2 applies 11-isogeny map for BLS12-381 G1 defined at draft-irtf-cfrg-hash-to-curve-06.
+func isogenyMapG2(e *fp2, x, y *fe2) {
+	if e == nil {
+		e = newFp2()
+	}
+	// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-08#appendix-C.2
+	params := isogenyConstantsG2
+	degree := 3
+	xNum := new(fe2).set(params[0][degree])
+	xDen := new(fe2).set(params[1][degree])
+	yNum := new(fe2).set(params[2][degree])
+	yDen := new(fe2).set(params[3][degree])
+	for i := degree - 1; i >= 0; i-- {
+		e.mul(xNum, xNum, x)
+		e.mul(xDen, xDen, x)
+		e.mul(yNum, yNum, x)
+		e.mul(yDen, yDen, x)
+		e.add(xNum, xNum, params[0][i])
+		e.add(xDen, xDen, params[1][i])
+		e.add(yNum, yNum, params[2][i])
+		e.add(yDen, yDen, params[3][i])
+	}
+	e.inverse(xDen, xDen)
+	e.inverse(yDen, yDen)
+	e.mul(xNum, xNum, xDen)
+	e.mul(yNum, yNum, yDen)
+	e.mul(yNum, yNum, y)
+	x.set(xNum)
+	y.set(yNum)
+}
+
+var isogenyConstansG1 = [4][16]*fe{
+	[16]*fe{
+		&fe{0x4d18b6f3af00131c, 0x19fa219793fee28c, 0x3f2885f1467f19ae, 0x23dcea34f2ffb304, 0xd15b58d2ffc00054, 0x0913be200a20bef4},
+		&fe{0x898985385cdbbd8b, 0x3c79e43cc7d966aa, 0x1597e193f4cd233a, 0x8637ef1e4d6623ad, 0x11b22deed20d827b, 0x07097bc5998784ad},
+		&fe{0xa542583a480b664b, 0xfc7169c026e568c6, 0x5ba2ef314ed8b5a6, 0x5b5491c05102f0e7, 0xdf6e99707d2a0079, 0x0784151ed7605524},
+		&fe{0x494e212870f72741, 0xab9be52fbda43021, 0x26f5577994e34c3d, 0x049dfee82aefbd60, 0x65dadd7828505289, 0x0e93d431ea011aeb},
+		&fe{0x90ee774bd6a74d45, 0x7ada1c8a41bfb185, 0x0f1a8953b325f464, 0x104c24211be4805c, 0x169139d319ea7a8f, 0x09f20ead8e532bf6},
+		&fe{0x6ddd93e2f43626b7, 0xa5482c9aa1ccd7bd, 0x143245631883f4bd, 0x2e0a94ccf77ec0db, 0xb0282d480e56489f, 0x18f4bfcbb4368929},
+		&fe{0x23c5f0c953402dfd, 0x7a43ff6958ce4fe9, 0x2c390d3d2da5df63, 0xd0df5c98e1f9d70f, 0xffd89869a572b297, 0x1277ffc72f25e8fe},
+		&fe{0x79f4f0490f06a8a6, 0x85f894a88030fd81, 0x12da3054b18b6410, 0xe2a57f6505880d65, 0xbba074f260e400f1, 0x08b76279f621d028},
+		&fe{0xe67245ba78d5b00b, 0x8456ba9a1f186475, 0x7888bff6e6b33bb4, 0xe21585b9a30f86cb, 0x05a69cdcef55feee, 0x09e699dd9adfa5ac},
+		&fe{0x0de5c357bff57107, 0x0a0db4ae6b1a10b2, 0xe256bb67b3b3cd8d, 0x8ad456574e9db24f, 0x0443915f50fd4179, 0x098c4bf7de8b6375},
+		&fe{0xe6b0617e7dd929c7, 0xfe6e37d442537375, 0x1dafdeda137a489e, 0xe4efd1ad3f767ceb, 0x4a51d8667f0fe1cf, 0x054fdf4bbf1d821c},
+		&fe{0x72db2a50658d767b, 0x8abf91faa257b3d5, 0xe969d6833764ab47, 0x464170142a1009eb, 0xb14f01aadb30be2f, 0x18ae6a856f40715d},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+	},
+	[16]*fe{
+		&fe{0xb962a077fdb0f945, 0xa6a9740fefda13a0, 0xc14d568c3ed6c544, 0xb43fc37b908b133e, 0x9c0b3ac929599016, 0x0165aa6c93ad115f},
+		&fe{0x23279a3ba506c1d9, 0x92cfca0a9465176a, 0x3b294ab13755f0ff, 0x116dda1c5070ae93, 0xed4530924cec2045, 0x083383d6ed81f1ce},
+		&fe{0x9885c2a6449fecfc, 0x4a2b54ccd37733f0, 0x17da9ffd8738c142, 0xa0fba72732b3fafd, 0xff364f36e54b6812, 0x0f29c13c660523e2},
+		&fe{0xe349cc118278f041, 0xd487228f2f3204fb, 0xc9d325849ade5150, 0x43a92bd69c15c2df, 0x1c2c7844bc417be4, 0x12025184f407440c},
+		&fe{0x587f65ae6acb057b, 0x1444ef325140201f, 0xfbf995e71270da49, 0xccda066072436a42, 0x7408904f0f186bb2, 0x13b93c63edf6c015},
+		&fe{0xfb918622cd141920, 0x4a4c64423ecaddb4, 0x0beb232927f7fb26, 0x30f94df6f83a3dc2, 0xaeedd424d780f388, 0x06cc402dd594bbeb},
+		&fe{0xd41f761151b23f8f, 0x32a92465435719b3, 0x64f436e888c62cb9, 0xdf70a9a1f757c6e4, 0x6933a38d5b594c81, 0x0c6f7f7237b46606},
+		&fe{0x693c08747876c8f7, 0x22c9850bf9cf80f0, 0x8e9071dab950c124, 0x89bc62d61c7baf23, 0xbc6be2d8dad57c23, 0x17916987aa14a122},
+		&fe{0x1be3ff439c1316fd, 0x9965243a7571dfa7, 0xc7f7f62962f5cd81, 0x32c6aa9af394361c, 0xbbc2ee18e1c227f4, 0x0c102cbac531bb34},
+		&fe{0x997614c97bacbf07, 0x61f86372b99192c0, 0x5b8c95fc14353fc3, 0xca2b066c2a87492f, 0x16178f5bbf698711, 0x12a6dcd7f0f4e0e8},
+		&fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+		&fe{0, 0, 0, 0, 0, 0},
+	},
+	[16]*fe{
+		&fe{0x2b567ff3e2837267, 0x1d4d9e57b958a767, 0xce028fea04bd7373, 0xcc31a30a0b6cd3df, 0x7d7b18a682692693, 0x0d300744d42a0310},
+		&fe{0x99c2555fa542493f, 0xfe7f53cc4874f878, 0x5df0608b8f97608a, 0x14e03832052b49c8, 0x706326a6957dd5a4, 0x0a8dadd9c2414555},
+		&fe{0x13d942922a5cf63a, 0x357e33e36e261e7d, 0xcf05a27c8456088d, 0x0000bd1de7ba50f0, 0x83d0c7532f8c1fde, 0x13f70bf38bbf2905},
+		&fe{0x5c57fd95bfafbdbb, 0x28a359a65e541707, 0x3983ceb4f6360b6d, 0xafe19ff6f97e6d53, 0xb3468f4550192bf7, 0x0bb6cde49d8ba257},
+		&fe{0x590b62c7ff8a513f, 0x314b4ce372cacefd, 0x6bef32ce94b8a800, 0x6ddf84a095713d5f, 0x64eace4cb0982191, 0x0386213c651b888d},
+		&fe{0xa5310a31111bbcdd, 0xa14ac0f5da148982, 0xf9ad9cc95423d2e9, 0xaa6ec095283ee4a7, 0xcf5b1f022e1c9107, 0x01fddf5aed881793},
+		&fe{0x65a572b0d7a7d950, 0xe25c2d8183473a19, 0xc2fcebe7cb877dbd, 0x05b2d36c769a89b0, 0xba12961be86e9efb, 0x07eb1b29c1dfde1f},
+		&fe{0x93e09572f7c4cd24, 0x364e929076795091, 0x8569467e68af51b5, 0xa47da89439f5340f, 0xf4fa918082e44d64, 0x0ad52ba3e6695a79},
+		&fe{0x911429844e0d5f54, 0xd03f51a3516bb233, 0x3d587e5640536e66, 0xfa86d2a3a9a73482, 0xa90ed5adf1ed5537, 0x149c9c326a5e7393},
+		&fe{0x462bbeb03c12921a, 0xdc9af5fa0a274a17, 0x9a558ebde836ebed, 0x649ef8f11a4fae46, 0x8100e1652b3cdc62, 0x1862bd62c291dacb},
+		&fe{0x05c9b8ca89f12c26, 0x0194160fa9b9ac4f, 0x6a643d5a6879fa2c, 0x14665bdd8846e19d, 0xbb1d0d53af3ff6bf, 0x12c7e1c3b28962e5},
+		&fe{0xb55ebf900b8a3e17, 0xfedc77ec1a9201c4, 0x1f07db10ea1a4df4, 0x0dfbd15dc41a594d, 0x389547f2334a5391, 0x02419f98165871a4},
+		&fe{0xb416af000745fc20, 0x8e563e9d1ea6d0f5, 0x7c763e17763a0652, 0x01458ef0159ebbef, 0x8346fe421f96bb13, 0x0d2d7b829ce324d2},
+		&fe{0x93096bb538d64615, 0x6f2a2619951d823a, 0x8f66b3ea59514fa4, 0xf563e63704f7092f, 0x724b136c4cf2d9fa, 0x046959cfcfd0bf49},
+		&fe{0xea748d4b6e405346, 0x91e9079c2c02d58f, 0x41064965946d9b59, 0xa06731f1d2bbe1ee, 0x07f897e267a33f1b, 0x1017290919210e5f},
+		&fe{0x872aa6c17d985097, 0xeecc53161264562a, 0x07afe37afff55002, 0x54759078e5be6838, 0xc4b92d15db8acca8, 0x106d87d1b51d13b9},
+	},
+	[16]*fe{
+		&fe{0xeb6c359d47e52b1c, 0x18ef5f8a10634d60, 0xddfa71a0889d5b7e, 0x723e71dcc5fc1323, 0x52f45700b70d5c69, 0x0a8b981ee47691f1},
+		&fe{0x616a3c4f5535b9fb, 0x6f5f037395dbd911, 0xf25f4cc5e35c65da, 0x3e50dffea3c62658, 0x6a33dca523560776, 0x0fadeff77b6bfe3e},
+		&fe{0x2be9b66df470059c, 0x24a2c159a3d36742, 0x115dbe7ad10c2a37, 0xb6634a652ee5884d, 0x04fe8bb2b8d81af4, 0x01c2a7a256fe9c41},
+		&fe{0xf27bf8ef3b75a386, 0x898b367476c9073f, 0x24482e6b8c2f4e5f, 0xc8e0bbd6fe110806, 0x59b0c17f7631448a, 0x11037cd58b3dbfbd},
+		&fe{0x31c7912ea267eec6, 0x1dbf6f1c5fcdb700, 0xd30d4fe3ba86fdb1, 0x3cae528fbee9a2a4, 0xb1cce69b6aa9ad9a, 0x044393bb632d94fb},
+		&fe{0xc66ef6efeeb5c7e8, 0x9824c289dd72bb55, 0x71b1a4d2f119981d, 0x104fc1aafb0919cc, 0x0e49df01d942a628, 0x096c3a09773272d4},
+		&fe{0x9abc11eb5fadeff4, 0x32dca50a885728f0, 0xfb1fa3721569734c, 0xc4b76271ea6506b3, 0xd466a75599ce728e, 0x0c81d4645f4cb6ed},
+		&fe{0x4199f10e5b8be45b, 0xda64e495b1e87930, 0xcb353efe9b33e4ff, 0x9e9efb24aa6424c6, 0xf08d33680a237465, 0x0d3378023e4c7406},
+		&fe{0x7eb4ae92ec74d3a5, 0xc341b4aa9fac3497, 0x5be603899e907687, 0x03bfd9cca75cbdeb, 0x564c2935a96bfa93, 0x0ef3c33371e2fdb5},
+		&fe{0x7ee91fd449f6ac2e, 0xe5d5bd5cb9357a30, 0x773a8ca5196b1380, 0xd0fda172174ed023, 0x6cb95e0fa776aead, 0x0d22d5a40cec7cff},
+		&fe{0xf727e09285fd8519, 0xdc9d55a83017897b, 0x7549d8bd057894ae, 0x178419613d90d8f8, 0xfce95ebdeb5b490a, 0x0467ffaef23fc49e},
+		&fe{0xc1769e6a7c385f1b, 0x79bc930deac01c03, 0x5461c75a23ede3b5, 0x6e20829e5c230c45, 0x828e0f1e772a53cd, 0x116aefa749127bff},
+		&fe{0x101c10bf2744c10a, 0xbbf18d053a6a3154, 0xa0ecf39ef026f602, 0xfc009d4996dc5153, 0xb9000209d5bd08d3, 0x189e5fe4470cd73c},
+		&fe{0x7ebd546ca1575ed2, 0xe47d5a981d081b55, 0x57b2b625b6d4ca21, 0xb0a1ba04228520cc, 0x98738983c2107ff3, 0x13dddbc4799d81d6},
+		&fe{0x09319f2e39834935, 0x039e952cbdb05c21, 0x55ba77a9a2f76493, 0xfd04e3dfc6086467, 0xfb95832e7d78742e, 0x0ef9c24eccaf5e0e},
+		&fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+	},
+}
+
+var isogenyConstantsG2 = [4][4]*fe2{
+	[4]*fe2{
+		&fe2{
+			fe{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
+			fe{0x47f671c71ce05e62, 0x06dd57071206393e, 0x7c80cd2af3fd71a2, 0x048103ea9e6cd062, 0xc54516acc8d037f6, 0x13808f550920ea41},
+		},
+		&fe2{
+			fe{0, 0, 0, 0, 0, 0},
+			fe{0x5fe55555554c71d0, 0x873fffdd236aaaa3, 0x6a6b4619b26ef918, 0x21c2888408874945, 0x2836cda7028cabc5, 0x0ac73310a7fd5abd},
+		},
+		&fe2{
+			fe{0x0a0c5555555971c3, 0xdb0c00101f9eaaae, 0xb1fb2f941d797997, 0xd3960742ef416e1c, 0xb70040e2c20556f4, 0x149d7861e581393b},
+			fe{0xaff2aaaaaaa638e8, 0x439fffee91b55551, 0xb535a30cd9377c8c, 0x90e144420443a4a2, 0x941b66d3814655e2, 0x0563998853fead5e},
+		},
+		&fe2{
+			fe{0x40aac71c71c725ed, 0x190955557a84e38e, 0xd817050a8f41abc3, 0xd86485d4c87f6fb1, 0x696eb479f885d059, 0x198e1a74328002d2},
+			fe{0, 0, 0, 0, 0, 0},
+		},
+	},
+	[4]*fe2{
+		&fe2{
+			fe{0, 0, 0, 0, 0, 0},
+			fe{0x1f3affffff13ab97, 0xf25bfc611da3ff3e, 0xca3757cb3819b208, 0x3e6427366f8cec18, 0x03977bc86095b089, 0x04f69db13f39a952},
+		},
+		&fe2{
+			fe{0x447600000027552e, 0xdcb8009a43480020, 0x6f7ee9ce4a6e8b59, 0xb10330b7c0a95bc6, 0x6140b1fcfb1e54b7, 0x0381be097f0bb4e1},
+			fe{0x7588ffffffd8557d, 0x41f3ff646e0bffdf, 0xf7b1e8d2ac426aca, 0xb3741acd32dbb6f8, 0xe9daf5b9482d581f, 0x167f53e0ba7431b8},
+		},
+		&fe2{
+			fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+			fe{0, 0, 0, 0, 0, 0},
+		},
+		&fe2{
+			fe{0, 0, 0, 0, 0, 0},
+			fe{0, 0, 0, 0, 0, 0},
+		},
+	},
+	[4]*fe2{
+		&fe2{
+			fe{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
+			fe{0x96d8f684bdfc77be, 0xb530e4f43b66d0e2, 0x184a88ff379652fd, 0x57cb23ecfae804e1, 0x0fd2e39eada3eba9, 0x08c8055e31c5d5c3},
+		},
+		&fe2{
+			fe{0, 0, 0, 0, 0, 0},
+			fe{0xbf0a71c71c91b406, 0x4d6d55d28b7638fd, 0x9d82f98e5f205aee, 0xa27aa27b1d1a18d5, 0x02c3b2b2d2938e86, 0x0c7d13420b09807f},
+		},
+		&fe2{
+			fe{0xd7f9555555531c74, 0x21cffff748daaaa8, 0x5a9ad1866c9bbe46, 0x4870a2210221d251, 0x4a0db369c0a32af1, 0x02b1ccc429ff56af},
+			fe{0xe205aaaaaaac8e37, 0xfcdc000768795556, 0x0c96011a8a1537dd, 0x1c06a963f163406e, 0x010df44c82a881e6, 0x174f45260f808feb},
+		},
+		&fe2{
+			fe{0xa470bda12f67f35c, 0xc0fe38e23327b425, 0xc9d3d0f2c6f0678d, 0x1c55c9935b5a982e, 0x27f6c0e2f0746764, 0x117c5e6e28aa9054},
+			fe{0, 0, 0, 0, 0, 0},
+		},
+	},
+	[4]*fe2{
+		&fe2{
+			fe{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
+			fe{0x0162fffffa765adf, 0x8f7bea480083fb75, 0x561b3c2259e93611, 0x11e19fc1a9c875d5, 0xca713efc00367660, 0x03c6a03d41da1151},
+		},
+		&fe2{
+			fe{0, 0, 0, 0, 0, 0},
+			fe{0x5db0fffffd3b02c5, 0xd713f52358ebfdba, 0x5ea60761a84d161a, 0xbb2c75a34ea6c44a, 0x0ac6735921c1119b, 0x0ee3d913bdacfbf6},
+		},
+		&fe2{
+			fe{0x66b10000003affc5, 0xcb1400e764ec0030, 0xa73e5eb56fa5d106, 0x8984c913a0fe09a9, 0x11e10afb78ad7f13, 0x05429d0e3e918f52},
+			fe{0x534dffffffc4aae6, 0x5397ff174c67ffcf, 0xbff273eb870b251d, 0xdaf2827152870915, 0x393a9cbaca9e2dc3, 0x14be74dbfaee5748},
+		},
+		&fe2{
+			fe{0x760900000002fffd, 0xebf4000bc40c0002, 0x5f48985753c758ba, 0x77ce585370525745, 0x5c071a97a256ec6d, 0x15f65ec3fa80e493},
+			fe{0, 0, 0, 0, 0, 0},
+		},
+	},
+}
diff --git a/pkg/core/curves/native/bls12-381/pairing.go b/pkg/core/curves/native/bls12-381/pairing.go
new file mode 100644
index 00000000..7eaeb803
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/pairing.go
@@ -0,0 +1,303 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import "errors"
+
+type pair struct {
+	g1 *PointG1
+	g2 *PointG2
+}
+
+func newPair(g1 *PointG1, g2 *PointG2) pair {
+	return pair{g1, g2}
+}
+
+// Engine is BLS12-381 elliptic curve pairing engine
+type Engine struct {
+	G1   *G1
+	G2   *G2
+	fp12 *fp12
+	fp2  *fp2
+	pairingEngineTemp
+	pairs []pair
+}
+
+// NewEngine creates new pairing engine insteace.
+func NewEngine() *Engine {
+	fp2 := newFp2()
+	fp6 := newFp6(fp2)
+	fp12 := newFp12(fp6)
+	g1 := NewG1()
+	g2 := newG2(fp2)
+	return &Engine{
+		fp2:               fp2,
+		fp12:              fp12,
+		G1:                g1,
+		G2:                g2,
+		pairingEngineTemp: newEngineTemp(),
+	}
+}
+
+type pairingEngineTemp struct {
+	t2  [10]*fe2
+	t12 [9]fe12
+}
+
+func newEngineTemp() pairingEngineTemp {
+	t2 := [10]*fe2{}
+	for i := 0; i < 10; i++ {
+		t2[i] = &fe2{}
+	}
+	t12 := [9]fe12{}
+	return pairingEngineTemp{t2, t12}
+}
+
+// AddPair adds a g1, g2 point pair to pairing engine
+// returns nil if no more pairs can be added
+func (e *Engine) AddPair(g1 *PointG1, g2 *PointG2) *Engine {
+	if len(e.pairs) > maxInputLength {
+		return nil
+	}
+	p := newPair(g1, g2)
+	if !e.isZero(p) {
+		e.affine(p)
+		e.pairs = append(e.pairs, p)
+	}
+	return e
+}
+
+// AddPairInv adds a G1, G2 point pair to pairing engine. G1 point is negated.
+// returns nil if no more pairs can be added
+func (e *Engine) AddPairInv(g1 *PointG1, g2 *PointG2) *Engine {
+	if len(e.pairs) > maxInputLength {
+		return nil
+	}
+	e.G1.Neg(g1, g1)
+	e.AddPair(g1, g2)
+	return e
+}
+
+// Reset deletes added pairs.
+func (e *Engine) Reset() *Engine {
+	e.pairs = []pair{}
+	return e
+}
+
+func (e *Engine) isZero(p pair) bool {
+	return e.G1.IsZero(p.g1) || e.G2.IsZero(p.g2)
+}
+
+func (e *Engine) affine(p pair) {
+	e.G1.Affine(p.g1)
+	e.G2.Affine(p.g2)
+}
+
+func (e *Engine) doublingStep(coeff *[3]fe2, r *PointG2) {
+	// Adaptation of Formula 3 in https://eprint.iacr.org/2010/526.pdf
+	fp2 := e.fp2
+	t := e.t2
+	fp2.mul(t[0], &r[0], &r[1])
+	fp2.mulByFq(t[0], t[0], twoInv)
+	fp2.square(t[1], &r[1])
+	fp2.square(t[2], &r[2])
+	fp2.double(t[7], t[2])
+	fp2.add(t[7], t[7], t[2])
+	fp2.mulByB(t[3], t[7])
+	fp2.double(t[4], t[3])
+	fp2.add(t[4], t[4], t[3])
+	fp2.add(t[5], t[1], t[4])
+	fp2.mulByFq(t[5], t[5], twoInv)
+	fp2.add(t[6], &r[1], &r[2])
+	fp2.square(t[6], t[6])
+	fp2.add(t[7], t[2], t[1])
+	fp2.sub(t[6], t[6], t[7])
+	fp2.sub(&coeff[0], t[3], t[1])
+	fp2.square(t[7], &r[0])
+	fp2.sub(t[4], t[1], t[4])
+	fp2.mul(&r[0], t[4], t[0])
+	fp2.square(t[2], t[3])
+	fp2.double(t[3], t[2])
+	fp2.add(t[3], t[3], t[2])
+	fp2.square(t[5], t[5])
+	fp2.sub(&r[1], t[5], t[3])
+	fp2.mul(&r[2], t[1], t[6])
+	fp2.double(t[0], t[7])
+	fp2.add(&coeff[1], t[0], t[7])
+	fp2.neg(&coeff[2], t[6])
+}
+
+func (e *Engine) additionStep(coeff *[3]fe2, r, q *PointG2) {
+	// Algorithm 12 in https://eprint.iacr.org/2010/526.pdf
+	fp2 := e.fp2
+	t := e.t2
+	fp2.mul(t[0], &q[1], &r[2])
+	fp2.neg(t[0], t[0])
+	fp2.add(t[0], t[0], &r[1])
+	fp2.mul(t[1], &q[0], &r[2])
+	fp2.neg(t[1], t[1])
+	fp2.add(t[1], t[1], &r[0])
+	fp2.square(t[2], t[0])
+	fp2.square(t[3], t[1])
+	fp2.mul(t[4], t[1], t[3])
+	fp2.mul(t[2], &r[2], t[2])
+	fp2.mul(t[3], &r[0], t[3])
+	fp2.double(t[5], t[3])
+	fp2.sub(t[5], t[4], t[5])
+	fp2.add(t[5], t[5], t[2])
+	fp2.mul(&r[0], t[1], t[5])
+	fp2.sub(t[2], t[3], t[5])
+	fp2.mul(t[2], t[2], t[0])
+	fp2.mul(t[3], &r[1], t[4])
+	fp2.sub(&r[1], t[2], t[3])
+	fp2.mul(&r[2], &r[2], t[4])
+	fp2.mul(t[2], t[1], &q[1])
+	fp2.mul(t[3], t[0], &q[0])
+	fp2.sub(&coeff[0], t[3], t[2])
+	fp2.neg(&coeff[1], t[0])
+	coeff[2].set(t[1])
+}
+
+func (e *Engine) preCompute(ellCoeffs *[68][3]fe2, twistPoint *PointG2) error {
+	// Algorithm 5 in  https://eprint.iacr.org/2019/077.pdf
+	if e.G2.IsZero(twistPoint) {
+		return nil
+	}
+	r := new(PointG2).Set(twistPoint)
+	j := 0
+	for i := int(x.BitLen() - 2); i >= 0; i-- {
+		if j > len(ellCoeffs) {
+			return errors.New("precompute: j index greater than len of ellCoeffs")
+		}
+		e.doublingStep(&ellCoeffs[j], r)
+		if x.Bit(i) != 0 {
+			j++
+			if j > len(ellCoeffs) {
+				return errors.New("precompute: j index greater than len of ellCoeffs")
+			}
+			ellCoeffs[j] = fe6{}
+			e.additionStep(&ellCoeffs[j], r, twistPoint)
+		}
+		j++
+	}
+	return nil
+}
+
+func (e *Engine) millerLoop(f *fe12) error {
+	pairs := e.pairs
+	ellCoeffs := make([][68][3]fe2, len(pairs))
+	for i := 0; i < len(pairs); i++ {
+		err := e.preCompute(&ellCoeffs[i], pairs[i].g2)
+		if err != nil {
+			return err
+		}
+	}
+	fp12, fp2 := e.fp12, e.fp2
+	t := e.t2
+	f.one()
+	j := 0
+	for i := 62; /* x.BitLen() - 2 */ i >= 0; i-- {
+		if i != 62 {
+			fp12.square(f, f)
+		}
+		for i := 0; i <= len(pairs)-1; i++ {
+			fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &pairs[i].g1[1])
+			fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &pairs[i].g1[0])
+			fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
+		}
+		if x.Bit(i) != 0 {
+			j++
+			for i := 0; i <= len(pairs)-1; i++ {
+				fp2.mulByFq(t[0], &ellCoeffs[i][j][2], &pairs[i].g1[1])
+				fp2.mulByFq(t[1], &ellCoeffs[i][j][1], &pairs[i].g1[0])
+				fp12.mulBy014Assign(f, &ellCoeffs[i][j][0], t[1], t[0])
+			}
+		}
+		j++
+	}
+	fp12.conjugate(f, f)
+	return nil
+}
+
+func (e *Engine) exp(c, a *fe12) {
+	fp12 := e.fp12
+	fp12.cyclotomicExp(c, a, x)
+	fp12.conjugate(c, c)
+}
+
+func (e *Engine) finalExp(f *fe12) {
+	fp12 := e.fp12
+	t := e.t12
+	// easy part
+	fp12.frobeniusMap(&t[0], f, 6)
+	fp12.inverse(&t[1], f)
+	fp12.mul(&t[2], &t[0], &t[1])
+	t[1].set(&t[2])
+	fp12.frobeniusMapAssign(&t[2], 2)
+	fp12.mulAssign(&t[2], &t[1])
+	fp12.cyclotomicSquare(&t[1], &t[2])
+	fp12.conjugate(&t[1], &t[1])
+	// hard part
+	e.exp(&t[3], &t[2])
+	fp12.cyclotomicSquare(&t[4], &t[3])
+	fp12.mul(&t[5], &t[1], &t[3])
+	e.exp(&t[1], &t[5])
+	e.exp(&t[0], &t[1])
+	e.exp(&t[6], &t[0])
+	fp12.mulAssign(&t[6], &t[4])
+	e.exp(&t[4], &t[6])
+	fp12.conjugate(&t[5], &t[5])
+	fp12.mulAssign(&t[4], &t[5])
+	fp12.mulAssign(&t[4], &t[2])
+	fp12.conjugate(&t[5], &t[2])
+	fp12.mulAssign(&t[1], &t[2])
+	fp12.frobeniusMapAssign(&t[1], 3)
+	fp12.mulAssign(&t[6], &t[5])
+	fp12.frobeniusMapAssign(&t[6], 1)
+	fp12.mulAssign(&t[3], &t[0])
+	fp12.frobeniusMapAssign(&t[3], 2)
+	fp12.mulAssign(&t[3], &t[1])
+	fp12.mulAssign(&t[3], &t[6])
+	fp12.mul(f, &t[3], &t[4])
+}
+
+func (e *Engine) calculate() (*fe12, error) {
+	f := e.fp12.one()
+	if len(e.pairs) == 0 {
+		return f, nil
+	}
+	err := e.millerLoop(f)
+	if err != nil {
+		return nil, err
+	}
+	e.finalExp(f)
+	return f, nil
+}
+
+// Check computes pairing and checks if result is equal to one
+func (e *Engine) Check() (bool, error) {
+	calc, err := e.calculate()
+	if err != nil {
+		return false, err
+	}
+	return calc.isOne(), nil
+}
+
+// Result computes pairing and returns target group element as result.
+func (e *Engine) Result() (*E, error) {
+	r, err := e.calculate()
+	if err != nil {
+		return nil, err
+	}
+	e.Reset()
+	return r, nil
+}
+
+// GT returns target group instance.
+func (e *Engine) GT() *GT {
+	return NewGT()
+}
diff --git a/pkg/core/curves/native/bls12-381/pairing_test.go b/pkg/core/curves/native/bls12-381/pairing_test.go
new file mode 100644
index 00000000..5f4373bb
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/pairing_test.go
@@ -0,0 +1,280 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"math/big"
+	"testing"
+)
+
+func TestPairingExpected(t *testing.T) {
+	bls := NewEngine()
+	G1, G2 := bls.G1, bls.G2
+	GT := bls.GT()
+	expected, err := GT.FromBytes(
+		fromHex(
+			48,
+			"0x0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631",
+			"0x04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef",
+			"0x03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2",
+			"0x11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57",
+			"0x06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a",
+			"0x19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d",
+			"0x018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6",
+			"0x01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5",
+			"0x193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f",
+			"0x1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87",
+			"0x089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f",
+			"0x1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
+		),
+	)
+	if err != nil {
+		t.Fatal(err)
+	}
+	r, err := bls.AddPair(G1.One(), G2.One()).Result()
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !r.Equal(expected) {
+		t.Fatal("bad pairing")
+	}
+	if !GT.IsValid(r) {
+		t.Fatal("element is not in correct subgroup")
+	}
+}
+
+func TestPairingNonDegeneracy(t *testing.T) {
+	bls := NewEngine()
+	G1, G2 := bls.G1, bls.G2
+	g1Zero, g2Zero, g1One, g2One := G1.Zero(), G2.Zero(), G1.One(), G2.One()
+	GT := bls.GT()
+	// e(g1^a, g2^b) != 1
+	bls.Reset()
+	{
+		bls.AddPair(g1One, g2One)
+		e, err := bls.Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if e.IsOne() {
+			t.Fatal("pairing result is not expected to be one")
+		}
+		if !GT.IsValid(e) {
+			t.Fatal("pairing result is not valid")
+		}
+	}
+	// e(g1^a, 0) == 1
+	bls.Reset()
+	{
+		bls.AddPair(g1One, g2Zero)
+		e, err := bls.Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !e.IsOne() {
+			t.Fatal("pairing result is expected to be one")
+		}
+	}
+	// e(0, g2^b) == 1
+	bls.Reset()
+	{
+		bls.AddPair(g1Zero, g2One)
+		e, err := bls.Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !e.IsOne() {
+			t.Fatal("pairing result is expected to be one")
+		}
+	}
+	//
+	bls.Reset()
+	{
+		bls.AddPair(g1Zero, g2One)
+		bls.AddPair(g1One, g2Zero)
+		bls.AddPair(g1Zero, g2Zero)
+		e, err := bls.Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !e.IsOne() {
+			t.Fatal("pairing result is expected to be one")
+		}
+	}
+	//
+	bls.Reset()
+	{
+		expected, err := GT.FromBytes(
+			fromHex(
+				48,
+				"0x0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631",
+				"0x04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef",
+				"0x03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2",
+				"0x11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57",
+				"0x06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a",
+				"0x19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d",
+				"0x018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6",
+				"0x01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5",
+				"0x193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f",
+				"0x1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87",
+				"0x089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f",
+				"0x1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6",
+			),
+		)
+		if err != nil {
+			t.Fatal(err)
+		}
+		bls.AddPair(g1Zero, g2One)
+		bls.AddPair(g1One, g2Zero)
+		bls.AddPair(g1Zero, g2Zero)
+		bls.AddPair(g1One, g2One)
+		e, err := bls.Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !e.Equal(expected) {
+			t.Fatal("bad pairing")
+		}
+	}
+}
+
+func TestPairingBilinearity(t *testing.T) {
+	bls := NewEngine()
+	g1, g2 := bls.G1, bls.G2
+	gt := bls.GT()
+	// e(a*G1, b*G2) = e(G1, G2)^c
+	{
+		a, b := big.NewInt(17), big.NewInt(117)
+		c := new(big.Int).Mul(a, b)
+		G1, G2 := g1.One(), g2.One()
+		e0, err := bls.AddPair(G1, G2).Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		P1, P2 := g1.New(), g2.New()
+		g1.MulScalar(P1, G1, a)
+		g2.MulScalar(P2, G2, b)
+		e1, err := bls.AddPair(P1, P2).Result()
+		if err != nil {
+			t.Fatal(err)
+		}
+		gt.Exp(e0, e0, c)
+		if !e0.Equal(e1) {
+			t.Fatal("bad pairing, 1")
+		}
+	}
+	// e(a * G1, b * G2) = e((a + b) * G1, G2)
+	{
+		// scalars
+		a, b := big.NewInt(17), big.NewInt(117)
+		c := new(big.Int).Mul(a, b)
+		// LHS
+		G1, G2 := g1.One(), g2.One()
+		g1.MulScalar(G1, G1, c)
+		bls.AddPair(G1, G2)
+		// RHS
+		P1, P2 := g1.One(), g2.One()
+		g1.MulScalar(P1, P1, a)
+		g2.MulScalar(P2, P2, b)
+		bls.AddPairInv(P1, P2)
+		// should be one
+		check, err := bls.Check()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !check {
+			t.Fatal("bad pairing, 2")
+		}
+	}
+	// e(a * G1, b * G2) = e((a + b) * G1, G2)
+	{
+		// scalars
+		a, b := big.NewInt(17), big.NewInt(117)
+		c := new(big.Int).Mul(a, b)
+		// LHS
+		G1, G2 := g1.One(), g2.One()
+		g2.MulScalar(G2, G2, c)
+		bls.AddPair(G1, G2)
+		// RHS
+		H1, H2 := g1.One(), g2.One()
+		g1.MulScalar(H1, H1, a)
+		g2.MulScalar(H2, H2, b)
+		bls.AddPairInv(H1, H2)
+		// should be one
+		check, err := bls.Check()
+		if err != nil {
+			t.Fatal(err)
+		}
+		if !check {
+			t.Fatal("bad pairing, 3")
+		}
+	}
+}
+
+func TestPairingMulti(t *testing.T) {
+	// e(G1, G2) ^ t == e(a01 * G1, a02 * G2) * e(a11 * G1, a12 * G2) * ... * e(an1 * G1, an2 * G2)
+	// where t = sum(ai1 * ai2)
+	bls := NewEngine()
+	g1, g2 := bls.G1, bls.G2
+	numOfPair := 100
+	targetExp := new(big.Int)
+	// RHS
+	for i := 0; i < numOfPair; i++ {
+		// (ai1 * G1, ai2 * G2)
+		a1, a2 := randScalar(q), randScalar(q)
+		P1, P2 := g1.One(), g2.One()
+		g1.MulScalar(P1, P1, a1)
+		g2.MulScalar(P2, P2, a2)
+		bls.AddPair(P1, P2)
+		// accumulate targetExp
+		// t += (ai1 * ai2)
+		a1.Mul(a1, a2)
+		targetExp.Add(targetExp, a1)
+	}
+	// LHS
+	// e(t * G1, G2)
+	T1, T2 := g1.One(), g2.One()
+	g1.MulScalar(T1, T1, targetExp)
+	bls.AddPairInv(T1, T2)
+	check, err := bls.Check()
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !check {
+		t.Fatal("fail multi pairing")
+	}
+}
+
+func TestPairingEmpty(t *testing.T) {
+	bls := NewEngine()
+	check, err := bls.Check()
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !check {
+		t.Fatal("empty check should be accepted")
+	}
+	res, err := bls.Result()
+	if err != nil {
+		t.Fatal(err)
+	}
+	if !res.IsOne() {
+		t.Fatal("empty pairing result should be one")
+	}
+}
+
+func BenchmarkPairing(t *testing.B) {
+	bls := NewEngine()
+	g1, g2, gt := bls.G1, bls.G2, bls.GT()
+	bls.AddPair(g1.One(), g2.One())
+	e := gt.New()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		e, _ = bls.calculate()
+	}
+	_ = e
+}
diff --git a/pkg/core/curves/native/bls12-381/swu.go b/pkg/core/curves/native/bls12-381/swu.go
new file mode 100644
index 00000000..c61fa7ab
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/swu.go
@@ -0,0 +1,148 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+// swuMapG1 is implementation of Simplified Shallue-van de Woestijne-Ulas Method
+// follows the implmentation at draft-irtf-cfrg-hash-to-curve-06.
+func swuMapG1(u *fe) (*fe, *fe) {
+	var params = swuParamsForG1
+	var tv [4]*fe
+	for i := 0; i < 4; i++ {
+		tv[i] = new(fe)
+	}
+	square(tv[0], u)
+	mul(tv[0], tv[0], params.z)
+	square(tv[1], tv[0])
+	x1 := new(fe)
+	add(x1, tv[0], tv[1])
+	inverse(x1, x1)
+	e1 := x1.isZero()
+	one := new(fe).one()
+	add(x1, x1, one)
+	if e1 {
+		x1.set(params.zInv)
+	}
+	mul(x1, x1, params.minusBOverA)
+	gx1 := new(fe)
+	square(gx1, x1)
+	add(gx1, gx1, params.a)
+	mul(gx1, gx1, x1)
+	add(gx1, gx1, params.b)
+	x2 := new(fe)
+	mul(x2, tv[0], x1)
+	mul(tv[1], tv[0], tv[1])
+	gx2 := new(fe)
+	mul(gx2, gx1, tv[1])
+	e2 := !isQuadraticNonResidue(gx1)
+	x, y2 := new(fe), new(fe)
+	if e2 {
+		x.set(x1)
+		y2.set(gx1)
+	} else {
+		x.set(x2)
+		y2.set(gx2)
+	}
+	y := new(fe)
+	sqrt(y, y2)
+	if y.sign() != u.sign() {
+		neg(y, y)
+	}
+	return x, y
+}
+
+// swuMapG2 is implementation of Simplified Shallue-van de Woestijne-Ulas Method
+// defined at draft-irtf-cfrg-hash-to-curve-06.
+func swuMapG2(e *fp2, u *fe2) (*fe2, *fe2) {
+	if e == nil {
+		e = newFp2()
+	}
+	params := swuParamsForG2
+	var tv [4]*fe2
+	for i := 0; i < 4; i++ {
+		tv[i] = e.new()
+	}
+	e.square(tv[0], u)
+	e.mul(tv[0], tv[0], params.z)
+	e.square(tv[1], tv[0])
+	x1 := e.new()
+	e.add(x1, tv[0], tv[1])
+	e.inverse(x1, x1)
+	e1 := x1.isZero()
+	e.add(x1, x1, e.one())
+	if e1 {
+		x1.set(params.zInv)
+	}
+	e.mul(x1, x1, params.minusBOverA)
+	gx1 := e.new()
+	e.square(gx1, x1)
+	e.add(gx1, gx1, params.a)
+	e.mul(gx1, gx1, x1)
+	e.add(gx1, gx1, params.b)
+	x2 := e.new()
+	e.mul(x2, tv[0], x1)
+	e.mul(tv[1], tv[0], tv[1])
+	gx2 := e.new()
+	e.mul(gx2, gx1, tv[1])
+	e2 := !e.isQuadraticNonResidue(gx1)
+	x, y2 := e.new(), e.new()
+	if e2 {
+		x.set(x1)
+		y2.set(gx1)
+	} else {
+		x.set(x2)
+		y2.set(gx2)
+	}
+	y := e.new()
+	e.sqrt(y, y2)
+	if y.sign() != u.sign() {
+		e.neg(y, y)
+	}
+	return x, y
+}
+
+var swuParamsForG1 = struct {
+	z           *fe
+	zInv        *fe
+	a           *fe
+	b           *fe
+	minusBOverA *fe
+}{
+	a:           &fe{0x2f65aa0e9af5aa51, 0x86464c2d1e8416c3, 0xb85ce591b7bd31e2, 0x27e11c91b5f24e7c, 0x28376eda6bfc1835, 0x155455c3e5071d85},
+	b:           &fe{0xfb996971fe22a1e0, 0x9aa93eb35b742d6f, 0x8c476013de99c5c4, 0x873e27c3a221e571, 0xca72b5e45a52d888, 0x06824061418a386b},
+	z:           &fe{0x886c00000023ffdc, 0x0f70008d3090001d, 0x77672417ed5828c3, 0x9dac23e943dc1740, 0x50553f1b9c131521, 0x078c712fbe0ab6e8},
+	zInv:        &fe{0x0e8a2e8ba2e83e10, 0x5b28ba2ca4d745d1, 0x678cd5473847377a, 0x4c506dd8a8076116, 0x9bcb227d79284139, 0x0e8d3154b0ba099a},
+	minusBOverA: &fe{0x052583c93555a7fe, 0x3b40d72430f93c82, 0x1b75faa0105ec983, 0x2527e7dc63851767, 0x99fffd1f34fc181d, 0x097cab54770ca0d3},
+}
+
+var swuParamsForG2 = struct {
+	z           *fe2
+	zInv        *fe2
+	a           *fe2
+	b           *fe2
+	minusBOverA *fe2
+}{
+	a: &fe2{
+		fe{0, 0, 0, 0, 0, 0},
+		fe{0xe53a000003135242, 0x01080c0fdef80285, 0xe7889edbe340f6bd, 0x0b51375126310601, 0x02d6985717c744ab, 0x1220b4e979ea5467},
+	},
+	b: &fe2{
+		fe{0x22ea00000cf89db2, 0x6ec832df71380aa4, 0x6e1b94403db5a66e, 0x75bf3c53a79473ba, 0x3dd3a569412c0a34, 0x125cdb5e74dc4fd1},
+		fe{0x22ea00000cf89db2, 0x6ec832df71380aa4, 0x6e1b94403db5a66e, 0x75bf3c53a79473ba, 0x3dd3a569412c0a34, 0x125cdb5e74dc4fd1},
+	},
+	z: &fe2{
+		fe{0x87ebfffffff9555c, 0x656fffe5da8ffffa, 0x0fd0749345d33ad2, 0xd951e663066576f4, 0xde291a3d41e980d3, 0x0815664c7dfe040d},
+		fe{0x43f5fffffffcaaae, 0x32b7fff2ed47fffd, 0x07e83a49a2e99d69, 0xeca8f3318332bb7a, 0xef148d1ea0f4c069, 0x040ab3263eff0206},
+	},
+	zInv: &fe2{
+		fe{0xacd0000000011110, 0x9dd9999dc88ccccd, 0xb5ca2ac9b76352bf, 0xf1b574bcf4bc90ce, 0x42dab41f28a77081, 0x132fc6ac14cd1e12},
+		fe{0xe396ffffffff2223, 0x4fbf332fcd0d9998, 0x0c4bbd3c1aff4cc4, 0x6b9c91267926ca58, 0x29ae4da6aef7f496, 0x10692e942f195791},
+	},
+	minusBOverA: &fe2{
+		fe{0x903c555555474fb3, 0x5f98cc95ce451105, 0x9f8e582eefe0fade, 0xc68946b6aebbd062, 0x467a4ad10ee6de53, 0x0e7146f483e23a05},
+		fe{0x29c2aaaaaab85af8, 0xbf133368e30eeefa, 0xc7a27a7206cffb45, 0x9dee04ce44c9425c, 0x04a15ce53464ce83, 0x0b8fcaf5b59dac95},
+	},
+}
diff --git a/pkg/core/curves/native/bls12-381/tests/README.md b/pkg/core/curves/native/bls12-381/tests/README.md
new file mode 100644
index 00000000..7c8d7376
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/tests/README.md
@@ -0,0 +1 @@
+Test vectors are copied from [zkcrypto/bls12_381](https://github.com/zkcrypto/bls12_381) @  _afe30519f862abfba3ab26ae1ed406dd779db22e_
\ No newline at end of file
diff --git a/pkg/core/curves/native/bls12-381/tests/g1_compressed_valid_test_vectors.dat b/pkg/core/curves/native/bls12-381/tests/g1_compressed_valid_test_vectors.dat
new file mode 100644
index 0000000000000000000000000000000000000000..ea8cd67652d133010e79df8488452450b6f5cb17
GIT binary patch
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diff --git a/pkg/core/curves/native/bls12-381/tests/g1_uncompressed_valid_test_vectors.dat b/pkg/core/curves/native/bls12-381/tests/g1_uncompressed_valid_test_vectors.dat
new file mode 100644
index 0000000000000000000000000000000000000000..86abfba945c7b701750d637bffe6701330e10e88
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diff --git a/pkg/core/curves/native/bls12-381/tests/g2_compressed_valid_test_vectors.dat b/pkg/core/curves/native/bls12-381/tests/g2_compressed_valid_test_vectors.dat
new file mode 100644
index 0000000000000000000000000000000000000000..a40bbe251d90e576060adb7eaa2456197878804c
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diff --git a/pkg/core/curves/native/bls12-381/tests/g2_uncompressed_valid_test_vectors.dat b/pkg/core/curves/native/bls12-381/tests/g2_uncompressed_valid_test_vectors.dat
new file mode 100644
index 0000000000000000000000000000000000000000..92e4bc528e8937a311b502e4940e5e363a1f7c57
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z9w<pdQ4xDbD2(N>wO29^aEI8%kHqYPD2><}d`JQBq5Px^1rr3}sqKZ%k>D$!;n(zU
zaYwk&0IP;<!W%I=v;yRH68RFm5bC|4apo+m_S7}Sn+J9HfPnKlFP2Hv=f<EsuNQBg
z@nU75^`FNs2+5w^5e#;$P@5O|c$;>ylKyUe?gKT$!>N&B^v3skN<v~0pLC8##wiQh
z3C={yq5CQTVZkf^lLR%i1xrD^<T@(XZ4R3*&QV1%j|r(aBjdX1RqPljPZZNFQ#MC6
zLRFmc6$%3oLM&1zm><^X;^|?LC<aNOAND+t^OP7-Xo=#pd{B{qy8y5$>mxGOAQRKI
z?rPFQ@Hw)M@Ou5!IM3R4>lPk~FLGhZS?=3k8ZZRhRsz+lXLKbM2;)*+P1Lq0#5d^k
zWF`z_B93G}JGsQYK>{@nVb91Io}VbK*!x38VtQ}5FhZ3yK$d<e;+5D&EEZ9OQWSpj
zN)pbhbE4$(T>?)tGc6?3q)f}sIFEfM+rr;`I{O}JObDwqe1I161^CL(r9`{01Vw-#
z1JKzE8WdH~sdUZSQ84P-UhshImBEj%=v&Ks;P<vrn)bct5cWrdlX~Egnot?D4p(3Y
za1bpt7LSi>ZK7hfbq~ui$=)H-VTDo-2cvzPUewFfRa&{us(`YQT|R5OsYOV6iw2aH
zT0ldq=R1ndeo!T!n+S@7T(Eu&^NEd>?XVk1+{bR*yy<@Ghmk*47vw=SAOSV!EiR@8
zQYV!9tr*@O)_C5?!KdB7*1&gcz}tV}mE5mm)FM5P4&#Uw4Wge*2?SFG8&UEyopEDE
z3a(gg?5(*CI(SpFD>*SL4p-#K)I$2rxZ^W4bY7?~Uinp*x(1j-!-0T5{_ZN6^S`={
zWW>@}3ZVTg2`z<YitYghjwW+Yy&rSCeVm}|_nt4jItfd|@-^X@x->GL@3S7LJfaXC
zbj@wQeaA+knY_IUx+%PJV;@sC0Ayxki#tUK5)LDR9L{}%p48baPc58K{)x)5a;rnM
z>w@reAfm5C1zRM85G9h@OI5~L_j8BQX$4pG5?y-?Q}X@Vnd<?E_Qp&7o$6cJMHb0#
zwN>WQ|M5Ur2m7pEF)r(c#!;6f1qthIKM8TGWO`iOZ0j5=^-L~()%RYE_^6&$Q%MfV
zf;i7sZfZ)N@T3VU&Z6M{W&l5BPx0U1Ax%iO$7T49f=QXt8Fo9tC;ao!CNwe5^UknS
zyyJwr6jTB9F84C^T^7f4*R$-xdZ_v=7MC0ZgaMLNGfN(E(K$3dPhW+T!uM^4{jkKG
zPwr-u{(ZQ&Xa+rKBFJQ{+?EPFXNpQWryi>Z<}s-n+LY^lk>tRFEPctF0NOk<1?_fM
z0odRe_ZenaGL1*YoulJ@FGwHv!H7}t0fH<D%70NJaH*DptGAWv9Q>VL`pu2B$Vs9x
zkOR<$*gvvp>&iRp+kNOmr-rZOtiP~w7X)c#jBbw0wXqGAzN{m2ooAZH9U+yc_6l+q
z2Kv%}RznKoc0Ti5YH(X|XNjsNW;ndseJiauqupQ*6^HS9SfVG4!&@VoHx-Y87T_+0
zXE)!>+R&%*0QeKbZ<;kUo_?k;tg?bkl6So{=2#v0J?itpCg&3IUJEbS>x$^&-%^3(
zdcR{d${xdb1`$Kfd>nvE*~AINEvq!gjh%S}sC7)TfqIk2>J{RV1*iVM*v%WK%#Cyb
zy6-<C63sqD#eQrEvH0?_I*azk{;I%YzSqZobH%@;=mCl@WGq<Tega;)yzO*yM1_E`
g+;ght)L|-d70?SDFO6{n3KP7a5Wqj)F^xR@qeTkEDF6Tf

literal 0
HcmV?d00001

diff --git a/pkg/core/curves/native/bls12-381/utils.go b/pkg/core/curves/native/bls12-381/utils.go
new file mode 100644
index 00000000..ba4cdfb0
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/utils.go
@@ -0,0 +1,22 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"math/big"
+)
+
+func bigFromHex(hex string) *big.Int {
+	if len(hex) > 1 && hex[:2] == "0x" {
+		hex = hex[2:]
+	}
+	n, success := new(big.Int).SetString(hex, 16)
+	if !success {
+		panic("bigFromHex: failed to convert hex to big")
+	}
+	return n
+}
diff --git a/pkg/core/curves/native/bls12-381/wnaf.go b/pkg/core/curves/native/bls12-381/wnaf.go
new file mode 100644
index 00000000..5746eaa0
--- /dev/null
+++ b/pkg/core/curves/native/bls12-381/wnaf.go
@@ -0,0 +1,41 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bls12381
+
+import (
+	"math/big"
+)
+
+func wnaf(e0 *big.Int, window uint) []int64 {
+	e := new(big.Int).Set(e0)
+	zero := big.NewInt(0)
+	if e.Cmp(zero) == 0 {
+		return []int64{}
+	}
+	max := int64(1 << window)
+	midpoint := int64(1 << (window - 1))
+	modulusMask := uint64(1<<window) - 1
+	var out []int64
+	for e.Cmp(zero) != 0 {
+		var z int64
+		if e.Bit(0)&1 == 1 {
+			maskedBits := int64(e.Uint64() & modulusMask)
+			if maskedBits > midpoint {
+				z = maskedBits - max
+				e.Add(e, new(big.Int).SetInt64(0-z))
+			} else {
+				z = maskedBits
+				e.Sub(e, new(big.Int).SetInt64(z))
+			}
+		} else {
+			z = 0
+		}
+		out = append(out, z)
+		e.Rsh(e, 1)
+	}
+	return out
+}
diff --git a/pkg/core/curves/native/pasta/README.md b/pkg/core/curves/native/pasta/README.md
new file mode 100755
index 00000000..e8ecfd36
--- /dev/null
+++ b/pkg/core/curves/native/pasta/README.md
@@ -0,0 +1,15 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# pasta
+
+```go
+import "github.com/coinbase/kryptology/pkg/core/curves/native/pasta"
+```
+
+## Index
+
+
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/curves/native/pasta/fp/README.md b/pkg/core/curves/native/pasta/fp/README.md
new file mode 100755
index 00000000..0d447813
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fp/README.md
@@ -0,0 +1,301 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# fp
+
+```go
+import "github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fp"
+```
+
+Autogenerated: '\./src/ExtractionOCaml/word\_by\_word\_montgomery' \-\-lang Go pasta\_fp 64 '2^254 \+ 45560315531419706090280762371685220353'
+
+curve description: pasta\_fp
+
+machine\_wordsize = 64 \(from "64"\)
+
+requested operations: \(all\)
+
+m = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001 \(from "2^254 \+ 45560315531419706090280762371685220353"\)
+
+NOTE: In addition to the bounds specified above each function\, all
+
+```
+functions synthesized for this Montgomery arithmetic require the
+
+input to be strictly less than the prime modulus (m), and also
+
+require the input to be in the unique saturated representation.
+
+All functions also ensure that these two properties are true of
+
+return values.
+```
+
+Computed values:
+
+```
+eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
+
+bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248)
+
+twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
+
+                         if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
+```
+
+## Index
+
+- [type Fp](<#type-fp>)
+  - [func (fp *Fp) Add(lhs, rhs *Fp) *Fp](<#func-fp-add>)
+  - [func (fp *Fp) BigInt() *big.Int](<#func-fp-bigint>)
+  - [func (fp *Fp) Bytes() [32]byte](<#func-fp-bytes>)
+  - [func (fp *Fp) CMove(lhs, rhs *Fp, choice int) *Fp](<#func-fp-cmove>)
+  - [func (fp *Fp) Cmp(rhs *Fp) int](<#func-fp-cmp>)
+  - [func (fp *Fp) Double(elem *Fp) *Fp](<#func-fp-double>)
+  - [func (fp *Fp) Equal(rhs *Fp) bool](<#func-fp-equal>)
+  - [func (fp *Fp) Exp(base, exp *Fp) *Fp](<#func-fp-exp>)
+  - [func (fp *Fp) Invert(elem *Fp) (*Fp, bool)](<#func-fp-invert>)
+  - [func (fp *Fp) IsOdd() bool](<#func-fp-isodd>)
+  - [func (fp *Fp) IsOne() bool](<#func-fp-isone>)
+  - [func (fp *Fp) IsZero() bool](<#func-fp-iszero>)
+  - [func (fp *Fp) Mul(lhs, rhs *Fp) *Fp](<#func-fp-mul>)
+  - [func (fp *Fp) Neg(elem *Fp) *Fp](<#func-fp-neg>)
+  - [func (fp *Fp) Set(rhs *Fp) *Fp](<#func-fp-set>)
+  - [func (fp *Fp) SetBigInt(bi *big.Int) *Fp](<#func-fp-setbigint>)
+  - [func (fp *Fp) SetBool(rhs bool) *Fp](<#func-fp-setbool>)
+  - [func (fp *Fp) SetBytes(input *[32]byte) (*Fp, error)](<#func-fp-setbytes>)
+  - [func (fp *Fp) SetBytesWide(input *[64]byte) *Fp](<#func-fp-setbyteswide>)
+  - [func (fp *Fp) SetOne() *Fp](<#func-fp-setone>)
+  - [func (fp *Fp) SetRaw(array *[4]uint64) *Fp](<#func-fp-setraw>)
+  - [func (fp *Fp) SetUint64(rhs uint64) *Fp](<#func-fp-setuint64>)
+  - [func (fp *Fp) SetZero() *Fp](<#func-fp-setzero>)
+  - [func (fp *Fp) Sqrt(elem *Fp) (*Fp, bool)](<#func-fp-sqrt>)
+  - [func (fp *Fp) Square(elem *Fp) *Fp](<#func-fp-square>)
+  - [func (fp *Fp) Sub(lhs, rhs *Fp) *Fp](<#func-fp-sub>)
+  - [func (fp *Fp) ToRaw() [4]uint64](<#func-fp-toraw>)
+
+
+## type [Fp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L16>)
+
+```go
+type Fp fiat_pasta_fp_montgomery_domain_field_element
+```
+
+### func \(\*Fp\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L316>)
+
+```go
+func (fp *Fp) Add(lhs, rhs *Fp) *Fp
+```
+
+Add returns the result from adding rhs to this element
+
+### func \(\*Fp\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L209>)
+
+```go
+func (fp *Fp) BigInt() *big.Int
+```
+
+BigInt converts this element into the big\.Int struct
+
+### func \(\*Fp\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L200>)
+
+```go
+func (fp *Fp) Bytes() [32]byte
+```
+
+Bytes converts this element into a byte representation in little endian byte order
+
+### func \(\*Fp\) [CMove](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L355>)
+
+```go
+func (fp *Fp) CMove(lhs, rhs *Fp, choice int) *Fp
+```
+
+CMove selects lhs if choice == 0 and rhs if choice == 1
+
+### func \(\*Fp\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L47>)
+
+```go
+func (fp *Fp) Cmp(rhs *Fp) int
+```
+
+Cmp returns \-1 if fp \< rhs 0 if fp == rhs 1 if fp \> rhs
+
+### func \(\*Fp\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L215>)
+
+```go
+func (fp *Fp) Double(elem *Fp) *Fp
+```
+
+Double this element
+
+### func \(\*Fp\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L58>)
+
+```go
+func (fp *Fp) Equal(rhs *Fp) bool
+```
+
+Equal returns true if fp == rhs
+
+### func \(\*Fp\) [Exp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L331>)
+
+```go
+func (fp *Fp) Exp(base, exp *Fp) *Fp
+```
+
+Exp exponentiates this element by exp
+
+### func \(\*Fp\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L289>)
+
+```go
+func (fp *Fp) Invert(elem *Fp) (*Fp, bool)
+```
+
+Invert this element i\.e\. compute the multiplicative inverse return false\, zero if this element is zero
+
+### func \(\*Fp\) [IsOdd](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L80>)
+
+```go
+func (fp *Fp) IsOdd() bool
+```
+
+### func \(\*Fp\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L76>)
+
+```go
+func (fp *Fp) IsOne() bool
+```
+
+IsOne returns true if fp == R
+
+### func \(\*Fp\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L67>)
+
+```go
+func (fp *Fp) IsZero() bool
+```
+
+IsZero returns true if fp == 0
+
+### func \(\*Fp\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L300>)
+
+```go
+func (fp *Fp) Mul(lhs, rhs *Fp) *Fp
+```
+
+Mul returns the result from multiplying this element by rhs
+
+### func \(\*Fp\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L324>)
+
+```go
+func (fp *Fp) Neg(elem *Fp) *Fp
+```
+
+Neg returns negation of this element
+
+### func \(\*Fp\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L87>)
+
+```go
+func (fp *Fp) Set(rhs *Fp) *Fp
+```
+
+Set fp == rhs
+
+### func \(\*Fp\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L182>)
+
+```go
+func (fp *Fp) SetBigInt(bi *big.Int) *Fp
+```
+
+SetBigInt initializes an element from big\.Int The value is reduced by the modulus
+
+### func \(\*Fp\) [SetBool](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L102>)
+
+```go
+func (fp *Fp) SetBool(rhs bool) *Fp
+```
+
+### func \(\*Fp\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L165>)
+
+```go
+func (fp *Fp) SetBytes(input *[32]byte) (*Fp, error)
+```
+
+SetBytes attempts to convert a little endian byte representation of a scalar into a \`Fp\`\, failing if input is not canonical
+
+### func \(\*Fp\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L140>)
+
+```go
+func (fp *Fp) SetBytesWide(input *[64]byte) *Fp
+```
+
+SetBytesWide takes 64 bytes as input and treats them as a 512\-bit number\. Attributed to https://github.com/zcash/pasta_curves/blob/main/src/fields/fp.rs#L255 We reduce an arbitrary 512\-bit number by decomposing it into two 256\-bit digits with the higher bits multiplied by 2^256\. Thus\, we perform two reductions
+
+1\. the lower bits are multiplied by R^2\, as normal 2\. the upper bits are multiplied by R^2 \* 2^256 = R^3
+
+and computing their sum in the field\. It remains to see that arbitrary 256\-bit numbers can be placed into Montgomery form safely using the reduction\. The reduction works so long as the product is less than R=2^256 multiplied by the modulus\. This holds because for any \`c\` smaller than the modulus\, we have that \(2^256 \- 1\)\*c is an acceptable product for the reduction\. Therefore\, the reduction always works so long as \`c\` is in the field; in this case it is either the constant \`r2\` or \`r3\`\.
+
+### func \(\*Fp\) [SetOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L112>)
+
+```go
+func (fp *Fp) SetOne() *Fp
+```
+
+SetOne fp == R
+
+### func \(\*Fp\) [SetRaw](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L193>)
+
+```go
+func (fp *Fp) SetRaw(array *[4]uint64) *Fp
+```
+
+SetRaw converts a raw array into a field element
+
+### func \(\*Fp\) [SetUint64](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L96>)
+
+```go
+func (fp *Fp) SetUint64(rhs uint64) *Fp
+```
+
+SetUint64 sets fp == rhs
+
+### func \(\*Fp\) [SetZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L117>)
+
+```go
+func (fp *Fp) SetZero() *Fp
+```
+
+SetZero fp == 0
+
+### func \(\*Fp\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L230>)
+
+```go
+func (fp *Fp) Sqrt(elem *Fp) (*Fp, bool)
+```
+
+Sqrt this element\, if it exists\. If true\, then value is a square root\. If false\, value is a QNR
+
+### func \(\*Fp\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L222>)
+
+```go
+func (fp *Fp) Square(elem *Fp) *Fp
+```
+
+Square this element
+
+### func \(\*Fp\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L308>)
+
+```go
+func (fp *Fp) Sub(lhs, rhs *Fp) *Fp
+```
+
+Sub returns the result from subtracting rhs from this element
+
+### func \(\*Fp\) [ToRaw](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fp/fp.go#L363>)
+
+```go
+func (fp *Fp) ToRaw() [4]uint64
+```
+
+ToRaw converts this element into the a \[4\]uint64
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/curves/native/pasta/fp/fp.go b/pkg/core/curves/native/pasta/fp/fp.go
new file mode 100644
index 00000000..5946a430
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fp/fp.go
@@ -0,0 +1,367 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package fp
+
+import (
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"math/big"
+)
+
+type Fp fiat_pasta_fp_montgomery_domain_field_element
+
+// r = 2^256 mod p
+var r = &Fp{0x34786d38fffffffd, 0x992c350be41914ad, 0xffffffffffffffff, 0x3fffffffffffffff}
+
+// r2 = 2^512 mod p
+var r2 = &Fp{0x8c78ecb30000000f, 0xd7d30dbd8b0de0e7, 0x7797a99bc3c95d18, 0x096d41af7b9cb714}
+
+// r3 = 2^768 mod p
+var r3 = &Fp{0xf185a5993a9e10f9, 0xf6a68f3b6ac5b1d1, 0xdf8d1014353fd42c, 0x2ae309222d2d9910}
+
+// generator = 5 mod p is a generator of the `p - 1` order multiplicative
+// subgroup, or in other words a primitive element of the field.
+var generator = &Fp{0xa1a55e68ffffffed, 0x74c2a54b4f4982f3, 0xfffffffffffffffd, 0x3fffffffffffffff}
+
+var s = 32
+
+// modulus representation
+// p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
+var modulus = &Fp{0x992d30ed00000001, 0x224698fc094cf91b, 0x0000000000000000, 0x4000000000000000}
+
+var biModulus = new(big.Int).SetBytes([]byte{
+	0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	0x22, 0x46, 0x98, 0xfc, 0x09, 0x4c, 0xf9, 0x1b,
+	0x99, 0x2d, 0x30, 0xed, 0x00, 0x00, 0x00, 0x01,
+})
+
+// Cmp returns -1 if fp < rhs
+// 0 if fp == rhs
+// 1 if fp > rhs
+func (fp *Fp) Cmp(rhs *Fp) int {
+	gt := 0
+	lt := 0
+	for i := len(fp) - 1; i >= 0; i-- {
+		gt |= int((rhs[i]-fp[i])>>63) &^ lt
+		lt |= int((fp[i]-rhs[i])>>63) &^ gt
+	}
+	return gt - lt
+}
+
+// Equal returns true if fp == rhs
+func (fp *Fp) Equal(rhs *Fp) bool {
+	t := fp[0] ^ rhs[0]
+	t |= fp[1] ^ rhs[1]
+	t |= fp[2] ^ rhs[2]
+	t |= fp[3] ^ rhs[3]
+	return t == 0
+}
+
+// IsZero returns true if fp == 0
+func (fp *Fp) IsZero() bool {
+	t := fp[0]
+	t |= fp[1]
+	t |= fp[2]
+	t |= fp[3]
+	return t == 0
+}
+
+// IsOne returns true if fp == R
+func (fp *Fp) IsOne() bool {
+	return fp.Equal(r)
+}
+
+func (fp *Fp) IsOdd() bool {
+	tv := new(fiat_pasta_fp_non_montgomery_domain_field_element)
+	fiat_pasta_fp_from_montgomery(tv, (*fiat_pasta_fp_montgomery_domain_field_element)(fp))
+	return tv[0]&0x01 == 0x01
+}
+
+// Set fp == rhs
+func (fp *Fp) Set(rhs *Fp) *Fp {
+	fp[0] = rhs[0]
+	fp[1] = rhs[1]
+	fp[2] = rhs[2]
+	fp[3] = rhs[3]
+	return fp
+}
+
+// SetUint64 sets fp == rhs
+func (fp *Fp) SetUint64(rhs uint64) *Fp {
+	r := &fiat_pasta_fp_non_montgomery_domain_field_element{rhs, 0, 0, 0}
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(fp), r)
+	return fp
+}
+
+func (fp *Fp) SetBool(rhs bool) *Fp {
+	if rhs {
+		fp.SetOne()
+	} else {
+		fp.SetZero()
+	}
+	return fp
+}
+
+// SetOne fp == R
+func (fp *Fp) SetOne() *Fp {
+	return fp.Set(r)
+}
+
+// SetZero fp == 0
+func (fp *Fp) SetZero() *Fp {
+	fp[0] = 0
+	fp[1] = 0
+	fp[2] = 0
+	fp[3] = 0
+	return fp
+}
+
+// SetBytesWide takes 64 bytes as input and treats them as a 512-bit number.
+// Attributed to https://github.com/zcash/pasta_curves/blob/main/src/fields/fp.rs#L255
+// We reduce an arbitrary 512-bit number by decomposing it into two 256-bit digits
+// with the higher bits multiplied by 2^256. Thus, we perform two reductions
+//
+// 1. the lower bits are multiplied by R^2, as normal
+// 2. the upper bits are multiplied by R^2 * 2^256 = R^3
+//
+// and computing their sum in the field. It remains to see that arbitrary 256-bit
+// numbers can be placed into Montgomery form safely using the reduction. The
+// reduction works so long as the product is less than R=2^256 multiplied by
+// the modulus. This holds because for any `c` smaller than the modulus, we have
+// that (2^256 - 1)*c is an acceptable product for the reduction. Therefore, the
+// reduction always works so long as `c` is in the field; in this case it is either the
+// constant `r2` or `r3`.
+func (fp *Fp) SetBytesWide(input *[64]byte) *Fp {
+	d0 := fiat_pasta_fp_montgomery_domain_field_element{
+		binary.LittleEndian.Uint64(input[:8]),
+		binary.LittleEndian.Uint64(input[8:16]),
+		binary.LittleEndian.Uint64(input[16:24]),
+		binary.LittleEndian.Uint64(input[24:32]),
+	}
+	d1 := fiat_pasta_fp_montgomery_domain_field_element{
+		binary.LittleEndian.Uint64(input[32:40]),
+		binary.LittleEndian.Uint64(input[40:48]),
+		binary.LittleEndian.Uint64(input[48:56]),
+		binary.LittleEndian.Uint64(input[56:64]),
+	}
+	// Convert to Montgomery form
+	tv1 := new(fiat_pasta_fp_montgomery_domain_field_element)
+	tv2 := new(fiat_pasta_fp_montgomery_domain_field_element)
+	// d0 * r2 + d1 * r3
+	fiat_pasta_fp_mul(tv1, &d0, (*fiat_pasta_fp_montgomery_domain_field_element)(r2))
+	fiat_pasta_fp_mul(tv2, &d1, (*fiat_pasta_fp_montgomery_domain_field_element)(r3))
+	fiat_pasta_fp_add((*fiat_pasta_fp_montgomery_domain_field_element)(fp), tv1, tv2)
+	return fp
+}
+
+// SetBytes attempts to convert a little endian byte representation
+// of a scalar into a `Fp`, failing if input is not canonical
+func (fp *Fp) SetBytes(input *[32]byte) (*Fp, error) {
+	d0 := &Fp{
+		binary.LittleEndian.Uint64(input[:8]),
+		binary.LittleEndian.Uint64(input[8:16]),
+		binary.LittleEndian.Uint64(input[16:24]),
+		binary.LittleEndian.Uint64(input[24:32]),
+	}
+	if d0.Cmp(modulus) != -1 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	fiat_pasta_fp_from_bytes((*[4]uint64)(fp), input)
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(fp), (*fiat_pasta_fp_non_montgomery_domain_field_element)(fp))
+	return fp, nil
+}
+
+// SetBigInt initializes an element from big.Int
+// The value is reduced by the modulus
+func (fp *Fp) SetBigInt(bi *big.Int) *Fp {
+	var buffer [32]byte
+	r := new(big.Int).Set(bi)
+	r.Mod(r, biModulus)
+	r.FillBytes(buffer[:])
+	copy(buffer[:], internal.ReverseScalarBytes(buffer[:]))
+	_, _ = fp.SetBytes(&buffer)
+	return fp
+}
+
+// SetRaw converts a raw array into a field element
+func (fp *Fp) SetRaw(array *[4]uint64) *Fp {
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(fp), (*fiat_pasta_fp_non_montgomery_domain_field_element)(array))
+	return fp
+}
+
+// Bytes converts this element into a byte representation
+// in little endian byte order
+func (fp *Fp) Bytes() [32]byte {
+	var output [32]byte
+	tv := new(fiat_pasta_fp_non_montgomery_domain_field_element)
+	fiat_pasta_fp_from_montgomery(tv, (*fiat_pasta_fp_montgomery_domain_field_element)(fp))
+	fiat_pasta_fp_to_bytes(&output, (*[4]uint64)(tv))
+	return output
+}
+
+// BigInt converts this element into the big.Int struct
+func (fp *Fp) BigInt() *big.Int {
+	buffer := fp.Bytes()
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(buffer[:]))
+}
+
+// Double this element
+func (fp *Fp) Double(elem *Fp) *Fp {
+	delem := (*fiat_pasta_fp_montgomery_domain_field_element)(elem)
+	fiat_pasta_fp_add((*fiat_pasta_fp_montgomery_domain_field_element)(fp), delem, delem)
+	return fp
+}
+
+// Square this element
+func (fp *Fp) Square(elem *Fp) *Fp {
+	delem := (*fiat_pasta_fp_montgomery_domain_field_element)(elem)
+	fiat_pasta_fp_square((*fiat_pasta_fp_montgomery_domain_field_element)(fp), delem)
+	return fp
+}
+
+// Sqrt this element, if it exists. If true, then value
+// is a square root. If false, value is a QNR
+func (fp *Fp) Sqrt(elem *Fp) (*Fp, bool) {
+	return fp.tonelliShanks(elem)
+}
+
+// See sqrt_ts_ct at
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-I.4
+func (fp *Fp) tonelliShanks(elem *Fp) (*Fp, bool) {
+	// c1 := 32
+	// c2 := (q - 1) / (2^c1)
+	// c2 := [4]uint64{
+	// 	0x094cf91b992d30ed,
+	// 	0x00000000224698fc,
+	// 	0x0000000000000000,
+	// 	0x0000000040000000,
+	// }
+	// c3 := (c2 - 1) / 2
+	c3 := [4]uint64{
+		0x04a67c8dcc969876,
+		0x0000000011234c7e,
+		0x0000000000000000,
+		0x0000000020000000,
+	}
+	// c4 := generator
+	// c5 := new(Fp).pow(&generator, c2)
+	c5 := &Fp{
+		0xa28db849bad6dbf0,
+		0x9083cd03d3b539df,
+		0xfba6b9ca9dc8448e,
+		0x3ec928747b89c6da,
+	}
+
+	z := new(Fp).pow(elem, c3)
+	t := new(Fp).Square(z)
+	t.Mul(t, elem)
+
+	z.Mul(z, elem)
+
+	b := new(Fp).Set(t)
+	c := new(Fp).Set(c5)
+	flags := map[bool]int{
+		true:  1,
+		false: 0,
+	}
+
+	for i := s; i >= 2; i-- {
+		for j := 1; j <= i-2; j++ {
+			b.Square(b)
+		}
+		z.CMove(z, new(Fp).Mul(z, c), flags[!b.IsOne()])
+		c.Square(c)
+		t.CMove(t, new(Fp).Mul(t, c), flags[!b.IsOne()])
+		b.Set(t)
+	}
+	wasSquare := c.Square(z).Equal(elem)
+	return fp.Set(z), wasSquare
+}
+
+// Invert this element i.e. compute the multiplicative inverse
+// return false, zero if this element is zero
+func (fp *Fp) Invert(elem *Fp) (*Fp, bool) {
+	// computes elem^(p - 2) mod p
+	exp := [4]uint64{
+		0x992d30ecffffffff,
+		0x224698fc094cf91b,
+		0x0000000000000000,
+		0x4000000000000000}
+	return fp.pow(elem, exp), !elem.IsZero()
+}
+
+// Mul returns the result from multiplying this element by rhs
+func (fp *Fp) Mul(lhs, rhs *Fp) *Fp {
+	dlhs := (*fiat_pasta_fp_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fp_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fp_mul((*fiat_pasta_fp_montgomery_domain_field_element)(fp), dlhs, drhs)
+	return fp
+}
+
+// Sub returns the result from subtracting rhs from this element
+func (fp *Fp) Sub(lhs, rhs *Fp) *Fp {
+	dlhs := (*fiat_pasta_fp_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fp_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fp_sub((*fiat_pasta_fp_montgomery_domain_field_element)(fp), dlhs, drhs)
+	return fp
+}
+
+// Add returns the result from adding rhs to this element
+func (fp *Fp) Add(lhs, rhs *Fp) *Fp {
+	dlhs := (*fiat_pasta_fp_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fp_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fp_add((*fiat_pasta_fp_montgomery_domain_field_element)(fp), dlhs, drhs)
+	return fp
+}
+
+// Neg returns negation of this element
+func (fp *Fp) Neg(elem *Fp) *Fp {
+	delem := (*fiat_pasta_fp_montgomery_domain_field_element)(elem)
+	fiat_pasta_fp_opp((*fiat_pasta_fp_montgomery_domain_field_element)(fp), delem)
+	return fp
+}
+
+// Exp exponentiates this element by exp
+func (fp *Fp) Exp(base, exp *Fp) *Fp {
+	// convert exponent to integer form
+	tv := &fiat_pasta_fp_non_montgomery_domain_field_element{}
+	fiat_pasta_fp_from_montgomery(tv, (*fiat_pasta_fp_montgomery_domain_field_element)(exp))
+
+	e := (*[4]uint64)(tv)
+	return fp.pow(base, *e)
+}
+
+func (fp *Fp) pow(base *Fp, exp [4]uint64) *Fp {
+	res := new(Fp).SetOne()
+	tmp := new(Fp)
+
+	for i := len(exp) - 1; i >= 0; i-- {
+		for j := 63; j >= 0; j-- {
+			res.Square(res)
+			tmp.Mul(res, base)
+			res.CMove(res, tmp, int(exp[i]>>j)&1)
+		}
+	}
+	return fp.Set(res)
+}
+
+// CMove selects lhs if choice == 0 and rhs if choice == 1
+func (fp *Fp) CMove(lhs, rhs *Fp, choice int) *Fp {
+	dlhs := (*[4]uint64)(lhs)
+	drhs := (*[4]uint64)(rhs)
+	fiat_pasta_fp_selectznz((*[4]uint64)(fp), fiat_pasta_fp_uint1(choice), dlhs, drhs)
+	return fp
+}
+
+// ToRaw converts this element into the a [4]uint64
+func (fp *Fp) ToRaw() [4]uint64 {
+	res := &fiat_pasta_fp_non_montgomery_domain_field_element{}
+	fiat_pasta_fp_from_montgomery(res, (*fiat_pasta_fp_montgomery_domain_field_element)(fp))
+	return *(*[4]uint64)(res)
+}
diff --git a/pkg/core/curves/native/pasta/fp/fp_test.go b/pkg/core/curves/native/pasta/fp/fp_test.go
new file mode 100644
index 00000000..a20dd6e4
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fp/fp_test.go
@@ -0,0 +1,248 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package fp
+
+import (
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"math/rand"
+	"testing"
+)
+
+func TestFpSetOne(t *testing.T) {
+	fp := new(Fp).SetOne()
+	assert.NotNil(t, fp)
+	assert.True(t, fp.Equal(r))
+}
+
+func TestFpSetUint64(t *testing.T) {
+	act := new(Fp).SetUint64(1 << 60)
+	assert.NotNil(t, act)
+	// Remember it will be in montgomery form
+	assert.Equal(t, int(act[0]), 0x592d30ed00000001)
+}
+
+func TestFpAdd(t *testing.T) {
+	lhs := new(Fp).SetOne()
+	rhs := new(Fp).SetOne()
+	exp := new(Fp).SetUint64(2)
+	res := new(Fp).Add(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint64() >> 2
+		r := rand.Uint64() >> 2
+		e := l + r
+		lhs.SetUint64(l)
+		rhs.SetUint64(r)
+		exp.SetUint64(e)
+
+		a := new(Fp).Add(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFpSub(t *testing.T) {
+	lhs := new(Fp).SetOne()
+	rhs := new(Fp).SetOne()
+	exp := new(Fp).SetZero()
+	res := new(Fp).Sub(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint64() >> 2
+		r := rand.Uint64() >> 2
+		if l < r {
+			l, r = r, l
+		}
+		e := l - r
+		lhs.SetUint64(l)
+		rhs.SetUint64(r)
+		exp.SetUint64(e)
+
+		a := new(Fp).Sub(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFpMul(t *testing.T) {
+	lhs := new(Fp).SetOne()
+	rhs := new(Fp).SetOne()
+	exp := new(Fp).SetOne()
+	res := new(Fp).Mul(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint32()
+		r := rand.Uint32()
+		e := uint64(l) * uint64(r)
+		lhs.SetUint64(uint64(l))
+		rhs.SetUint64(uint64(r))
+		exp.SetUint64(e)
+
+		a := new(Fp).Mul(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFpDouble(t *testing.T) {
+	a := new(Fp).SetUint64(2)
+	e := new(Fp).SetUint64(4)
+	assert.Equal(t, e, new(Fp).Double(a))
+
+	for i := 0; i < 25; i++ {
+		tv := rand.Uint32()
+		ttv := uint64(tv) * 2
+		a = new(Fp).SetUint64(uint64(tv))
+		e = new(Fp).SetUint64(ttv)
+		assert.Equal(t, e, new(Fp).Double(a))
+	}
+}
+
+func TestFpSquare(t *testing.T) {
+	a := new(Fp).SetUint64(4)
+	e := new(Fp).SetUint64(16)
+	assert.Equal(t, e, a.Square(a))
+
+	for i := 0; i < 25; i++ {
+		j := rand.Uint32()
+		exp := uint64(j) * uint64(j)
+		e.SetUint64(exp)
+		a.SetUint64(uint64(j))
+		assert.Equal(t, e, a.Square(a))
+	}
+}
+
+func TestFpNeg(t *testing.T) {
+	a := new(Fp).SetOne()
+	a.Neg(a)
+	e := &Fp{7256640077462241284, 9879318615658062958, 0, 0}
+	assert.Equal(t, e, a)
+	a.Neg(generator)
+	e = &Fp{0xf787d28400000014, 0xad83f3b0ba037627, 0x2, 0x0}
+	assert.Equal(t, e, a)
+}
+
+func TestFpExp(t *testing.T) {
+	e := new(Fp).SetUint64(8)
+	a := new(Fp).SetUint64(2)
+	by := new(Fp).SetUint64(3)
+	assert.Equal(t, e, a.Exp(a, by))
+}
+
+func TestFpSqrt(t *testing.T) {
+	t1 := new(Fp).SetUint64(2)
+	t2 := new(Fp).Neg(t1)
+	t3 := new(Fp).Square(t1)
+	_, wasSquare := t3.Sqrt(t3)
+	assert.True(t, wasSquare)
+	assert.True(t, t1.Equal(t3) || t2.Equal(t3))
+	t1.SetUint64(5)
+	_, wasSquare = new(Fp).Sqrt(t1)
+	assert.False(t, wasSquare)
+}
+
+func TestFpInvert(t *testing.T) {
+	twoInv := &Fp{0xcc96987680000001, 0x11234c7e04a67c8d, 0x0000000000000000, 0x2000000000000000}
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(twoInv), (*fiat_pasta_fp_non_montgomery_domain_field_element)(twoInv))
+	two := new(Fp).SetUint64(2)
+	a, inverted := new(Fp).Invert(two)
+	assert.True(t, inverted)
+	assert.Equal(t, a, twoInv)
+
+	rootOfUnity := &Fp{0xbdad6fabd87ea32f, 0xea322bf2b7bb7584, 0x362120830561f81a, 0x2bce74deac30ebda}
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(rootOfUnity), (*fiat_pasta_fp_non_montgomery_domain_field_element)(rootOfUnity))
+	rootOfUnityInv := &Fp{0xf0b87c7db2ce91f6, 0x84a0a1d8859f066f, 0xb4ed8e647196dad1, 0x2cd5282c53116b5c}
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(rootOfUnityInv), (*fiat_pasta_fp_non_montgomery_domain_field_element)(rootOfUnityInv))
+	a, inverted = new(Fp).Invert(rootOfUnity)
+	assert.True(t, inverted)
+	assert.Equal(t, a, rootOfUnityInv)
+
+	lhs := new(Fp).SetUint64(9)
+	rhs := new(Fp).SetUint64(3)
+	rhsInv, inverted := new(Fp).Invert(rhs)
+	assert.True(t, inverted)
+	assert.Equal(t, rhs, new(Fp).Mul(lhs, rhsInv))
+
+	rhs.SetZero()
+	_, inverted = new(Fp).Invert(rhs)
+	assert.False(t, inverted)
+}
+
+func TestFpCMove(t *testing.T) {
+	t1 := new(Fp).SetUint64(5)
+	t2 := new(Fp).SetUint64(10)
+	assert.Equal(t, t1, new(Fp).CMove(t1, t2, 0))
+	assert.Equal(t, t2, new(Fp).CMove(t1, t2, 1))
+}
+
+func TestFpBytes(t *testing.T) {
+	t1 := new(Fp).SetUint64(99)
+	seq := t1.Bytes()
+	t2, err := new(Fp).SetBytes(&seq)
+	assert.NoError(t, err)
+	assert.Equal(t, t1, t2)
+
+	for i := 0; i < 25; i++ {
+		t1.SetUint64(rand.Uint64())
+		seq = t1.Bytes()
+		_, err = t2.SetBytes(&seq)
+		assert.NoError(t, err)
+		assert.Equal(t, t1, t2)
+	}
+}
+
+func TestFpBigInt(t *testing.T) {
+	t1 := new(Fp).SetBigInt(big.NewInt(9999))
+	t2 := new(Fp).SetBigInt(t1.BigInt())
+	assert.Equal(t, t1, t2)
+
+	e := &Fp{0x8c6bc70550c87761, 0xce2c6c48e7063731, 0xf1275fd1e4607cd6, 0x3e6762e63501edbd}
+	b := new(big.Int).SetBytes([]byte{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9})
+	t1.SetBigInt(b)
+	assert.Equal(t, e, t1)
+	e[0] = 0xcc169e7af3788a0
+	e[1] = 0x541a2cb32246c1ea
+	e[2] = 0xed8a02e1b9f8329
+	e[3] = 0x1989d19cafe1242
+	b.Neg(b)
+	t1.SetBigInt(b)
+	assert.Equal(t, e, t1)
+}
+
+func TestFpSetBool(t *testing.T) {
+	assert.Equal(t, new(Fp).SetOne(), new(Fp).SetBool(true))
+	assert.Equal(t, new(Fp).SetZero(), new(Fp).SetBool(false))
+}
+
+func TestFpSetBytesWide(t *testing.T) {
+	e := &Fp{0x3daec14d565241d9, 0x0b7af45b6073944b, 0xea5b8bd611a5bd4c, 0x150160330625db3d}
+	fiat_pasta_fp_to_montgomery((*fiat_pasta_fp_montgomery_domain_field_element)(e), (*fiat_pasta_fp_non_montgomery_domain_field_element)(e))
+	a := new(Fp).SetBytesWide(&[64]byte{
+		0xa1, 0x78, 0x76, 0x29, 0x41, 0x56, 0x15, 0xee,
+		0x65, 0xbe, 0xfd, 0xdb, 0x6b, 0x15, 0x3e, 0xd8,
+		0xb5, 0xa0, 0x8b, 0xc6, 0x34, 0xd8, 0xcc, 0xd9,
+		0x58, 0x27, 0x27, 0x12, 0xe3, 0xed, 0x08, 0xf5,
+		0x89, 0x8e, 0x22, 0xf8, 0xcb, 0xf7, 0x8d, 0x03,
+		0x41, 0x4b, 0xc7, 0xa3, 0xe4, 0xa1, 0x05, 0x35,
+		0xb3, 0x2d, 0xb8, 0x5e, 0x77, 0x6f, 0xa4, 0xbf,
+		0x1d, 0x47, 0x2f, 0x26, 0x7e, 0xe2, 0xeb, 0x26,
+	})
+	assert.Equal(t, e, a)
+}
diff --git a/pkg/core/curves/native/pasta/fp/pasta_fp.go b/pkg/core/curves/native/pasta/fp/pasta_fp.go
new file mode 100644
index 00000000..36d7ec73
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fp/pasta_fp.go
@@ -0,0 +1,1432 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Autogenerated: './src/ExtractionOCaml/word_by_word_montgomery' --lang Go pasta_fp 64 '2^254 + 45560315531419706090280762371685220353'
+//
+// curve description: pasta_fp
+//
+// machine_wordsize = 64 (from "64")
+//
+// requested operations: (all)
+//
+// m = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001 (from "2^254 + 45560315531419706090280762371685220353")
+//
+//
+//
+// NOTE: In addition to the bounds specified above each function, all
+//
+//   functions synthesized for this Montgomery arithmetic require the
+//
+//   input to be strictly less than the prime modulus (m), and also
+//
+//   require the input to be in the unique saturated representation.
+//
+//   All functions also ensure that these two properties are true of
+//
+//   return values.
+//
+//
+//
+// Computed values:
+//
+//   eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
+//
+//   bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248)
+//
+//   twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
+//
+//                            if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
+package fp
+
+import "math/bits"
+
+type fiat_pasta_fp_uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+type fiat_pasta_fp_int1 int64   // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+
+// The type fiat_pasta_fp_montgomery_domain_field_element is a field element in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiat_pasta_fp_montgomery_domain_field_element [4]uint64
+
+// The type fiat_pasta_fp_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiat_pasta_fp_non_montgomery_domain_field_element [4]uint64
+
+// The function fiat_pasta_fp_addcarryx_u64 is a thin wrapper around bits.Add64 that uses fiat_pasta_fp_uint1 rather than uint64
+func fiat_pasta_fp_addcarryx_u64(x uint64, y uint64, carry fiat_pasta_fp_uint1) (uint64, fiat_pasta_fp_uint1) {
+	sum, carryOut := bits.Add64(x, y, uint64(carry))
+	return sum, fiat_pasta_fp_uint1(carryOut)
+}
+
+// The function fiat_pasta_fp_subborrowx_u64 is a thin wrapper around bits.Sub64 that uses fiat_pasta_fp_uint1 rather than uint64
+func fiat_pasta_fp_subborrowx_u64(x uint64, y uint64, carry fiat_pasta_fp_uint1) (uint64, fiat_pasta_fp_uint1) {
+	sum, carryOut := bits.Sub64(x, y, uint64(carry))
+	return sum, fiat_pasta_fp_uint1(carryOut)
+}
+
+// The function fiat_pasta_fp_cmovznz_u64 is a single-word conditional move.
+//
+// Postconditions:
+//   out1 = (if arg1 = 0 then arg2 else arg3)
+//
+// Input Bounds:
+//   arg1: [0x0 ~> 0x1]
+//   arg2: [0x0 ~> 0xffffffffffffffff]
+//   arg3: [0x0 ~> 0xffffffffffffffff]
+// Output Bounds:
+//   out1: [0x0 ~> 0xffffffffffffffff]
+func fiat_pasta_fp_cmovznz_u64(out1 *uint64, arg1 fiat_pasta_fp_uint1, arg2 uint64, arg3 uint64) {
+	x1 := arg1
+	x2 := (uint64((fiat_pasta_fp_int1(0x0) - fiat_pasta_fp_int1(x1))) & 0xffffffffffffffff)
+	x3 := ((x2 & arg3) | ((^x2) & arg2))
+	*out1 = x3
+}
+
+// The function fiat_pasta_fp_mul multiplies two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_mul(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element, arg2 *fiat_pasta_fp_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, arg2[3])
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, arg2[2])
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, arg2[1])
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, arg2[0])
+	var x13 uint64
+	var x14 fiat_pasta_fp_uint1
+	x13, x14 = fiat_pasta_fp_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fp_uint1
+	x15, x16 = fiat_pasta_fp_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fp_uint1
+	x17, x18 = fiat_pasta_fp_addcarryx_u64(x8, x5, x16)
+	x19 := (uint64(x18) + x6)
+	var x20 uint64
+	_, x20 = bits.Mul64(x11, 0x992d30ecffffffff)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x20, 0x4000000000000000)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x20, 0x224698fc094cf91b)
+	var x26 uint64
+	var x27 uint64
+	x27, x26 = bits.Mul64(x20, 0x992d30ed00000001)
+	var x28 uint64
+	var x29 fiat_pasta_fp_uint1
+	x28, x29 = fiat_pasta_fp_addcarryx_u64(x27, x24, 0x0)
+	x30 := (uint64(x29) + x25)
+	var x32 fiat_pasta_fp_uint1
+	_, x32 = fiat_pasta_fp_addcarryx_u64(x11, x26, 0x0)
+	var x33 uint64
+	var x34 fiat_pasta_fp_uint1
+	x33, x34 = fiat_pasta_fp_addcarryx_u64(x13, x28, x32)
+	var x35 uint64
+	var x36 fiat_pasta_fp_uint1
+	x35, x36 = fiat_pasta_fp_addcarryx_u64(x15, x30, x34)
+	var x37 uint64
+	var x38 fiat_pasta_fp_uint1
+	x37, x38 = fiat_pasta_fp_addcarryx_u64(x17, x22, x36)
+	var x39 uint64
+	var x40 fiat_pasta_fp_uint1
+	x39, x40 = fiat_pasta_fp_addcarryx_u64(x19, x23, x38)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, arg2[3])
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, arg2[2])
+	var x45 uint64
+	var x46 uint64
+	x46, x45 = bits.Mul64(x1, arg2[1])
+	var x47 uint64
+	var x48 uint64
+	x48, x47 = bits.Mul64(x1, arg2[0])
+	var x49 uint64
+	var x50 fiat_pasta_fp_uint1
+	x49, x50 = fiat_pasta_fp_addcarryx_u64(x48, x45, 0x0)
+	var x51 uint64
+	var x52 fiat_pasta_fp_uint1
+	x51, x52 = fiat_pasta_fp_addcarryx_u64(x46, x43, x50)
+	var x53 uint64
+	var x54 fiat_pasta_fp_uint1
+	x53, x54 = fiat_pasta_fp_addcarryx_u64(x44, x41, x52)
+	x55 := (uint64(x54) + x42)
+	var x56 uint64
+	var x57 fiat_pasta_fp_uint1
+	x56, x57 = fiat_pasta_fp_addcarryx_u64(x33, x47, 0x0)
+	var x58 uint64
+	var x59 fiat_pasta_fp_uint1
+	x58, x59 = fiat_pasta_fp_addcarryx_u64(x35, x49, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fp_uint1
+	x60, x61 = fiat_pasta_fp_addcarryx_u64(x37, x51, x59)
+	var x62 uint64
+	var x63 fiat_pasta_fp_uint1
+	x62, x63 = fiat_pasta_fp_addcarryx_u64(x39, x53, x61)
+	var x64 uint64
+	var x65 fiat_pasta_fp_uint1
+	x64, x65 = fiat_pasta_fp_addcarryx_u64(uint64(x40), x55, x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x56, 0x992d30ecffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc094cf91b)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x992d30ed00000001)
+	var x74 uint64
+	var x75 fiat_pasta_fp_uint1
+	x74, x75 = fiat_pasta_fp_addcarryx_u64(x73, x70, 0x0)
+	x76 := (uint64(x75) + x71)
+	var x78 fiat_pasta_fp_uint1
+	_, x78 = fiat_pasta_fp_addcarryx_u64(x56, x72, 0x0)
+	var x79 uint64
+	var x80 fiat_pasta_fp_uint1
+	x79, x80 = fiat_pasta_fp_addcarryx_u64(x58, x74, x78)
+	var x81 uint64
+	var x82 fiat_pasta_fp_uint1
+	x81, x82 = fiat_pasta_fp_addcarryx_u64(x60, x76, x80)
+	var x83 uint64
+	var x84 fiat_pasta_fp_uint1
+	x83, x84 = fiat_pasta_fp_addcarryx_u64(x62, x68, x82)
+	var x85 uint64
+	var x86 fiat_pasta_fp_uint1
+	x85, x86 = fiat_pasta_fp_addcarryx_u64(x64, x69, x84)
+	x87 := (uint64(x86) + uint64(x65))
+	var x88 uint64
+	var x89 uint64
+	x89, x88 = bits.Mul64(x2, arg2[3])
+	var x90 uint64
+	var x91 uint64
+	x91, x90 = bits.Mul64(x2, arg2[2])
+	var x92 uint64
+	var x93 uint64
+	x93, x92 = bits.Mul64(x2, arg2[1])
+	var x94 uint64
+	var x95 uint64
+	x95, x94 = bits.Mul64(x2, arg2[0])
+	var x96 uint64
+	var x97 fiat_pasta_fp_uint1
+	x96, x97 = fiat_pasta_fp_addcarryx_u64(x95, x92, 0x0)
+	var x98 uint64
+	var x99 fiat_pasta_fp_uint1
+	x98, x99 = fiat_pasta_fp_addcarryx_u64(x93, x90, x97)
+	var x100 uint64
+	var x101 fiat_pasta_fp_uint1
+	x100, x101 = fiat_pasta_fp_addcarryx_u64(x91, x88, x99)
+	x102 := (uint64(x101) + x89)
+	var x103 uint64
+	var x104 fiat_pasta_fp_uint1
+	x103, x104 = fiat_pasta_fp_addcarryx_u64(x79, x94, 0x0)
+	var x105 uint64
+	var x106 fiat_pasta_fp_uint1
+	x105, x106 = fiat_pasta_fp_addcarryx_u64(x81, x96, x104)
+	var x107 uint64
+	var x108 fiat_pasta_fp_uint1
+	x107, x108 = fiat_pasta_fp_addcarryx_u64(x83, x98, x106)
+	var x109 uint64
+	var x110 fiat_pasta_fp_uint1
+	x109, x110 = fiat_pasta_fp_addcarryx_u64(x85, x100, x108)
+	var x111 uint64
+	var x112 fiat_pasta_fp_uint1
+	x111, x112 = fiat_pasta_fp_addcarryx_u64(x87, x102, x110)
+	var x113 uint64
+	_, x113 = bits.Mul64(x103, 0x992d30ecffffffff)
+	var x115 uint64
+	var x116 uint64
+	x116, x115 = bits.Mul64(x113, 0x4000000000000000)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x113, 0x224698fc094cf91b)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x113, 0x992d30ed00000001)
+	var x121 uint64
+	var x122 fiat_pasta_fp_uint1
+	x121, x122 = fiat_pasta_fp_addcarryx_u64(x120, x117, 0x0)
+	x123 := (uint64(x122) + x118)
+	var x125 fiat_pasta_fp_uint1
+	_, x125 = fiat_pasta_fp_addcarryx_u64(x103, x119, 0x0)
+	var x126 uint64
+	var x127 fiat_pasta_fp_uint1
+	x126, x127 = fiat_pasta_fp_addcarryx_u64(x105, x121, x125)
+	var x128 uint64
+	var x129 fiat_pasta_fp_uint1
+	x128, x129 = fiat_pasta_fp_addcarryx_u64(x107, x123, x127)
+	var x130 uint64
+	var x131 fiat_pasta_fp_uint1
+	x130, x131 = fiat_pasta_fp_addcarryx_u64(x109, x115, x129)
+	var x132 uint64
+	var x133 fiat_pasta_fp_uint1
+	x132, x133 = fiat_pasta_fp_addcarryx_u64(x111, x116, x131)
+	x134 := (uint64(x133) + uint64(x112))
+	var x135 uint64
+	var x136 uint64
+	x136, x135 = bits.Mul64(x3, arg2[3])
+	var x137 uint64
+	var x138 uint64
+	x138, x137 = bits.Mul64(x3, arg2[2])
+	var x139 uint64
+	var x140 uint64
+	x140, x139 = bits.Mul64(x3, arg2[1])
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x3, arg2[0])
+	var x143 uint64
+	var x144 fiat_pasta_fp_uint1
+	x143, x144 = fiat_pasta_fp_addcarryx_u64(x142, x139, 0x0)
+	var x145 uint64
+	var x146 fiat_pasta_fp_uint1
+	x145, x146 = fiat_pasta_fp_addcarryx_u64(x140, x137, x144)
+	var x147 uint64
+	var x148 fiat_pasta_fp_uint1
+	x147, x148 = fiat_pasta_fp_addcarryx_u64(x138, x135, x146)
+	x149 := (uint64(x148) + x136)
+	var x150 uint64
+	var x151 fiat_pasta_fp_uint1
+	x150, x151 = fiat_pasta_fp_addcarryx_u64(x126, x141, 0x0)
+	var x152 uint64
+	var x153 fiat_pasta_fp_uint1
+	x152, x153 = fiat_pasta_fp_addcarryx_u64(x128, x143, x151)
+	var x154 uint64
+	var x155 fiat_pasta_fp_uint1
+	x154, x155 = fiat_pasta_fp_addcarryx_u64(x130, x145, x153)
+	var x156 uint64
+	var x157 fiat_pasta_fp_uint1
+	x156, x157 = fiat_pasta_fp_addcarryx_u64(x132, x147, x155)
+	var x158 uint64
+	var x159 fiat_pasta_fp_uint1
+	x158, x159 = fiat_pasta_fp_addcarryx_u64(x134, x149, x157)
+	var x160 uint64
+	_, x160 = bits.Mul64(x150, 0x992d30ecffffffff)
+	var x162 uint64
+	var x163 uint64
+	x163, x162 = bits.Mul64(x160, 0x4000000000000000)
+	var x164 uint64
+	var x165 uint64
+	x165, x164 = bits.Mul64(x160, 0x224698fc094cf91b)
+	var x166 uint64
+	var x167 uint64
+	x167, x166 = bits.Mul64(x160, 0x992d30ed00000001)
+	var x168 uint64
+	var x169 fiat_pasta_fp_uint1
+	x168, x169 = fiat_pasta_fp_addcarryx_u64(x167, x164, 0x0)
+	x170 := (uint64(x169) + x165)
+	var x172 fiat_pasta_fp_uint1
+	_, x172 = fiat_pasta_fp_addcarryx_u64(x150, x166, 0x0)
+	var x173 uint64
+	var x174 fiat_pasta_fp_uint1
+	x173, x174 = fiat_pasta_fp_addcarryx_u64(x152, x168, x172)
+	var x175 uint64
+	var x176 fiat_pasta_fp_uint1
+	x175, x176 = fiat_pasta_fp_addcarryx_u64(x154, x170, x174)
+	var x177 uint64
+	var x178 fiat_pasta_fp_uint1
+	x177, x178 = fiat_pasta_fp_addcarryx_u64(x156, x162, x176)
+	var x179 uint64
+	var x180 fiat_pasta_fp_uint1
+	x179, x180 = fiat_pasta_fp_addcarryx_u64(x158, x163, x178)
+	x181 := (uint64(x180) + uint64(x159))
+	var x182 uint64
+	var x183 fiat_pasta_fp_uint1
+	x182, x183 = fiat_pasta_fp_subborrowx_u64(x173, 0x992d30ed00000001, 0x0)
+	var x184 uint64
+	var x185 fiat_pasta_fp_uint1
+	x184, x185 = fiat_pasta_fp_subborrowx_u64(x175, 0x224698fc094cf91b, x183)
+	var x186 uint64
+	var x187 fiat_pasta_fp_uint1
+	x186, x187 = fiat_pasta_fp_subborrowx_u64(x177, uint64(0x0), x185)
+	var x188 uint64
+	var x189 fiat_pasta_fp_uint1
+	x188, x189 = fiat_pasta_fp_subborrowx_u64(x179, 0x4000000000000000, x187)
+	var x191 fiat_pasta_fp_uint1
+	_, x191 = fiat_pasta_fp_subborrowx_u64(x181, uint64(0x0), x189)
+	var x192 uint64
+	fiat_pasta_fp_cmovznz_u64(&x192, x191, x182, x173)
+	var x193 uint64
+	fiat_pasta_fp_cmovznz_u64(&x193, x191, x184, x175)
+	var x194 uint64
+	fiat_pasta_fp_cmovznz_u64(&x194, x191, x186, x177)
+	var x195 uint64
+	fiat_pasta_fp_cmovznz_u64(&x195, x191, x188, x179)
+	out1[0] = x192
+	out1[1] = x193
+	out1[2] = x194
+	out1[3] = x195
+}
+
+// The function fiat_pasta_fp_square squares a field element in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_square(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, arg1[3])
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, arg1[2])
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, arg1[1])
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, arg1[0])
+	var x13 uint64
+	var x14 fiat_pasta_fp_uint1
+	x13, x14 = fiat_pasta_fp_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fp_uint1
+	x15, x16 = fiat_pasta_fp_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fp_uint1
+	x17, x18 = fiat_pasta_fp_addcarryx_u64(x8, x5, x16)
+	x19 := (uint64(x18) + x6)
+	var x20 uint64
+	_, x20 = bits.Mul64(x11, 0x992d30ecffffffff)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x20, 0x4000000000000000)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x20, 0x224698fc094cf91b)
+	var x26 uint64
+	var x27 uint64
+	x27, x26 = bits.Mul64(x20, 0x992d30ed00000001)
+	var x28 uint64
+	var x29 fiat_pasta_fp_uint1
+	x28, x29 = fiat_pasta_fp_addcarryx_u64(x27, x24, 0x0)
+	x30 := (uint64(x29) + x25)
+	var x32 fiat_pasta_fp_uint1
+	_, x32 = fiat_pasta_fp_addcarryx_u64(x11, x26, 0x0)
+	var x33 uint64
+	var x34 fiat_pasta_fp_uint1
+	x33, x34 = fiat_pasta_fp_addcarryx_u64(x13, x28, x32)
+	var x35 uint64
+	var x36 fiat_pasta_fp_uint1
+	x35, x36 = fiat_pasta_fp_addcarryx_u64(x15, x30, x34)
+	var x37 uint64
+	var x38 fiat_pasta_fp_uint1
+	x37, x38 = fiat_pasta_fp_addcarryx_u64(x17, x22, x36)
+	var x39 uint64
+	var x40 fiat_pasta_fp_uint1
+	x39, x40 = fiat_pasta_fp_addcarryx_u64(x19, x23, x38)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, arg1[3])
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, arg1[2])
+	var x45 uint64
+	var x46 uint64
+	x46, x45 = bits.Mul64(x1, arg1[1])
+	var x47 uint64
+	var x48 uint64
+	x48, x47 = bits.Mul64(x1, arg1[0])
+	var x49 uint64
+	var x50 fiat_pasta_fp_uint1
+	x49, x50 = fiat_pasta_fp_addcarryx_u64(x48, x45, 0x0)
+	var x51 uint64
+	var x52 fiat_pasta_fp_uint1
+	x51, x52 = fiat_pasta_fp_addcarryx_u64(x46, x43, x50)
+	var x53 uint64
+	var x54 fiat_pasta_fp_uint1
+	x53, x54 = fiat_pasta_fp_addcarryx_u64(x44, x41, x52)
+	x55 := (uint64(x54) + x42)
+	var x56 uint64
+	var x57 fiat_pasta_fp_uint1
+	x56, x57 = fiat_pasta_fp_addcarryx_u64(x33, x47, 0x0)
+	var x58 uint64
+	var x59 fiat_pasta_fp_uint1
+	x58, x59 = fiat_pasta_fp_addcarryx_u64(x35, x49, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fp_uint1
+	x60, x61 = fiat_pasta_fp_addcarryx_u64(x37, x51, x59)
+	var x62 uint64
+	var x63 fiat_pasta_fp_uint1
+	x62, x63 = fiat_pasta_fp_addcarryx_u64(x39, x53, x61)
+	var x64 uint64
+	var x65 fiat_pasta_fp_uint1
+	x64, x65 = fiat_pasta_fp_addcarryx_u64(uint64(x40), x55, x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x56, 0x992d30ecffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc094cf91b)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x992d30ed00000001)
+	var x74 uint64
+	var x75 fiat_pasta_fp_uint1
+	x74, x75 = fiat_pasta_fp_addcarryx_u64(x73, x70, 0x0)
+	x76 := (uint64(x75) + x71)
+	var x78 fiat_pasta_fp_uint1
+	_, x78 = fiat_pasta_fp_addcarryx_u64(x56, x72, 0x0)
+	var x79 uint64
+	var x80 fiat_pasta_fp_uint1
+	x79, x80 = fiat_pasta_fp_addcarryx_u64(x58, x74, x78)
+	var x81 uint64
+	var x82 fiat_pasta_fp_uint1
+	x81, x82 = fiat_pasta_fp_addcarryx_u64(x60, x76, x80)
+	var x83 uint64
+	var x84 fiat_pasta_fp_uint1
+	x83, x84 = fiat_pasta_fp_addcarryx_u64(x62, x68, x82)
+	var x85 uint64
+	var x86 fiat_pasta_fp_uint1
+	x85, x86 = fiat_pasta_fp_addcarryx_u64(x64, x69, x84)
+	x87 := (uint64(x86) + uint64(x65))
+	var x88 uint64
+	var x89 uint64
+	x89, x88 = bits.Mul64(x2, arg1[3])
+	var x90 uint64
+	var x91 uint64
+	x91, x90 = bits.Mul64(x2, arg1[2])
+	var x92 uint64
+	var x93 uint64
+	x93, x92 = bits.Mul64(x2, arg1[1])
+	var x94 uint64
+	var x95 uint64
+	x95, x94 = bits.Mul64(x2, arg1[0])
+	var x96 uint64
+	var x97 fiat_pasta_fp_uint1
+	x96, x97 = fiat_pasta_fp_addcarryx_u64(x95, x92, 0x0)
+	var x98 uint64
+	var x99 fiat_pasta_fp_uint1
+	x98, x99 = fiat_pasta_fp_addcarryx_u64(x93, x90, x97)
+	var x100 uint64
+	var x101 fiat_pasta_fp_uint1
+	x100, x101 = fiat_pasta_fp_addcarryx_u64(x91, x88, x99)
+	x102 := (uint64(x101) + x89)
+	var x103 uint64
+	var x104 fiat_pasta_fp_uint1
+	x103, x104 = fiat_pasta_fp_addcarryx_u64(x79, x94, 0x0)
+	var x105 uint64
+	var x106 fiat_pasta_fp_uint1
+	x105, x106 = fiat_pasta_fp_addcarryx_u64(x81, x96, x104)
+	var x107 uint64
+	var x108 fiat_pasta_fp_uint1
+	x107, x108 = fiat_pasta_fp_addcarryx_u64(x83, x98, x106)
+	var x109 uint64
+	var x110 fiat_pasta_fp_uint1
+	x109, x110 = fiat_pasta_fp_addcarryx_u64(x85, x100, x108)
+	var x111 uint64
+	var x112 fiat_pasta_fp_uint1
+	x111, x112 = fiat_pasta_fp_addcarryx_u64(x87, x102, x110)
+	var x113 uint64
+	_, x113 = bits.Mul64(x103, 0x992d30ecffffffff)
+	var x115 uint64
+	var x116 uint64
+	x116, x115 = bits.Mul64(x113, 0x4000000000000000)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x113, 0x224698fc094cf91b)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x113, 0x992d30ed00000001)
+	var x121 uint64
+	var x122 fiat_pasta_fp_uint1
+	x121, x122 = fiat_pasta_fp_addcarryx_u64(x120, x117, 0x0)
+	x123 := (uint64(x122) + x118)
+	var x125 fiat_pasta_fp_uint1
+	_, x125 = fiat_pasta_fp_addcarryx_u64(x103, x119, 0x0)
+	var x126 uint64
+	var x127 fiat_pasta_fp_uint1
+	x126, x127 = fiat_pasta_fp_addcarryx_u64(x105, x121, x125)
+	var x128 uint64
+	var x129 fiat_pasta_fp_uint1
+	x128, x129 = fiat_pasta_fp_addcarryx_u64(x107, x123, x127)
+	var x130 uint64
+	var x131 fiat_pasta_fp_uint1
+	x130, x131 = fiat_pasta_fp_addcarryx_u64(x109, x115, x129)
+	var x132 uint64
+	var x133 fiat_pasta_fp_uint1
+	x132, x133 = fiat_pasta_fp_addcarryx_u64(x111, x116, x131)
+	x134 := (uint64(x133) + uint64(x112))
+	var x135 uint64
+	var x136 uint64
+	x136, x135 = bits.Mul64(x3, arg1[3])
+	var x137 uint64
+	var x138 uint64
+	x138, x137 = bits.Mul64(x3, arg1[2])
+	var x139 uint64
+	var x140 uint64
+	x140, x139 = bits.Mul64(x3, arg1[1])
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x3, arg1[0])
+	var x143 uint64
+	var x144 fiat_pasta_fp_uint1
+	x143, x144 = fiat_pasta_fp_addcarryx_u64(x142, x139, 0x0)
+	var x145 uint64
+	var x146 fiat_pasta_fp_uint1
+	x145, x146 = fiat_pasta_fp_addcarryx_u64(x140, x137, x144)
+	var x147 uint64
+	var x148 fiat_pasta_fp_uint1
+	x147, x148 = fiat_pasta_fp_addcarryx_u64(x138, x135, x146)
+	x149 := (uint64(x148) + x136)
+	var x150 uint64
+	var x151 fiat_pasta_fp_uint1
+	x150, x151 = fiat_pasta_fp_addcarryx_u64(x126, x141, 0x0)
+	var x152 uint64
+	var x153 fiat_pasta_fp_uint1
+	x152, x153 = fiat_pasta_fp_addcarryx_u64(x128, x143, x151)
+	var x154 uint64
+	var x155 fiat_pasta_fp_uint1
+	x154, x155 = fiat_pasta_fp_addcarryx_u64(x130, x145, x153)
+	var x156 uint64
+	var x157 fiat_pasta_fp_uint1
+	x156, x157 = fiat_pasta_fp_addcarryx_u64(x132, x147, x155)
+	var x158 uint64
+	var x159 fiat_pasta_fp_uint1
+	x158, x159 = fiat_pasta_fp_addcarryx_u64(x134, x149, x157)
+	var x160 uint64
+	_, x160 = bits.Mul64(x150, 0x992d30ecffffffff)
+	var x162 uint64
+	var x163 uint64
+	x163, x162 = bits.Mul64(x160, 0x4000000000000000)
+	var x164 uint64
+	var x165 uint64
+	x165, x164 = bits.Mul64(x160, 0x224698fc094cf91b)
+	var x166 uint64
+	var x167 uint64
+	x167, x166 = bits.Mul64(x160, 0x992d30ed00000001)
+	var x168 uint64
+	var x169 fiat_pasta_fp_uint1
+	x168, x169 = fiat_pasta_fp_addcarryx_u64(x167, x164, 0x0)
+	x170 := (uint64(x169) + x165)
+	var x172 fiat_pasta_fp_uint1
+	_, x172 = fiat_pasta_fp_addcarryx_u64(x150, x166, 0x0)
+	var x173 uint64
+	var x174 fiat_pasta_fp_uint1
+	x173, x174 = fiat_pasta_fp_addcarryx_u64(x152, x168, x172)
+	var x175 uint64
+	var x176 fiat_pasta_fp_uint1
+	x175, x176 = fiat_pasta_fp_addcarryx_u64(x154, x170, x174)
+	var x177 uint64
+	var x178 fiat_pasta_fp_uint1
+	x177, x178 = fiat_pasta_fp_addcarryx_u64(x156, x162, x176)
+	var x179 uint64
+	var x180 fiat_pasta_fp_uint1
+	x179, x180 = fiat_pasta_fp_addcarryx_u64(x158, x163, x178)
+	x181 := (uint64(x180) + uint64(x159))
+	var x182 uint64
+	var x183 fiat_pasta_fp_uint1
+	x182, x183 = fiat_pasta_fp_subborrowx_u64(x173, 0x992d30ed00000001, 0x0)
+	var x184 uint64
+	var x185 fiat_pasta_fp_uint1
+	x184, x185 = fiat_pasta_fp_subborrowx_u64(x175, 0x224698fc094cf91b, x183)
+	var x186 uint64
+	var x187 fiat_pasta_fp_uint1
+	x186, x187 = fiat_pasta_fp_subborrowx_u64(x177, uint64(0x0), x185)
+	var x188 uint64
+	var x189 fiat_pasta_fp_uint1
+	x188, x189 = fiat_pasta_fp_subborrowx_u64(x179, 0x4000000000000000, x187)
+	var x191 fiat_pasta_fp_uint1
+	_, x191 = fiat_pasta_fp_subborrowx_u64(x181, uint64(0x0), x189)
+	var x192 uint64
+	fiat_pasta_fp_cmovznz_u64(&x192, x191, x182, x173)
+	var x193 uint64
+	fiat_pasta_fp_cmovznz_u64(&x193, x191, x184, x175)
+	var x194 uint64
+	fiat_pasta_fp_cmovznz_u64(&x194, x191, x186, x177)
+	var x195 uint64
+	fiat_pasta_fp_cmovznz_u64(&x195, x191, x188, x179)
+	out1[0] = x192
+	out1[1] = x193
+	out1[2] = x194
+	out1[3] = x195
+}
+
+// The function fiat_pasta_fp_add adds two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_add(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element, arg2 *fiat_pasta_fp_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fp_uint1
+	x1, x2 = fiat_pasta_fp_addcarryx_u64(arg1[0], arg2[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fp_uint1
+	x3, x4 = fiat_pasta_fp_addcarryx_u64(arg1[1], arg2[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fp_uint1
+	x5, x6 = fiat_pasta_fp_addcarryx_u64(arg1[2], arg2[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fp_uint1
+	x7, x8 = fiat_pasta_fp_addcarryx_u64(arg1[3], arg2[3], x6)
+	var x9 uint64
+	var x10 fiat_pasta_fp_uint1
+	x9, x10 = fiat_pasta_fp_subborrowx_u64(x1, 0x992d30ed00000001, 0x0)
+	var x11 uint64
+	var x12 fiat_pasta_fp_uint1
+	x11, x12 = fiat_pasta_fp_subborrowx_u64(x3, 0x224698fc094cf91b, x10)
+	var x13 uint64
+	var x14 fiat_pasta_fp_uint1
+	x13, x14 = fiat_pasta_fp_subborrowx_u64(x5, uint64(0x0), x12)
+	var x15 uint64
+	var x16 fiat_pasta_fp_uint1
+	x15, x16 = fiat_pasta_fp_subborrowx_u64(x7, 0x4000000000000000, x14)
+	var x18 fiat_pasta_fp_uint1
+	_, x18 = fiat_pasta_fp_subborrowx_u64(uint64(x8), uint64(0x0), x16)
+	var x19 uint64
+	fiat_pasta_fp_cmovznz_u64(&x19, x18, x9, x1)
+	var x20 uint64
+	fiat_pasta_fp_cmovznz_u64(&x20, x18, x11, x3)
+	var x21 uint64
+	fiat_pasta_fp_cmovznz_u64(&x21, x18, x13, x5)
+	var x22 uint64
+	fiat_pasta_fp_cmovznz_u64(&x22, x18, x15, x7)
+	out1[0] = x19
+	out1[1] = x20
+	out1[2] = x21
+	out1[3] = x22
+}
+
+// The function fiat_pasta_fp_sub subtracts two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_sub(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element, arg2 *fiat_pasta_fp_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fp_uint1
+	x1, x2 = fiat_pasta_fp_subborrowx_u64(arg1[0], arg2[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fp_uint1
+	x3, x4 = fiat_pasta_fp_subborrowx_u64(arg1[1], arg2[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fp_uint1
+	x5, x6 = fiat_pasta_fp_subborrowx_u64(arg1[2], arg2[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fp_uint1
+	x7, x8 = fiat_pasta_fp_subborrowx_u64(arg1[3], arg2[3], x6)
+	var x9 uint64
+	fiat_pasta_fp_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
+	var x10 uint64
+	var x11 fiat_pasta_fp_uint1
+	x10, x11 = fiat_pasta_fp_addcarryx_u64(x1, (x9 & 0x992d30ed00000001), 0x0)
+	var x12 uint64
+	var x13 fiat_pasta_fp_uint1
+	x12, x13 = fiat_pasta_fp_addcarryx_u64(x3, (x9 & 0x224698fc094cf91b), x11)
+	var x14 uint64
+	var x15 fiat_pasta_fp_uint1
+	x14, x15 = fiat_pasta_fp_addcarryx_u64(x5, uint64(0x0), x13)
+	var x16 uint64
+	x16, _ = fiat_pasta_fp_addcarryx_u64(x7, (x9 & 0x4000000000000000), x15)
+	out1[0] = x10
+	out1[1] = x12
+	out1[2] = x14
+	out1[3] = x16
+}
+
+// The function fiat_pasta_fp_opp negates a field element in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_opp(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fp_uint1
+	x1, x2 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), arg1[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fp_uint1
+	x3, x4 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), arg1[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fp_uint1
+	x5, x6 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), arg1[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fp_uint1
+	x7, x8 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), arg1[3], x6)
+	var x9 uint64
+	fiat_pasta_fp_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
+	var x10 uint64
+	var x11 fiat_pasta_fp_uint1
+	x10, x11 = fiat_pasta_fp_addcarryx_u64(x1, (x9 & 0x992d30ed00000001), 0x0)
+	var x12 uint64
+	var x13 fiat_pasta_fp_uint1
+	x12, x13 = fiat_pasta_fp_addcarryx_u64(x3, (x9 & 0x224698fc094cf91b), x11)
+	var x14 uint64
+	var x15 fiat_pasta_fp_uint1
+	x14, x15 = fiat_pasta_fp_addcarryx_u64(x5, uint64(0x0), x13)
+	var x16 uint64
+	x16, _ = fiat_pasta_fp_addcarryx_u64(x7, (x9 & 0x4000000000000000), x15)
+	out1[0] = x10
+	out1[1] = x12
+	out1[2] = x14
+	out1[3] = x16
+}
+
+// The function fiat_pasta_fp_from_montgomery translates a field element out of the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_from_montgomery(out1 *fiat_pasta_fp_non_montgomery_domain_field_element, arg1 *fiat_pasta_fp_montgomery_domain_field_element) {
+	x1 := arg1[0]
+	var x2 uint64
+	_, x2 = bits.Mul64(x1, 0x992d30ecffffffff)
+	var x4 uint64
+	var x5 uint64
+	x5, x4 = bits.Mul64(x2, 0x4000000000000000)
+	var x6 uint64
+	var x7 uint64
+	x7, x6 = bits.Mul64(x2, 0x224698fc094cf91b)
+	var x8 uint64
+	var x9 uint64
+	x9, x8 = bits.Mul64(x2, 0x992d30ed00000001)
+	var x10 uint64
+	var x11 fiat_pasta_fp_uint1
+	x10, x11 = fiat_pasta_fp_addcarryx_u64(x9, x6, 0x0)
+	var x13 fiat_pasta_fp_uint1
+	_, x13 = fiat_pasta_fp_addcarryx_u64(x1, x8, 0x0)
+	var x14 uint64
+	var x15 fiat_pasta_fp_uint1
+	x14, x15 = fiat_pasta_fp_addcarryx_u64(uint64(0x0), x10, x13)
+	var x16 uint64
+	var x17 fiat_pasta_fp_uint1
+	x16, x17 = fiat_pasta_fp_addcarryx_u64(x14, arg1[1], 0x0)
+	var x18 uint64
+	_, x18 = bits.Mul64(x16, 0x992d30ecffffffff)
+	var x20 uint64
+	var x21 uint64
+	x21, x20 = bits.Mul64(x18, 0x4000000000000000)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x18, 0x224698fc094cf91b)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x18, 0x992d30ed00000001)
+	var x26 uint64
+	var x27 fiat_pasta_fp_uint1
+	x26, x27 = fiat_pasta_fp_addcarryx_u64(x25, x22, 0x0)
+	var x29 fiat_pasta_fp_uint1
+	_, x29 = fiat_pasta_fp_addcarryx_u64(x16, x24, 0x0)
+	var x30 uint64
+	var x31 fiat_pasta_fp_uint1
+	x30, x31 = fiat_pasta_fp_addcarryx_u64((uint64(x17) + (uint64(x15) + (uint64(x11) + x7))), x26, x29)
+	var x32 uint64
+	var x33 fiat_pasta_fp_uint1
+	x32, x33 = fiat_pasta_fp_addcarryx_u64(x4, (uint64(x27) + x23), x31)
+	var x34 uint64
+	var x35 fiat_pasta_fp_uint1
+	x34, x35 = fiat_pasta_fp_addcarryx_u64(x5, x20, x33)
+	var x36 uint64
+	var x37 fiat_pasta_fp_uint1
+	x36, x37 = fiat_pasta_fp_addcarryx_u64(x30, arg1[2], 0x0)
+	var x38 uint64
+	var x39 fiat_pasta_fp_uint1
+	x38, x39 = fiat_pasta_fp_addcarryx_u64(x32, uint64(0x0), x37)
+	var x40 uint64
+	var x41 fiat_pasta_fp_uint1
+	x40, x41 = fiat_pasta_fp_addcarryx_u64(x34, uint64(0x0), x39)
+	var x42 uint64
+	_, x42 = bits.Mul64(x36, 0x992d30ecffffffff)
+	var x44 uint64
+	var x45 uint64
+	x45, x44 = bits.Mul64(x42, 0x4000000000000000)
+	var x46 uint64
+	var x47 uint64
+	x47, x46 = bits.Mul64(x42, 0x224698fc094cf91b)
+	var x48 uint64
+	var x49 uint64
+	x49, x48 = bits.Mul64(x42, 0x992d30ed00000001)
+	var x50 uint64
+	var x51 fiat_pasta_fp_uint1
+	x50, x51 = fiat_pasta_fp_addcarryx_u64(x49, x46, 0x0)
+	var x53 fiat_pasta_fp_uint1
+	_, x53 = fiat_pasta_fp_addcarryx_u64(x36, x48, 0x0)
+	var x54 uint64
+	var x55 fiat_pasta_fp_uint1
+	x54, x55 = fiat_pasta_fp_addcarryx_u64(x38, x50, x53)
+	var x56 uint64
+	var x57 fiat_pasta_fp_uint1
+	x56, x57 = fiat_pasta_fp_addcarryx_u64(x40, (uint64(x51) + x47), x55)
+	var x58 uint64
+	var x59 fiat_pasta_fp_uint1
+	x58, x59 = fiat_pasta_fp_addcarryx_u64((uint64(x41) + (uint64(x35) + x21)), x44, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fp_uint1
+	x60, x61 = fiat_pasta_fp_addcarryx_u64(x54, arg1[3], 0x0)
+	var x62 uint64
+	var x63 fiat_pasta_fp_uint1
+	x62, x63 = fiat_pasta_fp_addcarryx_u64(x56, uint64(0x0), x61)
+	var x64 uint64
+	var x65 fiat_pasta_fp_uint1
+	x64, x65 = fiat_pasta_fp_addcarryx_u64(x58, uint64(0x0), x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x60, 0x992d30ecffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc094cf91b)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x992d30ed00000001)
+	var x74 uint64
+	var x75 fiat_pasta_fp_uint1
+	x74, x75 = fiat_pasta_fp_addcarryx_u64(x73, x70, 0x0)
+	var x77 fiat_pasta_fp_uint1
+	_, x77 = fiat_pasta_fp_addcarryx_u64(x60, x72, 0x0)
+	var x78 uint64
+	var x79 fiat_pasta_fp_uint1
+	x78, x79 = fiat_pasta_fp_addcarryx_u64(x62, x74, x77)
+	var x80 uint64
+	var x81 fiat_pasta_fp_uint1
+	x80, x81 = fiat_pasta_fp_addcarryx_u64(x64, (uint64(x75) + x71), x79)
+	var x82 uint64
+	var x83 fiat_pasta_fp_uint1
+	x82, x83 = fiat_pasta_fp_addcarryx_u64((uint64(x65) + (uint64(x59) + x45)), x68, x81)
+	x84 := (uint64(x83) + x69)
+	var x85 uint64
+	var x86 fiat_pasta_fp_uint1
+	x85, x86 = fiat_pasta_fp_subborrowx_u64(x78, 0x992d30ed00000001, 0x0)
+	var x87 uint64
+	var x88 fiat_pasta_fp_uint1
+	x87, x88 = fiat_pasta_fp_subborrowx_u64(x80, 0x224698fc094cf91b, x86)
+	var x89 uint64
+	var x90 fiat_pasta_fp_uint1
+	x89, x90 = fiat_pasta_fp_subborrowx_u64(x82, uint64(0x0), x88)
+	var x91 uint64
+	var x92 fiat_pasta_fp_uint1
+	x91, x92 = fiat_pasta_fp_subborrowx_u64(x84, 0x4000000000000000, x90)
+	var x94 fiat_pasta_fp_uint1
+	_, x94 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), uint64(0x0), x92)
+	var x95 uint64
+	fiat_pasta_fp_cmovznz_u64(&x95, x94, x85, x78)
+	var x96 uint64
+	fiat_pasta_fp_cmovznz_u64(&x96, x94, x87, x80)
+	var x97 uint64
+	fiat_pasta_fp_cmovznz_u64(&x97, x94, x89, x82)
+	var x98 uint64
+	fiat_pasta_fp_cmovznz_u64(&x98, x94, x91, x84)
+	out1[0] = x95
+	out1[1] = x96
+	out1[2] = x97
+	out1[3] = x98
+}
+
+// The function fiat_pasta_fp_to_montgomery translates a field element into the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = eval arg1 mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fp_to_montgomery(out1 *fiat_pasta_fp_montgomery_domain_field_element, arg1 *fiat_pasta_fp_non_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, 0x96d41af7b9cb714)
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, 0x7797a99bc3c95d18)
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, 0xd7d30dbd8b0de0e7)
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, 0x8c78ecb30000000f)
+	var x13 uint64
+	var x14 fiat_pasta_fp_uint1
+	x13, x14 = fiat_pasta_fp_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fp_uint1
+	x15, x16 = fiat_pasta_fp_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fp_uint1
+	x17, x18 = fiat_pasta_fp_addcarryx_u64(x8, x5, x16)
+	var x19 uint64
+	_, x19 = bits.Mul64(x11, 0x992d30ecffffffff)
+	var x21 uint64
+	var x22 uint64
+	x22, x21 = bits.Mul64(x19, 0x4000000000000000)
+	var x23 uint64
+	var x24 uint64
+	x24, x23 = bits.Mul64(x19, 0x224698fc094cf91b)
+	var x25 uint64
+	var x26 uint64
+	x26, x25 = bits.Mul64(x19, 0x992d30ed00000001)
+	var x27 uint64
+	var x28 fiat_pasta_fp_uint1
+	x27, x28 = fiat_pasta_fp_addcarryx_u64(x26, x23, 0x0)
+	var x30 fiat_pasta_fp_uint1
+	_, x30 = fiat_pasta_fp_addcarryx_u64(x11, x25, 0x0)
+	var x31 uint64
+	var x32 fiat_pasta_fp_uint1
+	x31, x32 = fiat_pasta_fp_addcarryx_u64(x13, x27, x30)
+	var x33 uint64
+	var x34 fiat_pasta_fp_uint1
+	x33, x34 = fiat_pasta_fp_addcarryx_u64(x15, (uint64(x28) + x24), x32)
+	var x35 uint64
+	var x36 fiat_pasta_fp_uint1
+	x35, x36 = fiat_pasta_fp_addcarryx_u64(x17, x21, x34)
+	var x37 uint64
+	var x38 uint64
+	x38, x37 = bits.Mul64(x1, 0x96d41af7b9cb714)
+	var x39 uint64
+	var x40 uint64
+	x40, x39 = bits.Mul64(x1, 0x7797a99bc3c95d18)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, 0xd7d30dbd8b0de0e7)
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, 0x8c78ecb30000000f)
+	var x45 uint64
+	var x46 fiat_pasta_fp_uint1
+	x45, x46 = fiat_pasta_fp_addcarryx_u64(x44, x41, 0x0)
+	var x47 uint64
+	var x48 fiat_pasta_fp_uint1
+	x47, x48 = fiat_pasta_fp_addcarryx_u64(x42, x39, x46)
+	var x49 uint64
+	var x50 fiat_pasta_fp_uint1
+	x49, x50 = fiat_pasta_fp_addcarryx_u64(x40, x37, x48)
+	var x51 uint64
+	var x52 fiat_pasta_fp_uint1
+	x51, x52 = fiat_pasta_fp_addcarryx_u64(x31, x43, 0x0)
+	var x53 uint64
+	var x54 fiat_pasta_fp_uint1
+	x53, x54 = fiat_pasta_fp_addcarryx_u64(x33, x45, x52)
+	var x55 uint64
+	var x56 fiat_pasta_fp_uint1
+	x55, x56 = fiat_pasta_fp_addcarryx_u64(x35, x47, x54)
+	var x57 uint64
+	var x58 fiat_pasta_fp_uint1
+	x57, x58 = fiat_pasta_fp_addcarryx_u64(((uint64(x36) + (uint64(x18) + x6)) + x22), x49, x56)
+	var x59 uint64
+	_, x59 = bits.Mul64(x51, 0x992d30ecffffffff)
+	var x61 uint64
+	var x62 uint64
+	x62, x61 = bits.Mul64(x59, 0x4000000000000000)
+	var x63 uint64
+	var x64 uint64
+	x64, x63 = bits.Mul64(x59, 0x224698fc094cf91b)
+	var x65 uint64
+	var x66 uint64
+	x66, x65 = bits.Mul64(x59, 0x992d30ed00000001)
+	var x67 uint64
+	var x68 fiat_pasta_fp_uint1
+	x67, x68 = fiat_pasta_fp_addcarryx_u64(x66, x63, 0x0)
+	var x70 fiat_pasta_fp_uint1
+	_, x70 = fiat_pasta_fp_addcarryx_u64(x51, x65, 0x0)
+	var x71 uint64
+	var x72 fiat_pasta_fp_uint1
+	x71, x72 = fiat_pasta_fp_addcarryx_u64(x53, x67, x70)
+	var x73 uint64
+	var x74 fiat_pasta_fp_uint1
+	x73, x74 = fiat_pasta_fp_addcarryx_u64(x55, (uint64(x68) + x64), x72)
+	var x75 uint64
+	var x76 fiat_pasta_fp_uint1
+	x75, x76 = fiat_pasta_fp_addcarryx_u64(x57, x61, x74)
+	var x77 uint64
+	var x78 uint64
+	x78, x77 = bits.Mul64(x2, 0x96d41af7b9cb714)
+	var x79 uint64
+	var x80 uint64
+	x80, x79 = bits.Mul64(x2, 0x7797a99bc3c95d18)
+	var x81 uint64
+	var x82 uint64
+	x82, x81 = bits.Mul64(x2, 0xd7d30dbd8b0de0e7)
+	var x83 uint64
+	var x84 uint64
+	x84, x83 = bits.Mul64(x2, 0x8c78ecb30000000f)
+	var x85 uint64
+	var x86 fiat_pasta_fp_uint1
+	x85, x86 = fiat_pasta_fp_addcarryx_u64(x84, x81, 0x0)
+	var x87 uint64
+	var x88 fiat_pasta_fp_uint1
+	x87, x88 = fiat_pasta_fp_addcarryx_u64(x82, x79, x86)
+	var x89 uint64
+	var x90 fiat_pasta_fp_uint1
+	x89, x90 = fiat_pasta_fp_addcarryx_u64(x80, x77, x88)
+	var x91 uint64
+	var x92 fiat_pasta_fp_uint1
+	x91, x92 = fiat_pasta_fp_addcarryx_u64(x71, x83, 0x0)
+	var x93 uint64
+	var x94 fiat_pasta_fp_uint1
+	x93, x94 = fiat_pasta_fp_addcarryx_u64(x73, x85, x92)
+	var x95 uint64
+	var x96 fiat_pasta_fp_uint1
+	x95, x96 = fiat_pasta_fp_addcarryx_u64(x75, x87, x94)
+	var x97 uint64
+	var x98 fiat_pasta_fp_uint1
+	x97, x98 = fiat_pasta_fp_addcarryx_u64(((uint64(x76) + (uint64(x58) + (uint64(x50) + x38))) + x62), x89, x96)
+	var x99 uint64
+	_, x99 = bits.Mul64(x91, 0x992d30ecffffffff)
+	var x101 uint64
+	var x102 uint64
+	x102, x101 = bits.Mul64(x99, 0x4000000000000000)
+	var x103 uint64
+	var x104 uint64
+	x104, x103 = bits.Mul64(x99, 0x224698fc094cf91b)
+	var x105 uint64
+	var x106 uint64
+	x106, x105 = bits.Mul64(x99, 0x992d30ed00000001)
+	var x107 uint64
+	var x108 fiat_pasta_fp_uint1
+	x107, x108 = fiat_pasta_fp_addcarryx_u64(x106, x103, 0x0)
+	var x110 fiat_pasta_fp_uint1
+	_, x110 = fiat_pasta_fp_addcarryx_u64(x91, x105, 0x0)
+	var x111 uint64
+	var x112 fiat_pasta_fp_uint1
+	x111, x112 = fiat_pasta_fp_addcarryx_u64(x93, x107, x110)
+	var x113 uint64
+	var x114 fiat_pasta_fp_uint1
+	x113, x114 = fiat_pasta_fp_addcarryx_u64(x95, (uint64(x108) + x104), x112)
+	var x115 uint64
+	var x116 fiat_pasta_fp_uint1
+	x115, x116 = fiat_pasta_fp_addcarryx_u64(x97, x101, x114)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x3, 0x96d41af7b9cb714)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x3, 0x7797a99bc3c95d18)
+	var x121 uint64
+	var x122 uint64
+	x122, x121 = bits.Mul64(x3, 0xd7d30dbd8b0de0e7)
+	var x123 uint64
+	var x124 uint64
+	x124, x123 = bits.Mul64(x3, 0x8c78ecb30000000f)
+	var x125 uint64
+	var x126 fiat_pasta_fp_uint1
+	x125, x126 = fiat_pasta_fp_addcarryx_u64(x124, x121, 0x0)
+	var x127 uint64
+	var x128 fiat_pasta_fp_uint1
+	x127, x128 = fiat_pasta_fp_addcarryx_u64(x122, x119, x126)
+	var x129 uint64
+	var x130 fiat_pasta_fp_uint1
+	x129, x130 = fiat_pasta_fp_addcarryx_u64(x120, x117, x128)
+	var x131 uint64
+	var x132 fiat_pasta_fp_uint1
+	x131, x132 = fiat_pasta_fp_addcarryx_u64(x111, x123, 0x0)
+	var x133 uint64
+	var x134 fiat_pasta_fp_uint1
+	x133, x134 = fiat_pasta_fp_addcarryx_u64(x113, x125, x132)
+	var x135 uint64
+	var x136 fiat_pasta_fp_uint1
+	x135, x136 = fiat_pasta_fp_addcarryx_u64(x115, x127, x134)
+	var x137 uint64
+	var x138 fiat_pasta_fp_uint1
+	x137, x138 = fiat_pasta_fp_addcarryx_u64(((uint64(x116) + (uint64(x98) + (uint64(x90) + x78))) + x102), x129, x136)
+	var x139 uint64
+	_, x139 = bits.Mul64(x131, 0x992d30ecffffffff)
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x139, 0x4000000000000000)
+	var x143 uint64
+	var x144 uint64
+	x144, x143 = bits.Mul64(x139, 0x224698fc094cf91b)
+	var x145 uint64
+	var x146 uint64
+	x146, x145 = bits.Mul64(x139, 0x992d30ed00000001)
+	var x147 uint64
+	var x148 fiat_pasta_fp_uint1
+	x147, x148 = fiat_pasta_fp_addcarryx_u64(x146, x143, 0x0)
+	var x150 fiat_pasta_fp_uint1
+	_, x150 = fiat_pasta_fp_addcarryx_u64(x131, x145, 0x0)
+	var x151 uint64
+	var x152 fiat_pasta_fp_uint1
+	x151, x152 = fiat_pasta_fp_addcarryx_u64(x133, x147, x150)
+	var x153 uint64
+	var x154 fiat_pasta_fp_uint1
+	x153, x154 = fiat_pasta_fp_addcarryx_u64(x135, (uint64(x148) + x144), x152)
+	var x155 uint64
+	var x156 fiat_pasta_fp_uint1
+	x155, x156 = fiat_pasta_fp_addcarryx_u64(x137, x141, x154)
+	x157 := ((uint64(x156) + (uint64(x138) + (uint64(x130) + x118))) + x142)
+	var x158 uint64
+	var x159 fiat_pasta_fp_uint1
+	x158, x159 = fiat_pasta_fp_subborrowx_u64(x151, 0x992d30ed00000001, 0x0)
+	var x160 uint64
+	var x161 fiat_pasta_fp_uint1
+	x160, x161 = fiat_pasta_fp_subborrowx_u64(x153, 0x224698fc094cf91b, x159)
+	var x162 uint64
+	var x163 fiat_pasta_fp_uint1
+	x162, x163 = fiat_pasta_fp_subborrowx_u64(x155, uint64(0x0), x161)
+	var x164 uint64
+	var x165 fiat_pasta_fp_uint1
+	x164, x165 = fiat_pasta_fp_subborrowx_u64(x157, 0x4000000000000000, x163)
+	var x167 fiat_pasta_fp_uint1
+	_, x167 = fiat_pasta_fp_subborrowx_u64(uint64(0x0), uint64(0x0), x165)
+	var x168 uint64
+	fiat_pasta_fp_cmovznz_u64(&x168, x167, x158, x151)
+	var x169 uint64
+	fiat_pasta_fp_cmovznz_u64(&x169, x167, x160, x153)
+	var x170 uint64
+	fiat_pasta_fp_cmovznz_u64(&x170, x167, x162, x155)
+	var x171 uint64
+	fiat_pasta_fp_cmovznz_u64(&x171, x167, x164, x157)
+	out1[0] = x168
+	out1[1] = x169
+	out1[2] = x170
+	out1[3] = x171
+}
+
+// The function fiat_pasta_fp_selectznz is a multi-limb conditional select.
+//
+// Postconditions:
+//   eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
+//
+// Input Bounds:
+//   arg1: [0x0 ~> 0x1]
+//   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+//   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+func fiat_pasta_fp_selectznz(out1 *[4]uint64, arg1 fiat_pasta_fp_uint1, arg2 *[4]uint64, arg3 *[4]uint64) {
+	var x1 uint64
+	fiat_pasta_fp_cmovznz_u64(&x1, arg1, arg2[0], arg3[0])
+	var x2 uint64
+	fiat_pasta_fp_cmovznz_u64(&x2, arg1, arg2[1], arg3[1])
+	var x3 uint64
+	fiat_pasta_fp_cmovznz_u64(&x3, arg1, arg2[2], arg3[2])
+	var x4 uint64
+	fiat_pasta_fp_cmovznz_u64(&x4, arg1, arg2[3], arg3[3])
+	out1[0] = x1
+	out1[1] = x2
+	out1[2] = x3
+	out1[3] = x4
+}
+
+// The function fiat_pasta_fp_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
+//
+// Input Bounds:
+//   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x7fffffffffffffff]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
+func fiat_pasta_fp_to_bytes(out1 *[32]uint8, arg1 *[4]uint64) {
+	x1 := arg1[3]
+	x2 := arg1[2]
+	x3 := arg1[1]
+	x4 := arg1[0]
+	x5 := (uint8(x4) & 0xff)
+	x6 := (x4 >> 8)
+	x7 := (uint8(x6) & 0xff)
+	x8 := (x6 >> 8)
+	x9 := (uint8(x8) & 0xff)
+	x10 := (x8 >> 8)
+	x11 := (uint8(x10) & 0xff)
+	x12 := (x10 >> 8)
+	x13 := (uint8(x12) & 0xff)
+	x14 := (x12 >> 8)
+	x15 := (uint8(x14) & 0xff)
+	x16 := (x14 >> 8)
+	x17 := (uint8(x16) & 0xff)
+	x18 := uint8((x16 >> 8))
+	x19 := (uint8(x3) & 0xff)
+	x20 := (x3 >> 8)
+	x21 := (uint8(x20) & 0xff)
+	x22 := (x20 >> 8)
+	x23 := (uint8(x22) & 0xff)
+	x24 := (x22 >> 8)
+	x25 := (uint8(x24) & 0xff)
+	x26 := (x24 >> 8)
+	x27 := (uint8(x26) & 0xff)
+	x28 := (x26 >> 8)
+	x29 := (uint8(x28) & 0xff)
+	x30 := (x28 >> 8)
+	x31 := (uint8(x30) & 0xff)
+	x32 := uint8((x30 >> 8))
+	x33 := (uint8(x2) & 0xff)
+	x34 := (x2 >> 8)
+	x35 := (uint8(x34) & 0xff)
+	x36 := (x34 >> 8)
+	x37 := (uint8(x36) & 0xff)
+	x38 := (x36 >> 8)
+	x39 := (uint8(x38) & 0xff)
+	x40 := (x38 >> 8)
+	x41 := (uint8(x40) & 0xff)
+	x42 := (x40 >> 8)
+	x43 := (uint8(x42) & 0xff)
+	x44 := (x42 >> 8)
+	x45 := (uint8(x44) & 0xff)
+	x46 := uint8((x44 >> 8))
+	x47 := (uint8(x1) & 0xff)
+	x48 := (x1 >> 8)
+	x49 := (uint8(x48) & 0xff)
+	x50 := (x48 >> 8)
+	x51 := (uint8(x50) & 0xff)
+	x52 := (x50 >> 8)
+	x53 := (uint8(x52) & 0xff)
+	x54 := (x52 >> 8)
+	x55 := (uint8(x54) & 0xff)
+	x56 := (x54 >> 8)
+	x57 := (uint8(x56) & 0xff)
+	x58 := (x56 >> 8)
+	x59 := (uint8(x58) & 0xff)
+	x60 := uint8((x58 >> 8))
+	out1[0] = x5
+	out1[1] = x7
+	out1[2] = x9
+	out1[3] = x11
+	out1[4] = x13
+	out1[5] = x15
+	out1[6] = x17
+	out1[7] = x18
+	out1[8] = x19
+	out1[9] = x21
+	out1[10] = x23
+	out1[11] = x25
+	out1[12] = x27
+	out1[13] = x29
+	out1[14] = x31
+	out1[15] = x32
+	out1[16] = x33
+	out1[17] = x35
+	out1[18] = x37
+	out1[19] = x39
+	out1[20] = x41
+	out1[21] = x43
+	out1[22] = x45
+	out1[23] = x46
+	out1[24] = x47
+	out1[25] = x49
+	out1[26] = x51
+	out1[27] = x53
+	out1[28] = x55
+	out1[29] = x57
+	out1[30] = x59
+	out1[31] = x60
+}
+
+// The function fiat_pasta_fp_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
+//
+// Preconditions:
+//   0 ≤ bytes_eval arg1 < m
+// Postconditions:
+//   eval out1 mod m = bytes_eval arg1 mod m
+//   0 ≤ eval out1 < m
+//
+// Input Bounds:
+//   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x7fffffffffffffff]]
+func fiat_pasta_fp_from_bytes(out1 *[4]uint64, arg1 *[32]uint8) {
+	x1 := (uint64(arg1[31]) << 56)
+	x2 := (uint64(arg1[30]) << 48)
+	x3 := (uint64(arg1[29]) << 40)
+	x4 := (uint64(arg1[28]) << 32)
+	x5 := (uint64(arg1[27]) << 24)
+	x6 := (uint64(arg1[26]) << 16)
+	x7 := (uint64(arg1[25]) << 8)
+	x8 := arg1[24]
+	x9 := (uint64(arg1[23]) << 56)
+	x10 := (uint64(arg1[22]) << 48)
+	x11 := (uint64(arg1[21]) << 40)
+	x12 := (uint64(arg1[20]) << 32)
+	x13 := (uint64(arg1[19]) << 24)
+	x14 := (uint64(arg1[18]) << 16)
+	x15 := (uint64(arg1[17]) << 8)
+	x16 := arg1[16]
+	x17 := (uint64(arg1[15]) << 56)
+	x18 := (uint64(arg1[14]) << 48)
+	x19 := (uint64(arg1[13]) << 40)
+	x20 := (uint64(arg1[12]) << 32)
+	x21 := (uint64(arg1[11]) << 24)
+	x22 := (uint64(arg1[10]) << 16)
+	x23 := (uint64(arg1[9]) << 8)
+	x24 := arg1[8]
+	x25 := (uint64(arg1[7]) << 56)
+	x26 := (uint64(arg1[6]) << 48)
+	x27 := (uint64(arg1[5]) << 40)
+	x28 := (uint64(arg1[4]) << 32)
+	x29 := (uint64(arg1[3]) << 24)
+	x30 := (uint64(arg1[2]) << 16)
+	x31 := (uint64(arg1[1]) << 8)
+	x32 := arg1[0]
+	x33 := (x31 + uint64(x32))
+	x34 := (x30 + x33)
+	x35 := (x29 + x34)
+	x36 := (x28 + x35)
+	x37 := (x27 + x36)
+	x38 := (x26 + x37)
+	x39 := (x25 + x38)
+	x40 := (x23 + uint64(x24))
+	x41 := (x22 + x40)
+	x42 := (x21 + x41)
+	x43 := (x20 + x42)
+	x44 := (x19 + x43)
+	x45 := (x18 + x44)
+	x46 := (x17 + x45)
+	x47 := (x15 + uint64(x16))
+	x48 := (x14 + x47)
+	x49 := (x13 + x48)
+	x50 := (x12 + x49)
+	x51 := (x11 + x50)
+	x52 := (x10 + x51)
+	x53 := (x9 + x52)
+	x54 := (x7 + uint64(x8))
+	x55 := (x6 + x54)
+	x56 := (x5 + x55)
+	x57 := (x4 + x56)
+	x58 := (x3 + x57)
+	x59 := (x2 + x58)
+	x60 := (x1 + x59)
+	out1[0] = x39
+	out1[1] = x46
+	out1[2] = x53
+	out1[3] = x60
+}
diff --git a/pkg/core/curves/native/pasta/fq/README.md b/pkg/core/curves/native/pasta/fq/README.md
new file mode 100755
index 00000000..30678c4a
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fq/README.md
@@ -0,0 +1,306 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# fq
+
+```go
+import "github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fq"
+```
+
+Autogenerated: '\./src/ExtractionOCaml/word\_by\_word\_montgomery' \-\-lang Go pasta\_fq 64 '2^254 \+ 45560315531506369815346746415080538113'
+
+curve description: pasta\_fq
+
+machine\_wordsize = 64 \(from "64"\)
+
+requested operations: \(all\)
+
+m = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 \(from "2^254 \+ 45560315531506369815346746415080538113"\)
+
+NOTE: In addition to the bounds specified above each function\, all
+
+```
+functions synthesized for this Montgomery arithmetic require the
+
+input to be strictly less than the prime modulus (m), and also
+
+require the input to be in the unique saturated representation.
+
+All functions also ensure that these two properties are true of
+
+return values.
+```
+
+Computed values:
+
+```
+eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
+
+bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248)
+
+twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
+
+                         if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
+```
+
+## Index
+
+- [Variables](<#variables>)
+- [type Fq](<#type-fq>)
+  - [func (fq *Fq) Add(lhs, rhs *Fq) *Fq](<#func-fq-add>)
+  - [func (fq *Fq) BigInt() *big.Int](<#func-fq-bigint>)
+  - [func (fq *Fq) Bytes() [32]byte](<#func-fq-bytes>)
+  - [func (fq *Fq) CMove(lhs, rhs *Fq, choice int) *Fq](<#func-fq-cmove>)
+  - [func (fq *Fq) Cmp(rhs *Fq) int](<#func-fq-cmp>)
+  - [func (fq *Fq) Double(elem *Fq) *Fq](<#func-fq-double>)
+  - [func (fq *Fq) Equal(rhs *Fq) bool](<#func-fq-equal>)
+  - [func (fq *Fq) Exp(base, exp *Fq) *Fq](<#func-fq-exp>)
+  - [func (fq *Fq) Invert(elem *Fq) (*Fq, bool)](<#func-fq-invert>)
+  - [func (fq *Fq) IsOne() bool](<#func-fq-isone>)
+  - [func (fq *Fq) IsZero() bool](<#func-fq-iszero>)
+  - [func (fq *Fq) Mul(lhs, rhs *Fq) *Fq](<#func-fq-mul>)
+  - [func (fq *Fq) Neg(elem *Fq) *Fq](<#func-fq-neg>)
+  - [func (fq *Fq) Set(rhs *Fq) *Fq](<#func-fq-set>)
+  - [func (fq *Fq) SetBigInt(bi *big.Int) *Fq](<#func-fq-setbigint>)
+  - [func (fq *Fq) SetBool(rhs bool) *Fq](<#func-fq-setbool>)
+  - [func (fq *Fq) SetBytes(input *[32]byte) (*Fq, error)](<#func-fq-setbytes>)
+  - [func (fq *Fq) SetBytesWide(input *[64]byte) *Fq](<#func-fq-setbyteswide>)
+  - [func (fq *Fq) SetOne() *Fq](<#func-fq-setone>)
+  - [func (fq *Fq) SetRaw(array *[4]uint64) *Fq](<#func-fq-setraw>)
+  - [func (fq *Fq) SetUint64(rhs uint64) *Fq](<#func-fq-setuint64>)
+  - [func (fq *Fq) SetZero() *Fq](<#func-fq-setzero>)
+  - [func (fq *Fq) Sqrt(elem *Fq) (*Fq, bool)](<#func-fq-sqrt>)
+  - [func (fq *Fq) Square(elem *Fq) *Fq](<#func-fq-square>)
+  - [func (fq *Fq) Sub(lhs, rhs *Fq) *Fq](<#func-fq-sub>)
+  - [func (fq *Fq) ToRaw() [4]uint64](<#func-fq-toraw>)
+
+
+## Variables
+
+```go
+var BiModulus = new(big.Int).SetBytes([]byte{
+    0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+    0x22, 0x46, 0x98, 0xfc, 0x09, 0x94, 0xa8, 0xdd,
+    0x8c, 0x46, 0xeb, 0x21, 0x00, 0x00, 0x00, 0x01,
+})
+```
+
+## type [Fq](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L16>)
+
+```go
+type Fq fiat_pasta_fq_montgomery_domain_field_element
+```
+
+### func \(\*Fq\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L310>)
+
+```go
+func (fq *Fq) Add(lhs, rhs *Fq) *Fq
+```
+
+Add returns the result from adding rhs to this element
+
+### func \(\*Fq\) [BigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L203>)
+
+```go
+func (fq *Fq) BigInt() *big.Int
+```
+
+BigInt converts this element into the big\.Int struct
+
+### func \(\*Fq\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L194>)
+
+```go
+func (fq *Fq) Bytes() [32]byte
+```
+
+Bytes converts this element into a byte representation in little endian byte order
+
+### func \(\*Fq\) [CMove](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L349>)
+
+```go
+func (fq *Fq) CMove(lhs, rhs *Fq, choice int) *Fq
+```
+
+CMove selects lhs if choice == 0 and rhs if choice == 1
+
+### func \(\*Fq\) [Cmp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L47>)
+
+```go
+func (fq *Fq) Cmp(rhs *Fq) int
+```
+
+Cmp returns \-1 if fp \< rhs 0 if fp == rhs 1 if fp \> rhs
+
+### func \(\*Fq\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L209>)
+
+```go
+func (fq *Fq) Double(elem *Fq) *Fq
+```
+
+Double this element
+
+### func \(\*Fq\) [Equal](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L58>)
+
+```go
+func (fq *Fq) Equal(rhs *Fq) bool
+```
+
+Equal returns true if fp == rhs
+
+### func \(\*Fq\) [Exp](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L325>)
+
+```go
+func (fq *Fq) Exp(base, exp *Fq) *Fq
+```
+
+Exp exponentiates this element by exp
+
+### func \(\*Fq\) [Invert](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L283>)
+
+```go
+func (fq *Fq) Invert(elem *Fq) (*Fq, bool)
+```
+
+Invert this element i\.e\. compute the multiplicative inverse return false\, zero if this element is zero
+
+### func \(\*Fq\) [IsOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L76>)
+
+```go
+func (fq *Fq) IsOne() bool
+```
+
+IsOne returns true if fp == r
+
+### func \(\*Fq\) [IsZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L67>)
+
+```go
+func (fq *Fq) IsZero() bool
+```
+
+IsZero returns true if fp == 0
+
+### func \(\*Fq\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L294>)
+
+```go
+func (fq *Fq) Mul(lhs, rhs *Fq) *Fq
+```
+
+Mul returns the result from multiplying this element by rhs
+
+### func \(\*Fq\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L318>)
+
+```go
+func (fq *Fq) Neg(elem *Fq) *Fq
+```
+
+Neg returns negation of this element
+
+### func \(\*Fq\) [Set](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L81>)
+
+```go
+func (fq *Fq) Set(rhs *Fq) *Fq
+```
+
+Set fp == rhs
+
+### func \(\*Fq\) [SetBigInt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L176>)
+
+```go
+func (fq *Fq) SetBigInt(bi *big.Int) *Fq
+```
+
+SetBigInt initializes an element from big\.Int The value is reduced by the modulus
+
+### func \(\*Fq\) [SetBool](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L96>)
+
+```go
+func (fq *Fq) SetBool(rhs bool) *Fq
+```
+
+### func \(\*Fq\) [SetBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L159>)
+
+```go
+func (fq *Fq) SetBytes(input *[32]byte) (*Fq, error)
+```
+
+SetBytes attempts to convert a little endian byte representation of a scalar into a \`Fq\`\, failing if input is not canonical
+
+### func \(\*Fq\) [SetBytesWide](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L134>)
+
+```go
+func (fq *Fq) SetBytesWide(input *[64]byte) *Fq
+```
+
+SetBytesWide takes 64 bytes as input and treats them as a 512\-bit number\. Attributed to https://github.com/zcash/pasta_curves/blob/main/src/fields/fq.rs#L255 We reduce an arbitrary 512\-bit number by decomposing it into two 256\-bit digits with the higher bits multiplied by 2^256\. Thus\, we perform two reductions
+
+1\. the lower bits are multiplied by r^2\, as normal 2\. the upper bits are multiplied by r^2 \* 2^256 = r^3
+
+and computing their sum in the field\. It remains to see that arbitrary 256\-bit numbers can be placed into Montgomery form safely using the reduction\. The reduction works so long as the product is less than r=2^256 multiplied by the modulus\. This holds because for any \`c\` smaller than the modulus\, we have that \(2^256 \- 1\)\*c is an acceptable product for the reduction\. Therefore\, the reduction always works so long as \`c\` is in the field; in this case it is either the constant \`r2\` or \`r3\`\.
+
+### func \(\*Fq\) [SetOne](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L106>)
+
+```go
+func (fq *Fq) SetOne() *Fq
+```
+
+SetOne fp == r
+
+### func \(\*Fq\) [SetRaw](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L187>)
+
+```go
+func (fq *Fq) SetRaw(array *[4]uint64) *Fq
+```
+
+SetRaw converts a raw array into a field element
+
+### func \(\*Fq\) [SetUint64](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L90>)
+
+```go
+func (fq *Fq) SetUint64(rhs uint64) *Fq
+```
+
+SetUint64 sets fp == rhs
+
+### func \(\*Fq\) [SetZero](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L111>)
+
+```go
+func (fq *Fq) SetZero() *Fq
+```
+
+SetZero fp == 0
+
+### func \(\*Fq\) [Sqrt](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L224>)
+
+```go
+func (fq *Fq) Sqrt(elem *Fq) (*Fq, bool)
+```
+
+Sqrt this element\, if it exists\. If true\, then value is a square root\. If false\, value is a QNR
+
+### func \(\*Fq\) [Square](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L216>)
+
+```go
+func (fq *Fq) Square(elem *Fq) *Fq
+```
+
+Square this element
+
+### func \(\*Fq\) [Sub](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L302>)
+
+```go
+func (fq *Fq) Sub(lhs, rhs *Fq) *Fq
+```
+
+Sub returns the result from subtracting rhs from this element
+
+### func \(\*Fq\) [ToRaw](<https://github.com/coinbase/kryptology/blob/master/pkg/core/curves/native/pasta/fq/fq.go#L357>)
+
+```go
+func (fq *Fq) ToRaw() [4]uint64
+```
+
+ToRaw converts this element into the a \[4\]uint64
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/core/curves/native/pasta/fq/fq.go b/pkg/core/curves/native/pasta/fq/fq.go
new file mode 100644
index 00000000..33deac8a
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fq/fq.go
@@ -0,0 +1,361 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package fq
+
+import (
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"math/big"
+)
+
+type Fq fiat_pasta_fq_montgomery_domain_field_element
+
+// r = 2^256 mod p
+var r = &Fq{0x5b2b3e9cfffffffd, 0x992c350be3420567, 0xffffffffffffffff, 0x3fffffffffffffff}
+
+// r2 = 2^512 mod p
+var r2 = &Fq{0xfc9678ff0000000f, 0x67bb433d891a16e3, 0x7fae231004ccf590, 0x096d41af7ccfdaa9}
+
+// r3 = 2^768 mod p
+var r3 = &Fq{0x008b421c249dae4c, 0xe13bda50dba41326, 0x88fececb8e15cb63, 0x07dd97a06e6792c8}
+
+// generator = 5 mod p is a generator of the `p - 1` order multiplicative
+// subgroup, or in other words a primitive element of the field.
+var generator = &Fq{0x96bc8c8cffffffed, 0x74c2a54b49f7778e, 0xfffffffffffffffd, 0x3fffffffffffffff}
+
+var s = 32
+
+// modulus representation
+// p = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
+var modulus = &Fq{0x8c46eb2100000001, 0x224698fc0994a8dd, 0x0000000000000000, 0x4000000000000000}
+
+var BiModulus = new(big.Int).SetBytes([]byte{
+	0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+	0x22, 0x46, 0x98, 0xfc, 0x09, 0x94, 0xa8, 0xdd,
+	0x8c, 0x46, 0xeb, 0x21, 0x00, 0x00, 0x00, 0x01,
+})
+
+// Cmp returns -1 if fp < rhs
+// 0 if fp == rhs
+// 1 if fp > rhs
+func (fq *Fq) Cmp(rhs *Fq) int {
+	gt := 0
+	lt := 0
+	for i := len(fq) - 1; i >= 0; i-- {
+		gt |= int((rhs[i]-fq[i])>>63) &^ lt
+		lt |= int((fq[i]-rhs[i])>>63) &^ gt
+	}
+	return gt - lt
+}
+
+// Equal returns true if fp == rhs
+func (fq *Fq) Equal(rhs *Fq) bool {
+	t := fq[0] ^ rhs[0]
+	t |= fq[1] ^ rhs[1]
+	t |= fq[2] ^ rhs[2]
+	t |= fq[3] ^ rhs[3]
+	return t == 0
+}
+
+// IsZero returns true if fp == 0
+func (fq *Fq) IsZero() bool {
+	t := fq[0]
+	t |= fq[1]
+	t |= fq[2]
+	t |= fq[3]
+	return t == 0
+}
+
+// IsOne returns true if fp == r
+func (fq *Fq) IsOne() bool {
+	return fq.Equal(r)
+}
+
+// Set fp == rhs
+func (fq *Fq) Set(rhs *Fq) *Fq {
+	fq[0] = rhs[0]
+	fq[1] = rhs[1]
+	fq[2] = rhs[2]
+	fq[3] = rhs[3]
+	return fq
+}
+
+// SetUint64 sets fp == rhs
+func (fq *Fq) SetUint64(rhs uint64) *Fq {
+	r := &fiat_pasta_fq_non_montgomery_domain_field_element{rhs, 0, 0, 0}
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(fq), r)
+	return fq
+}
+
+func (fq *Fq) SetBool(rhs bool) *Fq {
+	if rhs {
+		fq.SetOne()
+	} else {
+		fq.SetZero()
+	}
+	return fq
+}
+
+// SetOne fp == r
+func (fq *Fq) SetOne() *Fq {
+	return fq.Set(r)
+}
+
+// SetZero fp == 0
+func (fq *Fq) SetZero() *Fq {
+	fq[0] = 0
+	fq[1] = 0
+	fq[2] = 0
+	fq[3] = 0
+	return fq
+}
+
+// SetBytesWide takes 64 bytes as input and treats them as a 512-bit number.
+// Attributed to https://github.com/zcash/pasta_curves/blob/main/src/fields/fq.rs#L255
+// We reduce an arbitrary 512-bit number by decomposing it into two 256-bit digits
+// with the higher bits multiplied by 2^256. Thus, we perform two reductions
+//
+// 1. the lower bits are multiplied by r^2, as normal
+// 2. the upper bits are multiplied by r^2 * 2^256 = r^3
+//
+// and computing their sum in the field. It remains to see that arbitrary 256-bit
+// numbers can be placed into Montgomery form safely using the reduction. The
+// reduction works so long as the product is less than r=2^256 multiplied by
+// the modulus. This holds because for any `c` smaller than the modulus, we have
+// that (2^256 - 1)*c is an acceptable product for the reduction. Therefore, the
+// reduction always works so long as `c` is in the field; in this case it is either the
+// constant `r2` or `r3`.
+func (fq *Fq) SetBytesWide(input *[64]byte) *Fq {
+	d0 := fiat_pasta_fq_montgomery_domain_field_element{
+		binary.LittleEndian.Uint64(input[:8]),
+		binary.LittleEndian.Uint64(input[8:16]),
+		binary.LittleEndian.Uint64(input[16:24]),
+		binary.LittleEndian.Uint64(input[24:32]),
+	}
+	d1 := fiat_pasta_fq_montgomery_domain_field_element{
+		binary.LittleEndian.Uint64(input[32:40]),
+		binary.LittleEndian.Uint64(input[40:48]),
+		binary.LittleEndian.Uint64(input[48:56]),
+		binary.LittleEndian.Uint64(input[56:64]),
+	}
+	// Convert to Montgomery form
+	tv1 := &fiat_pasta_fq_montgomery_domain_field_element{}
+	tv2 := &fiat_pasta_fq_montgomery_domain_field_element{}
+	// d0 * r2 + d1 * r3
+	fiat_pasta_fq_mul(tv1, &d0, (*fiat_pasta_fq_montgomery_domain_field_element)(r2))
+	fiat_pasta_fq_mul(tv2, &d1, (*fiat_pasta_fq_montgomery_domain_field_element)(r3))
+	fiat_pasta_fq_add((*fiat_pasta_fq_montgomery_domain_field_element)(fq), tv1, tv2)
+	return fq
+}
+
+// SetBytes attempts to convert a little endian byte representation
+// of a scalar into a `Fq`, failing if input is not canonical
+func (fq *Fq) SetBytes(input *[32]byte) (*Fq, error) {
+	d0 := &Fq{
+		binary.LittleEndian.Uint64(input[:8]),
+		binary.LittleEndian.Uint64(input[8:16]),
+		binary.LittleEndian.Uint64(input[16:24]),
+		binary.LittleEndian.Uint64(input[24:32]),
+	}
+	if d0.Cmp(modulus) != -1 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	fiat_pasta_fq_from_bytes((*[4]uint64)(fq), input)
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(fq), (*fiat_pasta_fq_non_montgomery_domain_field_element)(fq))
+	return fq, nil
+}
+
+// SetBigInt initializes an element from big.Int
+// The value is reduced by the modulus
+func (fq *Fq) SetBigInt(bi *big.Int) *Fq {
+	var buffer [32]byte
+	r := new(big.Int).Set(bi)
+	r.Mod(r, BiModulus)
+	r.FillBytes(buffer[:])
+	copy(buffer[:], internal.ReverseScalarBytes(buffer[:]))
+	_, _ = fq.SetBytes(&buffer)
+	return fq
+}
+
+// SetRaw converts a raw array into a field element
+func (fq *Fq) SetRaw(array *[4]uint64) *Fq {
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(fq), (*fiat_pasta_fq_non_montgomery_domain_field_element)(array))
+	return fq
+}
+
+// Bytes converts this element into a byte representation
+// in little endian byte order
+func (fq *Fq) Bytes() [32]byte {
+	var output [32]byte
+	tv := &fiat_pasta_fq_non_montgomery_domain_field_element{}
+	fiat_pasta_fq_from_montgomery(tv, (*fiat_pasta_fq_montgomery_domain_field_element)(fq))
+	fiat_pasta_fq_to_bytes(&output, (*[4]uint64)(tv))
+	return output
+}
+
+// BigInt converts this element into the big.Int struct
+func (fq *Fq) BigInt() *big.Int {
+	buffer := fq.Bytes()
+	return new(big.Int).SetBytes(internal.ReverseScalarBytes(buffer[:]))
+}
+
+// Double this element
+func (fq *Fq) Double(elem *Fq) *Fq {
+	delem := (*fiat_pasta_fq_montgomery_domain_field_element)(elem)
+	fiat_pasta_fq_add((*fiat_pasta_fq_montgomery_domain_field_element)(fq), delem, delem)
+	return fq
+}
+
+// Square this element
+func (fq *Fq) Square(elem *Fq) *Fq {
+	delem := (*fiat_pasta_fq_montgomery_domain_field_element)(elem)
+	fiat_pasta_fq_square((*fiat_pasta_fq_montgomery_domain_field_element)(fq), delem)
+	return fq
+}
+
+// Sqrt this element, if it exists. If true, then value
+// is a square root. If false, value is a QNR
+func (fq *Fq) Sqrt(elem *Fq) (*Fq, bool) {
+	return fq.tonelliShanks(elem)
+}
+
+// See sqrt_ts_ct at
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-I.4
+func (fq *Fq) tonelliShanks(elem *Fq) (*Fq, bool) {
+	// c1 := 32
+	// c2 := (q - 1) / (2^c1)
+	//c2 := [4]uint64{
+	//	0x0994a8dd8c46eb21,
+	//	0x00000000224698fc,
+	//	0x0000000000000000,
+	//	0x0000000040000000,
+	//}
+	// c3 := (c2 - 1) / 2
+	c3 := [4]uint64{
+		0x04ca546ec6237590,
+		0x0000000011234c7e,
+		0x0000000000000000,
+		0x0000000020000000,
+	}
+	//c4 := generator
+	//c5 := new(Fq).pow(&generator, c2)
+	c5 := &Fq{
+		0x218077428c9942de,
+		0xcc49578921b60494,
+		0xac2e5d27b2efbee2,
+		0xb79fa897f2db056,
+	}
+
+	z := new(Fq).pow(elem, c3)
+	t := new(Fq).Square(z)
+	t.Mul(t, elem)
+
+	z.Mul(z, elem)
+
+	b := new(Fq).Set(t)
+	c := new(Fq).Set(c5)
+	flags := map[bool]int{
+		true:  1,
+		false: 0,
+	}
+
+	for i := s; i >= 2; i-- {
+		for j := 1; j <= i-2; j++ {
+			b.Square(b)
+		}
+		z.CMove(z, new(Fq).Mul(z, c), flags[!b.IsOne()])
+		c.Square(c)
+		t.CMove(t, new(Fq).Mul(t, c), flags[!b.IsOne()])
+		b.Set(t)
+	}
+	wasSquare := c.Square(z).Equal(elem)
+	return fq.Set(z), wasSquare
+}
+
+// Invert this element i.e. compute the multiplicative inverse
+// return false, zero if this element is zero
+func (fq *Fq) Invert(elem *Fq) (*Fq, bool) {
+	// computes elem^(p - 2) mod p
+	exp := [4]uint64{
+		0x8c46eb20ffffffff,
+		0x224698fc0994a8dd,
+		0x0000000000000000,
+		0x4000000000000000}
+	return fq.pow(elem, exp), !elem.IsZero()
+}
+
+// Mul returns the result from multiplying this element by rhs
+func (fq *Fq) Mul(lhs, rhs *Fq) *Fq {
+	dlhs := (*fiat_pasta_fq_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fq_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fq_mul((*fiat_pasta_fq_montgomery_domain_field_element)(fq), dlhs, drhs)
+	return fq
+}
+
+// Sub returns the result from subtracting rhs from this element
+func (fq *Fq) Sub(lhs, rhs *Fq) *Fq {
+	dlhs := (*fiat_pasta_fq_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fq_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fq_sub((*fiat_pasta_fq_montgomery_domain_field_element)(fq), dlhs, drhs)
+	return fq
+}
+
+// Add returns the result from adding rhs to this element
+func (fq *Fq) Add(lhs, rhs *Fq) *Fq {
+	dlhs := (*fiat_pasta_fq_montgomery_domain_field_element)(lhs)
+	drhs := (*fiat_pasta_fq_montgomery_domain_field_element)(rhs)
+	fiat_pasta_fq_add((*fiat_pasta_fq_montgomery_domain_field_element)(fq), dlhs, drhs)
+	return fq
+}
+
+// Neg returns negation of this element
+func (fq *Fq) Neg(elem *Fq) *Fq {
+	delem := (*fiat_pasta_fq_montgomery_domain_field_element)(elem)
+	fiat_pasta_fq_opp((*fiat_pasta_fq_montgomery_domain_field_element)(fq), delem)
+	return fq
+}
+
+// Exp exponentiates this element by exp
+func (fq *Fq) Exp(base, exp *Fq) *Fq {
+	// convert exponent to integer form
+	tv := &fiat_pasta_fq_non_montgomery_domain_field_element{}
+	fiat_pasta_fq_from_montgomery(tv, (*fiat_pasta_fq_montgomery_domain_field_element)(exp))
+
+	e := (*[4]uint64)(tv)
+	return fq.pow(base, *e)
+}
+
+func (fq *Fq) pow(base *Fq, exp [4]uint64) *Fq {
+	res := new(Fq).SetOne()
+	tmp := new(Fq)
+
+	for i := len(exp) - 1; i >= 0; i-- {
+		for j := 63; j >= 0; j-- {
+			res.Square(res)
+			tmp.Mul(res, base)
+			res.CMove(res, tmp, int(exp[i]>>j)&1)
+		}
+	}
+	return fq.Set(res)
+}
+
+// CMove selects lhs if choice == 0 and rhs if choice == 1
+func (fq *Fq) CMove(lhs, rhs *Fq, choice int) *Fq {
+	dlhs := (*[4]uint64)(lhs)
+	drhs := (*[4]uint64)(rhs)
+	fiat_pasta_fq_selectznz((*[4]uint64)(fq), fiat_pasta_fq_uint1(choice), dlhs, drhs)
+	return fq
+}
+
+// ToRaw converts this element into the a [4]uint64
+func (fq *Fq) ToRaw() [4]uint64 {
+	res := &fiat_pasta_fq_non_montgomery_domain_field_element{}
+	fiat_pasta_fq_from_montgomery(res, (*fiat_pasta_fq_montgomery_domain_field_element)(fq))
+	return *(*[4]uint64)(res)
+}
diff --git a/pkg/core/curves/native/pasta/fq/fq_test.go b/pkg/core/curves/native/pasta/fq/fq_test.go
new file mode 100644
index 00000000..50a86694
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fq/fq_test.go
@@ -0,0 +1,248 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package fq
+
+import (
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"math/rand"
+	"testing"
+)
+
+func TestFqSetOne(t *testing.T) {
+	fq := new(Fq).SetOne()
+	assert.NotNil(t, fq)
+	assert.True(t, fq.Equal(r))
+}
+
+func TestFqSetUint64(t *testing.T) {
+	act := new(Fq).SetUint64(1 << 60)
+	assert.NotNil(t, act)
+	// Remember it will be in montgomery form
+	assert.Equal(t, int(act[0]), 0x4c46eb2100000001)
+}
+
+func TestFqAdd(t *testing.T) {
+	lhs := new(Fq).SetOne()
+	rhs := new(Fq).SetOne()
+	exp := new(Fq).SetUint64(2)
+	res := new(Fq).Add(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint64() >> 2
+		r := rand.Uint64() >> 2
+		e := l + r
+		lhs.SetUint64(l)
+		rhs.SetUint64(r)
+		exp.SetUint64(e)
+
+		a := new(Fq).Add(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFqSub(t *testing.T) {
+	lhs := new(Fq).SetOne()
+	rhs := new(Fq).SetOne()
+	exp := new(Fq).SetZero()
+	res := new(Fq).Sub(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint64() >> 2
+		r := rand.Uint64() >> 2
+		if l < r {
+			l, r = r, l
+		}
+		e := l - r
+		lhs.SetUint64(l)
+		rhs.SetUint64(r)
+		exp.SetUint64(e)
+
+		a := new(Fq).Sub(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFqMul(t *testing.T) {
+	lhs := new(Fq).SetOne()
+	rhs := new(Fq).SetOne()
+	exp := new(Fq).SetOne()
+	res := new(Fq).Mul(lhs, rhs)
+	assert.NotNil(t, res)
+	assert.True(t, res.Equal(exp))
+
+	// Fuzz test
+	for i := 0; i < 25; i++ {
+		// Divide by 4 to prevent overflow false errors
+		l := rand.Uint32()
+		r := rand.Uint32()
+		e := uint64(l) * uint64(r)
+		lhs.SetUint64(uint64(l))
+		rhs.SetUint64(uint64(r))
+		exp.SetUint64(e)
+
+		a := new(Fq).Mul(lhs, rhs)
+		assert.NotNil(t, a)
+		assert.Equal(t, exp, a)
+	}
+}
+
+func TestFqDouble(t *testing.T) {
+	a := new(Fq).SetUint64(2)
+	e := new(Fq).SetUint64(4)
+	assert.Equal(t, e, new(Fq).Double(a))
+
+	for i := 0; i < 25; i++ {
+		tv := rand.Uint32()
+		ttv := uint64(tv) * 2
+		a = new(Fq).SetUint64(uint64(tv))
+		e = new(Fq).SetUint64(ttv)
+		assert.Equal(t, e, new(Fq).Double(a))
+	}
+}
+
+func TestFqSquare(t *testing.T) {
+	a := new(Fq).SetUint64(4)
+	e := new(Fq).SetUint64(16)
+	assert.Equal(t, e, a.Square(a))
+
+	for i := 0; i < 25; i++ {
+		j := rand.Uint32()
+		exp := uint64(j) * uint64(j)
+		e.SetUint64(exp)
+		a.SetUint64(uint64(j))
+		assert.Equal(t, e, a.Square(a))
+	}
+}
+
+func TestFqNeg(t *testing.T) {
+	a := new(Fq).SetOne()
+	a.Neg(a)
+	e := &Fq{0x311bac8400000004, 0x891a63f02652a376, 0, 0}
+	assert.Equal(t, e, a)
+	a.Neg(generator)
+	e = &Fq{0xf58a5e9400000014, 0xad83f3b0bf9d314e, 0x2, 0x0}
+	assert.Equal(t, e, a)
+}
+
+func TestFqExp(t *testing.T) {
+	e := new(Fq).SetUint64(8)
+	a := new(Fq).SetUint64(2)
+	by := new(Fq).SetUint64(3)
+	assert.Equal(t, e, a.Exp(a, by))
+}
+
+func TestFqSqrt(t *testing.T) {
+	t1 := new(Fq).SetUint64(2)
+	t2 := new(Fq).Neg(t1)
+	t3 := new(Fq).Square(t1)
+	_, wasSquare := t3.Sqrt(t3)
+	assert.True(t, wasSquare)
+	assert.True(t, t1.Equal(t3) || t2.Equal(t3))
+	t1.SetUint64(5)
+	_, wasSquare = new(Fq).Sqrt(t1)
+	assert.False(t, wasSquare)
+}
+
+func TestFqInvert(t *testing.T) {
+	twoInv := &Fq{0xc623759080000001, 0x11234c7e04ca546e, 0x0000000000000000, 0x2000000000000000}
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(twoInv), (*fiat_pasta_fq_non_montgomery_domain_field_element)(twoInv))
+	two := new(Fq).SetUint64(2)
+	a, inverted := new(Fq).Invert(two)
+	assert.True(t, inverted)
+	assert.Equal(t, a, twoInv)
+
+	rootOfUnity := &Fq{0xa70e2c1102b6d05f, 0x9bb97ea3c106f049, 0x9e5c4dfd492ae26e, 0x2de6a9b8746d3f58}
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(rootOfUnity), (*fiat_pasta_fq_non_montgomery_domain_field_element)(rootOfUnity))
+	rootOfUnityInv := &Fq{0x57eecda0a84b6836, 0x4ad38b9084b8a80c, 0xf4c8f353124086c1, 0x2235e1a7415bf936}
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(rootOfUnityInv), (*fiat_pasta_fq_non_montgomery_domain_field_element)(rootOfUnityInv))
+	a, inverted = new(Fq).Invert(rootOfUnity)
+	assert.True(t, inverted)
+	assert.Equal(t, a, rootOfUnityInv)
+
+	lhs := new(Fq).SetUint64(9)
+	rhs := new(Fq).SetUint64(3)
+	rhsInv, inverted := new(Fq).Invert(rhs)
+	assert.True(t, inverted)
+	assert.Equal(t, rhs, new(Fq).Mul(lhs, rhsInv))
+
+	rhs.SetZero()
+	_, inverted = new(Fq).Invert(rhs)
+	assert.False(t, inverted)
+}
+
+func TestFqCMove(t *testing.T) {
+	t1 := new(Fq).SetUint64(5)
+	t2 := new(Fq).SetUint64(10)
+	assert.Equal(t, t1, new(Fq).CMove(t1, t2, 0))
+	assert.Equal(t, t2, new(Fq).CMove(t1, t2, 1))
+}
+
+func TestFqBytes(t *testing.T) {
+	t1 := new(Fq).SetUint64(99)
+	seq := t1.Bytes()
+	t2, err := new(Fq).SetBytes(&seq)
+	assert.NoError(t, err)
+	assert.Equal(t, t1, t2)
+
+	for i := 0; i < 25; i++ {
+		t1.SetUint64(rand.Uint64())
+		seq = t1.Bytes()
+		_, err = t2.SetBytes(&seq)
+		assert.NoError(t, err)
+		assert.Equal(t, t1, t2)
+	}
+}
+
+func TestFqBigInt(t *testing.T) {
+	t1 := new(Fq).SetBigInt(big.NewInt(9999))
+	t2 := new(Fq).SetBigInt(t1.BigInt())
+	assert.Equal(t, t1, t2)
+
+	e := &Fq{0x7bb1416dea3d6ae3, 0x62f9108a340aa525, 0x303b3f30fcaa477f, 0x11c9ef5422d80a4d}
+	b := new(big.Int).SetBytes([]byte{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9})
+	t1.SetBigInt(b)
+	assert.Equal(t, e, t1)
+	e[0] = 0x1095a9b315c2951e
+	e[1] = 0xbf4d8871d58a03b8
+	e[2] = 0xcfc4c0cf0355b880
+	e[3] = 0x2e3610abdd27f5b2
+	b.Neg(b)
+	t1.SetBigInt(b)
+	assert.Equal(t, e, t1)
+}
+
+func TestFqSetBool(t *testing.T) {
+	assert.Equal(t, new(Fq).SetOne(), new(Fq).SetBool(true))
+	assert.Equal(t, new(Fq).SetZero(), new(Fq).SetBool(false))
+}
+
+func TestFqSetBytesWide(t *testing.T) {
+	e := &Fq{0xe22bd0d1b22cc43e, 0x6b84e5b52490a7c8, 0x264262941ac9e229, 0x27dcfdf361ce4254}
+	fiat_pasta_fq_to_montgomery((*fiat_pasta_fq_montgomery_domain_field_element)(e), (*fiat_pasta_fq_non_montgomery_domain_field_element)(e))
+	a := new(Fq).SetBytesWide(&[64]byte{
+		0x69, 0x23, 0x5a, 0x0b, 0xce, 0x0c, 0xa8, 0x64,
+		0x3c, 0x78, 0xbc, 0x01, 0x05, 0xef, 0xf2, 0x84,
+		0xde, 0xbb, 0x6b, 0xc8, 0x63, 0x5e, 0x6e, 0x69,
+		0x62, 0xcc, 0xc6, 0x2d, 0xf5, 0x72, 0x40, 0x92,
+		0x28, 0x11, 0xd6, 0xc8, 0x07, 0xa5, 0x88, 0x82,
+		0xfe, 0xe3, 0x97, 0xf6, 0x1e, 0xfb, 0x2e, 0x3b,
+		0x27, 0x5f, 0x85, 0x06, 0x8d, 0x99, 0xa4, 0x75,
+		0xc0, 0x2c, 0x71, 0x69, 0x9e, 0x58, 0xea, 0x52,
+	})
+	assert.Equal(t, e, a)
+}
diff --git a/pkg/core/curves/native/pasta/fq/pasta_fq.go b/pkg/core/curves/native/pasta/fq/pasta_fq.go
new file mode 100644
index 00000000..ac98cbfe
--- /dev/null
+++ b/pkg/core/curves/native/pasta/fq/pasta_fq.go
@@ -0,0 +1,1432 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Autogenerated: './src/ExtractionOCaml/word_by_word_montgomery' --lang Go pasta_fq 64 '2^254 + 45560315531506369815346746415080538113'
+//
+// curve description: pasta_fq
+//
+// machine_wordsize = 64 (from "64")
+//
+// requested operations: (all)
+//
+// m = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001 (from "2^254 + 45560315531506369815346746415080538113")
+//
+//
+//
+// NOTE: In addition to the bounds specified above each function, all
+//
+//   functions synthesized for this Montgomery arithmetic require the
+//
+//   input to be strictly less than the prime modulus (m), and also
+//
+//   require the input to be in the unique saturated representation.
+//
+//   All functions also ensure that these two properties are true of
+//
+//   return values.
+//
+//
+//
+// Computed values:
+//
+//   eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192)
+//
+//   bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248)
+//
+//   twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in
+//
+//                            if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
+package fq
+
+import "math/bits"
+
+type fiat_pasta_fq_uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+type fiat_pasta_fq_int1 int64   // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927
+
+// The type fiat_pasta_fq_montgomery_domain_field_element is a field element in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiat_pasta_fq_montgomery_domain_field_element [4]uint64
+
+// The type fiat_pasta_fq_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain.
+//
+// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+type fiat_pasta_fq_non_montgomery_domain_field_element [4]uint64
+
+// The function fiat_pasta_fq_addcarryx_u64 is a thin wrapper around bits.Add64 that uses fiat_pasta_fq_uint1 rather than uint64
+func fiat_pasta_fq_addcarryx_u64(x uint64, y uint64, carry fiat_pasta_fq_uint1) (uint64, fiat_pasta_fq_uint1) {
+	sum, carryOut := bits.Add64(x, y, uint64(carry))
+	return sum, fiat_pasta_fq_uint1(carryOut)
+}
+
+// The function fiat_pasta_fq_subborrowx_u64 is a thin wrapper around bits.Sub64 that uses fiat_pasta_fq_uint1 rather than uint64
+func fiat_pasta_fq_subborrowx_u64(x uint64, y uint64, carry fiat_pasta_fq_uint1) (uint64, fiat_pasta_fq_uint1) {
+	sum, carryOut := bits.Sub64(x, y, uint64(carry))
+	return sum, fiat_pasta_fq_uint1(carryOut)
+}
+
+// The function fiat_pasta_fq_cmovznz_u64 is a single-word conditional move.
+//
+// Postconditions:
+//   out1 = (if arg1 = 0 then arg2 else arg3)
+//
+// Input Bounds:
+//   arg1: [0x0 ~> 0x1]
+//   arg2: [0x0 ~> 0xffffffffffffffff]
+//   arg3: [0x0 ~> 0xffffffffffffffff]
+// Output Bounds:
+//   out1: [0x0 ~> 0xffffffffffffffff]
+func fiat_pasta_fq_cmovznz_u64(out1 *uint64, arg1 fiat_pasta_fq_uint1, arg2 uint64, arg3 uint64) {
+	x1 := arg1
+	x2 := (uint64((fiat_pasta_fq_int1(0x0) - fiat_pasta_fq_int1(x1))) & 0xffffffffffffffff)
+	x3 := ((x2 & arg3) | ((^x2) & arg2))
+	*out1 = x3
+}
+
+// The function fiat_pasta_fq_mul multiplies two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_mul(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element, arg2 *fiat_pasta_fq_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, arg2[3])
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, arg2[2])
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, arg2[1])
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, arg2[0])
+	var x13 uint64
+	var x14 fiat_pasta_fq_uint1
+	x13, x14 = fiat_pasta_fq_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fq_uint1
+	x15, x16 = fiat_pasta_fq_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fq_uint1
+	x17, x18 = fiat_pasta_fq_addcarryx_u64(x8, x5, x16)
+	x19 := (uint64(x18) + x6)
+	var x20 uint64
+	_, x20 = bits.Mul64(x11, 0x8c46eb20ffffffff)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x20, 0x4000000000000000)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x20, 0x224698fc0994a8dd)
+	var x26 uint64
+	var x27 uint64
+	x27, x26 = bits.Mul64(x20, 0x8c46eb2100000001)
+	var x28 uint64
+	var x29 fiat_pasta_fq_uint1
+	x28, x29 = fiat_pasta_fq_addcarryx_u64(x27, x24, 0x0)
+	x30 := (uint64(x29) + x25)
+	var x32 fiat_pasta_fq_uint1
+	_, x32 = fiat_pasta_fq_addcarryx_u64(x11, x26, 0x0)
+	var x33 uint64
+	var x34 fiat_pasta_fq_uint1
+	x33, x34 = fiat_pasta_fq_addcarryx_u64(x13, x28, x32)
+	var x35 uint64
+	var x36 fiat_pasta_fq_uint1
+	x35, x36 = fiat_pasta_fq_addcarryx_u64(x15, x30, x34)
+	var x37 uint64
+	var x38 fiat_pasta_fq_uint1
+	x37, x38 = fiat_pasta_fq_addcarryx_u64(x17, x22, x36)
+	var x39 uint64
+	var x40 fiat_pasta_fq_uint1
+	x39, x40 = fiat_pasta_fq_addcarryx_u64(x19, x23, x38)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, arg2[3])
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, arg2[2])
+	var x45 uint64
+	var x46 uint64
+	x46, x45 = bits.Mul64(x1, arg2[1])
+	var x47 uint64
+	var x48 uint64
+	x48, x47 = bits.Mul64(x1, arg2[0])
+	var x49 uint64
+	var x50 fiat_pasta_fq_uint1
+	x49, x50 = fiat_pasta_fq_addcarryx_u64(x48, x45, 0x0)
+	var x51 uint64
+	var x52 fiat_pasta_fq_uint1
+	x51, x52 = fiat_pasta_fq_addcarryx_u64(x46, x43, x50)
+	var x53 uint64
+	var x54 fiat_pasta_fq_uint1
+	x53, x54 = fiat_pasta_fq_addcarryx_u64(x44, x41, x52)
+	x55 := (uint64(x54) + x42)
+	var x56 uint64
+	var x57 fiat_pasta_fq_uint1
+	x56, x57 = fiat_pasta_fq_addcarryx_u64(x33, x47, 0x0)
+	var x58 uint64
+	var x59 fiat_pasta_fq_uint1
+	x58, x59 = fiat_pasta_fq_addcarryx_u64(x35, x49, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fq_uint1
+	x60, x61 = fiat_pasta_fq_addcarryx_u64(x37, x51, x59)
+	var x62 uint64
+	var x63 fiat_pasta_fq_uint1
+	x62, x63 = fiat_pasta_fq_addcarryx_u64(x39, x53, x61)
+	var x64 uint64
+	var x65 fiat_pasta_fq_uint1
+	x64, x65 = fiat_pasta_fq_addcarryx_u64(uint64(x40), x55, x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x56, 0x8c46eb20ffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc0994a8dd)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x8c46eb2100000001)
+	var x74 uint64
+	var x75 fiat_pasta_fq_uint1
+	x74, x75 = fiat_pasta_fq_addcarryx_u64(x73, x70, 0x0)
+	x76 := (uint64(x75) + x71)
+	var x78 fiat_pasta_fq_uint1
+	_, x78 = fiat_pasta_fq_addcarryx_u64(x56, x72, 0x0)
+	var x79 uint64
+	var x80 fiat_pasta_fq_uint1
+	x79, x80 = fiat_pasta_fq_addcarryx_u64(x58, x74, x78)
+	var x81 uint64
+	var x82 fiat_pasta_fq_uint1
+	x81, x82 = fiat_pasta_fq_addcarryx_u64(x60, x76, x80)
+	var x83 uint64
+	var x84 fiat_pasta_fq_uint1
+	x83, x84 = fiat_pasta_fq_addcarryx_u64(x62, x68, x82)
+	var x85 uint64
+	var x86 fiat_pasta_fq_uint1
+	x85, x86 = fiat_pasta_fq_addcarryx_u64(x64, x69, x84)
+	x87 := (uint64(x86) + uint64(x65))
+	var x88 uint64
+	var x89 uint64
+	x89, x88 = bits.Mul64(x2, arg2[3])
+	var x90 uint64
+	var x91 uint64
+	x91, x90 = bits.Mul64(x2, arg2[2])
+	var x92 uint64
+	var x93 uint64
+	x93, x92 = bits.Mul64(x2, arg2[1])
+	var x94 uint64
+	var x95 uint64
+	x95, x94 = bits.Mul64(x2, arg2[0])
+	var x96 uint64
+	var x97 fiat_pasta_fq_uint1
+	x96, x97 = fiat_pasta_fq_addcarryx_u64(x95, x92, 0x0)
+	var x98 uint64
+	var x99 fiat_pasta_fq_uint1
+	x98, x99 = fiat_pasta_fq_addcarryx_u64(x93, x90, x97)
+	var x100 uint64
+	var x101 fiat_pasta_fq_uint1
+	x100, x101 = fiat_pasta_fq_addcarryx_u64(x91, x88, x99)
+	x102 := (uint64(x101) + x89)
+	var x103 uint64
+	var x104 fiat_pasta_fq_uint1
+	x103, x104 = fiat_pasta_fq_addcarryx_u64(x79, x94, 0x0)
+	var x105 uint64
+	var x106 fiat_pasta_fq_uint1
+	x105, x106 = fiat_pasta_fq_addcarryx_u64(x81, x96, x104)
+	var x107 uint64
+	var x108 fiat_pasta_fq_uint1
+	x107, x108 = fiat_pasta_fq_addcarryx_u64(x83, x98, x106)
+	var x109 uint64
+	var x110 fiat_pasta_fq_uint1
+	x109, x110 = fiat_pasta_fq_addcarryx_u64(x85, x100, x108)
+	var x111 uint64
+	var x112 fiat_pasta_fq_uint1
+	x111, x112 = fiat_pasta_fq_addcarryx_u64(x87, x102, x110)
+	var x113 uint64
+	_, x113 = bits.Mul64(x103, 0x8c46eb20ffffffff)
+	var x115 uint64
+	var x116 uint64
+	x116, x115 = bits.Mul64(x113, 0x4000000000000000)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x113, 0x224698fc0994a8dd)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x113, 0x8c46eb2100000001)
+	var x121 uint64
+	var x122 fiat_pasta_fq_uint1
+	x121, x122 = fiat_pasta_fq_addcarryx_u64(x120, x117, 0x0)
+	x123 := (uint64(x122) + x118)
+	var x125 fiat_pasta_fq_uint1
+	_, x125 = fiat_pasta_fq_addcarryx_u64(x103, x119, 0x0)
+	var x126 uint64
+	var x127 fiat_pasta_fq_uint1
+	x126, x127 = fiat_pasta_fq_addcarryx_u64(x105, x121, x125)
+	var x128 uint64
+	var x129 fiat_pasta_fq_uint1
+	x128, x129 = fiat_pasta_fq_addcarryx_u64(x107, x123, x127)
+	var x130 uint64
+	var x131 fiat_pasta_fq_uint1
+	x130, x131 = fiat_pasta_fq_addcarryx_u64(x109, x115, x129)
+	var x132 uint64
+	var x133 fiat_pasta_fq_uint1
+	x132, x133 = fiat_pasta_fq_addcarryx_u64(x111, x116, x131)
+	x134 := (uint64(x133) + uint64(x112))
+	var x135 uint64
+	var x136 uint64
+	x136, x135 = bits.Mul64(x3, arg2[3])
+	var x137 uint64
+	var x138 uint64
+	x138, x137 = bits.Mul64(x3, arg2[2])
+	var x139 uint64
+	var x140 uint64
+	x140, x139 = bits.Mul64(x3, arg2[1])
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x3, arg2[0])
+	var x143 uint64
+	var x144 fiat_pasta_fq_uint1
+	x143, x144 = fiat_pasta_fq_addcarryx_u64(x142, x139, 0x0)
+	var x145 uint64
+	var x146 fiat_pasta_fq_uint1
+	x145, x146 = fiat_pasta_fq_addcarryx_u64(x140, x137, x144)
+	var x147 uint64
+	var x148 fiat_pasta_fq_uint1
+	x147, x148 = fiat_pasta_fq_addcarryx_u64(x138, x135, x146)
+	x149 := (uint64(x148) + x136)
+	var x150 uint64
+	var x151 fiat_pasta_fq_uint1
+	x150, x151 = fiat_pasta_fq_addcarryx_u64(x126, x141, 0x0)
+	var x152 uint64
+	var x153 fiat_pasta_fq_uint1
+	x152, x153 = fiat_pasta_fq_addcarryx_u64(x128, x143, x151)
+	var x154 uint64
+	var x155 fiat_pasta_fq_uint1
+	x154, x155 = fiat_pasta_fq_addcarryx_u64(x130, x145, x153)
+	var x156 uint64
+	var x157 fiat_pasta_fq_uint1
+	x156, x157 = fiat_pasta_fq_addcarryx_u64(x132, x147, x155)
+	var x158 uint64
+	var x159 fiat_pasta_fq_uint1
+	x158, x159 = fiat_pasta_fq_addcarryx_u64(x134, x149, x157)
+	var x160 uint64
+	_, x160 = bits.Mul64(x150, 0x8c46eb20ffffffff)
+	var x162 uint64
+	var x163 uint64
+	x163, x162 = bits.Mul64(x160, 0x4000000000000000)
+	var x164 uint64
+	var x165 uint64
+	x165, x164 = bits.Mul64(x160, 0x224698fc0994a8dd)
+	var x166 uint64
+	var x167 uint64
+	x167, x166 = bits.Mul64(x160, 0x8c46eb2100000001)
+	var x168 uint64
+	var x169 fiat_pasta_fq_uint1
+	x168, x169 = fiat_pasta_fq_addcarryx_u64(x167, x164, 0x0)
+	x170 := (uint64(x169) + x165)
+	var x172 fiat_pasta_fq_uint1
+	_, x172 = fiat_pasta_fq_addcarryx_u64(x150, x166, 0x0)
+	var x173 uint64
+	var x174 fiat_pasta_fq_uint1
+	x173, x174 = fiat_pasta_fq_addcarryx_u64(x152, x168, x172)
+	var x175 uint64
+	var x176 fiat_pasta_fq_uint1
+	x175, x176 = fiat_pasta_fq_addcarryx_u64(x154, x170, x174)
+	var x177 uint64
+	var x178 fiat_pasta_fq_uint1
+	x177, x178 = fiat_pasta_fq_addcarryx_u64(x156, x162, x176)
+	var x179 uint64
+	var x180 fiat_pasta_fq_uint1
+	x179, x180 = fiat_pasta_fq_addcarryx_u64(x158, x163, x178)
+	x181 := (uint64(x180) + uint64(x159))
+	var x182 uint64
+	var x183 fiat_pasta_fq_uint1
+	x182, x183 = fiat_pasta_fq_subborrowx_u64(x173, 0x8c46eb2100000001, 0x0)
+	var x184 uint64
+	var x185 fiat_pasta_fq_uint1
+	x184, x185 = fiat_pasta_fq_subborrowx_u64(x175, 0x224698fc0994a8dd, x183)
+	var x186 uint64
+	var x187 fiat_pasta_fq_uint1
+	x186, x187 = fiat_pasta_fq_subborrowx_u64(x177, uint64(0x0), x185)
+	var x188 uint64
+	var x189 fiat_pasta_fq_uint1
+	x188, x189 = fiat_pasta_fq_subborrowx_u64(x179, 0x4000000000000000, x187)
+	var x191 fiat_pasta_fq_uint1
+	_, x191 = fiat_pasta_fq_subborrowx_u64(x181, uint64(0x0), x189)
+	var x192 uint64
+	fiat_pasta_fq_cmovznz_u64(&x192, x191, x182, x173)
+	var x193 uint64
+	fiat_pasta_fq_cmovznz_u64(&x193, x191, x184, x175)
+	var x194 uint64
+	fiat_pasta_fq_cmovznz_u64(&x194, x191, x186, x177)
+	var x195 uint64
+	fiat_pasta_fq_cmovznz_u64(&x195, x191, x188, x179)
+	out1[0] = x192
+	out1[1] = x193
+	out1[2] = x194
+	out1[3] = x195
+}
+
+// The function fiat_pasta_fq_square squares a field element in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_square(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, arg1[3])
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, arg1[2])
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, arg1[1])
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, arg1[0])
+	var x13 uint64
+	var x14 fiat_pasta_fq_uint1
+	x13, x14 = fiat_pasta_fq_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fq_uint1
+	x15, x16 = fiat_pasta_fq_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fq_uint1
+	x17, x18 = fiat_pasta_fq_addcarryx_u64(x8, x5, x16)
+	x19 := (uint64(x18) + x6)
+	var x20 uint64
+	_, x20 = bits.Mul64(x11, 0x8c46eb20ffffffff)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x20, 0x4000000000000000)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x20, 0x224698fc0994a8dd)
+	var x26 uint64
+	var x27 uint64
+	x27, x26 = bits.Mul64(x20, 0x8c46eb2100000001)
+	var x28 uint64
+	var x29 fiat_pasta_fq_uint1
+	x28, x29 = fiat_pasta_fq_addcarryx_u64(x27, x24, 0x0)
+	x30 := (uint64(x29) + x25)
+	var x32 fiat_pasta_fq_uint1
+	_, x32 = fiat_pasta_fq_addcarryx_u64(x11, x26, 0x0)
+	var x33 uint64
+	var x34 fiat_pasta_fq_uint1
+	x33, x34 = fiat_pasta_fq_addcarryx_u64(x13, x28, x32)
+	var x35 uint64
+	var x36 fiat_pasta_fq_uint1
+	x35, x36 = fiat_pasta_fq_addcarryx_u64(x15, x30, x34)
+	var x37 uint64
+	var x38 fiat_pasta_fq_uint1
+	x37, x38 = fiat_pasta_fq_addcarryx_u64(x17, x22, x36)
+	var x39 uint64
+	var x40 fiat_pasta_fq_uint1
+	x39, x40 = fiat_pasta_fq_addcarryx_u64(x19, x23, x38)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, arg1[3])
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, arg1[2])
+	var x45 uint64
+	var x46 uint64
+	x46, x45 = bits.Mul64(x1, arg1[1])
+	var x47 uint64
+	var x48 uint64
+	x48, x47 = bits.Mul64(x1, arg1[0])
+	var x49 uint64
+	var x50 fiat_pasta_fq_uint1
+	x49, x50 = fiat_pasta_fq_addcarryx_u64(x48, x45, 0x0)
+	var x51 uint64
+	var x52 fiat_pasta_fq_uint1
+	x51, x52 = fiat_pasta_fq_addcarryx_u64(x46, x43, x50)
+	var x53 uint64
+	var x54 fiat_pasta_fq_uint1
+	x53, x54 = fiat_pasta_fq_addcarryx_u64(x44, x41, x52)
+	x55 := (uint64(x54) + x42)
+	var x56 uint64
+	var x57 fiat_pasta_fq_uint1
+	x56, x57 = fiat_pasta_fq_addcarryx_u64(x33, x47, 0x0)
+	var x58 uint64
+	var x59 fiat_pasta_fq_uint1
+	x58, x59 = fiat_pasta_fq_addcarryx_u64(x35, x49, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fq_uint1
+	x60, x61 = fiat_pasta_fq_addcarryx_u64(x37, x51, x59)
+	var x62 uint64
+	var x63 fiat_pasta_fq_uint1
+	x62, x63 = fiat_pasta_fq_addcarryx_u64(x39, x53, x61)
+	var x64 uint64
+	var x65 fiat_pasta_fq_uint1
+	x64, x65 = fiat_pasta_fq_addcarryx_u64(uint64(x40), x55, x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x56, 0x8c46eb20ffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc0994a8dd)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x8c46eb2100000001)
+	var x74 uint64
+	var x75 fiat_pasta_fq_uint1
+	x74, x75 = fiat_pasta_fq_addcarryx_u64(x73, x70, 0x0)
+	x76 := (uint64(x75) + x71)
+	var x78 fiat_pasta_fq_uint1
+	_, x78 = fiat_pasta_fq_addcarryx_u64(x56, x72, 0x0)
+	var x79 uint64
+	var x80 fiat_pasta_fq_uint1
+	x79, x80 = fiat_pasta_fq_addcarryx_u64(x58, x74, x78)
+	var x81 uint64
+	var x82 fiat_pasta_fq_uint1
+	x81, x82 = fiat_pasta_fq_addcarryx_u64(x60, x76, x80)
+	var x83 uint64
+	var x84 fiat_pasta_fq_uint1
+	x83, x84 = fiat_pasta_fq_addcarryx_u64(x62, x68, x82)
+	var x85 uint64
+	var x86 fiat_pasta_fq_uint1
+	x85, x86 = fiat_pasta_fq_addcarryx_u64(x64, x69, x84)
+	x87 := (uint64(x86) + uint64(x65))
+	var x88 uint64
+	var x89 uint64
+	x89, x88 = bits.Mul64(x2, arg1[3])
+	var x90 uint64
+	var x91 uint64
+	x91, x90 = bits.Mul64(x2, arg1[2])
+	var x92 uint64
+	var x93 uint64
+	x93, x92 = bits.Mul64(x2, arg1[1])
+	var x94 uint64
+	var x95 uint64
+	x95, x94 = bits.Mul64(x2, arg1[0])
+	var x96 uint64
+	var x97 fiat_pasta_fq_uint1
+	x96, x97 = fiat_pasta_fq_addcarryx_u64(x95, x92, 0x0)
+	var x98 uint64
+	var x99 fiat_pasta_fq_uint1
+	x98, x99 = fiat_pasta_fq_addcarryx_u64(x93, x90, x97)
+	var x100 uint64
+	var x101 fiat_pasta_fq_uint1
+	x100, x101 = fiat_pasta_fq_addcarryx_u64(x91, x88, x99)
+	x102 := (uint64(x101) + x89)
+	var x103 uint64
+	var x104 fiat_pasta_fq_uint1
+	x103, x104 = fiat_pasta_fq_addcarryx_u64(x79, x94, 0x0)
+	var x105 uint64
+	var x106 fiat_pasta_fq_uint1
+	x105, x106 = fiat_pasta_fq_addcarryx_u64(x81, x96, x104)
+	var x107 uint64
+	var x108 fiat_pasta_fq_uint1
+	x107, x108 = fiat_pasta_fq_addcarryx_u64(x83, x98, x106)
+	var x109 uint64
+	var x110 fiat_pasta_fq_uint1
+	x109, x110 = fiat_pasta_fq_addcarryx_u64(x85, x100, x108)
+	var x111 uint64
+	var x112 fiat_pasta_fq_uint1
+	x111, x112 = fiat_pasta_fq_addcarryx_u64(x87, x102, x110)
+	var x113 uint64
+	_, x113 = bits.Mul64(x103, 0x8c46eb20ffffffff)
+	var x115 uint64
+	var x116 uint64
+	x116, x115 = bits.Mul64(x113, 0x4000000000000000)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x113, 0x224698fc0994a8dd)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x113, 0x8c46eb2100000001)
+	var x121 uint64
+	var x122 fiat_pasta_fq_uint1
+	x121, x122 = fiat_pasta_fq_addcarryx_u64(x120, x117, 0x0)
+	x123 := (uint64(x122) + x118)
+	var x125 fiat_pasta_fq_uint1
+	_, x125 = fiat_pasta_fq_addcarryx_u64(x103, x119, 0x0)
+	var x126 uint64
+	var x127 fiat_pasta_fq_uint1
+	x126, x127 = fiat_pasta_fq_addcarryx_u64(x105, x121, x125)
+	var x128 uint64
+	var x129 fiat_pasta_fq_uint1
+	x128, x129 = fiat_pasta_fq_addcarryx_u64(x107, x123, x127)
+	var x130 uint64
+	var x131 fiat_pasta_fq_uint1
+	x130, x131 = fiat_pasta_fq_addcarryx_u64(x109, x115, x129)
+	var x132 uint64
+	var x133 fiat_pasta_fq_uint1
+	x132, x133 = fiat_pasta_fq_addcarryx_u64(x111, x116, x131)
+	x134 := (uint64(x133) + uint64(x112))
+	var x135 uint64
+	var x136 uint64
+	x136, x135 = bits.Mul64(x3, arg1[3])
+	var x137 uint64
+	var x138 uint64
+	x138, x137 = bits.Mul64(x3, arg1[2])
+	var x139 uint64
+	var x140 uint64
+	x140, x139 = bits.Mul64(x3, arg1[1])
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x3, arg1[0])
+	var x143 uint64
+	var x144 fiat_pasta_fq_uint1
+	x143, x144 = fiat_pasta_fq_addcarryx_u64(x142, x139, 0x0)
+	var x145 uint64
+	var x146 fiat_pasta_fq_uint1
+	x145, x146 = fiat_pasta_fq_addcarryx_u64(x140, x137, x144)
+	var x147 uint64
+	var x148 fiat_pasta_fq_uint1
+	x147, x148 = fiat_pasta_fq_addcarryx_u64(x138, x135, x146)
+	x149 := (uint64(x148) + x136)
+	var x150 uint64
+	var x151 fiat_pasta_fq_uint1
+	x150, x151 = fiat_pasta_fq_addcarryx_u64(x126, x141, 0x0)
+	var x152 uint64
+	var x153 fiat_pasta_fq_uint1
+	x152, x153 = fiat_pasta_fq_addcarryx_u64(x128, x143, x151)
+	var x154 uint64
+	var x155 fiat_pasta_fq_uint1
+	x154, x155 = fiat_pasta_fq_addcarryx_u64(x130, x145, x153)
+	var x156 uint64
+	var x157 fiat_pasta_fq_uint1
+	x156, x157 = fiat_pasta_fq_addcarryx_u64(x132, x147, x155)
+	var x158 uint64
+	var x159 fiat_pasta_fq_uint1
+	x158, x159 = fiat_pasta_fq_addcarryx_u64(x134, x149, x157)
+	var x160 uint64
+	_, x160 = bits.Mul64(x150, 0x8c46eb20ffffffff)
+	var x162 uint64
+	var x163 uint64
+	x163, x162 = bits.Mul64(x160, 0x4000000000000000)
+	var x164 uint64
+	var x165 uint64
+	x165, x164 = bits.Mul64(x160, 0x224698fc0994a8dd)
+	var x166 uint64
+	var x167 uint64
+	x167, x166 = bits.Mul64(x160, 0x8c46eb2100000001)
+	var x168 uint64
+	var x169 fiat_pasta_fq_uint1
+	x168, x169 = fiat_pasta_fq_addcarryx_u64(x167, x164, 0x0)
+	x170 := (uint64(x169) + x165)
+	var x172 fiat_pasta_fq_uint1
+	_, x172 = fiat_pasta_fq_addcarryx_u64(x150, x166, 0x0)
+	var x173 uint64
+	var x174 fiat_pasta_fq_uint1
+	x173, x174 = fiat_pasta_fq_addcarryx_u64(x152, x168, x172)
+	var x175 uint64
+	var x176 fiat_pasta_fq_uint1
+	x175, x176 = fiat_pasta_fq_addcarryx_u64(x154, x170, x174)
+	var x177 uint64
+	var x178 fiat_pasta_fq_uint1
+	x177, x178 = fiat_pasta_fq_addcarryx_u64(x156, x162, x176)
+	var x179 uint64
+	var x180 fiat_pasta_fq_uint1
+	x179, x180 = fiat_pasta_fq_addcarryx_u64(x158, x163, x178)
+	x181 := (uint64(x180) + uint64(x159))
+	var x182 uint64
+	var x183 fiat_pasta_fq_uint1
+	x182, x183 = fiat_pasta_fq_subborrowx_u64(x173, 0x8c46eb2100000001, 0x0)
+	var x184 uint64
+	var x185 fiat_pasta_fq_uint1
+	x184, x185 = fiat_pasta_fq_subborrowx_u64(x175, 0x224698fc0994a8dd, x183)
+	var x186 uint64
+	var x187 fiat_pasta_fq_uint1
+	x186, x187 = fiat_pasta_fq_subborrowx_u64(x177, uint64(0x0), x185)
+	var x188 uint64
+	var x189 fiat_pasta_fq_uint1
+	x188, x189 = fiat_pasta_fq_subborrowx_u64(x179, 0x4000000000000000, x187)
+	var x191 fiat_pasta_fq_uint1
+	_, x191 = fiat_pasta_fq_subborrowx_u64(x181, uint64(0x0), x189)
+	var x192 uint64
+	fiat_pasta_fq_cmovznz_u64(&x192, x191, x182, x173)
+	var x193 uint64
+	fiat_pasta_fq_cmovznz_u64(&x193, x191, x184, x175)
+	var x194 uint64
+	fiat_pasta_fq_cmovznz_u64(&x194, x191, x186, x177)
+	var x195 uint64
+	fiat_pasta_fq_cmovznz_u64(&x195, x191, x188, x179)
+	out1[0] = x192
+	out1[1] = x193
+	out1[2] = x194
+	out1[3] = x195
+}
+
+// The function fiat_pasta_fq_add adds two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_add(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element, arg2 *fiat_pasta_fq_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fq_uint1
+	x1, x2 = fiat_pasta_fq_addcarryx_u64(arg1[0], arg2[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fq_uint1
+	x3, x4 = fiat_pasta_fq_addcarryx_u64(arg1[1], arg2[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fq_uint1
+	x5, x6 = fiat_pasta_fq_addcarryx_u64(arg1[2], arg2[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fq_uint1
+	x7, x8 = fiat_pasta_fq_addcarryx_u64(arg1[3], arg2[3], x6)
+	var x9 uint64
+	var x10 fiat_pasta_fq_uint1
+	x9, x10 = fiat_pasta_fq_subborrowx_u64(x1, 0x8c46eb2100000001, 0x0)
+	var x11 uint64
+	var x12 fiat_pasta_fq_uint1
+	x11, x12 = fiat_pasta_fq_subborrowx_u64(x3, 0x224698fc0994a8dd, x10)
+	var x13 uint64
+	var x14 fiat_pasta_fq_uint1
+	x13, x14 = fiat_pasta_fq_subborrowx_u64(x5, uint64(0x0), x12)
+	var x15 uint64
+	var x16 fiat_pasta_fq_uint1
+	x15, x16 = fiat_pasta_fq_subborrowx_u64(x7, 0x4000000000000000, x14)
+	var x18 fiat_pasta_fq_uint1
+	_, x18 = fiat_pasta_fq_subborrowx_u64(uint64(x8), uint64(0x0), x16)
+	var x19 uint64
+	fiat_pasta_fq_cmovznz_u64(&x19, x18, x9, x1)
+	var x20 uint64
+	fiat_pasta_fq_cmovznz_u64(&x20, x18, x11, x3)
+	var x21 uint64
+	fiat_pasta_fq_cmovznz_u64(&x21, x18, x13, x5)
+	var x22 uint64
+	fiat_pasta_fq_cmovznz_u64(&x22, x18, x15, x7)
+	out1[0] = x19
+	out1[1] = x20
+	out1[2] = x21
+	out1[3] = x22
+}
+
+// The function fiat_pasta_fq_sub subtracts two field elements in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+//   0 ≤ eval arg2 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_sub(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element, arg2 *fiat_pasta_fq_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fq_uint1
+	x1, x2 = fiat_pasta_fq_subborrowx_u64(arg1[0], arg2[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fq_uint1
+	x3, x4 = fiat_pasta_fq_subborrowx_u64(arg1[1], arg2[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fq_uint1
+	x5, x6 = fiat_pasta_fq_subborrowx_u64(arg1[2], arg2[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fq_uint1
+	x7, x8 = fiat_pasta_fq_subborrowx_u64(arg1[3], arg2[3], x6)
+	var x9 uint64
+	fiat_pasta_fq_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
+	var x10 uint64
+	var x11 fiat_pasta_fq_uint1
+	x10, x11 = fiat_pasta_fq_addcarryx_u64(x1, (x9 & 0x8c46eb2100000001), 0x0)
+	var x12 uint64
+	var x13 fiat_pasta_fq_uint1
+	x12, x13 = fiat_pasta_fq_addcarryx_u64(x3, (x9 & 0x224698fc0994a8dd), x11)
+	var x14 uint64
+	var x15 fiat_pasta_fq_uint1
+	x14, x15 = fiat_pasta_fq_addcarryx_u64(x5, uint64(0x0), x13)
+	var x16 uint64
+	x16, _ = fiat_pasta_fq_addcarryx_u64(x7, (x9 & 0x4000000000000000), x15)
+	out1[0] = x10
+	out1[1] = x12
+	out1[2] = x14
+	out1[3] = x16
+}
+
+// The function fiat_pasta_fq_opp negates a field element in the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = -eval (from_montgomery arg1) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_opp(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element) {
+	var x1 uint64
+	var x2 fiat_pasta_fq_uint1
+	x1, x2 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), arg1[0], 0x0)
+	var x3 uint64
+	var x4 fiat_pasta_fq_uint1
+	x3, x4 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), arg1[1], x2)
+	var x5 uint64
+	var x6 fiat_pasta_fq_uint1
+	x5, x6 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), arg1[2], x4)
+	var x7 uint64
+	var x8 fiat_pasta_fq_uint1
+	x7, x8 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), arg1[3], x6)
+	var x9 uint64
+	fiat_pasta_fq_cmovznz_u64(&x9, x8, uint64(0x0), 0xffffffffffffffff)
+	var x10 uint64
+	var x11 fiat_pasta_fq_uint1
+	x10, x11 = fiat_pasta_fq_addcarryx_u64(x1, (x9 & 0x8c46eb2100000001), 0x0)
+	var x12 uint64
+	var x13 fiat_pasta_fq_uint1
+	x12, x13 = fiat_pasta_fq_addcarryx_u64(x3, (x9 & 0x224698fc0994a8dd), x11)
+	var x14 uint64
+	var x15 fiat_pasta_fq_uint1
+	x14, x15 = fiat_pasta_fq_addcarryx_u64(x5, uint64(0x0), x13)
+	var x16 uint64
+	x16, _ = fiat_pasta_fq_addcarryx_u64(x7, (x9 & 0x4000000000000000), x15)
+	out1[0] = x10
+	out1[1] = x12
+	out1[2] = x14
+	out1[3] = x16
+}
+
+// The function fiat_pasta_fq_from_montgomery translates a field element out of the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_from_montgomery(out1 *fiat_pasta_fq_non_montgomery_domain_field_element, arg1 *fiat_pasta_fq_montgomery_domain_field_element) {
+	x1 := arg1[0]
+	var x2 uint64
+	_, x2 = bits.Mul64(x1, 0x8c46eb20ffffffff)
+	var x4 uint64
+	var x5 uint64
+	x5, x4 = bits.Mul64(x2, 0x4000000000000000)
+	var x6 uint64
+	var x7 uint64
+	x7, x6 = bits.Mul64(x2, 0x224698fc0994a8dd)
+	var x8 uint64
+	var x9 uint64
+	x9, x8 = bits.Mul64(x2, 0x8c46eb2100000001)
+	var x10 uint64
+	var x11 fiat_pasta_fq_uint1
+	x10, x11 = fiat_pasta_fq_addcarryx_u64(x9, x6, 0x0)
+	var x13 fiat_pasta_fq_uint1
+	_, x13 = fiat_pasta_fq_addcarryx_u64(x1, x8, 0x0)
+	var x14 uint64
+	var x15 fiat_pasta_fq_uint1
+	x14, x15 = fiat_pasta_fq_addcarryx_u64(uint64(0x0), x10, x13)
+	var x16 uint64
+	var x17 fiat_pasta_fq_uint1
+	x16, x17 = fiat_pasta_fq_addcarryx_u64(x14, arg1[1], 0x0)
+	var x18 uint64
+	_, x18 = bits.Mul64(x16, 0x8c46eb20ffffffff)
+	var x20 uint64
+	var x21 uint64
+	x21, x20 = bits.Mul64(x18, 0x4000000000000000)
+	var x22 uint64
+	var x23 uint64
+	x23, x22 = bits.Mul64(x18, 0x224698fc0994a8dd)
+	var x24 uint64
+	var x25 uint64
+	x25, x24 = bits.Mul64(x18, 0x8c46eb2100000001)
+	var x26 uint64
+	var x27 fiat_pasta_fq_uint1
+	x26, x27 = fiat_pasta_fq_addcarryx_u64(x25, x22, 0x0)
+	var x29 fiat_pasta_fq_uint1
+	_, x29 = fiat_pasta_fq_addcarryx_u64(x16, x24, 0x0)
+	var x30 uint64
+	var x31 fiat_pasta_fq_uint1
+	x30, x31 = fiat_pasta_fq_addcarryx_u64((uint64(x17) + (uint64(x15) + (uint64(x11) + x7))), x26, x29)
+	var x32 uint64
+	var x33 fiat_pasta_fq_uint1
+	x32, x33 = fiat_pasta_fq_addcarryx_u64(x4, (uint64(x27) + x23), x31)
+	var x34 uint64
+	var x35 fiat_pasta_fq_uint1
+	x34, x35 = fiat_pasta_fq_addcarryx_u64(x5, x20, x33)
+	var x36 uint64
+	var x37 fiat_pasta_fq_uint1
+	x36, x37 = fiat_pasta_fq_addcarryx_u64(x30, arg1[2], 0x0)
+	var x38 uint64
+	var x39 fiat_pasta_fq_uint1
+	x38, x39 = fiat_pasta_fq_addcarryx_u64(x32, uint64(0x0), x37)
+	var x40 uint64
+	var x41 fiat_pasta_fq_uint1
+	x40, x41 = fiat_pasta_fq_addcarryx_u64(x34, uint64(0x0), x39)
+	var x42 uint64
+	_, x42 = bits.Mul64(x36, 0x8c46eb20ffffffff)
+	var x44 uint64
+	var x45 uint64
+	x45, x44 = bits.Mul64(x42, 0x4000000000000000)
+	var x46 uint64
+	var x47 uint64
+	x47, x46 = bits.Mul64(x42, 0x224698fc0994a8dd)
+	var x48 uint64
+	var x49 uint64
+	x49, x48 = bits.Mul64(x42, 0x8c46eb2100000001)
+	var x50 uint64
+	var x51 fiat_pasta_fq_uint1
+	x50, x51 = fiat_pasta_fq_addcarryx_u64(x49, x46, 0x0)
+	var x53 fiat_pasta_fq_uint1
+	_, x53 = fiat_pasta_fq_addcarryx_u64(x36, x48, 0x0)
+	var x54 uint64
+	var x55 fiat_pasta_fq_uint1
+	x54, x55 = fiat_pasta_fq_addcarryx_u64(x38, x50, x53)
+	var x56 uint64
+	var x57 fiat_pasta_fq_uint1
+	x56, x57 = fiat_pasta_fq_addcarryx_u64(x40, (uint64(x51) + x47), x55)
+	var x58 uint64
+	var x59 fiat_pasta_fq_uint1
+	x58, x59 = fiat_pasta_fq_addcarryx_u64((uint64(x41) + (uint64(x35) + x21)), x44, x57)
+	var x60 uint64
+	var x61 fiat_pasta_fq_uint1
+	x60, x61 = fiat_pasta_fq_addcarryx_u64(x54, arg1[3], 0x0)
+	var x62 uint64
+	var x63 fiat_pasta_fq_uint1
+	x62, x63 = fiat_pasta_fq_addcarryx_u64(x56, uint64(0x0), x61)
+	var x64 uint64
+	var x65 fiat_pasta_fq_uint1
+	x64, x65 = fiat_pasta_fq_addcarryx_u64(x58, uint64(0x0), x63)
+	var x66 uint64
+	_, x66 = bits.Mul64(x60, 0x8c46eb20ffffffff)
+	var x68 uint64
+	var x69 uint64
+	x69, x68 = bits.Mul64(x66, 0x4000000000000000)
+	var x70 uint64
+	var x71 uint64
+	x71, x70 = bits.Mul64(x66, 0x224698fc0994a8dd)
+	var x72 uint64
+	var x73 uint64
+	x73, x72 = bits.Mul64(x66, 0x8c46eb2100000001)
+	var x74 uint64
+	var x75 fiat_pasta_fq_uint1
+	x74, x75 = fiat_pasta_fq_addcarryx_u64(x73, x70, 0x0)
+	var x77 fiat_pasta_fq_uint1
+	_, x77 = fiat_pasta_fq_addcarryx_u64(x60, x72, 0x0)
+	var x78 uint64
+	var x79 fiat_pasta_fq_uint1
+	x78, x79 = fiat_pasta_fq_addcarryx_u64(x62, x74, x77)
+	var x80 uint64
+	var x81 fiat_pasta_fq_uint1
+	x80, x81 = fiat_pasta_fq_addcarryx_u64(x64, (uint64(x75) + x71), x79)
+	var x82 uint64
+	var x83 fiat_pasta_fq_uint1
+	x82, x83 = fiat_pasta_fq_addcarryx_u64((uint64(x65) + (uint64(x59) + x45)), x68, x81)
+	x84 := (uint64(x83) + x69)
+	var x85 uint64
+	var x86 fiat_pasta_fq_uint1
+	x85, x86 = fiat_pasta_fq_subborrowx_u64(x78, 0x8c46eb2100000001, 0x0)
+	var x87 uint64
+	var x88 fiat_pasta_fq_uint1
+	x87, x88 = fiat_pasta_fq_subborrowx_u64(x80, 0x224698fc0994a8dd, x86)
+	var x89 uint64
+	var x90 fiat_pasta_fq_uint1
+	x89, x90 = fiat_pasta_fq_subborrowx_u64(x82, uint64(0x0), x88)
+	var x91 uint64
+	var x92 fiat_pasta_fq_uint1
+	x91, x92 = fiat_pasta_fq_subborrowx_u64(x84, 0x4000000000000000, x90)
+	var x94 fiat_pasta_fq_uint1
+	_, x94 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), uint64(0x0), x92)
+	var x95 uint64
+	fiat_pasta_fq_cmovznz_u64(&x95, x94, x85, x78)
+	var x96 uint64
+	fiat_pasta_fq_cmovznz_u64(&x96, x94, x87, x80)
+	var x97 uint64
+	fiat_pasta_fq_cmovznz_u64(&x97, x94, x89, x82)
+	var x98 uint64
+	fiat_pasta_fq_cmovznz_u64(&x98, x94, x91, x84)
+	out1[0] = x95
+	out1[1] = x96
+	out1[2] = x97
+	out1[3] = x98
+}
+
+// The function fiat_pasta_fq_to_montgomery translates a field element into the Montgomery domain.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   eval (from_montgomery out1) mod m = eval arg1 mod m
+//   0 ≤ eval out1 < m
+//
+func fiat_pasta_fq_to_montgomery(out1 *fiat_pasta_fq_montgomery_domain_field_element, arg1 *fiat_pasta_fq_non_montgomery_domain_field_element) {
+	x1 := arg1[1]
+	x2 := arg1[2]
+	x3 := arg1[3]
+	x4 := arg1[0]
+	var x5 uint64
+	var x6 uint64
+	x6, x5 = bits.Mul64(x4, 0x96d41af7ccfdaa9)
+	var x7 uint64
+	var x8 uint64
+	x8, x7 = bits.Mul64(x4, 0x7fae231004ccf590)
+	var x9 uint64
+	var x10 uint64
+	x10, x9 = bits.Mul64(x4, 0x67bb433d891a16e3)
+	var x11 uint64
+	var x12 uint64
+	x12, x11 = bits.Mul64(x4, 0xfc9678ff0000000f)
+	var x13 uint64
+	var x14 fiat_pasta_fq_uint1
+	x13, x14 = fiat_pasta_fq_addcarryx_u64(x12, x9, 0x0)
+	var x15 uint64
+	var x16 fiat_pasta_fq_uint1
+	x15, x16 = fiat_pasta_fq_addcarryx_u64(x10, x7, x14)
+	var x17 uint64
+	var x18 fiat_pasta_fq_uint1
+	x17, x18 = fiat_pasta_fq_addcarryx_u64(x8, x5, x16)
+	var x19 uint64
+	_, x19 = bits.Mul64(x11, 0x8c46eb20ffffffff)
+	var x21 uint64
+	var x22 uint64
+	x22, x21 = bits.Mul64(x19, 0x4000000000000000)
+	var x23 uint64
+	var x24 uint64
+	x24, x23 = bits.Mul64(x19, 0x224698fc0994a8dd)
+	var x25 uint64
+	var x26 uint64
+	x26, x25 = bits.Mul64(x19, 0x8c46eb2100000001)
+	var x27 uint64
+	var x28 fiat_pasta_fq_uint1
+	x27, x28 = fiat_pasta_fq_addcarryx_u64(x26, x23, 0x0)
+	var x30 fiat_pasta_fq_uint1
+	_, x30 = fiat_pasta_fq_addcarryx_u64(x11, x25, 0x0)
+	var x31 uint64
+	var x32 fiat_pasta_fq_uint1
+	x31, x32 = fiat_pasta_fq_addcarryx_u64(x13, x27, x30)
+	var x33 uint64
+	var x34 fiat_pasta_fq_uint1
+	x33, x34 = fiat_pasta_fq_addcarryx_u64(x15, (uint64(x28) + x24), x32)
+	var x35 uint64
+	var x36 fiat_pasta_fq_uint1
+	x35, x36 = fiat_pasta_fq_addcarryx_u64(x17, x21, x34)
+	var x37 uint64
+	var x38 uint64
+	x38, x37 = bits.Mul64(x1, 0x96d41af7ccfdaa9)
+	var x39 uint64
+	var x40 uint64
+	x40, x39 = bits.Mul64(x1, 0x7fae231004ccf590)
+	var x41 uint64
+	var x42 uint64
+	x42, x41 = bits.Mul64(x1, 0x67bb433d891a16e3)
+	var x43 uint64
+	var x44 uint64
+	x44, x43 = bits.Mul64(x1, 0xfc9678ff0000000f)
+	var x45 uint64
+	var x46 fiat_pasta_fq_uint1
+	x45, x46 = fiat_pasta_fq_addcarryx_u64(x44, x41, 0x0)
+	var x47 uint64
+	var x48 fiat_pasta_fq_uint1
+	x47, x48 = fiat_pasta_fq_addcarryx_u64(x42, x39, x46)
+	var x49 uint64
+	var x50 fiat_pasta_fq_uint1
+	x49, x50 = fiat_pasta_fq_addcarryx_u64(x40, x37, x48)
+	var x51 uint64
+	var x52 fiat_pasta_fq_uint1
+	x51, x52 = fiat_pasta_fq_addcarryx_u64(x31, x43, 0x0)
+	var x53 uint64
+	var x54 fiat_pasta_fq_uint1
+	x53, x54 = fiat_pasta_fq_addcarryx_u64(x33, x45, x52)
+	var x55 uint64
+	var x56 fiat_pasta_fq_uint1
+	x55, x56 = fiat_pasta_fq_addcarryx_u64(x35, x47, x54)
+	var x57 uint64
+	var x58 fiat_pasta_fq_uint1
+	x57, x58 = fiat_pasta_fq_addcarryx_u64(((uint64(x36) + (uint64(x18) + x6)) + x22), x49, x56)
+	var x59 uint64
+	_, x59 = bits.Mul64(x51, 0x8c46eb20ffffffff)
+	var x61 uint64
+	var x62 uint64
+	x62, x61 = bits.Mul64(x59, 0x4000000000000000)
+	var x63 uint64
+	var x64 uint64
+	x64, x63 = bits.Mul64(x59, 0x224698fc0994a8dd)
+	var x65 uint64
+	var x66 uint64
+	x66, x65 = bits.Mul64(x59, 0x8c46eb2100000001)
+	var x67 uint64
+	var x68 fiat_pasta_fq_uint1
+	x67, x68 = fiat_pasta_fq_addcarryx_u64(x66, x63, 0x0)
+	var x70 fiat_pasta_fq_uint1
+	_, x70 = fiat_pasta_fq_addcarryx_u64(x51, x65, 0x0)
+	var x71 uint64
+	var x72 fiat_pasta_fq_uint1
+	x71, x72 = fiat_pasta_fq_addcarryx_u64(x53, x67, x70)
+	var x73 uint64
+	var x74 fiat_pasta_fq_uint1
+	x73, x74 = fiat_pasta_fq_addcarryx_u64(x55, (uint64(x68) + x64), x72)
+	var x75 uint64
+	var x76 fiat_pasta_fq_uint1
+	x75, x76 = fiat_pasta_fq_addcarryx_u64(x57, x61, x74)
+	var x77 uint64
+	var x78 uint64
+	x78, x77 = bits.Mul64(x2, 0x96d41af7ccfdaa9)
+	var x79 uint64
+	var x80 uint64
+	x80, x79 = bits.Mul64(x2, 0x7fae231004ccf590)
+	var x81 uint64
+	var x82 uint64
+	x82, x81 = bits.Mul64(x2, 0x67bb433d891a16e3)
+	var x83 uint64
+	var x84 uint64
+	x84, x83 = bits.Mul64(x2, 0xfc9678ff0000000f)
+	var x85 uint64
+	var x86 fiat_pasta_fq_uint1
+	x85, x86 = fiat_pasta_fq_addcarryx_u64(x84, x81, 0x0)
+	var x87 uint64
+	var x88 fiat_pasta_fq_uint1
+	x87, x88 = fiat_pasta_fq_addcarryx_u64(x82, x79, x86)
+	var x89 uint64
+	var x90 fiat_pasta_fq_uint1
+	x89, x90 = fiat_pasta_fq_addcarryx_u64(x80, x77, x88)
+	var x91 uint64
+	var x92 fiat_pasta_fq_uint1
+	x91, x92 = fiat_pasta_fq_addcarryx_u64(x71, x83, 0x0)
+	var x93 uint64
+	var x94 fiat_pasta_fq_uint1
+	x93, x94 = fiat_pasta_fq_addcarryx_u64(x73, x85, x92)
+	var x95 uint64
+	var x96 fiat_pasta_fq_uint1
+	x95, x96 = fiat_pasta_fq_addcarryx_u64(x75, x87, x94)
+	var x97 uint64
+	var x98 fiat_pasta_fq_uint1
+	x97, x98 = fiat_pasta_fq_addcarryx_u64(((uint64(x76) + (uint64(x58) + (uint64(x50) + x38))) + x62), x89, x96)
+	var x99 uint64
+	_, x99 = bits.Mul64(x91, 0x8c46eb20ffffffff)
+	var x101 uint64
+	var x102 uint64
+	x102, x101 = bits.Mul64(x99, 0x4000000000000000)
+	var x103 uint64
+	var x104 uint64
+	x104, x103 = bits.Mul64(x99, 0x224698fc0994a8dd)
+	var x105 uint64
+	var x106 uint64
+	x106, x105 = bits.Mul64(x99, 0x8c46eb2100000001)
+	var x107 uint64
+	var x108 fiat_pasta_fq_uint1
+	x107, x108 = fiat_pasta_fq_addcarryx_u64(x106, x103, 0x0)
+	var x110 fiat_pasta_fq_uint1
+	_, x110 = fiat_pasta_fq_addcarryx_u64(x91, x105, 0x0)
+	var x111 uint64
+	var x112 fiat_pasta_fq_uint1
+	x111, x112 = fiat_pasta_fq_addcarryx_u64(x93, x107, x110)
+	var x113 uint64
+	var x114 fiat_pasta_fq_uint1
+	x113, x114 = fiat_pasta_fq_addcarryx_u64(x95, (uint64(x108) + x104), x112)
+	var x115 uint64
+	var x116 fiat_pasta_fq_uint1
+	x115, x116 = fiat_pasta_fq_addcarryx_u64(x97, x101, x114)
+	var x117 uint64
+	var x118 uint64
+	x118, x117 = bits.Mul64(x3, 0x96d41af7ccfdaa9)
+	var x119 uint64
+	var x120 uint64
+	x120, x119 = bits.Mul64(x3, 0x7fae231004ccf590)
+	var x121 uint64
+	var x122 uint64
+	x122, x121 = bits.Mul64(x3, 0x67bb433d891a16e3)
+	var x123 uint64
+	var x124 uint64
+	x124, x123 = bits.Mul64(x3, 0xfc9678ff0000000f)
+	var x125 uint64
+	var x126 fiat_pasta_fq_uint1
+	x125, x126 = fiat_pasta_fq_addcarryx_u64(x124, x121, 0x0)
+	var x127 uint64
+	var x128 fiat_pasta_fq_uint1
+	x127, x128 = fiat_pasta_fq_addcarryx_u64(x122, x119, x126)
+	var x129 uint64
+	var x130 fiat_pasta_fq_uint1
+	x129, x130 = fiat_pasta_fq_addcarryx_u64(x120, x117, x128)
+	var x131 uint64
+	var x132 fiat_pasta_fq_uint1
+	x131, x132 = fiat_pasta_fq_addcarryx_u64(x111, x123, 0x0)
+	var x133 uint64
+	var x134 fiat_pasta_fq_uint1
+	x133, x134 = fiat_pasta_fq_addcarryx_u64(x113, x125, x132)
+	var x135 uint64
+	var x136 fiat_pasta_fq_uint1
+	x135, x136 = fiat_pasta_fq_addcarryx_u64(x115, x127, x134)
+	var x137 uint64
+	var x138 fiat_pasta_fq_uint1
+	x137, x138 = fiat_pasta_fq_addcarryx_u64(((uint64(x116) + (uint64(x98) + (uint64(x90) + x78))) + x102), x129, x136)
+	var x139 uint64
+	_, x139 = bits.Mul64(x131, 0x8c46eb20ffffffff)
+	var x141 uint64
+	var x142 uint64
+	x142, x141 = bits.Mul64(x139, 0x4000000000000000)
+	var x143 uint64
+	var x144 uint64
+	x144, x143 = bits.Mul64(x139, 0x224698fc0994a8dd)
+	var x145 uint64
+	var x146 uint64
+	x146, x145 = bits.Mul64(x139, 0x8c46eb2100000001)
+	var x147 uint64
+	var x148 fiat_pasta_fq_uint1
+	x147, x148 = fiat_pasta_fq_addcarryx_u64(x146, x143, 0x0)
+	var x150 fiat_pasta_fq_uint1
+	_, x150 = fiat_pasta_fq_addcarryx_u64(x131, x145, 0x0)
+	var x151 uint64
+	var x152 fiat_pasta_fq_uint1
+	x151, x152 = fiat_pasta_fq_addcarryx_u64(x133, x147, x150)
+	var x153 uint64
+	var x154 fiat_pasta_fq_uint1
+	x153, x154 = fiat_pasta_fq_addcarryx_u64(x135, (uint64(x148) + x144), x152)
+	var x155 uint64
+	var x156 fiat_pasta_fq_uint1
+	x155, x156 = fiat_pasta_fq_addcarryx_u64(x137, x141, x154)
+	x157 := ((uint64(x156) + (uint64(x138) + (uint64(x130) + x118))) + x142)
+	var x158 uint64
+	var x159 fiat_pasta_fq_uint1
+	x158, x159 = fiat_pasta_fq_subborrowx_u64(x151, 0x8c46eb2100000001, 0x0)
+	var x160 uint64
+	var x161 fiat_pasta_fq_uint1
+	x160, x161 = fiat_pasta_fq_subborrowx_u64(x153, 0x224698fc0994a8dd, x159)
+	var x162 uint64
+	var x163 fiat_pasta_fq_uint1
+	x162, x163 = fiat_pasta_fq_subborrowx_u64(x155, uint64(0x0), x161)
+	var x164 uint64
+	var x165 fiat_pasta_fq_uint1
+	x164, x165 = fiat_pasta_fq_subborrowx_u64(x157, 0x4000000000000000, x163)
+	var x167 fiat_pasta_fq_uint1
+	_, x167 = fiat_pasta_fq_subborrowx_u64(uint64(0x0), uint64(0x0), x165)
+	var x168 uint64
+	fiat_pasta_fq_cmovznz_u64(&x168, x167, x158, x151)
+	var x169 uint64
+	fiat_pasta_fq_cmovznz_u64(&x169, x167, x160, x153)
+	var x170 uint64
+	fiat_pasta_fq_cmovznz_u64(&x170, x167, x162, x155)
+	var x171 uint64
+	fiat_pasta_fq_cmovznz_u64(&x171, x167, x164, x157)
+	out1[0] = x168
+	out1[1] = x169
+	out1[2] = x170
+	out1[3] = x171
+}
+
+// The function fiat_pasta_fq_selectznz is a multi-limb conditional select.
+//
+// Postconditions:
+//   eval out1 = (if arg1 = 0 then eval arg2 else eval arg3)
+//
+// Input Bounds:
+//   arg1: [0x0 ~> 0x1]
+//   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+//   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+func fiat_pasta_fq_selectznz(out1 *[4]uint64, arg1 fiat_pasta_fq_uint1, arg2 *[4]uint64, arg3 *[4]uint64) {
+	var x1 uint64
+	fiat_pasta_fq_cmovznz_u64(&x1, arg1, arg2[0], arg3[0])
+	var x2 uint64
+	fiat_pasta_fq_cmovznz_u64(&x2, arg1, arg2[1], arg3[1])
+	var x3 uint64
+	fiat_pasta_fq_cmovznz_u64(&x3, arg1, arg2[2], arg3[2])
+	var x4 uint64
+	fiat_pasta_fq_cmovznz_u64(&x4, arg1, arg2[3], arg3[3])
+	out1[0] = x1
+	out1[1] = x2
+	out1[2] = x3
+	out1[3] = x4
+}
+
+// The function fiat_pasta_fq_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
+//
+// Preconditions:
+//   0 ≤ eval arg1 < m
+// Postconditions:
+//   out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31]
+//
+// Input Bounds:
+//   arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x7fffffffffffffff]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
+func fiat_pasta_fq_to_bytes(out1 *[32]uint8, arg1 *[4]uint64) {
+	x1 := arg1[3]
+	x2 := arg1[2]
+	x3 := arg1[1]
+	x4 := arg1[0]
+	x5 := (uint8(x4) & 0xff)
+	x6 := (x4 >> 8)
+	x7 := (uint8(x6) & 0xff)
+	x8 := (x6 >> 8)
+	x9 := (uint8(x8) & 0xff)
+	x10 := (x8 >> 8)
+	x11 := (uint8(x10) & 0xff)
+	x12 := (x10 >> 8)
+	x13 := (uint8(x12) & 0xff)
+	x14 := (x12 >> 8)
+	x15 := (uint8(x14) & 0xff)
+	x16 := (x14 >> 8)
+	x17 := (uint8(x16) & 0xff)
+	x18 := uint8((x16 >> 8))
+	x19 := (uint8(x3) & 0xff)
+	x20 := (x3 >> 8)
+	x21 := (uint8(x20) & 0xff)
+	x22 := (x20 >> 8)
+	x23 := (uint8(x22) & 0xff)
+	x24 := (x22 >> 8)
+	x25 := (uint8(x24) & 0xff)
+	x26 := (x24 >> 8)
+	x27 := (uint8(x26) & 0xff)
+	x28 := (x26 >> 8)
+	x29 := (uint8(x28) & 0xff)
+	x30 := (x28 >> 8)
+	x31 := (uint8(x30) & 0xff)
+	x32 := uint8((x30 >> 8))
+	x33 := (uint8(x2) & 0xff)
+	x34 := (x2 >> 8)
+	x35 := (uint8(x34) & 0xff)
+	x36 := (x34 >> 8)
+	x37 := (uint8(x36) & 0xff)
+	x38 := (x36 >> 8)
+	x39 := (uint8(x38) & 0xff)
+	x40 := (x38 >> 8)
+	x41 := (uint8(x40) & 0xff)
+	x42 := (x40 >> 8)
+	x43 := (uint8(x42) & 0xff)
+	x44 := (x42 >> 8)
+	x45 := (uint8(x44) & 0xff)
+	x46 := uint8((x44 >> 8))
+	x47 := (uint8(x1) & 0xff)
+	x48 := (x1 >> 8)
+	x49 := (uint8(x48) & 0xff)
+	x50 := (x48 >> 8)
+	x51 := (uint8(x50) & 0xff)
+	x52 := (x50 >> 8)
+	x53 := (uint8(x52) & 0xff)
+	x54 := (x52 >> 8)
+	x55 := (uint8(x54) & 0xff)
+	x56 := (x54 >> 8)
+	x57 := (uint8(x56) & 0xff)
+	x58 := (x56 >> 8)
+	x59 := (uint8(x58) & 0xff)
+	x60 := uint8((x58 >> 8))
+	out1[0] = x5
+	out1[1] = x7
+	out1[2] = x9
+	out1[3] = x11
+	out1[4] = x13
+	out1[5] = x15
+	out1[6] = x17
+	out1[7] = x18
+	out1[8] = x19
+	out1[9] = x21
+	out1[10] = x23
+	out1[11] = x25
+	out1[12] = x27
+	out1[13] = x29
+	out1[14] = x31
+	out1[15] = x32
+	out1[16] = x33
+	out1[17] = x35
+	out1[18] = x37
+	out1[19] = x39
+	out1[20] = x41
+	out1[21] = x43
+	out1[22] = x45
+	out1[23] = x46
+	out1[24] = x47
+	out1[25] = x49
+	out1[26] = x51
+	out1[27] = x53
+	out1[28] = x55
+	out1[29] = x57
+	out1[30] = x59
+	out1[31] = x60
+}
+
+// The function fiat_pasta_fq_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
+//
+// Preconditions:
+//   0 ≤ bytes_eval arg1 < m
+// Postconditions:
+//   eval out1 mod m = bytes_eval arg1 mod m
+//   0 ≤ eval out1 < m
+//
+// Input Bounds:
+//   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0x7f]]
+// Output Bounds:
+//   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0x7fffffffffffffff]]
+func fiat_pasta_fq_from_bytes(out1 *[4]uint64, arg1 *[32]uint8) {
+	x1 := (uint64(arg1[31]) << 56)
+	x2 := (uint64(arg1[30]) << 48)
+	x3 := (uint64(arg1[29]) << 40)
+	x4 := (uint64(arg1[28]) << 32)
+	x5 := (uint64(arg1[27]) << 24)
+	x6 := (uint64(arg1[26]) << 16)
+	x7 := (uint64(arg1[25]) << 8)
+	x8 := arg1[24]
+	x9 := (uint64(arg1[23]) << 56)
+	x10 := (uint64(arg1[22]) << 48)
+	x11 := (uint64(arg1[21]) << 40)
+	x12 := (uint64(arg1[20]) << 32)
+	x13 := (uint64(arg1[19]) << 24)
+	x14 := (uint64(arg1[18]) << 16)
+	x15 := (uint64(arg1[17]) << 8)
+	x16 := arg1[16]
+	x17 := (uint64(arg1[15]) << 56)
+	x18 := (uint64(arg1[14]) << 48)
+	x19 := (uint64(arg1[13]) << 40)
+	x20 := (uint64(arg1[12]) << 32)
+	x21 := (uint64(arg1[11]) << 24)
+	x22 := (uint64(arg1[10]) << 16)
+	x23 := (uint64(arg1[9]) << 8)
+	x24 := arg1[8]
+	x25 := (uint64(arg1[7]) << 56)
+	x26 := (uint64(arg1[6]) << 48)
+	x27 := (uint64(arg1[5]) << 40)
+	x28 := (uint64(arg1[4]) << 32)
+	x29 := (uint64(arg1[3]) << 24)
+	x30 := (uint64(arg1[2]) << 16)
+	x31 := (uint64(arg1[1]) << 8)
+	x32 := arg1[0]
+	x33 := (x31 + uint64(x32))
+	x34 := (x30 + x33)
+	x35 := (x29 + x34)
+	x36 := (x28 + x35)
+	x37 := (x27 + x36)
+	x38 := (x26 + x37)
+	x39 := (x25 + x38)
+	x40 := (x23 + uint64(x24))
+	x41 := (x22 + x40)
+	x42 := (x21 + x41)
+	x43 := (x20 + x42)
+	x44 := (x19 + x43)
+	x45 := (x18 + x44)
+	x46 := (x17 + x45)
+	x47 := (x15 + uint64(x16))
+	x48 := (x14 + x47)
+	x49 := (x13 + x48)
+	x50 := (x12 + x49)
+	x51 := (x11 + x50)
+	x52 := (x10 + x51)
+	x53 := (x9 + x52)
+	x54 := (x7 + uint64(x8))
+	x55 := (x6 + x54)
+	x56 := (x5 + x55)
+	x57 := (x4 + x56)
+	x58 := (x3 + x57)
+	x59 := (x2 + x58)
+	x60 := (x1 + x59)
+	out1[0] = x39
+	out1[1] = x46
+	out1[2] = x53
+	out1[3] = x60
+}
diff --git a/pkg/core/curves/native/pasta/pallas.go b/pkg/core/curves/native/pasta/pallas.go
new file mode 100644
index 00000000..d90bc3d9
--- /dev/null
+++ b/pkg/core/curves/native/pasta/pallas.go
@@ -0,0 +1,7 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package pasta
diff --git a/pkg/core/curves/p256_curve.go b/pkg/core/curves/p256_curve.go
new file mode 100644
index 00000000..057d6065
--- /dev/null
+++ b/pkg/core/curves/p256_curve.go
@@ -0,0 +1,604 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core"
+	"io"
+	"math/big"
+)
+
+type ScalarP256 struct {
+	value *big.Int
+}
+
+type PointP256 struct {
+	x, y *big.Int
+}
+
+func (s *ScalarP256) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarP256) Hash(bytes []byte) Scalar {
+	xmd, err := expandMsgXmd(sha256.New(), bytes, []byte("P256_XMD:SHA-256_SSWU_RO_"), 48)
+	if err != nil {
+		return nil
+	}
+	v := new(big.Int).SetBytes(xmd)
+	return &ScalarP256{
+		value: v.Mod(v, elliptic.P256().Params().N),
+	}
+}
+
+func (s *ScalarP256) Zero() Scalar {
+	return &ScalarP256{
+		value: big.NewInt(0),
+	}
+}
+
+func (s *ScalarP256) One() Scalar {
+	return &ScalarP256{
+		value: big.NewInt(1),
+	}
+}
+
+func (s *ScalarP256) IsZero() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{}) == 1
+}
+
+func (s *ScalarP256) IsOne() bool {
+	return subtle.ConstantTimeCompare(s.value.Bytes(), []byte{1}) == 1
+}
+
+func (s *ScalarP256) IsOdd() bool {
+	return s.value.Bit(0) == 1
+}
+
+func (s *ScalarP256) IsEven() bool {
+	return s.value.Bit(0) == 0
+}
+
+func (s *ScalarP256) New(value int) Scalar {
+	v := big.NewInt(int64(value))
+	if value < 0 {
+		v.Mod(v, elliptic.P256().Params().N)
+	}
+	return &ScalarP256{
+		value: v,
+	}
+}
+
+func (s *ScalarP256) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		return s.value.Cmp(r.value)
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarP256) Square() Scalar {
+	return &ScalarP256{
+		value: new(big.Int).Exp(s.value, big.NewInt(2), elliptic.P256().Params().N),
+	}
+}
+
+func (s *ScalarP256) Double() Scalar {
+	v := new(big.Int).Add(s.value, s.value)
+	return &ScalarP256{
+		value: v.Mod(v, elliptic.P256().Params().N),
+	}
+}
+
+func (s *ScalarP256) Invert() (Scalar, error) {
+	return &ScalarP256{
+		value: new(big.Int).ModInverse(s.value, elliptic.P256().Params().N),
+	}, nil
+}
+
+func (s *ScalarP256) Sqrt() (Scalar, error) {
+	return &ScalarP256{
+		value: new(big.Int).ModSqrt(s.value, elliptic.P256().Params().N),
+	}, nil
+}
+
+func (s *ScalarP256) Cube() Scalar {
+	return &ScalarP256{
+		value: new(big.Int).Exp(s.value, big.NewInt(3), elliptic.P256().Params().N),
+	}
+}
+
+func (s *ScalarP256) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		v := new(big.Int).Add(s.value, r.value)
+		return &ScalarP256{
+			value: v.Mod(v, elliptic.P256().Params().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarP256) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		v := new(big.Int).Sub(s.value, r.value)
+		return &ScalarP256{
+			value: v.Mod(v, elliptic.P256().Params().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarP256) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		v := new(big.Int).Mul(s.value, r.value)
+		return &ScalarP256{
+			value: v.Mod(v, elliptic.P256().Params().N),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarP256) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarP256) Div(rhs Scalar) Scalar {
+	n := elliptic.P256().Params().N
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		v := new(big.Int).ModInverse(r.value, n)
+		v.Mul(v, s.value)
+		return &ScalarP256{
+			value: v.Mod(v, n),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarP256) Neg() Scalar {
+	z := new(big.Int).Neg(s.value)
+	return &ScalarP256{
+		value: z.Mod(z, elliptic.P256().Params().N),
+	}
+}
+
+func (s *ScalarP256) SetBigInt(v *big.Int) (Scalar, error) {
+	if v == nil {
+		return nil, fmt.Errorf("invalid value")
+	}
+	t := new(big.Int).Mod(v, elliptic.P256().Params().N)
+	if t.Cmp(v) != 0 {
+		return nil, fmt.Errorf("invalid value")
+	}
+	return &ScalarP256{
+		value: t,
+	}, nil
+}
+
+func (s *ScalarP256) BigInt() *big.Int {
+	return new(big.Int).Set(s.value)
+}
+
+func (s *ScalarP256) Bytes() []byte {
+	var out [32]byte
+	return s.value.FillBytes(out[:])
+}
+
+func (s *ScalarP256) SetBytes(bytes []byte) (Scalar, error) {
+	value := new(big.Int).SetBytes(bytes)
+	t := new(big.Int).Mod(value, elliptic.P256().Params().N)
+	if t.Cmp(value) != 0 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	return &ScalarP256{
+		value: t,
+	}, nil
+}
+
+func (s *ScalarP256) SetBytesWide(bytes []byte) (Scalar, error) {
+	if len(bytes) < 32 || len(bytes) > 128 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	value := new(big.Int).SetBytes(bytes)
+	value.Mod(value, elliptic.P256().Params().N)
+	return &ScalarP256{
+		value,
+	}, nil
+}
+
+func (s *ScalarP256) Point() Point {
+	return new(PointP256).Identity()
+}
+
+func (s *ScalarP256) Clone() Scalar {
+	return &ScalarP256{
+		value: new(big.Int).Set(s.value),
+	}
+}
+
+func (s *ScalarP256) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarP256) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarP256)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarP256) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarP256) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarP256)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarP256) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarP256) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarP256)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+func (p *PointP256) Random(reader io.Reader) Point {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *PointP256) Hash(bytes []byte) Point {
+	curve := elliptic.P256().Params()
+
+	var domain = []byte("P256_XMD:SHA-256_SSWU_RO_")
+	uniformBytes, _ := expandMsgXmd(sha256.New(), bytes, domain, 96)
+
+	u0 := new(big.Int).SetBytes(uniformBytes[:48])
+	u1 := new(big.Int).SetBytes(uniformBytes[48:])
+
+	u0.Mod(u0, curve.P)
+	u1.Mod(u1, curve.P)
+
+	ssParams := p256SswuParams()
+	q0x, q0y := osswu3mod4(u0, ssParams)
+	q1x, q1y := osswu3mod4(u1, ssParams)
+
+	// Since P-256 does not require the isogeny map just add the points
+	x, y := curve.Add(q0x, q0y, q1x, q1y)
+
+	return &PointP256{
+		x, y,
+	}
+}
+
+func (p *PointP256) Identity() Point {
+	return &PointP256{
+		x: big.NewInt(0), y: big.NewInt(0),
+	}
+}
+
+func (p *PointP256) Generator() Point {
+	curve := elliptic.P256().Params()
+	return &PointP256{
+		x: new(big.Int).Set(curve.Gx),
+		y: new(big.Int).Set(curve.Gy),
+	}
+}
+
+func (p *PointP256) IsIdentity() bool {
+	x := core.ConstantTimeEqByte(p.x, core.Zero)
+	y := core.ConstantTimeEqByte(p.y, core.Zero)
+	return (x & y) == 1
+}
+
+func (p *PointP256) IsNegative() bool {
+	return p.y.Bit(0) == 1
+}
+
+func (p *PointP256) IsOnCurve() bool {
+	return elliptic.P256().IsOnCurve(p.x, p.y)
+}
+
+func (p *PointP256) Double() Point {
+	curve := elliptic.P256()
+	x, y := curve.Double(p.x, p.y)
+	return &PointP256{x, y}
+}
+
+func (p *PointP256) Scalar() Scalar {
+	return new(ScalarP256).Zero()
+}
+
+func (p *PointP256) Neg() Point {
+	y := new(big.Int).Sub(elliptic.P256().Params().P, p.y)
+	y.Mod(y, elliptic.P256().Params().P)
+	return &PointP256{x: p.x, y: y}
+}
+
+func (p *PointP256) Add(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*PointP256)
+	if ok {
+		x, y := elliptic.P256().Add(p.x, p.y, r.x, r.y)
+		return &PointP256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointP256) Sub(rhs Point) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.Neg().(*PointP256)
+	if ok {
+		x, y := elliptic.P256().Add(p.x, p.y, r.x, r.y)
+		return &PointP256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointP256) Mul(rhs Scalar) Point {
+	if rhs == nil {
+		return nil
+	}
+	r, ok := rhs.(*ScalarP256)
+	if ok {
+		x, y := elliptic.P256().ScalarMult(p.x, p.y, r.value.Bytes())
+		return &PointP256{x, y}
+	} else {
+		return nil
+	}
+}
+
+func (p *PointP256) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointP256)
+	if ok {
+		x := core.ConstantTimeEqByte(p.x, r.x)
+		y := core.ConstantTimeEqByte(p.y, r.y)
+		return (x & y) == 1
+	} else {
+		return false
+	}
+}
+
+func (p *PointP256) Set(x, y *big.Int) (Point, error) {
+	// check is identity or on curve
+	xx := subtle.ConstantTimeCompare(x.Bytes(), []byte{})
+	yy := subtle.ConstantTimeCompare(y.Bytes(), []byte{})
+	// Checks are constant time
+	onCurve := elliptic.P256().IsOnCurve(x, y)
+	if !onCurve && (xx&yy) != 1 {
+		return nil, fmt.Errorf("invalid coordinates")
+	}
+	x = new(big.Int).Set(x)
+	y = new(big.Int).Set(y)
+	return &PointP256{x, y}, nil
+}
+
+func (p *PointP256) ToAffineCompressed() []byte {
+	var x [33]byte
+	x[0] = byte(2)
+	x[0] |= byte(p.y.Bit(0))
+	p.x.FillBytes(x[1:])
+	return x[:]
+}
+
+func (p *PointP256) ToAffineUncompressed() []byte {
+	var out [65]byte
+	out[0] = byte(4)
+	p.x.FillBytes(out[1:33])
+	p.y.FillBytes(out[33:])
+	return out[:]
+}
+
+func (p *PointP256) FromAffineCompressed(bytes []byte) (Point, error) {
+	if len(bytes) != 33 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	sign := int(bytes[0])
+	if sign != 2 && sign != 3 {
+		return nil, fmt.Errorf("invalid sign byte")
+	}
+	sign &= 0x1
+
+	x := new(big.Int).SetBytes(bytes[1:])
+	rhs := rhsP256(x, elliptic.P256().Params())
+	// test that rhs is quadratic residue
+	// if not, then this Point is at infinity
+	y := new(big.Int).ModSqrt(rhs, elliptic.P256().Params().P)
+	if y != nil {
+		// fix the sign
+		if int(y.Bit(0)) != sign {
+			y.Neg(y)
+			y.Mod(y, elliptic.P256().Params().P)
+		}
+	} else {
+		x = new(big.Int)
+		y = new(big.Int)
+	}
+	return &PointP256{
+		x, y,
+	}, nil
+}
+
+func (p *PointP256) FromAffineUncompressed(bytes []byte) (Point, error) {
+	if len(bytes) != 65 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+	if bytes[0] != 4 {
+		return nil, fmt.Errorf("invalid sign byte")
+	}
+	x := new(big.Int).SetBytes(bytes[1:33])
+	y := new(big.Int).SetBytes(bytes[33:])
+	return &PointP256{x, y}, nil
+}
+
+func (p *PointP256) CurveName() string {
+	return elliptic.P256().Params().Name
+}
+
+func (p *PointP256) SumOfProducts(points []Point, scalars []Scalar) Point {
+	nScalars := make([]*big.Int, len(scalars))
+	for i, sc := range scalars {
+		s, ok := sc.(*ScalarP256)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = s.value
+	}
+	return sumOfProductsPippenger(points, nScalars)
+}
+
+func (p *PointP256) X() *big.Int {
+	return new(big.Int).Set(p.x)
+}
+
+func (p *PointP256) Y() *big.Int {
+	return new(big.Int).Set(p.y)
+}
+
+func (p *PointP256) Params() *elliptic.CurveParams {
+	return elliptic.P256().Params()
+}
+
+func (p *PointP256) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointP256) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointP256)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.x = ppt.x
+	p.y = ppt.y
+	return nil
+}
+
+func (p *PointP256) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointP256) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointP256)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.x = ppt.x
+	p.y = ppt.y
+	return nil
+}
+
+func (p *PointP256) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointP256) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointP256)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.x = P.x
+	p.y = P.y
+	return nil
+}
+
+// Take from https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-8.2
+func p256SswuParams() *sswuParams {
+	params := elliptic.P256().Params()
+
+	// c1 = (q - 3) / 4
+	c1 := new(big.Int).Set(params.P)
+	c1.Sub(c1, big.NewInt(3))
+	c1.Rsh(c1, 2)
+
+	a := big.NewInt(-3)
+	a.Mod(a, params.P)
+	b := new(big.Int).Set(params.B)
+	z := big.NewInt(-10)
+	z.Mod(z, params.P)
+	// sqrt(-Z^3)
+	zTmp := new(big.Int).Exp(z, big.NewInt(3), nil)
+	zTmp = zTmp.Neg(zTmp)
+	zTmp.Mod(zTmp, params.P)
+	c2 := new(big.Int).ModSqrt(zTmp, params.P)
+
+	return &sswuParams{
+		params, c1, c2, a, b, z,
+	}
+}
+
+// rhs of the curve equation
+func rhsP256(x *big.Int, params *elliptic.CurveParams) *big.Int {
+	f := NewField(params.P)
+	r := f.NewElement(x)
+	r2 := r.Mul(r)
+
+	// x^3-3x+B
+	a := r.Mul(f.NewElement(big.NewInt(3)))
+	r = r2.Mul(r)
+	return r.Add(a.Neg()).Add(f.NewElement(params.B)).Value
+}
diff --git a/pkg/core/curves/p256_curve_test.go b/pkg/core/curves/p256_curve_test.go
new file mode 100644
index 00000000..128067ef
--- /dev/null
+++ b/pkg/core/curves/p256_curve_test.go
@@ -0,0 +1,364 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	crand "crypto/rand"
+	"github.com/stretchr/testify/assert"
+	"math/big"
+	"testing"
+)
+
+func TestScalarP256Random(t *testing.T) {
+	p256 := P256()
+	sc := p256.Scalar.Random(testRng())
+	s, ok := sc.(*ScalarP256)
+	assert.True(t, ok)
+	expected := bhex("02ca487e56f8cb1ad9666027b2282d1159792d39a5e05f0bc696f85de5acc6d4")
+	assert.Equal(t, s.value, expected)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := p256.Scalar.Random(crand.Reader)
+		_, ok := sc.(*ScalarP256)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsZero())
+	}
+}
+
+func TestScalarP256Hash(t *testing.T) {
+	var b [32]byte
+	p256 := P256()
+	sc := p256.Scalar.Hash(b[:])
+	s, ok := sc.(*ScalarP256)
+	assert.True(t, ok)
+	expected := bhex("43ca74a23022b221e60c8499781afff2a2776ec23362712df90a3080b5557f90")
+	assert.Equal(t, s.value, expected)
+}
+
+func TestScalarP256Zero(t *testing.T) {
+	p256 := P256()
+	sc := p256.Scalar.Zero()
+	assert.True(t, sc.IsZero())
+	assert.True(t, sc.IsEven())
+}
+
+func TestScalarP256One(t *testing.T) {
+	p256 := P256()
+	sc := p256.Scalar.One()
+	assert.True(t, sc.IsOne())
+	assert.True(t, sc.IsOdd())
+}
+
+func TestScalarP256New(t *testing.T) {
+	p256 := P256()
+	three := p256.Scalar.New(3)
+	assert.True(t, three.IsOdd())
+	four := p256.Scalar.New(4)
+	assert.True(t, four.IsEven())
+	neg1 := p256.Scalar.New(-1)
+	assert.True(t, neg1.IsEven())
+	neg2 := p256.Scalar.New(-2)
+	assert.True(t, neg2.IsOdd())
+}
+
+func TestScalarP256Square(t *testing.T) {
+	p256 := P256()
+	three := p256.Scalar.New(3)
+	nine := p256.Scalar.New(9)
+	assert.Equal(t, three.Square().Cmp(nine), 0)
+}
+
+func TestScalarP256Cube(t *testing.T) {
+	p256 := P256()
+	three := p256.Scalar.New(3)
+	twentySeven := p256.Scalar.New(27)
+	assert.Equal(t, three.Cube().Cmp(twentySeven), 0)
+}
+
+func TestScalarP256Double(t *testing.T) {
+	p256 := P256()
+	three := p256.Scalar.New(3)
+	six := p256.Scalar.New(6)
+	assert.Equal(t, three.Double().Cmp(six), 0)
+}
+
+func TestScalarP256Neg(t *testing.T) {
+	p256 := P256()
+	one := p256.Scalar.One()
+	neg1 := p256.Scalar.New(-1)
+	assert.Equal(t, one.Neg().Cmp(neg1), 0)
+	lotsOfThrees := p256.Scalar.New(333333)
+	expected := p256.Scalar.New(-333333)
+	assert.Equal(t, lotsOfThrees.Neg().Cmp(expected), 0)
+}
+
+func TestScalarP256Invert(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	actual, _ := nine.Invert()
+	sa, _ := actual.(*ScalarP256)
+	bn := bhex("8e38e38daaaaaaab38e38e38e38e38e368f2197ceb0d1f2d6af570a536e1bf66")
+	expected, err := p256.Scalar.SetBigInt(bn)
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarP256Sqrt(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	actual, err := nine.Sqrt()
+	sa, _ := actual.(*ScalarP256)
+	expected := p256.Scalar.New(3)
+	assert.NoError(t, err)
+	assert.Equal(t, sa.Cmp(expected), 0)
+}
+
+func TestScalarP256Add(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	six := p256.Scalar.New(6)
+	fifteen := nine.Add(six)
+	assert.NotNil(t, fifteen)
+	expected := p256.Scalar.New(15)
+	assert.Equal(t, expected.Cmp(fifteen), 0)
+	n := new(big.Int).Set(elliptic.P256().Params().N)
+	n.Sub(n, big.NewInt(3))
+
+	upper, err := p256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := upper.Add(nine)
+	assert.NotNil(t, actual)
+	assert.Equal(t, actual.Cmp(six), 0)
+}
+
+func TestScalarP256Sub(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	six := p256.Scalar.New(6)
+	n := new(big.Int).Set(elliptic.P256().Params().N)
+	n.Sub(n, big.NewInt(3))
+
+	expected, err := p256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	actual := six.Sub(nine)
+	assert.Equal(t, expected.Cmp(actual), 0)
+
+	actual = nine.Sub(six)
+	assert.Equal(t, actual.Cmp(p256.Scalar.New(3)), 0)
+}
+
+func TestScalarP256Mul(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	six := p256.Scalar.New(6)
+	actual := nine.Mul(six)
+	assert.Equal(t, actual.Cmp(p256.Scalar.New(54)), 0)
+	n := new(big.Int).Set(elliptic.P256().Params().N)
+	n.Sub(n, big.NewInt(1))
+	upper, err := p256.Scalar.SetBigInt(n)
+	assert.NoError(t, err)
+	assert.Equal(t, upper.Mul(upper).Cmp(p256.Scalar.New(1)), 0)
+}
+
+func TestScalarP256Div(t *testing.T) {
+	p256 := P256()
+	nine := p256.Scalar.New(9)
+	actual := nine.Div(nine)
+	assert.Equal(t, actual.Cmp(p256.Scalar.New(1)), 0)
+	assert.Equal(t, p256.Scalar.New(54).Div(nine).Cmp(p256.Scalar.New(6)), 0)
+}
+
+func TestScalarP256Serialize(t *testing.T) {
+	p256 := P256()
+	sc := p256.Scalar.New(255)
+	sequence := sc.Bytes()
+	assert.Equal(t, len(sequence), 32)
+	assert.Equal(t, sequence, []byte{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0xff})
+	ret, err := p256.Scalar.SetBytes(sequence)
+	assert.NoError(t, err)
+	assert.Equal(t, ret.Cmp(sc), 0)
+
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc = p256.Scalar.Random(crand.Reader)
+		sequence = sc.Bytes()
+		assert.Equal(t, len(sequence), 32)
+		ret, err = p256.Scalar.SetBytes(sequence)
+		assert.NoError(t, err)
+		assert.Equal(t, ret.Cmp(sc), 0)
+	}
+}
+
+func TestScalarP256Nil(t *testing.T) {
+	p256 := P256()
+	one := p256.Scalar.New(1)
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, one.Div(nil))
+	assert.Nil(t, p256.Scalar.Random(nil))
+	assert.Equal(t, one.Cmp(nil), -2)
+	_, err := p256.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointP256Random(t *testing.T) {
+	p256 := P256()
+	sc := p256.Point.Random(testRng())
+	s, ok := sc.(*PointP256)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("7d31a079d75687cd0dd1118996f726c3e4d52806a5124d23c1faeee9fadb2201", 16)
+	expectedY, _ := new(big.Int).SetString("da62629181a0e2ec6943c263bbe81f53d87cb94d0039a707309f415f04d47bab", 16)
+	assert.Equal(t, s.x, expectedX)
+	assert.Equal(t, s.y, expectedY)
+	// Try 10 random values
+	for i := 0; i < 10; i++ {
+		sc := p256.Point.Random(crand.Reader)
+		_, ok := sc.(*PointP256)
+		assert.True(t, ok)
+		assert.True(t, !sc.IsIdentity())
+	}
+}
+
+func TestPointP256Hash(t *testing.T) {
+	var b [32]byte
+	p256 := P256()
+	sc := p256.Point.Hash(b[:])
+	s, ok := sc.(*PointP256)
+	assert.True(t, ok)
+	expectedX, _ := new(big.Int).SetString("10f1699c24cf20f5322b92bfab4fdf14814ee1472ffc6b1ef2ec36be3051925d", 16)
+	expectedY, _ := new(big.Int).SetString("99efe055f13c3e5e3fc65be12043a89d0482b806c7a9945c276b7aee887c1de0", 16)
+	assert.Equal(t, s.x, expectedX)
+	assert.Equal(t, s.y, expectedY)
+}
+
+func TestPointP256Identity(t *testing.T) {
+	p256 := P256()
+	sc := p256.Point.Identity()
+	assert.True(t, sc.IsIdentity())
+	assert.Equal(t, sc.ToAffineCompressed(), []byte{2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
+}
+
+func TestPointP256Generator(t *testing.T) {
+	p256 := P256()
+	sc := p256.Point.Generator()
+	s, ok := sc.(*PointP256)
+	assert.True(t, ok)
+	assert.Equal(t, s.x.Cmp(elliptic.P256().Params().Gx), 0)
+	assert.Equal(t, s.y.Cmp(elliptic.P256().Params().Gy), 0)
+}
+
+func TestPointP256Set(t *testing.T) {
+	p256 := P256()
+	iden, err := p256.Point.Set(big.NewInt(0), big.NewInt(0))
+	assert.NoError(t, err)
+	assert.True(t, iden.IsIdentity())
+	_, err = p256.Point.Set(elliptic.P256().Params().Gx, elliptic.P256().Params().Gy)
+	assert.NoError(t, err)
+}
+
+func TestPointP256Double(t *testing.T) {
+	p256 := P256()
+	g := p256.Point.Generator()
+	g2 := g.Double()
+	assert.True(t, g2.Equal(g.Mul(p256.Scalar.New(2))))
+	i := p256.Point.Identity()
+	assert.True(t, i.Double().Equal(i))
+}
+
+func TestPointP256Neg(t *testing.T) {
+	p256 := P256()
+	g := p256.Point.Generator().Neg()
+	assert.True(t, g.Neg().Equal(p256.Point.Generator()))
+	assert.True(t, p256.Point.Identity().Neg().Equal(p256.Point.Identity()))
+}
+
+func TestPointP256Add(t *testing.T) {
+	p256 := P256()
+	pt := p256.Point.Generator()
+	assert.True(t, pt.Add(pt).Equal(pt.Double()))
+	assert.True(t, pt.Mul(p256.Scalar.New(3)).Equal(pt.Add(pt).Add(pt)))
+}
+
+func TestPointP256Sub(t *testing.T) {
+	p256 := P256()
+	g := p256.Point.Generator()
+	pt := p256.Point.Generator().Mul(p256.Scalar.New(4))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Equal(g))
+	assert.True(t, pt.Sub(g).Sub(g).Sub(g).Sub(g).IsIdentity())
+}
+
+func TestPointP256Mul(t *testing.T) {
+	p256 := P256()
+	g := p256.Point.Generator()
+	pt := p256.Point.Generator().Mul(p256.Scalar.New(4))
+	assert.True(t, g.Double().Double().Equal(pt))
+}
+
+func TestPointP256Serialize(t *testing.T) {
+	p256 := P256()
+	ss := p256.Scalar.Random(testRng())
+	g := p256.Point.Generator()
+
+	ppt := g.Mul(ss)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0x3, 0x1b, 0xfa, 0x44, 0xfb, 0x6, 0xa4, 0x6d, 0xe1, 0x38, 0x72, 0x39, 0x9a, 0x69, 0xd4, 0x71, 0x38, 0x3f, 0x8b, 0x13, 0x39, 0x60, 0xdc, 0x61, 0x91, 0x22, 0x70, 0x58, 0x7c, 0xdf, 0x82, 0x33, 0xba})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x4, 0x1b, 0xfa, 0x44, 0xfb, 0x6, 0xa4, 0x6d, 0xe1, 0x38, 0x72, 0x39, 0x9a, 0x69, 0xd4, 0x71, 0x38, 0x3f, 0x8b, 0x13, 0x39, 0x60, 0xdc, 0x61, 0x91, 0x22, 0x70, 0x58, 0x7c, 0xdf, 0x82, 0x33, 0xba, 0x48, 0xdf, 0x58, 0xac, 0x70, 0xf3, 0x9b, 0x9d, 0x5d, 0x84, 0x6e, 0x2d, 0x75, 0xc9, 0x6, 0x1e, 0xd9, 0x62, 0x8b, 0x15, 0x0, 0x65, 0x69, 0x79, 0xfb, 0x42, 0xc, 0x35, 0xce, 0x2e, 0x8b, 0xfd})
+	retP, err := ppt.FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = ppt.FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := p256.Scalar.Random(crand.Reader)
+		pt := g.Mul(s)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 33)
+		retC, err := pt.FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 65)
+		retU, err := pt.FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointP256Nil(t *testing.T) {
+	p256 := P256()
+	one := p256.Point.Generator()
+	assert.Nil(t, one.Add(nil))
+	assert.Nil(t, one.Sub(nil))
+	assert.Nil(t, one.Mul(nil))
+	assert.Nil(t, p256.Scalar.Random(nil))
+	assert.False(t, one.Equal(nil))
+	_, err := p256.Scalar.SetBigInt(nil)
+	assert.Error(t, err)
+}
+
+func TestPointP256SumOfProducts(t *testing.T) {
+	lhs := new(PointP256).Generator().Mul(new(ScalarP256).New(50))
+	points := make([]Point, 5)
+	for i := range points {
+		points[i] = new(PointP256).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarP256).New(8),
+		new(ScalarP256).New(9),
+		new(ScalarP256).New(10),
+		new(ScalarP256).New(11),
+		new(ScalarP256).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
diff --git a/pkg/core/curves/pallas_curve.go b/pkg/core/curves/pallas_curve.go
new file mode 100644
index 00000000..c24ce61f
--- /dev/null
+++ b/pkg/core/curves/pallas_curve.go
@@ -0,0 +1,1163 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	"crypto/elliptic"
+	crand "crypto/rand"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fp"
+	"github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fq"
+	"golang.org/x/crypto/blake2b"
+	"io"
+	"math/big"
+	"sync"
+)
+
+var b = new(fp.Fp).SetUint64(5)
+var three = &fp.Fp{0x6b0ee5d0fffffff5, 0x86f76d2b99b14bd0, 0xfffffffffffffffe, 0x3fffffffffffffff}
+var eight = &fp.Fp{0x7387134cffffffe1, 0xd973797adfadd5a8, 0xfffffffffffffffb, 0x3fffffffffffffff}
+var bool2int = map[bool]int{
+	true:  1,
+	false: 0,
+}
+
+var isomapper = [13]*fp.Fp{
+	new(fp.Fp).SetRaw(&[4]uint64{0x775f6034aaaaaaab, 0x4081775473d8375b, 0xe38e38e38e38e38e, 0x0e38e38e38e38e38}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x8cf863b02814fb76, 0x0f93b82ee4b99495, 0x267c7ffa51cf412a, 0x3509afd51872d88e}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x0eb64faef37ea4f7, 0x380af066cfeb6d69, 0x98c7d7ac3d98fd13, 0x17329b9ec5253753}),
+	new(fp.Fp).SetRaw(&[4]uint64{0xeebec06955555580, 0x8102eea8e7b06eb6, 0xc71c71c71c71c71c, 0x1c71c71c71c71c71}),
+	new(fp.Fp).SetRaw(&[4]uint64{0xc47f2ab668bcd71f, 0x9c434ac1c96b6980, 0x5a607fcce0494a79, 0x1d572e7ddc099cff}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x2aa3af1eae5b6604, 0xb4abf9fb9a1fc81c, 0x1d13bf2a7f22b105, 0x325669becaecd5d1}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x5ad985b5e38e38e4, 0x7642b01ad461bad2, 0x4bda12f684bda12f, 0x1a12f684bda12f68}),
+	new(fp.Fp).SetRaw(&[4]uint64{0xc67c31d8140a7dbb, 0x07c9dc17725cca4a, 0x133e3ffd28e7a095, 0x1a84d7ea8c396c47}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x02e2be87d225b234, 0x1765e924f7459378, 0x303216cce1db9ff1, 0x3fb98ff0d2ddcadd}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x93e53ab371c71c4f, 0x0ac03e8e134eb3e4, 0x7b425ed097b425ed, 0x025ed097b425ed09}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x5a28279b1d1b42ae, 0x5941a3a4a97aa1b3, 0x0790bfb3506defb6, 0x0c02c5bcca0e6b7f}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x4d90ab820b12320a, 0xd976bbfabbc5661d, 0x573b3d7f7d681310, 0x17033d3c60c68173}),
+	new(fp.Fp).SetRaw(&[4]uint64{0x992d30ecfffffde5, 0x224698fc094cf91b, 0x0000000000000000, 0x4000000000000000}),
+}
+var isoa = new(fp.Fp).SetRaw(&[4]uint64{0x92bb4b0b657a014b, 0xb74134581a27a59f, 0x49be2d7258370742, 0x18354a2eb0ea8c9c})
+var isob = new(fp.Fp).SetRaw(&[4]uint64{1265, 0, 0, 0})
+var z = new(fp.Fp).SetRaw(&[4]uint64{0x992d30ecfffffff4, 0x224698fc094cf91b, 0x0000000000000000, 0x4000000000000000})
+
+var oldPallasInitonce sync.Once
+var oldPallas PallasCurve
+
+type PallasCurve struct {
+	*elliptic.CurveParams
+}
+
+func oldPallasInitAll() {
+	oldPallas.CurveParams = new(elliptic.CurveParams)
+	oldPallas.P = new(big.Int).SetBytes([]byte{
+		0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x22, 0x46, 0x98, 0xfc, 0x09, 0x4c, 0xf9, 0x1b,
+		0x99, 0x2d, 0x30, 0xed, 0x00, 0x00, 0x00, 0x01,
+	})
+	oldPallas.N = new(big.Int).SetBytes([]byte{
+		0x40, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+		0x22, 0x46, 0x98, 0xfc, 0x09, 0x94, 0xa8, 0xdd,
+		0x8c, 0x46, 0xeb, 0x21, 0x00, 0x00, 0x00, 0x01,
+	})
+	g := new(Ep).Generator()
+	oldPallas.Gx = g.x.BigInt()
+	oldPallas.Gy = g.y.BigInt()
+	oldPallas.B = big.NewInt(5)
+	oldPallas.BitSize = 255
+	pallas.Name = PallasName
+}
+
+func Pallas() *PallasCurve {
+	oldPallasInitonce.Do(oldPallasInitAll)
+	return &oldPallas
+}
+
+func (curve *PallasCurve) Params() *elliptic.CurveParams {
+	return curve.CurveParams
+}
+
+func (curve *PallasCurve) IsOnCurve(x, y *big.Int) bool {
+	p := new(Ep)
+	p.x = new(fp.Fp).SetBigInt(x)
+	p.y = new(fp.Fp).SetBigInt(y)
+	p.z = new(fp.Fp).SetOne()
+
+	return p.IsOnCurve()
+}
+
+func (curve *PallasCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	p := new(Ep)
+	p.x = new(fp.Fp).SetBigInt(x1)
+	p.y = new(fp.Fp).SetBigInt(y1)
+	p.z = new(fp.Fp).SetOne()
+	if p.x.IsZero() && p.y.IsZero() {
+		p.z.SetZero()
+	}
+
+	q := new(Ep)
+	q.x = new(fp.Fp).SetBigInt(x2)
+	q.y = new(fp.Fp).SetBigInt(y2)
+	q.z = new(fp.Fp).SetOne()
+	if q.x.IsZero() && q.y.IsZero() {
+		q.z.SetZero()
+	}
+	p.Add(p, q)
+	p.toAffine()
+	return p.x.BigInt(), p.y.BigInt()
+}
+
+func (curve *PallasCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	p := new(Ep)
+	p.x = new(fp.Fp).SetBigInt(x1)
+	p.y = new(fp.Fp).SetBigInt(y1)
+	p.z = new(fp.Fp).SetOne()
+	if p.x.IsZero() && p.y.IsZero() {
+		p.z.SetZero()
+	}
+	p.Double(p)
+	p.toAffine()
+	return p.x.BigInt(), p.y.BigInt()
+}
+
+func (curve *PallasCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	p := new(Ep)
+	p.x = new(fp.Fp).SetBigInt(Bx)
+	p.y = new(fp.Fp).SetBigInt(By)
+	p.z = new(fp.Fp).SetOne()
+	if p.x.IsZero() && p.y.IsZero() {
+		p.z.SetZero()
+	}
+	var t [32]byte
+	copy(t[:], k)
+	ss := new(big.Int).SetBytes(k)
+	sc := new(fq.Fq).SetBigInt(ss)
+	p.Mul(p, sc)
+	p.toAffine()
+	return p.x.BigInt(), p.y.BigInt()
+}
+
+func (curve *PallasCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	p := new(Ep).Generator()
+	var t [32]byte
+	copy(t[:], k)
+	ss := new(big.Int).SetBytes(k)
+	sc := new(fq.Fq).SetBigInt(ss)
+	p.Mul(p, sc)
+	p.toAffine()
+	return p.x.BigInt(), p.y.BigInt()
+}
+
+// PallasScalar - Old interface
+type PallasScalar struct{}
+
+func NewPallasScalar() *PallasScalar {
+	return &PallasScalar{}
+}
+
+func (k PallasScalar) Add(x, y *big.Int) *big.Int {
+	r := new(big.Int).Add(x, y)
+	return r.Mod(r, fq.BiModulus)
+}
+
+func (k PallasScalar) Sub(x, y *big.Int) *big.Int {
+	r := new(big.Int).Sub(x, y)
+	return r.Mod(r, fq.BiModulus)
+}
+
+func (k PallasScalar) Neg(x *big.Int) *big.Int {
+	r := new(big.Int).Neg(x)
+	return r.Mod(r, fq.BiModulus)
+}
+
+func (k PallasScalar) Mul(x, y *big.Int) *big.Int {
+	r := new(big.Int).Mul(x, y)
+	return r.Mod(r, fq.BiModulus)
+}
+
+func (k PallasScalar) Div(x, y *big.Int) *big.Int {
+	r := new(big.Int).ModInverse(y, fq.BiModulus)
+	r.Mul(r, x)
+	return r.Mod(r, fq.BiModulus)
+}
+
+func (k PallasScalar) Hash(input []byte) *big.Int {
+	return new(ScalarPallas).Hash(input).(*ScalarPallas).value.BigInt()
+}
+
+func (k PallasScalar) Bytes(x *big.Int) []byte {
+	return x.Bytes()
+}
+
+func (k PallasScalar) Random() (*big.Int, error) {
+	s := new(ScalarPallas).Random(crand.Reader).(*ScalarPallas)
+	return s.value.BigInt(), nil
+}
+
+func (k PallasScalar) IsValid(x *big.Int) bool {
+	return x.Cmp(fq.BiModulus) == -1
+}
+
+// ScalarPallas - New interface
+type ScalarPallas struct {
+	value *fq.Fq
+}
+
+func (s *ScalarPallas) Random(reader io.Reader) Scalar {
+	if reader == nil {
+		return nil
+	}
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return s.Hash(seed[:])
+}
+
+func (s *ScalarPallas) Hash(bytes []byte) Scalar {
+	h, _ := blake2b.New(64, []byte{})
+	xmd, err := expandMsgXmd(h, bytes, []byte("pallas_XMD:BLAKE2b_SSWU_RO_"), 64)
+	if err != nil {
+		return nil
+	}
+	var t [64]byte
+	copy(t[:], xmd)
+	return &ScalarPallas{
+		value: new(fq.Fq).SetBytesWide(&t),
+	}
+}
+
+func (s *ScalarPallas) Zero() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).SetZero(),
+	}
+}
+
+func (s *ScalarPallas) One() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).SetOne(),
+	}
+}
+
+func (s *ScalarPallas) IsZero() bool {
+	return s.value.IsZero()
+}
+
+func (s *ScalarPallas) IsOne() bool {
+	return s.value.IsOne()
+}
+
+func (s *ScalarPallas) IsOdd() bool {
+	return (s.value[0] & 1) == 1
+}
+
+func (s *ScalarPallas) IsEven() bool {
+	return (s.value[0] & 1) == 0
+}
+
+func (s *ScalarPallas) New(value int) Scalar {
+	v := big.NewInt(int64(value))
+	return &ScalarPallas{
+		value: new(fq.Fq).SetBigInt(v),
+	}
+}
+
+func (s *ScalarPallas) Cmp(rhs Scalar) int {
+	r, ok := rhs.(*ScalarPallas)
+	if ok {
+		return s.value.Cmp(r.value)
+	} else {
+		return -2
+	}
+}
+
+func (s *ScalarPallas) Square() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).Square(s.value),
+	}
+}
+
+func (s *ScalarPallas) Double() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).Double(s.value),
+	}
+}
+
+func (s *ScalarPallas) Invert() (Scalar, error) {
+	value, wasInverted := new(fq.Fq).Invert(s.value)
+	if !wasInverted {
+		return nil, fmt.Errorf("inverse doesn't exist")
+	}
+	return &ScalarPallas{
+		value,
+	}, nil
+}
+
+func (s *ScalarPallas) Sqrt() (Scalar, error) {
+	value, wasSquare := new(fq.Fq).Sqrt(s.value)
+	if !wasSquare {
+		return nil, fmt.Errorf("not a square")
+	}
+	return &ScalarPallas{
+		value,
+	}, nil
+}
+
+func (s *ScalarPallas) Cube() Scalar {
+	value := new(fq.Fq).Mul(s.value, s.value)
+	value.Mul(value, s.value)
+	return &ScalarPallas{
+		value,
+	}
+}
+
+func (s *ScalarPallas) Add(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarPallas)
+	if ok {
+		return &ScalarPallas{
+			value: new(fq.Fq).Add(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarPallas) Sub(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarPallas)
+	if ok {
+		return &ScalarPallas{
+			value: new(fq.Fq).Sub(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarPallas) Mul(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarPallas)
+	if ok {
+		return &ScalarPallas{
+			value: new(fq.Fq).Mul(s.value, r.value),
+		}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarPallas) MulAdd(y, z Scalar) Scalar {
+	return s.Mul(y).Add(z)
+}
+
+func (s *ScalarPallas) Div(rhs Scalar) Scalar {
+	r, ok := rhs.(*ScalarPallas)
+	if ok {
+		v, wasInverted := new(fq.Fq).Invert(r.value)
+		if !wasInverted {
+			return nil
+		}
+		v.Mul(v, s.value)
+		return &ScalarPallas{value: v}
+	} else {
+		return nil
+	}
+}
+
+func (s *ScalarPallas) Neg() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).Neg(s.value),
+	}
+}
+
+func (s *ScalarPallas) SetBigInt(v *big.Int) (Scalar, error) {
+	return &ScalarPallas{
+		value: new(fq.Fq).SetBigInt(v),
+	}, nil
+}
+
+func (s *ScalarPallas) BigInt() *big.Int {
+	return s.value.BigInt()
+}
+
+func (s *ScalarPallas) Bytes() []byte {
+	t := s.value.Bytes()
+	return t[:]
+}
+
+func (s *ScalarPallas) SetBytes(bytes []byte) (Scalar, error) {
+	if len(bytes) != 32 {
+		return nil, fmt.Errorf("invalid length")
+	}
+	var seq [32]byte
+	copy(seq[:], bytes)
+	value, err := new(fq.Fq).SetBytes(&seq)
+	if err != nil {
+		return nil, err
+	}
+	return &ScalarPallas{
+		value,
+	}, nil
+}
+
+func (s *ScalarPallas) SetBytesWide(bytes []byte) (Scalar, error) {
+	if len(bytes) != 64 {
+		return nil, fmt.Errorf("invalid length")
+	}
+	var seq [64]byte
+	copy(seq[:], bytes)
+	return &ScalarPallas{
+		value: new(fq.Fq).SetBytesWide(&seq),
+	}, nil
+}
+
+func (s *ScalarPallas) Point() Point {
+	return new(PointPallas).Identity()
+}
+
+func (s *ScalarPallas) Clone() Scalar {
+	return &ScalarPallas{
+		value: new(fq.Fq).Set(s.value),
+	}
+}
+
+func (s *ScalarPallas) GetFq() *fq.Fq {
+	return new(fq.Fq).Set(s.value)
+}
+
+func (s *ScalarPallas) SetFq(fq *fq.Fq) *ScalarPallas {
+	s.value = fq
+	return s
+}
+
+func (s *ScalarPallas) MarshalBinary() ([]byte, error) {
+	return scalarMarshalBinary(s)
+}
+
+func (s *ScalarPallas) UnmarshalBinary(input []byte) error {
+	sc, err := scalarUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarPallas)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarPallas) MarshalText() ([]byte, error) {
+	return scalarMarshalText(s)
+}
+
+func (s *ScalarPallas) UnmarshalText(input []byte) error {
+	sc, err := scalarUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ss, ok := sc.(*ScalarPallas)
+	if !ok {
+		return fmt.Errorf("invalid scalar")
+	}
+	s.value = ss.value
+	return nil
+}
+
+func (s *ScalarPallas) MarshalJSON() ([]byte, error) {
+	return scalarMarshalJson(s)
+}
+
+func (s *ScalarPallas) UnmarshalJSON(input []byte) error {
+	sc, err := scalarUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	S, ok := sc.(*ScalarPallas)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	s.value = S.value
+	return nil
+}
+
+type PointPallas struct {
+	value *Ep
+}
+
+func (p *PointPallas) Random(reader io.Reader) Point {
+	return &PointPallas{new(Ep).Random(reader)}
+}
+
+func (p *PointPallas) Hash(bytes []byte) Point {
+	return &PointPallas{new(Ep).Hash(bytes)}
+}
+
+func (p *PointPallas) Identity() Point {
+	return &PointPallas{new(Ep).Identity()}
+}
+
+func (p *PointPallas) Generator() Point {
+	return &PointPallas{new(Ep).Generator()}
+}
+
+func (p *PointPallas) IsIdentity() bool {
+	return p.value.IsIdentity()
+}
+
+func (p *PointPallas) IsNegative() bool {
+	return p.value.Y().IsOdd()
+}
+
+func (p *PointPallas) IsOnCurve() bool {
+	return p.value.IsOnCurve()
+}
+
+func (p *PointPallas) Double() Point {
+	return &PointPallas{new(Ep).Double(p.value)}
+}
+
+func (p *PointPallas) Scalar() Scalar {
+	return &ScalarPallas{new(fq.Fq).SetZero()}
+}
+
+func (p *PointPallas) Neg() Point {
+	return &PointPallas{new(Ep).Neg(p.value)}
+}
+
+func (p *PointPallas) Add(rhs Point) Point {
+	r, ok := rhs.(*PointPallas)
+	if !ok {
+		return nil
+	}
+	return &PointPallas{new(Ep).Add(p.value, r.value)}
+}
+
+func (p *PointPallas) Sub(rhs Point) Point {
+	r, ok := rhs.(*PointPallas)
+	if !ok {
+		return nil
+	}
+	return &PointPallas{new(Ep).Sub(p.value, r.value)}
+}
+
+func (p *PointPallas) Mul(rhs Scalar) Point {
+	s, ok := rhs.(*ScalarPallas)
+	if !ok {
+		return nil
+	}
+	return &PointPallas{new(Ep).Mul(p.value, s.value)}
+}
+
+func (p *PointPallas) Equal(rhs Point) bool {
+	r, ok := rhs.(*PointPallas)
+	if !ok {
+		return false
+	}
+	return p.value.Equal(r.value)
+}
+
+func (p *PointPallas) Set(x, y *big.Int) (Point, error) {
+	xx := subtle.ConstantTimeCompare(x.Bytes(), []byte{})
+	yy := subtle.ConstantTimeCompare(y.Bytes(), []byte{})
+	xElem := new(fp.Fp).SetBigInt(x)
+	var data [32]byte
+	if yy == 1 {
+		if xx == 1 {
+			return &PointPallas{new(Ep).Identity()}, nil
+		}
+		data = xElem.Bytes()
+		return p.FromAffineCompressed(data[:])
+	}
+	yElem := new(fp.Fp).SetBigInt(y)
+	value := &Ep{xElem, yElem, new(fp.Fp).SetOne()}
+	if !value.IsOnCurve() {
+		return nil, fmt.Errorf("point is not on the curve")
+	}
+	return &PointPallas{value}, nil
+}
+
+func (p *PointPallas) ToAffineCompressed() []byte {
+	return p.value.ToAffineCompressed()
+}
+
+func (p *PointPallas) ToAffineUncompressed() []byte {
+	return p.value.ToAffineUncompressed()
+}
+
+func (p *PointPallas) FromAffineCompressed(bytes []byte) (Point, error) {
+	value, err := new(Ep).FromAffineCompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointPallas{value}, nil
+}
+
+func (p *PointPallas) FromAffineUncompressed(bytes []byte) (Point, error) {
+	value, err := new(Ep).FromAffineUncompressed(bytes)
+	if err != nil {
+		return nil, err
+	}
+	return &PointPallas{value}, nil
+}
+
+func (p *PointPallas) CurveName() string {
+	return PallasName
+}
+
+func (p *PointPallas) SumOfProducts(points []Point, scalars []Scalar) Point {
+	eps := make([]*Ep, len(points))
+	for i, pt := range points {
+		ps, ok := pt.(*PointPallas)
+		if !ok {
+			return nil
+		}
+		eps[i] = ps.value
+	}
+	value := p.value.SumOfProducts(eps, scalars)
+	return &PointPallas{value}
+}
+
+func (p *PointPallas) MarshalBinary() ([]byte, error) {
+	return pointMarshalBinary(p)
+}
+
+func (p *PointPallas) UnmarshalBinary(input []byte) error {
+	pt, err := pointUnmarshalBinary(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointPallas)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointPallas) MarshalText() ([]byte, error) {
+	return pointMarshalText(p)
+}
+
+func (p *PointPallas) UnmarshalText(input []byte) error {
+	pt, err := pointUnmarshalText(input)
+	if err != nil {
+		return err
+	}
+	ppt, ok := pt.(*PointPallas)
+	if !ok {
+		return fmt.Errorf("invalid point")
+	}
+	p.value = ppt.value
+	return nil
+}
+
+func (p *PointPallas) MarshalJSON() ([]byte, error) {
+	return pointMarshalJson(p)
+}
+
+func (p *PointPallas) UnmarshalJSON(input []byte) error {
+	pt, err := pointUnmarshalJson(input)
+	if err != nil {
+		return err
+	}
+	P, ok := pt.(*PointPallas)
+	if !ok {
+		return fmt.Errorf("invalid type")
+	}
+	p.value = P.value
+	return nil
+}
+
+func (p *PointPallas) X() *fp.Fp {
+	return p.value.X()
+}
+
+func (p *PointPallas) Y() *fp.Fp {
+	return p.value.Y()
+}
+
+func (p *PointPallas) GetEp() *Ep {
+	return new(Ep).Set(p.value)
+}
+
+type Ep struct {
+	x *fp.Fp
+	y *fp.Fp
+	z *fp.Fp
+}
+
+func (p *Ep) Random(reader io.Reader) *Ep {
+	var seed [64]byte
+	_, _ = reader.Read(seed[:])
+	return p.Hash(seed[:])
+}
+
+func (p *Ep) Hash(bytes []byte) *Ep {
+	if bytes == nil {
+		bytes = []byte{}
+	}
+	h, _ := blake2b.New(64, []byte{})
+	u, _ := expandMsgXmd(h, bytes, []byte("pallas_XMD:BLAKE2b_SSWU_RO_"), 128)
+	var buf [64]byte
+	copy(buf[:], u[:64])
+	u0 := new(fp.Fp).SetBytesWide(&buf)
+	copy(buf[:], u[64:])
+	u1 := new(fp.Fp).SetBytesWide(&buf)
+
+	q0 := mapSswu(u0)
+	q1 := mapSswu(u1)
+	r1 := isoMap(q0)
+	r2 := isoMap(q1)
+	return p.Identity().Add(r1, r2)
+}
+
+func (p *Ep) Identity() *Ep {
+	p.x = new(fp.Fp).SetZero()
+	p.y = new(fp.Fp).SetZero()
+	p.z = new(fp.Fp).SetZero()
+	return p
+}
+
+func (p *Ep) Generator() *Ep {
+	p.x = new(fp.Fp).SetOne()
+	p.y = &fp.Fp{0x2f474795455d409d, 0xb443b9b74b8255d9, 0x270c412f2c9a5d66, 0x8e00f71ba43dd6b}
+	p.z = new(fp.Fp).SetOne()
+	return p
+}
+
+func (p *Ep) IsIdentity() bool {
+	return p.z.IsZero()
+}
+
+func (p *Ep) Double(other *Ep) *Ep {
+	if other.IsIdentity() {
+		p.Set(other)
+		return p
+	}
+	r := new(Ep)
+	// essentially paraphrased https://github.com/MinaProtocol/c-reference-signer/blob/master/crypto.c#L306-L337
+	a := new(fp.Fp).Square(other.x)
+	b := new(fp.Fp).Square(other.y)
+	c := new(fp.Fp).Square(b)
+	r.x = new(fp.Fp).Add(other.x, b)
+	r.y = new(fp.Fp).Square(r.x)
+	r.z = new(fp.Fp).Sub(r.y, a)
+	r.x.Sub(r.z, c)
+	d := new(fp.Fp).Double(r.x)
+	e := new(fp.Fp).Mul(three, a)
+	f := new(fp.Fp).Square(e)
+	r.y.Double(d)
+	r.x.Sub(f, r.y)
+	r.y.Sub(d, r.x)
+	f.Mul(eight, c)
+	r.z.Mul(e, r.y)
+	r.y.Sub(r.z, f)
+	f.Mul(other.y, other.z)
+	r.z.Double(f)
+	p.Set(r)
+	return p
+}
+
+func (p *Ep) Neg(other *Ep) *Ep {
+	p.x = new(fp.Fp).Set(other.x)
+	p.y = new(fp.Fp).Neg(other.y)
+	p.z = new(fp.Fp).Set(other.z)
+	return p
+}
+
+func (p *Ep) Add(lhs *Ep, rhs *Ep) *Ep {
+	if lhs.IsIdentity() {
+		return p.Set(rhs)
+	}
+	if rhs.IsIdentity() {
+		return p.Set(lhs)
+	}
+	z1z1 := new(fp.Fp).Square(lhs.z)
+	z2z2 := new(fp.Fp).Square(rhs.z)
+	u1 := new(fp.Fp).Mul(lhs.x, z2z2)
+	u2 := new(fp.Fp).Mul(rhs.x, z1z1)
+	s1 := new(fp.Fp).Mul(lhs.y, z2z2)
+	s1.Mul(s1, rhs.z)
+	s2 := new(fp.Fp).Mul(rhs.y, z1z1)
+	s2.Mul(s2, lhs.z)
+
+	if u1.Equal(u2) {
+		if s1.Equal(s2) {
+			return p.Double(lhs)
+		} else {
+			return p.Identity()
+		}
+	} else {
+		h := new(fp.Fp).Sub(u2, u1)
+		i := new(fp.Fp).Double(h)
+		i.Square(i)
+		j := new(fp.Fp).Mul(i, h)
+		r := new(fp.Fp).Sub(s2, s1)
+		r.Double(r)
+		v := new(fp.Fp).Mul(u1, i)
+		x3 := new(fp.Fp).Square(r)
+		x3.Sub(x3, j)
+		x3.Sub(x3, new(fp.Fp).Double(v))
+		s1.Mul(s1, j)
+		s1.Double(s1)
+		y3 := new(fp.Fp).Mul(r, new(fp.Fp).Sub(v, x3))
+		y3.Sub(y3, s1)
+		z3 := new(fp.Fp).Add(lhs.z, rhs.z)
+		z3.Square(z3)
+		z3.Sub(z3, z1z1)
+		z3.Sub(z3, z2z2)
+		z3.Mul(z3, h)
+		p.x = new(fp.Fp).Set(x3)
+		p.y = new(fp.Fp).Set(y3)
+		p.z = new(fp.Fp).Set(z3)
+
+		return p
+	}
+}
+
+func (p *Ep) Sub(lhs, rhs *Ep) *Ep {
+	return p.Add(lhs, new(Ep).Neg(rhs))
+}
+
+func (p *Ep) Mul(point *Ep, scalar *fq.Fq) *Ep {
+	bytes := scalar.Bytes()
+	precomputed := [16]*Ep{}
+	precomputed[0] = new(Ep).Identity()
+	precomputed[1] = new(Ep).Set(point)
+	for i := 2; i < 16; i += 2 {
+		precomputed[i] = new(Ep).Double(precomputed[i>>1])
+		precomputed[i+1] = new(Ep).Add(precomputed[i], point)
+	}
+	p.Identity()
+	for i := 0; i < 256; i += 4 {
+		// Brouwer / windowing method. window size of 4.
+		for j := 0; j < 4; j++ {
+			p.Double(p)
+		}
+		window := bytes[32-1-i>>3] >> (4 - i&0x04) & 0x0F
+		p.Add(p, precomputed[window])
+	}
+	return p
+}
+
+func (p *Ep) Equal(other *Ep) bool {
+	// warning: requires converting both to affine
+	// could save slightly by modifying one so that its z-value equals the other
+	// this would save one inversion and a handful of multiplications
+	// but this is more subtle and error-prone, so going to just convert both to affine.
+	lhs := new(Ep).Set(p)
+	rhs := new(Ep).Set(other)
+	lhs.toAffine()
+	rhs.toAffine()
+	return lhs.x.Equal(rhs.x) && lhs.y.Equal(rhs.y)
+}
+
+func (p *Ep) Set(other *Ep) *Ep {
+	// check is identity or on curve
+	p.x = new(fp.Fp).Set(other.x)
+	p.y = new(fp.Fp).Set(other.y)
+	p.z = new(fp.Fp).Set(other.z)
+	return p
+}
+
+func (p *Ep) toAffine() *Ep {
+	// mutates `p` in-place to convert it to "affine" form.
+	if p.IsIdentity() {
+		// warning: control flow / not constant-time
+		p.x.SetZero()
+		p.y.SetZero()
+		p.z.SetOne()
+		return p
+	}
+	zInv3, _ := new(fp.Fp).Invert(p.z) // z is necessarily nonzero
+	zInv2 := new(fp.Fp).Square(zInv3)
+	zInv3.Mul(zInv3, zInv2)
+	p.x.Mul(p.x, zInv2)
+	p.y.Mul(p.y, zInv3)
+	p.z.SetOne()
+	return p
+}
+
+func (p *Ep) ToAffineCompressed() []byte {
+	// Use ZCash encoding where infinity is all zeros
+	// and the top bit represents the sign of y and the
+	// remainder represent the x-coordinate
+	var inf [32]byte
+	p1 := new(Ep).Set(p)
+	p1.toAffine()
+	x := p1.x.Bytes()
+	x[31] |= (p1.y.Bytes()[0] & 1) << 7
+	subtle.ConstantTimeCopy(bool2int[p1.IsIdentity()], x[:], inf[:])
+	return x[:]
+}
+
+func (p *Ep) ToAffineUncompressed() []byte {
+	p1 := new(Ep).Set(p)
+	p1.toAffine()
+	x := p1.x.Bytes()
+	y := p1.y.Bytes()
+	return append(x[:], y[:]...)
+}
+
+func (p *Ep) FromAffineCompressed(bytes []byte) (*Ep, error) {
+	if len(bytes) != 32 {
+		return nil, fmt.Errorf("invalid byte sequence")
+	}
+
+	var input [32]byte
+	copy(input[:], bytes)
+	sign := (input[31] >> 7) & 1
+	input[31] &= 0x7F
+
+	x := new(fp.Fp)
+	if _, err := x.SetBytes(&input); err != nil {
+		return nil, err
+	}
+	rhs := rhsPallas(x)
+	if _, square := rhs.Sqrt(rhs); !square {
+		return nil, fmt.Errorf("rhs of given x-coordinate is not a square")
+	}
+	if rhs.Bytes()[0]&1 != sign {
+		rhs.Neg(rhs)
+	}
+	p.x = x
+	p.y = rhs
+	p.z = new(fp.Fp).SetOne()
+	if !p.IsOnCurve() {
+		return nil, fmt.Errorf("invalid point")
+	}
+	return p, nil
+}
+
+func (p *Ep) FromAffineUncompressed(bytes []byte) (*Ep, error) {
+	if len(bytes) != 64 {
+		return nil, fmt.Errorf("invalid length")
+	}
+	p.z = new(fp.Fp).SetOne()
+	p.x = new(fp.Fp)
+	p.y = new(fp.Fp)
+	var x, y [32]byte
+	copy(x[:], bytes[:32])
+	copy(y[:], bytes[32:])
+	if _, err := p.x.SetBytes(&x); err != nil {
+		return nil, err
+	}
+	if _, err := p.y.SetBytes(&y); err != nil {
+		return nil, err
+	}
+	if !p.IsOnCurve() {
+		return nil, fmt.Errorf("invalid point")
+	}
+	return p, nil
+}
+
+// rhs of the curve equation
+func rhsPallas(x *fp.Fp) *fp.Fp {
+	x2 := new(fp.Fp).Square(x)
+	x3 := new(fp.Fp).Mul(x, x2)
+	return new(fp.Fp).Add(x3, b)
+}
+
+func (p Ep) CurveName() string {
+	return "pallas"
+}
+
+func (p Ep) SumOfProducts(points []*Ep, scalars []Scalar) *Ep {
+	nScalars := make([]*big.Int, len(scalars))
+	for i, s := range scalars {
+		sc, ok := s.(*ScalarPallas)
+		if !ok {
+			return nil
+		}
+		nScalars[i] = sc.value.BigInt()
+	}
+	return sumOfProductsPippengerPallas(points, nScalars)
+}
+
+func (p *Ep) X() *fp.Fp {
+	t := new(Ep).Set(p)
+	t.toAffine()
+	return new(fp.Fp).Set(t.x)
+}
+
+func (p *Ep) Y() *fp.Fp {
+	t := new(Ep).Set(p)
+	t.toAffine()
+	return new(fp.Fp).Set(t.y)
+}
+
+func (p *Ep) IsOnCurve() bool {
+	// y^2 = x^3 + axz^4 + bz^6
+	// a = 0
+	// b = 5
+	z2 := new(fp.Fp).Square(p.z)
+	z4 := new(fp.Fp).Square(z2)
+	z6 := new(fp.Fp).Mul(z2, z4)
+	x2 := new(fp.Fp).Square(p.x)
+	x3 := new(fp.Fp).Mul(x2, p.x)
+
+	lhs := new(fp.Fp).Square(p.y)
+	rhs := new(fp.Fp).SetUint64(5)
+	rhs.Mul(rhs, z6)
+	rhs.Add(rhs, x3)
+	return p.z.IsZero() || lhs.Equal(rhs)
+}
+
+func (p *Ep) CMove(lhs, rhs *Ep, condition int) *Ep {
+	p.x = new(fp.Fp).CMove(lhs.x, rhs.x, condition)
+	p.y = new(fp.Fp).CMove(lhs.y, rhs.y, condition)
+	p.z = new(fp.Fp).CMove(lhs.z, rhs.z, condition)
+	return p
+}
+
+func sumOfProductsPippengerPallas(points []*Ep, scalars []*big.Int) *Ep {
+	if len(points) != len(scalars) {
+		return nil
+	}
+
+	const w = 6
+
+	bucketSize := (1 << w) - 1
+	windows := make([]*Ep, 255/w+1)
+	for i := range windows {
+		windows[i] = new(Ep).Identity()
+	}
+	bucket := make([]*Ep, bucketSize)
+
+	for j := 0; j < len(windows); j++ {
+		for i := 0; i < bucketSize; i++ {
+			bucket[i] = new(Ep).Identity()
+		}
+
+		for i := 0; i < len(scalars); i++ {
+			index := bucketSize & int(new(big.Int).Rsh(scalars[i], uint(w*j)).Int64())
+			if index != 0 {
+				bucket[index-1].Add(bucket[index-1], points[i])
+			}
+		}
+
+		acc, sum := new(Ep).Identity(), new(Ep).Identity()
+
+		for i := bucketSize - 1; i >= 0; i-- {
+			sum.Add(sum, bucket[i])
+			acc.Add(acc, sum)
+		}
+		windows[j] = acc
+	}
+
+	acc := new(Ep).Identity()
+	for i := len(windows) - 1; i >= 0; i-- {
+		for j := 0; j < w; j++ {
+			acc.Double(acc)
+		}
+		acc.Add(acc, windows[i])
+	}
+	return acc
+}
+
+// Implements a degree 3 isogeny map.
+// The input and output are in Jacobian coordinates, using the method
+// in "Avoiding inversions" [WB2019, section 4.3].
+func isoMap(p *Ep) *Ep {
+	var z [4]*fp.Fp
+	z[0] = new(fp.Fp).Square(p.z)    //z^2
+	z[1] = new(fp.Fp).Mul(z[0], p.z) // z^3
+	z[2] = new(fp.Fp).Square(z[0])   // z^4
+	z[3] = new(fp.Fp).Square(z[1])   // z^6
+
+	// ((iso[0] * x + iso[1] * z^2) * x + iso[2] * z^4) * x + iso[3] * z^6
+	numX := new(fp.Fp).Set(isomapper[0])
+	numX.Mul(numX, p.x)
+	numX.Add(numX, new(fp.Fp).Mul(isomapper[1], z[0]))
+	numX.Mul(numX, p.x)
+	numX.Add(numX, new(fp.Fp).Mul(isomapper[2], z[2]))
+	numX.Mul(numX, p.x)
+	numX.Add(numX, new(fp.Fp).Mul(isomapper[3], z[3]))
+
+	// (z^2 * x + iso[4] * z^4) * x + iso[5] * z^6
+	divX := new(fp.Fp).Set(z[0])
+	divX.Mul(divX, p.x)
+	divX.Add(divX, new(fp.Fp).Mul(isomapper[4], z[2]))
+	divX.Mul(divX, p.x)
+	divX.Add(divX, new(fp.Fp).Mul(isomapper[5], z[3]))
+
+	// (((iso[6] * x + iso[7] * z2) * x + iso[8] * z4) * x + iso[9] * z6) * y
+	numY := new(fp.Fp).Set(isomapper[6])
+	numY.Mul(numY, p.x)
+	numY.Add(numY, new(fp.Fp).Mul(isomapper[7], z[0]))
+	numY.Mul(numY, p.x)
+	numY.Add(numY, new(fp.Fp).Mul(isomapper[8], z[2]))
+	numY.Mul(numY, p.x)
+	numY.Add(numY, new(fp.Fp).Mul(isomapper[9], z[3]))
+	numY.Mul(numY, p.y)
+
+	// (((x + iso[10] * z2) * x + iso[11] * z4) * x + iso[12] * z6) * z3
+	divY := new(fp.Fp).Set(p.x)
+	divY.Add(divY, new(fp.Fp).Mul(isomapper[10], z[0]))
+	divY.Mul(divY, p.x)
+	divY.Add(divY, new(fp.Fp).Mul(isomapper[11], z[2]))
+	divY.Mul(divY, p.x)
+	divY.Add(divY, new(fp.Fp).Mul(isomapper[12], z[3]))
+	divY.Mul(divY, z[1])
+
+	z0 := new(fp.Fp).Mul(divX, divY)
+	x := new(fp.Fp).Mul(numX, divY)
+	x.Mul(x, z0)
+	y := new(fp.Fp).Mul(numY, divX)
+	y.Mul(y, new(fp.Fp).Square(z0))
+
+	return &Ep{
+		x, y, z0,
+	}
+}
+
+func mapSswu(u *fp.Fp) *Ep {
+	//c1 := new(fp.Fp).Neg(isoa)
+	//c1.Invert(c1)
+	//c1.Mul(isob, c1)
+	c1 := &fp.Fp{
+		0x1ee770ce078456ec,
+		0x48cfd64c2ce76be0,
+		0x43d5774c0ab79e2f,
+		0x23368d2bdce28cf3,
+	}
+	//c2 := new(fp.Fp).Neg(z)
+	//c2.Invert(c2)
+	c2 := &fp.Fp{
+		0x03df915f89d89d8a,
+		0x8f1e8db09ef82653,
+		0xd89d89d89d89d89d,
+		0x1d89d89d89d89d89,
+	}
+
+	u2 := new(fp.Fp).Square(u)
+	tv1 := new(fp.Fp).Mul(z, u2)
+	tv2 := new(fp.Fp).Square(tv1)
+	x1 := new(fp.Fp).Add(tv1, tv2)
+	x1.Invert(x1)
+	e1 := bool2int[x1.IsZero()]
+	x1.Add(x1, new(fp.Fp).SetOne())
+	x1.CMove(x1, c2, e1)
+	x1.Mul(x1, c1)
+	gx1 := new(fp.Fp).Square(x1)
+	gx1.Add(gx1, isoa)
+	gx1.Mul(gx1, x1)
+	gx1.Add(gx1, isob)
+	x2 := new(fp.Fp).Mul(tv1, x1)
+	tv2.Mul(tv1, tv2)
+	gx2 := new(fp.Fp).Mul(gx1, tv2)
+	gx1Sqrt, e2 := new(fp.Fp).Sqrt(gx1)
+	x := new(fp.Fp).CMove(x2, x1, bool2int[e2])
+	gx2Sqrt, _ := new(fp.Fp).Sqrt(gx2)
+	y := new(fp.Fp).CMove(gx2Sqrt, gx1Sqrt, bool2int[e2])
+	e3 := u.IsOdd() == y.IsOdd()
+	y.CMove(new(fp.Fp).Neg(y), y, bool2int[e3])
+
+	return &Ep{
+		x: x, y: y, z: new(fp.Fp).SetOne(),
+	}
+}
diff --git a/pkg/core/curves/pallas_curve_test.go b/pkg/core/curves/pallas_curve_test.go
new file mode 100644
index 00000000..8dec7ec3
--- /dev/null
+++ b/pkg/core/curves/pallas_curve_test.go
@@ -0,0 +1,136 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package curves
+
+import (
+	crand "crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fp"
+	"github.com/coinbase/kryptology/pkg/core/curves/native/pasta/fq"
+	"github.com/stretchr/testify/assert"
+	"testing"
+)
+
+func TestPointPallasAddDoubleMul(t *testing.T) {
+	g := new(Ep).Generator()
+	id := new(Ep).Identity()
+	assert.Equal(t, g.Add(g, id), g)
+
+	g2 := new(Ep).Add(g, g)
+	assert.True(t, new(Ep).Double(g).Equal(g2))
+	assert.Equal(t, new(Ep).Double(g), new(Ep).Add(g, g))
+	g3 := new(Ep).Add(g, g2)
+	assert.True(t, g3.Equal(new(Ep).Mul(g, new(fq.Fq).SetUint64(3))))
+
+	g4 := new(Ep).Add(g3, g)
+	assert.True(t, g4.Equal(new(Ep).Double(g2)))
+	assert.True(t, g4.Equal(new(Ep).Mul(g, new(fq.Fq).SetUint64(4))))
+}
+
+func TestPointPallasHash(t *testing.T) {
+	h0 := new(Ep).Hash(nil)
+	assert.True(t, h0.IsOnCurve())
+	h1 := new(Ep).Hash([]byte{})
+	assert.True(t, h1.IsOnCurve())
+	assert.True(t, h0.Equal(h1))
+	h2 := new(Ep).Hash([]byte{1})
+	assert.True(t, h2.IsOnCurve())
+}
+
+func TestPointPallasNeg(t *testing.T) {
+	g := new(Ep).Generator()
+	g.Neg(g)
+	assert.True(t, g.Neg(g).Equal(new(Ep).Generator()))
+	id := new(Ep).Identity()
+	assert.True(t, new(Ep).Neg(id).Equal(id))
+}
+
+func TestPointPallasRandom(t *testing.T) {
+	a := new(Ep).Random(testRng())
+	assert.NotNil(t, a.x)
+	assert.NotNil(t, a.y)
+	assert.NotNil(t, a.z)
+	assert.True(t, a.IsOnCurve())
+	e := &Ep{
+		x: &fp.Fp{
+			0x7263083d01d4859c,
+			0x65a03323b5a3d204,
+			0xe71d73222b136668,
+			0x1d1b1bcf1256b539,
+		},
+		y: &fp.Fp{
+			0x8cc2516ffe23e1bb,
+			0x5418f941eeaca812,
+			0x16c9af658a846f29,
+			0x11c572091c418668,
+		},
+		z: &fp.Fp{
+			0xa879589adb77a88e,
+			0x5444a531a19f2406,
+			0x637ff77c51dda524,
+			0x0369e90d219ce821,
+		},
+	}
+	assert.True(t, a.Equal(e))
+}
+
+func TestPointPallasSerialize(t *testing.T) {
+	ss := new(ScalarPallas).Random(testRng()).(*ScalarPallas)
+	g := new(Ep).Generator()
+
+	ppt := new(Ep).Mul(g, ss.value)
+	assert.Equal(t, ppt.ToAffineCompressed(), []byte{0x1c, 0x6d, 0x47, 0x1f, 0x4a, 0x81, 0xcd, 0x8, 0x4e, 0xb3, 0x17, 0x9a, 0xcd, 0x17, 0xe2, 0x9a, 0x24, 0x69, 0xb, 0x4e, 0x69, 0x5f, 0x35, 0x1a, 0x92, 0x12, 0x95, 0xc9, 0xe6, 0xd3, 0x7a, 0x0})
+	assert.Equal(t, ppt.ToAffineUncompressed(), []byte{0x1c, 0x6d, 0x47, 0x1f, 0x4a, 0x81, 0xcd, 0x8, 0x4e, 0xb3, 0x17, 0x9a, 0xcd, 0x17, 0xe2, 0x9a, 0x24, 0x69, 0xb, 0x4e, 0x69, 0x5f, 0x35, 0x1a, 0x92, 0x12, 0x95, 0xc9, 0xe6, 0xd3, 0x7a, 0x0, 0x80, 0x5c, 0xa1, 0x56, 0x6d, 0x1b, 0x87, 0x5f, 0xb0, 0x2e, 0xae, 0x85, 0x4e, 0x86, 0xa9, 0xcd, 0xde, 0x37, 0x6a, 0xc8, 0x4a, 0x80, 0xf6, 0x43, 0xaa, 0xe6, 0x2c, 0x2d, 0x15, 0xdb, 0xda, 0x29})
+	retP, err := new(Ep).FromAffineCompressed(ppt.ToAffineCompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+	retP, err = new(Ep).FromAffineUncompressed(ppt.ToAffineUncompressed())
+	assert.NoError(t, err)
+	assert.True(t, ppt.Equal(retP))
+
+	// smoke test
+	for i := 0; i < 25; i++ {
+		s := new(ScalarPallas).Random(crand.Reader).(*ScalarPallas)
+		pt := new(Ep).Mul(g, s.value)
+		cmprs := pt.ToAffineCompressed()
+		assert.Equal(t, len(cmprs), 32)
+		retC, err := new(Ep).FromAffineCompressed(cmprs)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retC))
+
+		un := pt.ToAffineUncompressed()
+		assert.Equal(t, len(un), 64)
+		retU, err := new(Ep).FromAffineUncompressed(un)
+		assert.NoError(t, err)
+		assert.True(t, pt.Equal(retU))
+	}
+}
+
+func TestPointPallasCMove(t *testing.T) {
+	a := new(Ep).Random(crand.Reader)
+	b := new(Ep).Random(crand.Reader)
+	assert.True(t, new(Ep).CMove(a, b, 1).Equal(b))
+	assert.True(t, new(Ep).CMove(a, b, 0).Equal(a))
+}
+
+func TestPointPallasSumOfProducts(t *testing.T) {
+	lhs := new(Ep).Generator()
+	lhs.Mul(lhs, new(fq.Fq).SetUint64(50))
+	points := make([]*Ep, 5)
+	for i := range points {
+		points[i] = new(Ep).Generator()
+	}
+	scalars := []Scalar{
+		new(ScalarPallas).New(8),
+		new(ScalarPallas).New(9),
+		new(ScalarPallas).New(10),
+		new(ScalarPallas).New(11),
+		new(ScalarPallas).New(12),
+	}
+	rhs := lhs.SumOfProducts(points, scalars)
+	assert.NotNil(t, rhs)
+	assert.True(t, lhs.Equal(rhs))
+}
diff --git a/pkg/core/hash.go b/pkg/core/hash.go
new file mode 100644
index 00000000..94e7d977
--- /dev/null
+++ b/pkg/core/hash.go
@@ -0,0 +1,272 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"bytes"
+	"crypto/elliptic"
+	"crypto/sha256"
+	"fmt"
+	"hash"
+	"math"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"golang.org/x/crypto/hkdf"
+
+	"github.com/btcsuite/btcd/btcec"
+)
+
+type HashField struct {
+	// F_p^k
+	Order           *big.Int // p^k
+	Characteristic  *big.Int // p
+	ExtensionDegree *big.Int // k
+}
+
+type Params struct {
+	F                 *HashField
+	SecurityParameter int
+	Hash              func() hash.Hash
+	L                 int
+}
+
+func getParams(curve elliptic.Curve) (*Params, error) {
+	switch curve.Params().Name {
+	case btcec.S256().Name, elliptic.P256().Params().Name:
+		return &Params{
+			F: &HashField{
+				Order:           curve.Params().P,
+				Characteristic:  curve.Params().P,
+				ExtensionDegree: new(big.Int).SetInt64(1),
+			},
+			SecurityParameter: 128,
+			Hash:              sha256.New,
+			L:                 48,
+		}, nil
+	case "Bls12381G1":
+		return &Params{
+			F: &HashField{
+				Order:           curve.Params().P,
+				Characteristic:  curve.Params().P,
+				ExtensionDegree: new(big.Int).SetInt64(1),
+			},
+			SecurityParameter: 128,
+			Hash:              sha256.New,
+			L:                 48,
+		}, nil
+	case "ed25519":
+		return &Params{
+			F: &HashField{
+				Order:           curve.Params().P,
+				Characteristic:  curve.Params().P,
+				ExtensionDegree: new(big.Int).SetInt64(1),
+			},
+			SecurityParameter: 128,
+			Hash:              sha256.New,
+			L:                 48,
+		}, nil
+	default:
+		return nil, fmt.Errorf("Not implemented: %s", curve.Params().Name)
+	}
+}
+
+func I2OSP(b, n int) []byte {
+	os := new(big.Int).SetInt64(int64(b)).Bytes()
+	if n > len(os) {
+		var buf bytes.Buffer
+		buf.Write(make([]byte, n-len(os)))
+		buf.Write(os)
+		return buf.Bytes()
+	}
+	return os[:n]
+}
+
+func OS2IP(os []byte) *big.Int {
+	return new(big.Int).SetBytes(os)
+}
+
+func hashThis(f func() hash.Hash, this []byte) ([]byte, error) {
+	h := f()
+	w, err := h.Write(this)
+	if w != len(this) {
+		return nil, fmt.Errorf("bytes written to hash doesn't match expected")
+	} else if err != nil {
+		return nil, err
+	}
+	v := h.Sum(nil)
+	return v, nil
+}
+
+func concat(xs ...[]byte) []byte {
+	var result []byte
+	for _, x := range xs {
+		result = append(result, x...)
+	}
+	return result
+}
+
+func xor(b1, b2 []byte) []byte {
+	// b1 and b2 must be same length
+	result := make([]byte, len(b1))
+	for i := range b1 {
+		result[i] = b1[i] ^ b2[i]
+	}
+
+	return result
+}
+
+func ExpandMessageXmd(f func() hash.Hash, msg, DST []byte, lenInBytes int) ([]byte, error) {
+	// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-5.4.1
+
+	// step 1
+	ell := int(math.Ceil(float64(lenInBytes) / float64(f().Size())))
+
+	//step 2
+	if ell > 255 {
+		return nil, fmt.Errorf("ell > 255")
+	}
+
+	// step 3
+	dstPrime := append(DST, I2OSP(len(DST), 1)...)
+
+	// step 4
+	zPad := I2OSP(0, f().BlockSize())
+
+	// step 5 & 6
+	msgPrime := concat(zPad, msg, I2OSP(lenInBytes, 2), I2OSP(0, 1), dstPrime)
+
+	var err error
+
+	b := make([][]byte, ell+1)
+
+	// step 7
+	b[0], err = hashThis(f, msgPrime)
+	if err != nil {
+		return nil, err
+	}
+
+	// step 8
+	b[1], err = hashThis(f, concat(b[0], I2OSP(1, 1), dstPrime))
+	if err != nil {
+		return nil, err
+	}
+
+	// step 9
+	for i := 2; i <= ell; i++ {
+		// step 10
+		b[i], err = hashThis(f, concat(xor(b[0], b[i-1]), I2OSP(i, 1), dstPrime))
+		if err != nil {
+			return nil, err
+		}
+	}
+	// step 11
+	uniformBytes := concat(b[1:]...)
+
+	// step 12
+	return uniformBytes[:lenInBytes], nil
+}
+
+func hashToField(msg []byte, count int, curve elliptic.Curve) ([][]*big.Int, error) {
+	// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-5.3
+
+	parameters, err := getParams(curve)
+	if err != nil {
+		return nil, err
+	}
+
+	f := parameters.Hash
+
+	DST := []byte("Coinbase_tECDSA")
+
+	m := int(parameters.F.ExtensionDegree.Int64())
+	L := parameters.L
+
+	// step 1
+	lenInBytes := count * m * L
+
+	// step 2
+	uniformBytes, err := ExpandMessageXmd(f, msg, DST, lenInBytes)
+	if err != nil {
+		return nil, err
+	}
+
+	u := make([][]*big.Int, count)
+
+	// step 3
+	for i := 0; i < count; i++ {
+		e := make([]*big.Int, m)
+		// step 4
+		for j := 0; j < m; j++ {
+			// step 5
+			elmOffset := L * (j + i*m)
+			// step 6
+			tv := uniformBytes[elmOffset : elmOffset+L]
+			// step 7
+			e[j] = new(big.Int).Mod(OS2IP(tv), parameters.F.Characteristic)
+
+		}
+		// step 8
+		u[i] = e
+	}
+	// step 9
+	return u, nil
+}
+
+func Hash(msg []byte, curve elliptic.Curve) (*big.Int, error) {
+	u, err := hashToField(msg, 1, curve)
+	if err != nil {
+		return nil, err
+	}
+	return u[0][0], nil
+}
+
+// fiatShamir computes the HKDF over many values
+// iteratively such that each value is hashed separately
+// and based on preceding values
+//
+// The first value is computed as okm_0 = KDF(f || value) where
+// f is a byte slice of 32 0xFF
+// salt is zero-filled byte slice with length equal to the hash output length
+// info is the protocol name
+// okm is the 32 byte output
+//
+// The each subsequent iteration is computed by as okm_i = KDF(f_i || value || okm_{i-1})
+// where f_i = 2^b - 1 - i such that there are 0xFF bytes prior to the value.
+// f_1 changes the first byte to 0xFE, f_2 to 0xFD. The previous okm is appended to the value
+// to provide cryptographic domain separation
+// See https://signal.org/docs/specifications/x3dh/#cryptographic-notation
+// and https://signal.org/docs/specifications/xeddsa/#hash-functions
+// for more details.
+// This uses the KDF function similar to X3DH for each `value`
+// But changes the key just like XEdDSA where the prefix bytes change by a single bit
+func FiatShamir(values ...*big.Int) ([]byte, error) {
+	// Don't accept any nil arguments
+	if AnyNil(values...) {
+		return nil, internal.ErrNilArguments
+	}
+
+	info := []byte("Coinbase tECDSA 1.0")
+	salt := make([]byte, 32)
+	okm := make([]byte, 32)
+	f := bytes.Repeat([]byte{0xFF}, 32)
+
+	for _, b := range values {
+		ikm := append(f, b.Bytes()...)
+		ikm = append(ikm, okm...)
+		kdf := hkdf.New(sha256.New, ikm, salt, info)
+		n, err := kdf.Read(okm)
+		if err != nil {
+			return nil, err
+		}
+		if n != len(okm) {
+			return nil, fmt.Errorf("unable to read expected number of bytes want=%v got=%v", len(okm), n)
+		}
+		internal.ByteSub(f)
+	}
+	return okm, nil
+}
diff --git a/pkg/core/hash_test.go b/pkg/core/hash_test.go
new file mode 100644
index 00000000..b2b25f54
--- /dev/null
+++ b/pkg/core/hash_test.go
@@ -0,0 +1,132 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"crypto/sha256"
+	"crypto/sha512"
+	"encoding/hex"
+	"fmt"
+	"hash"
+	"math/big"
+	"strconv"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestExpandMessageXmd(t *testing.T) {
+	// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#appendix-K.1
+	tests := []struct {
+		f             func() hash.Hash
+		msg           []byte
+		lenInBytesHex string
+		expectedHex   string
+	}{
+		{sha256.New, []byte(""), "20", "f659819a6473c1835b25ea59e3d38914c98b374f0970b7e4c92181df928fca88"},
+		{sha256.New, []byte("abc"), "20", "1c38f7c211ef233367b2420d04798fa4698080a8901021a795a1151775fe4da7"},
+		{sha256.New, []byte("abcdef0123456789"), "20", "8f7e7b66791f0da0dbb5ec7c22ec637f79758c0a48170bfb7c4611bd304ece89"},
+		{sha256.New, []byte("q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq"), "20", "72d5aa5ec810370d1f0013c0df2f1d65699494ee2a39f72e1716b1b964e1c642"},
+		{sha256.New, []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"), "20", "3b8e704fc48336aca4c2a12195b720882f2162a4b7b13a9c350db46f429b771b"},
+		{sha256.New, []byte(""), "80", "8bcffd1a3cae24cf9cd7ab85628fd111bb17e3739d3b53f89580d217aa79526f1708354a76a402d3569d6a9d19ef3de4d0b991e4f54b9f20dcde9b95a66824cbdf6c1a963a1913d43fd7ac443a02fc5d9d8d77e2071b86ab114a9f34150954a7531da568a1ea8c760861c0cde2005afc2c114042ee7b5848f5303f0611cf297f"},
+		{sha256.New, []byte("abc"), "80", "fe994ec51bdaa821598047b3121c149b364b178606d5e72bfbb713933acc29c186f316baecf7ea22212f2496ef3f785a27e84a40d8b299cec56032763eceeff4c61bd1fe65ed81decafff4a31d0198619c0aa0c6c51fca15520789925e813dcfd318b542f8799441271f4db9ee3b8092a7a2e8d5b75b73e28fb1ab6b4573c192"},
+		{sha256.New, []byte("abcdef0123456789"), "80", "c9ec7941811b1e19ce98e21db28d22259354d4d0643e301175e2f474e030d32694e9dd5520dde93f3600d8edad94e5c364903088a7228cc9eff685d7eaac50d5a5a8229d083b51de4ccc3733917f4b9535a819b445814890b7029b5de805bf62b33a4dc7e24acdf2c924e9fe50d55a6b832c8c84c7f82474b34e48c6d43867be"},
+		{sha256.New, []byte("q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq"), "80", "48e256ddba722053ba462b2b93351fc966026e6d6db493189798181c5f3feea377b5a6f1d8368d7453faef715f9aecb078cd402cbd548c0e179c4ed1e4c7e5b048e0a39d31817b5b24f50db58bb3720fe96ba53db947842120a068816ac05c159bb5266c63658b4f000cbf87b1209a225def8ef1dca917bcda79a1e42acd8069"},
+		{sha256.New, []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"), "80", "396962db47f749ec3b5042ce2452b619607f27fd3939ece2746a7614fb83a1d097f554df3927b084e55de92c7871430d6b95c2a13896d8a33bc48587b1f66d21b128a1a8240d5b0c26dfe795a1a842a0807bb148b77c2ef82ed4b6c9f7fcb732e7f94466c8b51e52bf378fba044a31f5cb44583a892f5969dcd73b3fa128816e"},
+
+		{sha512.New, []byte(""), "20", "2eaa1f7b5715f4736e6a5dbe288257abf1faa028680c1d938cd62ac699ead642"},
+		{sha512.New, []byte("abc"), "20", "0eeda81f69376c80c0f8986496f22f21124cb3c562cf1dc608d2c13005553b0f"},
+		{sha512.New, []byte("abcdef0123456789"), "20", "2e375fc05e05e80dbf3083796fde2911789d9e8847e1fcebf4ca4b36e239b338"},
+		{sha512.New, []byte("q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq"), "20", "c37f9095fe7fe4f01c03c3540c1229e6ac8583b07510085920f62ec66acc0197"},
+		{sha512.New, []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"), "20", "af57a7f56e9ed2aa88c6eab45c8c6e7638ae02da7c92cc04f6648c874ebd560e"},
+		{sha512.New, []byte(""), "80", "0687ce02eba5eb3faf1c3c539d1f04babd3c0f420edae244eeb2253b6c6d6865145c31458e824b4e87ca61c3442dc7c8c9872b0b7250aa33e0668ccebbd2b386de658ca11a1dcceb51368721ae6dcd2d4bc86eaebc4e0d11fa02ad053289c9b28a03da6c942b2e12c14e88dbde3b0ba619d6214f47212b628f3e1b537b66efcf"},
+		{sha512.New, []byte("abc"), "80", "779ae4fd8a92f365e4df96b9fde97b40486bb005c1a2096c86f55f3d92875d89045fbdbc4a0e9f2d3e1e6bcd870b2d7131d868225b6fe72881a81cc5166b5285393f71d2e68bb0ac603479959370d06bdbe5f0d8bfd9af9494d1e4029bd68ab35a561341dd3f866b3ef0c95c1fdfaab384ce24a23427803dda1db0c7d8d5344a"},
+		{sha512.New, []byte("abcdef0123456789"), "80", "f0953d28846a50e9f88b7ae35b643fc43733c9618751b569a73960c655c068db7b9f044ad5a40d49d91c62302eaa26163c12abfa982e2b5d753049e000adf7630ae117aeb1fb9b61fc724431ac68b369e12a9481b4294384c3c890d576a79264787bc8076e7cdabe50c044130e480501046920ff090c1a091c88391502f0fbac"},
+		{sha512.New, []byte("q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq"), "80", "64d3e59f0bc3c5e653011c914b419ba8310390a9585311fddb26791d26663bd71971c347e1b5e88ba9274d2445ed9dcf48eea9528d807b7952924159b7c27caa4f25a2ea94df9508e70a7012dfce0e8021b37e59ea21b80aa9af7f1a1f2efa4fbe523c4266ce7d342acaacd438e452c501c131156b4945515e9008d2b155c258"},
+		{sha512.New, []byte("a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"), "80", "01524feea5b22f6509f6b1e805c97df94faf4d821b01aadeebc89e9daaed0733b4544e50852fd3e019d58eaad6d267a134c8bc2c08bc46c10bfeff3ee03110bcd8a0d695d75a34092bd8b677bdd369a13325549abab54f4ac907b712bdd3567f38c4554c51902b735b81f43a7ef6f938c7690d107c052c7e7b795ac635b3200a"},
+	}
+
+	for _, test := range tests {
+		t.Run(fmt.Sprintf("msg: %s", test.msg), func(t *testing.T) {
+			DST := []byte("QUUX-V01-CS02-with-expander")
+			lenInBytes, err := strconv.ParseInt(test.lenInBytesHex, 16, 64)
+			assert.NoError(t, err)
+			expected, err := hex.DecodeString(test.expectedHex)
+			assert.NoError(t, err)
+			actual, err := ExpandMessageXmd(test.f, test.msg, DST, int(lenInBytes))
+			assert.NoError(t, err)
+			assert.Equal(t, actual, expected)
+		})
+	}
+}
+func TestFiatShamirDeterministic(t *testing.T) {
+	a := big.NewInt(1)
+	hash, err := FiatShamir(a)
+	assert.Nil(t, err)
+	assert.Equal(t, hash, []byte{0x3d, 0x95, 0xc0, 0x9f, 0x41, 0x33, 0x25, 0xbb, 0x10, 0x77, 0x2d, 0x83, 0x1d, 0x3e, 0x67, 0x98, 0xce, 0x7b, 0xde, 0xd5, 0x7f, 0x9, 0x7e, 0xfc, 0x77, 0x23, 0xfc, 0x49, 0x36, 0x82, 0xdd, 0x6a})
+
+	a = big.NewInt(0xaaa)
+	hash, err = FiatShamir(a)
+	assert.Nil(t, err)
+	assert.Equal(t, hash, []byte{0x61, 0xa9, 0x7f, 0x6, 0x74, 0xec, 0x47, 0xf5, 0xac, 0x30, 0xa0, 0x4c, 0x34, 0xdb, 0x51, 0x97, 0x60, 0x7e, 0xb2, 0x4a, 0x97, 0x9, 0xa5, 0xb9, 0x1c, 0x89, 0x30, 0x39, 0xb7, 0x29, 0xe6, 0x30})
+}
+
+func TestFiatShamirEqual(t *testing.T) {
+	pi, err := FiatShamir(One)
+	assert.Nil(t, err)
+	pi_, err := FiatShamir(One)
+	assert.Nil(t, err)
+	assert.Equal(t, pi, pi_)
+}
+
+func TestFiatShamirNotEqual(t *testing.T) {
+	pi, err := FiatShamir(One)
+	assert.Nil(t, err)
+	pi_, err := FiatShamir(Two)
+	assert.Nil(t, err)
+	assert.NotEqual(t, pi, pi_)
+}
+
+func TestFiatShamirOrderDependent(t *testing.T) {
+	a := big.NewInt(1)
+	b := big.NewInt(100)
+
+	pi, err := FiatShamir(a, b)
+	assert.Nil(t, err)
+	pi_, err := FiatShamir(a, b)
+	assert.Nil(t, err)
+	assert.Equal(t, pi, pi_)
+
+	q, _ := FiatShamir(b, a)
+	assert.NotEqual(t, pi, q)
+}
+
+func TestFiatShamirExtensionAttackResistance(t *testing.T) {
+	a := big.NewInt(0x00FF)
+	b := big.NewInt(0xFF00)
+
+	c := big.NewInt(0x00)
+	d := big.NewInt(0xFFFF00)
+
+	pi, err := FiatShamir(a, b)
+	assert.Nil(t, err)
+	pi_, err := FiatShamir(c, d)
+	assert.Nil(t, err)
+	assert.NotEqual(t, pi, pi_)
+
+	a = big.NewInt(0x0000)
+	b = big.NewInt(0xFFFF)
+
+	c = big.NewInt(0x0000F)
+	d = big.NewInt(0xFFF)
+
+	q, err := FiatShamir(a, b)
+	assert.Nil(t, err)
+	q_, err := FiatShamir(c, d)
+	assert.Nil(t, err)
+	assert.NotEqual(t, q, q_)
+}
diff --git a/pkg/core/mod.go b/pkg/core/mod.go
new file mode 100644
index 00000000..c99176f2
--- /dev/null
+++ b/pkg/core/mod.go
@@ -0,0 +1,175 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+// Package core contains convenience functions for modular arithmetic.
+
+package core
+
+import (
+	crand "crypto/rand"
+	"crypto/subtle"
+	"fmt"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+var (
+	// Zero is additive identity in the set of integers
+	Zero = big.NewInt(0)
+
+	// One is the multiplicative identity in the set of integers
+	One = big.NewInt(1)
+
+	// Two is the odd prime
+	Two = big.NewInt(2)
+)
+
+// ConstantTimeEqByte determines if a, b have identical byte serialization
+// and signs. It uses the crypto/subtle package to get a constant time comparison
+// over byte representations. Return value is a byte which may be
+// useful in bitwise operations. Returns 0x1 if the two values have the
+// identical sign and byte representation; 0x0 otherwise.
+func ConstantTimeEqByte(a, b *big.Int) byte {
+	if a == nil && a == b {
+		return 1
+	}
+	if a == nil || b == nil {
+		return 0
+	}
+	// Determine if the byte representations are the same
+	var sameBytes byte
+	if subtle.ConstantTimeCompare(a.Bytes(), b.Bytes()) == 1 {
+		sameBytes = 1
+	} else {
+		sameBytes = 0
+	}
+
+	// Determine if the signs are the same
+	var sameSign byte
+	if a.Sign() == b.Sign() {
+		sameSign = 1
+	} else {
+		sameSign = 0
+	}
+
+	// Report the conjunction
+	return sameBytes & sameSign
+}
+
+// ConstantTimeEq determines if a, b have identical byte serialization
+// and uses the crypto/subtle package to get a constant time comparison
+// over byte representations.
+func ConstantTimeEq(a, b *big.Int) bool {
+	return ConstantTimeEqByte(a, b) == 1
+}
+
+// In determines ring membership before modular reduction: x ∈ Z_m
+// returns nil if 0 ≤ x < m
+func In(x, m *big.Int) error {
+	if AnyNil(x, m) {
+		return internal.ErrNilArguments
+	}
+	// subtle doesn't support constant time big.Int compare
+	// just use big.Cmp for now
+	// x ∈ Z_m ⇔ 0 ≤ x < m
+	if x.Cmp(Zero) != -1 && x.Cmp(m) == -1 {
+		return nil
+	}
+	return internal.ErrZmMembership
+}
+
+// Add (modular addition): z = x+y (modulo m)
+func Add(x, y, m *big.Int) (*big.Int, error) {
+	if AnyNil(x, y) {
+		return nil, internal.ErrNilArguments
+	}
+	z := new(big.Int).Add(x, y)
+	// Compute the residue if one is specified, otherwise
+	// we leave the value as an unbound integer
+	if m != nil {
+		z.Mod(z, m)
+	}
+	return z, nil
+}
+
+// Mul (modular multiplication): z = x*y (modulo m)
+func Mul(x, y, m *big.Int) (*big.Int, error) {
+	if AnyNil(x, y) {
+		return nil, internal.ErrNilArguments
+	}
+	z := new(big.Int).Mul(x, y)
+
+	// Compute the residue if one is specified, otherwise
+	// we leave the value as an unbound integer
+	if m != nil {
+		z.Mod(z, m)
+	}
+	return z, nil
+}
+
+// Exp (modular exponentiation): z = x^y (modulo m)
+func Exp(x, y, m *big.Int) (*big.Int, error) {
+	if AnyNil(x, y) {
+		return nil, internal.ErrNilArguments
+	}
+	// This wrapper looks silly, but it makes the calling code read more consistently.
+	return new(big.Int).Exp(x, y, m), nil
+}
+
+// Neg (modular negation): z = -x (modulo m)
+func Neg(x, m *big.Int) (*big.Int, error) {
+	if AnyNil(x, m) {
+		return nil, internal.ErrNilArguments
+	}
+	z := new(big.Int).Neg(x)
+	z.Mod(z, m)
+	return z, nil
+}
+
+// Inv (modular inverse): returns y such that xy = 1 (modulo m).
+func Inv(x, m *big.Int) (*big.Int, error) {
+	if AnyNil(x, m) {
+		return nil, internal.ErrNilArguments
+	}
+	z := new(big.Int).ModInverse(x, m)
+	if z == nil {
+		return nil, fmt.Errorf("cannot compute the multiplicative inverse")
+	}
+	return z, nil
+}
+
+// Rand generates a cryptographically secure random integer in the range: 1 < r < m.
+func Rand(m *big.Int) (*big.Int, error) {
+	if m == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Select a random element, but not zero or one
+	// The reason is the random element may be used as a Scalar or an exponent.
+	// An exponent of 1 is generally acceptable because the generator can't be
+	// 1. If a Scalar is combined with another Scalar like in fiat-shamir, it
+	// offers no hiding properties when multiplied.
+	for {
+		result, err := crand.Int(crand.Reader, m)
+		if err != nil {
+			return nil, err
+		}
+
+		if result.Cmp(One) == 1 { // result > 1
+			return result, nil
+		}
+	}
+}
+
+// AnyNil determines if any of values are nil
+func AnyNil(values ...*big.Int) bool {
+	for _, x := range values {
+		if x == nil {
+			return true
+		}
+	}
+	return false
+}
diff --git a/pkg/core/mod_test.go b/pkg/core/mod_test.go
new file mode 100644
index 00000000..318e2086
--- /dev/null
+++ b/pkg/core/mod_test.go
@@ -0,0 +1,564 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"github.com/coinbase/kryptology/internal"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+var (
+	four = big.NewInt(4)
+
+	// Large numbers for testing -- computing with independent tooling
+	// x,y 100-digit numbers
+	x, _     = new(big.Int).SetString("7146643783615963513942641287213372249533955323510461217840179896547799100626220786140425637990097431", 10)
+	y, _     = new(big.Int).SetString("1747698065194620177681258504464368264357359841192790848951902311522815739310792522712583635858354245", 10)
+	sumxy, _ = new(big.Int).SetString("8894341848810583691623899791677740513891315164703252066792082208070614839937013308853009273848451676", 10)
+	xy, _    = new(big.Int).SetString("12490175513260779219420155073726764321605372267033815716483640700978475653623775696463227582174703069158832890348206546318843052423532258178885792744599932977235221784868792263260215861775082862444595", 10)
+
+	// 101-digit modulus
+	m, _ = new(big.Int).SetString("85832751158419329546684678412285185885848111422509523329716452068504806021136687603399722116388773253", 10)
+
+	// 99-digit modulus
+	n, _ = new(big.Int).SetString("604464499356780653111583485887412477603580949137220100557796699530113283915988830359783807274682723", 10)
+)
+
+func TestConstantTimeEqByteSound(t *testing.T) {
+	hundoDigit := internal.B10("3593421565679030456559622742114065111786271367498220644136232358421457354322411370928949366452183472")
+	tests := []struct {
+		name     string
+		a, b     *big.Int
+		expected byte
+	}{
+		{"positive: 5", internal.B10("5"), internal.B10("5"), 1},
+		{"positive: 100", internal.B10("100"), internal.B10("100"), 1},
+		{"positive: -1204", internal.B10("-1204"), internal.B10("-1204"), 1},
+		{"positive: 100 digits", hundoDigit, hundoDigit, 1},
+		{"positive: 0", internal.B10("0"), internal.B10("0"), 1},
+		{"positive: 0/-0", internal.B10("0"), internal.B10("-0"), 1},
+		{"positive: -0/-0", internal.B10("-0"), internal.B10("-0"), 1},
+
+		{"negative: 5/-5", internal.B10("5"), internal.B10("-5"), 0},
+		{"negative: 5/500", internal.B10("5"), internal.B10("500"), 0},
+		{"negative: 100/100 digit", internal.B10("100"), hundoDigit, 0},
+		{"negative: -1204/-5", internal.B10("-1204"), internal.B10("-15"), 0},
+		{"negative: 0/-5 digits", internal.B10("0"), internal.B10("-5"), 0},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			actual := ConstantTimeEqByte(test.a, test.b)
+			assert.Equal(t, test.expected, actual)
+		})
+	}
+}
+
+func TestConstantTimeEqSound(t *testing.T) {
+	hundoDigit := internal.B10("3593421565679030456559622742114065111786271367498220644136232358421457354322411370928949366452183472")
+	tests := []struct {
+		name     string
+		a, b     *big.Int
+		expected bool
+	}{
+		{"positive: 5", internal.B10("5"), internal.B10("5"), true},
+		{"positive: 100", internal.B10("100"), internal.B10("100"), true},
+		{"positive: -1204", internal.B10("-1204"), internal.B10("-1204"), true},
+		{"positive: 100 digits", hundoDigit, hundoDigit, true},
+		{"positive: 0", internal.B10("0"), internal.B10("0"), true},
+		{"positive: 0/-0", internal.B10("0"), internal.B10("-0"), true},
+		{"positive: -0/-0", internal.B10("-0"), internal.B10("-0"), true},
+
+		{"negative: 5/-5", internal.B10("5"), internal.B10("-5"), false},
+		{"negative: 5/500", internal.B10("5"), internal.B10("500"), false},
+		{"negative: 100/100 digit", internal.B10("100"), hundoDigit, false},
+		{"negative: -1204/-5", internal.B10("-1204"), internal.B10("-15"), false},
+		{"negative: 0/-5 digits", internal.B10("0"), internal.B10("-5"), false},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			actual := ConstantTimeEq(test.a, test.b)
+			assert.Equal(t, test.expected, actual)
+		})
+	}
+}
+
+// Ring membership tests
+func TestIn(t *testing.T) {
+	// Some large numbers for testing
+	x, _ := new(big.Int).SetString("21888242871839275222246405745257275088696311157297823662689037894645226208583", 10)
+	y, _ := new(big.Int).SetString("32168432167132168106409840321684604654063138460840123871234181628904319728058", 10)
+	N := new(big.Int).Mul(x, y)  // N = xy
+	NN := new(big.Int).Mul(N, N) // N^2 = N*N = x^2y^2
+	errMember := internal.ErrZmMembership
+
+	var tests = []struct {
+		x        *big.Int
+		m        *big.Int
+		expected error
+	}{
+		//
+		// Completist test for: Z_4
+		//
+		// Too small:  -x ∉ Z_4, \forall \x \in \N
+		{big.NewInt(-4), four, errMember},
+		{big.NewInt(-3), four, errMember},
+		{big.NewInt(-2), four, errMember},
+		{big.NewInt(-1), four, errMember},
+
+		// Just right: {0,1,2,3} = Z_4
+		{big.NewInt(0), four, nil},
+		{big.NewInt(1), four, nil},
+		{big.NewInt(2), four, nil},
+		{big.NewInt(3), four, nil},
+
+		// Too big: {4,5,6,7} ∉ Z_4
+		{big.NewInt(4), four, errMember},
+		{big.NewInt(5), four, errMember},
+		{big.NewInt(6), four, errMember},
+		{big.NewInt(7), four, errMember},
+
+		//
+		// Large numbers
+		//
+		// x,y,N < N^2
+		{x, NN, nil},
+		{y, NN, nil},
+		{N, NN, nil},
+
+		// N+x,N+y,2N < N^2 ⇒ x ∈ Z_N^2
+		{big.NewInt(0).Add(N, x), NN, nil},
+		{big.NewInt(0).Add(N, y), NN, nil},
+		{big.NewInt(0).Add(N, N), NN, nil},
+
+		// Nx,Ny < N^2 ⇒ x ∈ Z_N^2
+		{big.NewInt(0).Mul(N, x), NN, nil},
+		{big.NewInt(0).Mul(N, y), NN, nil},
+
+		// -x,-y,-N ∉ Z_N^2
+		{big.NewInt(0).Neg(x), NN, errMember},
+		{big.NewInt(0).Neg(y), NN, errMember},
+		{big.NewInt(0).Neg(N), NN, errMember},
+
+		// N^2 ∉ Z_N^2
+		{NN, NN, errMember},
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		actual := In(test.x, test.m)
+		assert.Equal(t, test.expected, actual)
+	}
+}
+
+// Tests for modular addition with known answers
+func TestAdd(t *testing.T) {
+	// Pre-compute some values
+	sumXyModn, err := Add(x, y, n)
+	assert.Nil(t, err)
+
+	var tests = []struct {
+		x, y, m, expected *big.Int // inputs: x,y,m
+	}{
+		// Small number tests
+		{big.NewInt(-1), big.NewInt(1), four, big.NewInt(0)},
+		{big.NewInt(2), big.NewInt(1), four, big.NewInt(3)},
+		{big.NewInt(0), big.NewInt(2), four, big.NewInt(2)},
+		{big.NewInt(2), big.NewInt(4), four, big.NewInt(2)},
+		{big.NewInt(15), big.NewInt(15), four, big.NewInt(2)},
+
+		// Large number tests
+		{x, y, m, sumxy},
+		{y, x, m, sumxy},
+
+		// Large number Zero tests
+		{Zero, x, m, x},
+		{x, Zero, m, x},
+		{Zero, y, m, y},
+		{y, Zero, m, y},
+
+		// Commutative
+		{x, y, m, sumxy},
+		{y, x, m, sumxy},
+		{x, y, n, sumXyModn},
+		{y, x, n, sumXyModn},
+		{sumXyModn, Zero, n, sumXyModn},
+		{Zero, sumXyModn, n, sumXyModn},
+	}
+	// All the tests!
+	for _, test := range tests {
+		actual, err := Add(test.x, test.y, test.m)
+		internal.AssertNoError(t, err)
+		internal.AssertBigIntEq(t, actual, test.expected)
+	}
+}
+
+// Tests for modular addition according to known invariants
+func TestAddInvariants(t *testing.T) {
+	inputs := []*big.Int{x, y, Zero, One, new(big.Int).Neg(x), new(big.Int).Neg(y)}
+	moduli := []*big.Int{m, n, big.NewInt(10001)}
+
+	// Run all combinations of the inputs/moduli
+	for _, x := range inputs {
+		for _, y := range inputs {
+			for _, m := range moduli {
+
+				// Addition is commutative
+				z0, err := Add(x, y, m)
+				internal.AssertNoError(t, err)
+				z1, err := Add(y, x, m)
+				internal.AssertNoError(t, err)
+				internal.AssertBigIntEq(t, z0, z1)
+
+				// Addition is transitive: x+x+y == y+x+x == x+y+x
+				a0, _ := Add(x, x, m)
+				a0, _ = Add(a0, y, m)
+
+				a1, _ := Add(y, x, m)
+				a1, _ = Add(a1, x, m)
+
+				a2, _ := Add(x, y, m)
+				a2, _ = Add(a2, x, m)
+
+				internal.AssertBigIntEq(t, a0, a1)
+				internal.AssertBigIntEq(t, a1, a2)
+			}
+		}
+	}
+}
+
+// Tests modular multiplication with known answers
+func TestMul(t *testing.T) {
+	// Pre-compute some values
+	xyModm := new(big.Int).Mod(xy, m)
+
+	var tests = []struct {
+		x, y, m, expected *big.Int // inputs: x,y,m
+	}{
+		// Small number tests
+		{big.NewInt(-1), big.NewInt(1), four, big.NewInt(3)},
+		{big.NewInt(2), big.NewInt(1), four, big.NewInt(2)},
+		{big.NewInt(0), big.NewInt(2), four, big.NewInt(0)},
+		{big.NewInt(2), big.NewInt(4), four, big.NewInt(0)},
+		{big.NewInt(15), big.NewInt(15), four, big.NewInt(1)},
+
+		// Large number tests
+		{x, y, m, xyModm},
+		{y, x, m, xyModm},
+
+		// Large number Zero tests
+		{Zero, x, m, Zero},
+		{x, Zero, m, Zero},
+		{Zero, y, n, Zero},
+	}
+	// All the tests!
+	for _, test := range tests {
+		z, err := Mul(test.x, test.y, test.m)
+		internal.AssertNoError(t, err)
+		internal.AssertBigIntEq(t, z, test.expected)
+	}
+}
+
+// Tests for modular multiplication according to known invariants
+func TestMulInvariants(t *testing.T) {
+	inputs := []*big.Int{x, y, Zero, One, new(big.Int).Neg(x), new(big.Int).Neg(y)}
+	moduli := []*big.Int{m, n, big.NewInt(10001)}
+
+	// Run all combinations of the inputs/moduli
+	for _, x := range inputs {
+		for _, y := range inputs {
+			for _, m := range moduli {
+
+				// Mul is commutative
+				a, err := Mul(x, y, m)
+				internal.AssertNoError(t, err)
+				aʹ, err := Mul(y, x, m)
+				internal.AssertNoError(t, err)
+				internal.AssertBigIntEq(t, a, aʹ)
+
+				// Mul is transitive: (xx)y == (xy)x
+				z, _ := Mul(x, x, m)
+				z, _ = Mul(z, y, m)
+
+				zʹ, _ := Mul(x, y, m)
+				zʹ, _ = Mul(zʹ, x, m)
+				internal.AssertBigIntEq(t, z, zʹ)
+			}
+		}
+	}
+}
+
+// Tests modular negation with known answers
+func TestNeg(t *testing.T) {
+	var tests = []struct {
+		x, m, e *big.Int
+	}{
+		{big.NewInt(1), big.NewInt(7), big.NewInt(6)},
+		{big.NewInt(2), big.NewInt(7), big.NewInt(5)},
+		{big.NewInt(3), big.NewInt(7), big.NewInt(4)},
+		{big.NewInt(4), big.NewInt(7), big.NewInt(3)},
+		{big.NewInt(5), big.NewInt(7), big.NewInt(2)},
+		{big.NewInt(6), big.NewInt(7), big.NewInt(1)},
+
+		{big.NewInt(-1), big.NewInt(7), big.NewInt(1)},
+		{big.NewInt(-2), big.NewInt(7), big.NewInt(2)},
+		{big.NewInt(-3), big.NewInt(7), big.NewInt(3)},
+		{big.NewInt(-4), big.NewInt(7), big.NewInt(4)},
+		{big.NewInt(-5), big.NewInt(7), big.NewInt(5)},
+		{big.NewInt(-6), big.NewInt(7), big.NewInt(6)},
+
+		{big.NewInt(8), big.NewInt(7), big.NewInt(6)},
+		{big.NewInt(9), big.NewInt(7), big.NewInt(5)},
+		{big.NewInt(10), big.NewInt(7), big.NewInt(4)},
+		{big.NewInt(11), big.NewInt(7), big.NewInt(3)},
+		{big.NewInt(12), big.NewInt(7), big.NewInt(2)},
+		{big.NewInt(13), big.NewInt(7), big.NewInt(1)},
+	}
+
+	for _, test := range tests {
+		r, err := Neg(test.x, test.m)
+		internal.AssertNoError(t, err)
+		if r.Cmp(test.e) != 0 {
+			t.Errorf("TestNeg failed. Expected %v, got: %v ", test.e, r)
+		}
+	}
+}
+
+func TestNegInvariants(t *testing.T) {
+	var tests = []struct {
+		x, m, e *big.Int
+	}{
+		{big.NewInt(0), big.NewInt(7), big.NewInt(0)},
+		{big.NewInt(7), big.NewInt(7), big.NewInt(0)},
+		{big.NewInt(-7), big.NewInt(7), big.NewInt(0)},
+	}
+
+	for _, test := range tests {
+		r, err := Neg(test.x, test.m)
+		internal.AssertNoError(t, err)
+		if r.Cmp(test.e) != 0 {
+			t.Errorf("TestNeg failed. Expected %v, got: %v ", test.e, r)
+		}
+	}
+}
+
+// Simple test for distinct Rand output
+func TestRandDistinct(t *testing.T) {
+	// Each value should be distinct
+	a, _ := Rand(n)
+	b, _ := Rand(n)
+	c, _ := Rand(n)
+
+	// ❄️❄️❄️
+	internal.AssertBigIntNe(t, a, b)
+	internal.AssertBigIntNe(t, a, c)
+	internal.AssertBigIntNe(t, b, c)
+}
+
+// Rand values should be O(log2(m)) bits
+func TestRandIsExpectedLength(t *testing.T) {
+	trials := 1000
+	max := big.NewInt(-1)
+
+	// Generate many nonces, keep the max
+	for i := 0; i < trials; i++ {
+		r, err := Rand(m)
+		internal.AssertNoError(t, err)
+
+		// Nonces should be < m
+		if r.Cmp(m) != -1 {
+			t.Errorf("nonce too large, require %v < %v", r, m)
+		}
+
+		if r.Cmp(max) == 1 {
+			max = r
+		}
+	}
+
+	// With high probability, the max nonce should be very close N
+	lowerBound := new(big.Int).Rsh(m, 1)
+	if max.Cmp(lowerBound) == -1 {
+		t.Errorf("Expected max nonce: %v > %v", max, lowerBound)
+	}
+}
+
+// Randomly selected nonces with a large modulus will be unique with overwhelming probability
+func TestRandDistinctWithLargeModulus(t *testing.T) {
+	const iterations = 1000
+	testUnique(t, iterations, func() *big.Int {
+		r, _ := Rand(m)
+		return r
+	})
+}
+
+// Calls sampleFunc() n times and asserts that the lower 64B of each output are unique.
+func testUnique(t *testing.T, iterations int, sampleFunc func() *big.Int) {
+	// For simplicity, we test only the lower 64B of each nonce. This is sufficient
+	// to prove uniqueness and go-lang doesn't hash slices (no slices in maps)
+	const size = 256 / 8
+	seen := make(map[[size]byte]bool)
+	var x [size]byte
+
+	// Check the pre-computed commitments for uniquness
+	for i := 0; i < iterations; i++ {
+		// Retrieve a sample
+		sample := sampleFunc()
+		internal.AssertNotNil(t, sample)
+
+		// Copy the bytes from slice>array
+		copy(x[:], sample.Bytes())
+
+		// Ensure each sample is unique
+		if seen[x] {
+			t.Errorf("duplicate sample found: %v", x)
+		}
+		seen[x] = true
+	}
+}
+
+// Ensure Rand never returns 0 or 1.
+func TestRandNotZeroNotOne(t *testing.T) {
+	// Test for non-zero only useful when iterations >> |Z_m|
+	const iterations = 1000
+	m := big.NewInt(5)
+
+	for i := 0; i < iterations; i++ {
+		r, err := Rand(m)
+		internal.AssertNoError(t, err)
+		// Not 0 or 1
+		internal.AssertBigIntNe(t, r, Zero)
+		internal.AssertBigIntNe(t, r, One)
+	}
+}
+
+func TestRand_NilModulusErrors(t *testing.T) {
+	r, err := Rand(nil)
+	internal.AssertNil(t, r)
+	internal.AssertError(t, err, internal.ErrNilArguments.Error())
+}
+
+// Double-inverse is the identity function in fields
+func TestInvRoundTrip(t *testing.T) {
+	m := internal.B10("1031") // Prime-order modulus
+
+	for _, a := range []*big.Int{
+		internal.B10("500"),
+		internal.B10("-500"),
+		internal.B10("1"),
+		internal.B10("1030"),
+	} {
+		// Our expected value is the modular reduction of the test value
+		expected := a.Mod(a, m)
+
+		// Invert and check
+		aInv, err := Inv(a, m)
+		assert.NoError(t, err, "a=%v", a)
+		assert.NotNil(t, aInv)
+
+		// Invert again and check
+		a_, err := Inv(aInv, m)
+		if assert.NoError(t, err) {
+			assert.Equal(t, expected, a_)
+		}
+	}
+}
+
+// Tests values for which there is no inverse in the given field
+func TestInvNotFound(t *testing.T) {
+	m := internal.B10("1024") // m = 2^10
+	// 0 and even numbers will not have inverse in this ring
+
+	for _, a := range []*big.Int{
+		internal.B10("500"),
+		internal.B10("-500"),
+		internal.B10("0"),
+		internal.B10("1024"),
+		internal.B10("512"),
+		internal.B10("300000000"),
+	} {
+		// Invert and check
+		aInv, err := Inv(a, m)
+		assert.Error(t, err, "a=%v", a)
+		assert.Nil(t, aInv)
+	}
+}
+
+func TestExpKnownAnswer(t *testing.T) {
+	p := internal.B10("1031") // prime-order field
+	pMinus1 := internal.B10("1030")
+	tests := []struct {
+		name     string
+		x, e, m  *big.Int
+		expected *big.Int
+	}{
+		{"fermat's little thm: 500", internal.B10("500"), p, p, internal.B10("500")},
+		{"fermat's little thm (p-1): 500", internal.B10("500"), pMinus1, p, One},
+		{"fermat's little thm (p-1): 5000", internal.B10("5000"), pMinus1, p, One},
+		{"399^0 = 1", internal.B10("399"), Zero, p, One},
+		{"673^1 = 673", internal.B10("673"), One, p, internal.B10("673")},
+	}
+
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			actual, err := Exp(test.x, test.e, test.m)
+			if assert.NoError(t, err) {
+				assert.Equal(t, test.expected, actual)
+			}
+		})
+	}
+}
+
+// A product of two 1024b safe primes
+var N1024 = internal.B10("22657252520748253292205422817162431301953923432914829530688424232913850279325496327198502914522231560238552529734156383924448818535517634061008476071362010781638360092704508943571866960229942049437914690556866055765377519627454975682400206932320319743805083072214857842762721537739950074695623974079312071498296625705376593890814889314744719469735809152488403143751157723139035869185892099006348653635981206799193781030834368833947197930944812082594326193527332208252230115672713914945889734620959932802893197325106135662762752470236627025599443912886530954179753873735786171937758916890000958846322096261981191349917")
+
+// A product of two 256b safe primes
+var N256 = internal.B10("10815068324662993508164204692909269429257853772524581783499643160896147777579932560873002543907262462663453338979819981987639157192530671167315407970757417")
+
+func Benchmark_rand1024(b *testing.B) {
+	if testing.Short() {
+		b.Skip("skipping test in short mode.")
+	}
+
+	for i := 0; i < b.N; i++ {
+		Rand(N1024) // nolint
+	}
+}
+
+func BenchmarkRand1024(b *testing.B) {
+	if testing.Short() {
+		b.Skip("skipping test in short mode.")
+	}
+
+	for i := 0; i < b.N; i++ {
+		Rand(N1024) // nolint
+	}
+}
+
+func Benchmark_rand256(b *testing.B) {
+	if testing.Short() {
+		b.Skip("skipping test in short mode.")
+	}
+
+	for i := 0; i < b.N; i++ {
+		Rand(N256) // nolint
+	}
+}
+
+func BenchmarkRandStar256(b *testing.B) {
+	if testing.Short() {
+		b.Skip("skipping test in short mode.")
+	}
+
+	for i := 0; i < b.N; i++ {
+		Rand(N256) // nolint
+	}
+}
diff --git a/pkg/core/primes.go b/pkg/core/primes.go
new file mode 100644
index 00000000..24ae766e
--- /dev/null
+++ b/pkg/core/primes.go
@@ -0,0 +1,42 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package core
+
+import (
+	"crypto/rand"
+	"fmt"
+	"math"
+	"math/big"
+)
+
+// GenerateSafePrime creates a prime number `p`
+// where (`p`-1)/2 is also prime with at least `bits`
+func GenerateSafePrime(bits uint) (*big.Int, error) {
+	if bits < 3 {
+		return nil, fmt.Errorf("safe prime size must be at least 3-bits")
+	}
+
+	var p *big.Int
+	var err error
+	checks := int(math.Max(float64(bits)/16, 8))
+	for {
+		// rand.Prime throws an error if bits < 2
+		// -1 so the Sophie-Germain prime is 1023 bits
+		// and the Safe prime is 1024
+		p, err = rand.Prime(rand.Reader, int(bits)-1)
+		if err != nil {
+			return nil, err
+		}
+		p.Add(p.Lsh(p, 1), One)
+
+		if p.ProbablyPrime(checks) {
+			break
+		}
+	}
+
+	return p, nil
+}
diff --git a/pkg/dkg/README.md b/pkg/dkg/README.md
new file mode 100644
index 00000000..0b711995
--- /dev/null
+++ b/pkg/dkg/README.md
@@ -0,0 +1,230 @@
+# Distributed Key Generation
+
+```go
+import "github.com/coinbase/kryptology/pkg/dkg"
+```
+
+Package `dkg` is intended to contain implementations of distributed key generation (DKG) protocols. 
+Besides the DKG protocol we introduced in `github.com/coinbase/kryptology/pkg/tecdsa/README.md`, currently
+package `dkg` contains the following distributed key generation implementations. 
+
+- Gennaro DKG: an adapted version [[overleaf]](https://www.overleaf.com/project/60915c0df1d6917f5cde6657) of 
+DKG by Gennaro et al. [[GennaroDKG]](https://link.springer.com/content/pdf/10.1007/s00145-006-0347-3.pdf). (We call it
+GennaroDKG for convenience in the following context.)
+  
+- FROST DKG: the distributed key generation protocol used in [FROST tSchnorr signature](https://tools.ietf.org/pdf/draft-komlo-frost-00.pdf). We also 
+have its [pseudocode write-up](https://www.overleaf.com/read/nvmyjwsnbrwj). We call it FROST DKG in the following context.  
+
+## GennaroDKG
+### Participant
+Gennaro DKG is run by multiple participants distributedly. We define necessary types and 
+functions used by each participant under `dkg/gennaro/participant.go`.
+
+#### type Participant
+```go
+type Participant struct {
+    round                  int
+    curve                  elliptic.Curve
+    scalar                 crypto.EcScalar
+    otherParticipantShares map[uint32]*dkgParticipantData
+    id                     uint32
+    skShare                *sharing.Element
+    verificationKey        *sharing.ShareVerifier
+    feldman                *sharing.Feldman
+    pedersen               *sharing.Pedersen
+    pedersenResult         *sharing.PedersenResult
+}
+```
+`Participant` is a DKG player that contains information needed to perform DKG rounds
+and yield a secret key share and public key when finished.
+
+#### dkgParticipantData
+```go
+type dkgParticipantData struct {
+	Id        uint32
+	Share     *sharing.ShamirShare
+	Verifiers []*sharing.ShareVerifier
+}
+```
+`dkgParticipantData` contains values that need to be stored by each participant in
+the `otherParticipantShares` field. 
+
+#### func NewParticipant
+```go
+func NewParticipant(id, threshold uint32, generator *crypto.EcPoint, scalar crypto.EcScalar, otherParticipants ...uint32) (*Participant, error)
+```
+`NewParticipant` creates a participant ready to perform a DKG.
+- `id` is the integer value identifier for this participant
+- `threshold` is the minimum bound for the secret sharing scheme
+- `generator` is the blinding factor generator used by pedersen's verifiable secret sharing
+- `otherParticipants` is the integer value identifiers for the other participants
+
+### DKG Round 1
+#### type Round1Bcast
+```go
+type Round1Bcast = []*sharing.ShareVerifier
+```
+`Round1Bcast` are the values that are broadcast to all other participants
+after round1 completes.
+
+#### type Round1P2PSend
+```go
+type Round1P2PSend = map[uint32]*Round1P2PSendPacket
+```
+`Round1P2PSend` are the values that are sent to individual participants based
+on the id.
+
+#### type Round1P2PSendPacket
+```go
+type Round1P2PSendPacket struct {
+	secretShare   *sharing.ShamirShare
+	blindingShare *sharing.ShamirShare
+}
+```
+`Round1P2PSendPacket` are the shares generated from the secret for a specific participant.
+
+#### func (*Participant) Round1
+```go
+func (dp *Participant) Round1(secret []byte) (Round1Bcast, Round1P2PSend, error)
+```
+`Round1` computes the first round for the Gennaro DKG. 
+
+NOTE: if `secret` is nil, a new secret is generated which creates a new key
+if `secret` is set, then this performs key resharing aka proactive secret sharing update.
+
+### DKG Round 2
+#### type Round2Bcast
+```go
+type Round2Bcast = []*sharing.ShareVerifier
+```
+`Round2Bcast` contains the values that will be broadcast to other participants
+after completion of DKG Round 2. 
+
+#### func (*Participant) Round2
+```go
+func (dp *Participant) Round2(bcast map[uint32]Round1Bcast, p2p map[uint32]*Round1P2PSendPacket) (Round2Bcast, error)
+```
+Round2 computes the second round for Gennaro DKG. See Algorithm 3 - Gennaro DKG Round 2 in [[overleaf]](https://www.overleaf.com/project/60915c0df1d6917f5cde6657).
+- `bcast` contains all Round1 broadcast from other participants to this participant.
+- `p2p` contains all Round1 P2P send message from other participants to this participant.
+
+### DKG Round 3
+#### type Round3Bcast
+```go
+type Round3Bcast struct {
+	VerificationKey *sharing.ShareVerifier
+	Success         bool
+}
+```
+`Round3Bcast` contains values that will be broadcast to other participants.
+
+#### func (*Participant) Round3
+```go
+func (dp *Participant) Round3(bcast map[uint32]Round2Bcast) (*Round3Bcast, *sharing.ShamirShare, error)
+```
+`Round3` computes the third round for Gennaro DKG. See Algorithm 4 - Gennaro DKG Round 3 in [[overleaf]](https://www.overleaf.com/project/60915c0df1d6917f5cde6657).
+- `bcast` contains all Round2 broadcast from other participants to this participant.
+
+### DKG Round 4
+#### func (*Participant) Round4
+```go
+func (dp *Participant) Round4() (map[uint32]*crypto.EcPoint, error)
+```
+`Round4` computes the public shares used by tECDSA during signing
+that are converted to additive shares once the signing participants
+are known. This function is idempotent. See Algorithm 5 - Gennaro DKG Round 4 in [[overleaf]](https://www.overleaf.com/project/60915c0df1d6917f5cde6657).
+
+## FROST DKG
+### Participant
+FROST DKG is run by multiple participants distributedly. We define necessary types and functions used by
+each participant under `dkg/frost/participant.go`
+
+#### type DkgParticipant
+```go
+type DkgParticipant struct {
+	round                  int
+	curve                  elliptic.Curve
+	scalar                 core.EcScalar
+	otherParticipantShares map[uint32]*dkgParticipantData
+	id                     uint32
+	SkShare                *sharing.Element
+	verificationKey        *sharing.ShareVerifier
+	vkShare                *sharing.ShareVerifier
+	feldman                *sharing.Feldman
+	verifiers              []*sharing.ShareVerifier
+	secretShares           []*sharing.ShamirShare
+	ctx                    byte
+}
+```
+`DkgParticipant` is a FROST DKG player that contains information needed to perform DKG rounds and yield
+a secret key share and public key when finished. 
+
+#### dkgParticipantData
+```go
+type dkgParticipantData struct {
+	Id        uint32
+	Share     *sharing.ShamirShare
+	Verifiers []*sharing.ShareVerifier
+}
+```
+`dkgParticipantData` contains values that need to be stored by each participant in
+the `otherParticipantShares` field. 
+
+#### var Ctx
+```go
+Ctx = "fixed context string"
+```
+`Ctx` is simply a fixed context string that will be used in FROST DKG. It can be any fixed context string. 
+
+#### func NewDkgParticipant
+```go
+func NewDkgParticipant(id, threshold uint32, ctx string, generator *core.EcPoint, scalar core.EcScalar, otherParticipants ...uint32) (*DkgParticipant, error)
+```
+`NewDkgParticipant` creates a participant ready to perform FROST DKG.
+- `id` is the integer value identifier for this participant.
+- `threshold` is the minimum bound for the underlying secret sharing scheme. 
+- `ctx` is the fixed context string. 
+- `generator` is the blinding factor generator used by Feldman's VSS
+- `otherParticipants` is the integer value identifiers for the other participants. 
+
+### DKG Round 1
+#### type Round1Bcast
+```go
+type Round1Bcast struct {
+	verifiers []*sharing.ShareVerifier
+	wi        *big.Int
+	ci        *big.Int
+}
+```
+`Round1Bcast` are the values that are broadcast to all other participants after round 1 completes.
+
+#### type Round1P2PSend
+```go
+type Round1P2PSend = map[uint32]*sharing.ShamirShare
+```
+`Round1P2PSend` are the values that are sent to individual participants based on the id. 
+
+#### func (*DkgParticipant) Round1
+```go
+func (dp *DkgParticipant) Round1(secret []byte) (*Round1Bcast, Round1P2PSend, error)
+```
+`Round1` computes the first round for the FROST DKG.
+
+NOTE: if `secret` is nil, a new secret is generated which creates a new key. If `secret` is set, then 
+this performs key resharing a.k.a, proactive secret sharing update. 
+
+### DKG Round 2
+#### type Round2Bcast
+```go
+type Round2Bcast struct {
+	VerificationKey *sharing.ShareVerifier
+	VkShare         *sharing.ShareVerifier
+}
+```
+`Round2Bcast` contains the values that will be broadcast to other participants after completion of DKG Round 2. 
+
+#### func (*DkgParticipant) Round2
+```go
+func (dp *DkgParticipant) Round2(bcast map[uint32]*Round1Bcast, p2psend map[uint32]*sharing.ShamirShare) (*Round2Bcast, error)
+```
+Round2 computes the second round for FROST DKG. 
\ No newline at end of file
diff --git a/pkg/dkg/benchmarks.txt b/pkg/dkg/benchmarks.txt
new file mode 100644
index 00000000..b82f3c04
--- /dev/null
+++ b/pkg/dkg/benchmarks.txt
@@ -0,0 +1,111 @@
+------test Gennaro DKG TestAllGennaroDkgRounds for 1 time------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.888s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	0.778s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.460s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.622s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.470s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.179s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	1.033s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 10 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.865s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	0.602s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.617s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.513s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.380s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	0.986s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	0.746s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 50 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.542s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	1.598s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.419s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.788s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.403s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.028s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	0.919s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 100 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	1.019s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	2.401s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.666s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.794s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.441s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.250s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	1.142s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 500 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.567s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	9.806s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.680s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.464s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.395s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.045s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	0.924s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 1000 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.300s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	18.662s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.181s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.665s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.172s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	0.765s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	0.529s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 5000 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	1.017s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	94.413s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.461s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.904s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.461s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.104s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	0.762s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
+
+------test Gennaro DKG TestAllGennaroDkgRounds for 10000 times------
+
+?   	github.com/coinbase/kryptology/internal	[no test files]
+ok  	github.com/coinbase/kryptology/pkg/core	0.514s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/dkg/gennaro	192.149s
+ok  	github.com/coinbase/kryptology/pkg/paillier	0.742s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/sharing	0.962s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/dealer	0.470s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/participant	1.199s [no tests to run]
+ok  	github.com/coinbase/kryptology/pkg/tecdsa/proof	1.055s [no tests to run]
+?   	github.com/coinbase/kryptology/test/dkg/bls	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/ed25519	[no test files]
+?   	github.com/coinbase/kryptology/test/dkg/k256	[no test files]
diff --git a/pkg/dkg/frost/README.md b/pkg/dkg/frost/README.md
new file mode 100755
index 00000000..97f902dd
--- /dev/null
+++ b/pkg/dkg/frost/README.md
@@ -0,0 +1,88 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# frost
+
+```go
+import "github.com/coinbase/kryptology/pkg/dkg/frost"
+```
+
+## Index
+
+- [type DkgParticipant](<#type-dkgparticipant>)
+  - [func NewDkgParticipant(id, threshold uint32, ctx string, curve *curves.Curve, otherParticipants ...uint32) (*DkgParticipant, error)](<#func-newdkgparticipant>)
+  - [func (dp *DkgParticipant) Round1(secret []byte) (*Round1Bcast, Round1P2PSend, error)](<#func-dkgparticipant-round1>)
+  - [func (dp *DkgParticipant) Round2(bcast map[uint32]*Round1Bcast, p2psend map[uint32]*sharing.ShamirShare) (*Round2Bcast, error)](<#func-dkgparticipant-round2>)
+- [type Round1Bcast](<#type-round1bcast>)
+- [type Round1P2PSend](<#type-round1p2psend>)
+- [type Round2Bcast](<#type-round2bcast>)
+
+
+## type [DkgParticipant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/participant.go#L17-L29>)
+
+```go
+type DkgParticipant struct {
+    Curve *curves.Curve
+
+    Id              uint32
+    SkShare         curves.Scalar
+    VerificationKey curves.Point
+    VkShare         curves.Point
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewDkgParticipant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/participant.go#L37>)
+
+```go
+func NewDkgParticipant(id, threshold uint32, ctx string, curve *curves.Curve, otherParticipants ...uint32) (*DkgParticipant, error)
+```
+
+### func \(\*DkgParticipant\) [Round1](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/dkg_round1.go#L30>)
+
+```go
+func (dp *DkgParticipant) Round1(secret []byte) (*Round1Bcast, Round1P2PSend, error)
+```
+
+Round1 implements dkg round 1 of FROST
+
+### func \(\*DkgParticipant\) [Round2](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/dkg_round2.go#L24>)
+
+```go
+func (dp *DkgParticipant) Round2(bcast map[uint32]*Round1Bcast, p2psend map[uint32]*sharing.ShamirShare) (*Round2Bcast, error)
+```
+
+Round2 implements dkg round 2 of FROST
+
+## type [Round1Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/dkg_round1.go#L20-L23>)
+
+Round1Bcast are values that are broadcast to all other participants after round1 completes
+
+```go
+type Round1Bcast struct {
+    Verifiers *sharing.FeldmanVerifier
+    Wi, Ci    curves.Scalar
+}
+```
+
+## type [Round1P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/dkg_round1.go#L27>)
+
+Round1P2PSend are values that are P2PSend to all other participants after round1 completes
+
+```go
+type Round1P2PSend = map[uint32]*sharing.ShamirShare
+```
+
+## type [Round2Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/frost/dkg_round2.go#L18-L21>)
+
+Round2Bcast are values that are broadcast to all other participants after round2 completes
+
+```go
+type Round2Bcast struct {
+    VerificationKey curves.Point
+    VkShare         curves.Point
+}
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/dkg/frost/dkg_round1.go b/pkg/dkg/frost/dkg_round1.go
new file mode 100644
index 00000000..df6459c5
--- /dev/null
+++ b/pkg/dkg/frost/dkg_round1.go
@@ -0,0 +1,118 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	crand "crypto/rand"
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"reflect"
+)
+
+// Round1Bcast are values that are broadcast to all other participants
+// after round1 completes
+type Round1Bcast struct {
+	Verifiers *sharing.FeldmanVerifier
+	Wi, Ci    curves.Scalar
+}
+
+// Round1P2PSend are values that are P2PSend to all other participants
+// after round1 completes
+type Round1P2PSend = map[uint32]*sharing.ShamirShare
+
+// Round1 implements dkg round 1 of FROST
+func (dp *DkgParticipant) Round1(secret []byte) (*Round1Bcast, Round1P2PSend, error) {
+	// Make sure dkg participant is not empty
+	if dp == nil || dp.Curve == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+
+	// Make sure round number is correct
+	if dp.round != 1 {
+		return nil, nil, internal.ErrInvalidRound
+	}
+
+	// Check number of participants
+	if uint32(len(dp.otherParticipantShares)+1) > dp.feldman.Limit || uint32(len(dp.otherParticipantShares)+1) < dp.feldman.Threshold {
+		return nil, nil, fmt.Errorf("length of dp.otherParticipantShares + 1 should be equal to feldman limit")
+	}
+
+	// If secret is nil, sample a new one
+	// If not, check secret is valid
+	var s curves.Scalar
+	var err error
+	if secret == nil {
+		s = dp.Curve.Scalar.Random(crand.Reader)
+	} else {
+		s, err = dp.Curve.Scalar.SetBytes(secret)
+		if err != nil {
+			return nil, nil, err
+		}
+		if s.IsZero() {
+			return nil, nil, internal.ErrZeroValue
+		}
+	}
+
+	// Step 1 - (Aj0,...Ajt), (xi1,...,xin) <- FeldmanShare(s)
+	// We should validate types of Feldman curve scalar and participant's curve scalar.
+	if reflect.TypeOf(dp.feldman.Curve.Scalar) != reflect.TypeOf(dp.Curve.Scalar) {
+		return nil, nil, fmt.Errorf("feldman scalar should have the same type as the dkg participant scalar")
+	}
+	verifiers, shares, err := dp.feldman.Split(s, crand.Reader)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Store Verifiers and shares
+	dp.verifiers = verifiers
+	dp.secretShares = shares
+
+	// Step 2 - Sample ki <- Z_q
+	ki := dp.Curve.Scalar.Random(crand.Reader)
+
+	// Step 3 - Compute Ri = ki*G
+	Ri := dp.Curve.ScalarBaseMult(ki)
+
+	// Step 4 - Compute Ci = H(i, CTX, g^{a_(i,0)}, R_i), where CTX is fixed context string
+	var msg []byte
+	// Append participant id
+	msg = append(msg, byte(dp.Id))
+	// Append CTX
+	msg = append(msg, dp.ctx)
+	// Append a_{i,0}*G
+	msg = append(msg, verifiers.Commitments[0].ToAffineCompressed()...)
+	// Append Ri
+	msg = append(msg, Ri.ToAffineCompressed()...)
+	// Hash the message and get Ci
+	ci := dp.Curve.Scalar.Hash(msg)
+
+	// Step 5 - Compute Wi = ki+a_{i,0}*c_i mod q. Note that a_{i,0} is the secret.
+	// Note: We have to compute scalar in the following way when using ed25519 curve, rather than scalar := dp.Scalar.Mul(s, Ci)
+	// there is an invalid encoding error when we compute scalar as above.
+	wi := s.MulAdd(ci, ki)
+
+	// Step 6 - Broadcast (Ci, Wi, Ci) to other participants
+	round1Bcast := &Round1Bcast{
+		verifiers,
+		wi,
+		ci,
+	}
+
+	// Step 7 - P2PSend f_i(j) to each participant Pj and keep (i, f_j(i)) for himself
+	p2pSend := make(Round1P2PSend, len(dp.otherParticipantShares))
+	for id := range dp.otherParticipantShares {
+		p2pSend[id] = shares[id-1]
+	}
+
+	// Update internal state
+	dp.round = 2
+
+	// return
+	return round1Bcast, p2pSend, nil
+}
diff --git a/pkg/dkg/frost/dkg_round2.go b/pkg/dkg/frost/dkg_round2.go
new file mode 100644
index 00000000..025de620
--- /dev/null
+++ b/pkg/dkg/frost/dkg_round2.go
@@ -0,0 +1,157 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+)
+
+// Round2Bcast are values that are broadcast to all other participants
+// after round2 completes
+type Round2Bcast struct {
+	VerificationKey curves.Point
+	VkShare         curves.Point
+}
+
+// Round2 implements dkg round 2 of FROST
+func (dp *DkgParticipant) Round2(bcast map[uint32]*Round1Bcast, p2psend map[uint32]*sharing.ShamirShare) (*Round2Bcast, error) {
+	// Make sure dkg participant is not empty
+	if dp == nil || dp.Curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Check dkg participant has the correct dkg round number
+	if dp.round != 2 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Check the input is valid
+	if bcast == nil || p2psend == nil || len(p2psend) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Check length of bcast and p2psend
+	if uint32(len(bcast)) > dp.feldman.Limit || uint32(len(bcast)) < dp.feldman.Threshold-1 {
+		return nil, fmt.Errorf("invalid broadcast length")
+	}
+
+	if uint32(len(p2psend)) > dp.feldman.Limit-1 || uint32(len(p2psend)) < dp.feldman.Threshold-1 {
+		return nil, fmt.Errorf("invalid p2pSend length")
+	}
+
+	// We should validate Wi and Ci values in Round1Bcast
+	for id := range bcast {
+		// ci should be within the range 1 to q-1, q is the group order.
+		if bcast[id].Ci.IsZero() {
+			return nil, fmt.Errorf("ci should not be zero from participant %d\n", id)
+		}
+	}
+	// Validate each received commitment is on curve
+	for id := range bcast {
+		for _, com := range bcast[id].Verifiers.Commitments {
+			if !com.IsOnCurve() || com.IsIdentity() {
+				return nil, fmt.Errorf("some commitment is not on curve from participant %d\n", id)
+			}
+		}
+	}
+
+	var err error
+
+	// Step 2 - for j in 1,...,n
+	for id := range bcast {
+
+		// Step 3 - if j == i, continue
+		if id == dp.Id {
+			continue
+		}
+
+		// Step 4 - Check equation c_j = H(j, CTX, A_{j,0}, g^{w_j}*A_{j,0}^{-c_j}
+		// Get Aj0
+		Aj0 := bcast[id].Verifiers.Commitments[0]
+		// Compute g^{w_j}
+		prod1 := dp.Curve.ScalarBaseMult(bcast[id].Wi)
+		// Compute A_{j,0}^{-c_j}
+		prod2 := Aj0.Mul(bcast[id].Ci.Neg())
+
+		// We need to check Aj0 and prod2 are points on the same curve.
+		if !Aj0.IsOnCurve() || Aj0.IsIdentity() || !prod2.IsOnCurve() || prod2.IsIdentity() || Aj0.CurveName() != prod2.CurveName() {
+			return nil, fmt.Errorf("invalid Aj0 or prod2 which is not on the same curve")
+		}
+		if prod2 == nil {
+			return nil, fmt.Errorf("invalid should not be nil")
+		}
+
+		prod := prod1.Add(prod2)
+		var msg []byte
+		// Append participant id
+		msg = append(msg, byte(id))
+		// Append CTX
+		msg = append(msg, dp.ctx)
+		// Append Aj0
+		msg = append(msg, Aj0.ToAffineCompressed()...)
+		// Append prod
+		msg = append(msg, prod.ToAffineCompressed()...)
+		// Hash the message and get cj
+		cj := dp.Curve.Scalar.Hash(msg)
+		// Check equation
+		if cj.Cmp(bcast[id].Ci) != 0 {
+			return nil, fmt.Errorf("Hash check fails for participant with id %d\n", id)
+		}
+
+		// Step 5 - FeldmanVerify
+		fji := p2psend[id]
+		if err = bcast[id].Verifiers.Verify(fji); err != nil {
+			return nil, fmt.Errorf("feldman verify fails for participant with id %d\n", id)
+		}
+	}
+
+	sk, err := dp.Curve.Scalar.SetBytes(dp.secretShares[dp.Id-1].Value)
+	if err != nil {
+		return nil, err
+	}
+	vk := dp.verifiers.Commitments[0]
+	// Step 6 - Compute signing key share ski = \sum_{j=1}^n xji
+	for id := range bcast {
+		if id == dp.Id {
+			continue
+		}
+		t2, err := dp.Curve.Scalar.SetBytes(p2psend[id].Value)
+		if err != nil {
+			return nil, err
+		}
+		sk = sk.Add(t2)
+	}
+
+	// Step 8 - Compute verification key vk = sum(A_{j,0}), j = 1,...,n
+	for id := range bcast {
+		if id == dp.Id {
+			continue
+		}
+		vk = vk.Add(bcast[id].Verifiers.Commitments[0])
+	}
+
+	// Store signing key share
+	dp.SkShare = sk
+
+	// Step 7 - Compute verification key share vki = ski*G and store
+	dp.VkShare = dp.Curve.ScalarBaseMult(sk)
+
+	// Store verification key
+	dp.VerificationKey = vk
+
+	// Update round number
+	dp.round = 3
+
+	// Broadcast
+	return &Round2Bcast{
+		vk,
+		dp.VkShare,
+	}, nil
+}
diff --git a/pkg/dkg/frost/dkg_rounds_test.go b/pkg/dkg/frost/dkg_rounds_test.go
new file mode 100644
index 00000000..890ff6da
--- /dev/null
+++ b/pkg/dkg/frost/dkg_rounds_test.go
@@ -0,0 +1,167 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	testCurve = curves.ED25519()
+	Ctx       = "string to prevent replay attack"
+)
+
+// Test dkg round1 works for 2 participants
+func TestDkgRound1Works(t *testing.T) {
+	p1, err := NewDkgParticipant(1, 2, Ctx, testCurve, 2)
+	require.NoError(t, err)
+	bcast, p2psend, err := p1.Round1(nil)
+	require.NoError(t, err)
+	require.NotNil(t, bcast)
+	require.NotNil(t, p2psend)
+	require.NotNil(t, p1.ctx)
+	require.Equal(t, len(p2psend), 1)
+	require.Equal(t, p1.round, 2)
+	_, ok := p2psend[2]
+	require.True(t, ok)
+}
+
+func TestDkgRound1RepeatCall(t *testing.T) {
+	p1, err := NewDkgParticipant(1, 2, Ctx, testCurve, 2)
+	require.NoError(t, err)
+	_, _, err = p1.Round1(nil)
+	require.NoError(t, err)
+	_, _, err = p1.Round1(nil)
+	require.Error(t, err)
+}
+
+func TestDkgRound1BadSecret(t *testing.T) {
+	p1, err := NewDkgParticipant(1, 2, Ctx, testCurve, 2)
+	require.NoError(t, err)
+	// secret == 0
+	secret := []byte{0}
+	_, _, err = p1.Round1(secret)
+	require.Error(t, err)
+	// secret too big
+	secret = []byte{7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7}
+	_, _, err = p1.Round1(secret)
+	require.Error(t, err)
+}
+
+func PrepareRound2Input(t *testing.T) (*DkgParticipant, *DkgParticipant, *Round1Bcast, *Round1Bcast, Round1P2PSend, Round1P2PSend) {
+	// Prepare round 1 output of 2 participants
+	p1, err := NewDkgParticipant(1, 2, Ctx, testCurve, 2)
+	require.NoError(t, err)
+	require.Equal(t, p1.otherParticipantShares[2].Id, uint32(2))
+	p2, err := NewDkgParticipant(2, 2, Ctx, testCurve, 1)
+	require.NoError(t, err)
+	require.Equal(t, p2.otherParticipantShares[1].Id, uint32(1))
+	bcast1, p2psend1, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	return p1, p2, bcast1, bcast2, p2psend1, p2psend2
+}
+
+// Test FROST DKG round 2 works
+func TestDkgRound2Works(t *testing.T) {
+	// Prepare Dkg Round1 output
+	p1, _, bcast1, bcast2, _, p2psend2 := PrepareRound2Input(t)
+	// Actual Test
+	require.NotNil(t, bcast1)
+	require.NotNil(t, bcast2)
+	require.NotNil(t, p2psend2[1])
+	bcast := make(map[uint32]*Round1Bcast)
+	p2p := make(map[uint32]*sharing.ShamirShare)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	round2Out, err := p1.Round2(bcast, p2p)
+	require.NoError(t, err)
+	require.NotNil(t, round2Out)
+	require.NotNil(t, p1.SkShare)
+	require.NotNil(t, p1.VkShare)
+	require.NotNil(t, p1.VerificationKey)
+	require.NotNil(t, p1.otherParticipantShares)
+}
+
+// Test FROST DKG round 2 repeat call
+func TestDkgRound2RepeatCall(t *testing.T) {
+	// Prepare round 1 output
+	p1, _, bcast1, bcast2, _, p2psend2 := PrepareRound2Input(t)
+	// Actual Test
+	require.NotNil(t, bcast1)
+	require.NotNil(t, bcast2)
+	require.NotNil(t, p2psend2[1])
+	bcast := make(map[uint32]*Round1Bcast)
+	p2p := make(map[uint32]*sharing.ShamirShare)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	_, err := p1.Round2(bcast, p2p)
+	require.NoError(t, err)
+	_, err = p1.Round2(bcast, p2p)
+	require.Error(t, err)
+}
+
+// Test FROST Dkg Round 2 Bad Input
+func TestDkgRound2BadInput(t *testing.T) {
+	// Prepare Dkg Round 1 output
+	p1, _, _, _, _, _ := PrepareRound2Input(t)
+	bcast := make(map[uint32]*Round1Bcast)
+	p2p := make(map[uint32]*sharing.ShamirShare)
+
+	// Test empty bcast and p2p
+	_, err := p1.Round2(bcast, p2p)
+	require.Error(t, err)
+
+	// Test nil bcast and p2p
+	p1, _, _, _, _, _ = PrepareRound2Input(t)
+	_, err = p1.Round2(nil, nil)
+	require.Error(t, err)
+
+	// Test tampered input bcast and p2p
+	p1, _, bcast1, bcast2, _, p2psend2 := PrepareRound2Input(t)
+	bcast = make(map[uint32]*Round1Bcast)
+	p2p = make(map[uint32]*sharing.ShamirShare)
+
+	// Tamper p2psend2 by doubling the value
+	tmp, _ := testCurve.Scalar.SetBytes(p2psend2[1].Value)
+	p2psend2[1].Value = tmp.Double().Bytes()
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	_, err = p1.Round2(bcast, p2p)
+	require.Error(t, err)
+}
+
+// Test full round works
+func TestFullDkgRoundsWorks(t *testing.T) {
+	// Initiate two participants and running round 1
+	p1, p2, bcast1, bcast2, p2psend1, p2psend2 := PrepareRound2Input(t)
+	bcast := make(map[uint32]*Round1Bcast)
+	p2p1 := make(map[uint32]*sharing.ShamirShare)
+	p2p2 := make(map[uint32]*sharing.ShamirShare)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p1[2] = p2psend2[1]
+	p2p2[1] = p2psend1[2]
+
+	// Running round 2
+	round2Out1, _ := p1.Round2(bcast, p2p1)
+	round2Out2, _ := p2.Round2(bcast, p2p2)
+	require.Equal(t, round2Out1.VerificationKey, round2Out2.VerificationKey)
+	s, _ := sharing.NewShamir(2, 2, testCurve)
+	sk, err := s.Combine(&sharing.ShamirShare{Id: p1.Id, Value: p1.SkShare.Bytes()},
+		&sharing.ShamirShare{Id: p2.Id, Value: p2.SkShare.Bytes()})
+	require.NoError(t, err)
+
+	vk := testCurve.ScalarBaseMult(sk)
+	require.True(t, vk.Equal(p1.VerificationKey))
+}
diff --git a/pkg/dkg/frost/participant.go b/pkg/dkg/frost/participant.go
new file mode 100644
index 00000000..98837287
--- /dev/null
+++ b/pkg/dkg/frost/participant.go
@@ -0,0 +1,64 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"strconv"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+type DkgParticipant struct {
+	round                  int
+	Curve                  *curves.Curve
+	otherParticipantShares map[uint32]*dkgParticipantData
+	Id                     uint32
+	SkShare                curves.Scalar
+	VerificationKey        curves.Point
+	VkShare                curves.Point
+	feldman                *sharing.Feldman
+	verifiers              *sharing.FeldmanVerifier
+	secretShares           []*sharing.ShamirShare
+	ctx                    byte
+}
+
+type dkgParticipantData struct {
+	Id        uint32
+	Share     *sharing.ShamirShare
+	Verifiers *sharing.FeldmanVerifier
+}
+
+func NewDkgParticipant(id, threshold uint32, ctx string, curve *curves.Curve, otherParticipants ...uint32) (*DkgParticipant, error) {
+	if curve == nil || len(otherParticipants) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+	limit := uint32(len(otherParticipants)) + 1
+	feldman, err := sharing.NewFeldman(threshold, limit, curve)
+	if err != nil {
+		return nil, err
+	}
+	otherParticipantShares := make(map[uint32]*dkgParticipantData, len(otherParticipants))
+	for _, id := range otherParticipants {
+		otherParticipantShares[id] = &dkgParticipantData{
+			Id: id,
+		}
+	}
+
+	// SetBigInt the common fixed string
+	ctxV, _ := strconv.Atoi(ctx)
+
+	return &DkgParticipant{
+		Id:                     id,
+		round:                  1,
+		Curve:                  curve,
+		feldman:                feldman,
+		otherParticipantShares: otherParticipantShares,
+		ctx:                    byte(ctxV),
+	}, nil
+}
diff --git a/pkg/dkg/gennaro/README.md b/pkg/dkg/gennaro/README.md
new file mode 100755
index 00000000..2be4820f
--- /dev/null
+++ b/pkg/dkg/gennaro/README.md
@@ -0,0 +1,117 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# gennaro
+
+```go
+import "github.com/coinbase/kryptology/pkg/dkg/gennaro"
+```
+
+## Index
+
+- [type Participant](<#type-participant>)
+  - [func NewParticipant(id, threshold uint32, generator *curves.EcPoint, scalar curves.EcScalar, otherParticipants ...uint32) (*Participant, error)](<#func-newparticipant>)
+  - [func (dp *Participant) Round1(secret []byte) (Round1Bcast, Round1P2PSend, error)](<#func-participant-round1>)
+  - [func (dp *Participant) Round2(bcast map[uint32]Round1Bcast, p2p map[uint32]*Round1P2PSendPacket) (Round2Bcast, error)](<#func-participant-round2>)
+  - [func (dp *Participant) Round3(bcast map[uint32]Round2Bcast) (*Round3Bcast, *v1.ShamirShare, error)](<#func-participant-round3>)
+  - [func (dp *Participant) Round4() (map[uint32]*curves.EcPoint, error)](<#func-participant-round4>)
+- [type Round1Bcast](<#type-round1bcast>)
+- [type Round1P2PSend](<#type-round1p2psend>)
+- [type Round1P2PSendPacket](<#type-round1p2psendpacket>)
+- [type Round2Bcast](<#type-round2bcast>)
+- [type Round3Bcast](<#type-round3bcast>)
+
+
+## type [Participant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/participant.go#L20-L31>)
+
+Participant is a DKG player that contains information needed to perform DKG rounds and yield a secret key share and public key when finished
+
+```go
+type Participant struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewParticipant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/participant.go#L39>)
+
+```go
+func NewParticipant(id, threshold uint32, generator *curves.EcPoint, scalar curves.EcScalar, otherParticipants ...uint32) (*Participant, error)
+```
+
+NewParticipant creates a participant ready to perform a DKG \`id\` is the integer value identifier for this participant \`threshold\` is the minimum bound for the secret sharing scheme \`generator\` is the blinding factor generator used by pedersen's verifiable secret sharing \`otherParticipants\` is the integer value identifiers for the other participants \`id\` and \`otherParticipants\` must be the set of integers 1\,2\,\.\.\.\.\,n
+
+### func \(\*Participant\) [Round1](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round1.go#L36>)
+
+```go
+func (dp *Participant) Round1(secret []byte) (Round1Bcast, Round1P2PSend, error)
+```
+
+Round1 computes the first round for the DKG \`secret\` can be nil NOTE: if \`secret\` is nil\, a new secret is generated which creates a new key if \`secret\` is set\, then this performs key resharing aka proactive secret sharing update
+
+### func \(\*Participant\) [Round2](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round2.go#L22>)
+
+```go
+func (dp *Participant) Round2(bcast map[uint32]Round1Bcast, p2p map[uint32]*Round1P2PSendPacket) (Round2Bcast, error)
+```
+
+Round2 computes the second round for Gennaro DKG Algorithm 3 \- Gennaro DKG Round 2 bcast contains all Round1 broadcast from other participants to this participant p2p contains all Round1 P2P send message from other participants to this participant
+
+### func \(\*Participant\) [Round3](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round3.go#L22>)
+
+```go
+func (dp *Participant) Round3(bcast map[uint32]Round2Bcast) (*Round3Bcast, *v1.ShamirShare, error)
+```
+
+Round3 computes the third round for Gennaro DKG Algorithm 4 \- Gennaro DKG Round 3 bcast contains all Round2 broadcast from other participants to this participant\.
+
+### func \(\*Participant\) [Round4](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round4.go#L21>)
+
+```go
+func (dp *Participant) Round4() (map[uint32]*curves.EcPoint, error)
+```
+
+Round4 computes the public shares used by tECDSA during signing that are converted to additive shares once the signing participants are known\. This function is idempotent
+
+## type [Round1Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round1.go#L20>)
+
+Round1Bcast are the values that are broadcast to all other participants after round1 completes
+
+```go
+type Round1Bcast = []*v1.ShareVerifier
+```
+
+## type [Round1P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round1.go#L24>)
+
+Round1P2PSend are the values that are sent to individual participants based on the id
+
+```go
+type Round1P2PSend = map[uint32]*Round1P2PSendPacket
+```
+
+## type [Round1P2PSendPacket](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round1.go#L27-L30>)
+
+Round1P2PSendPacket are the shares generated from the secret for a specific participant
+
+```go
+type Round1P2PSendPacket struct {
+    SecretShare   *v1.ShamirShare
+    BlindingShare *v1.ShamirShare
+}
+```
+
+## type [Round2Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round2.go#L16>)
+
+```go
+type Round2Bcast = []*v1.ShareVerifier
+```
+
+## type [Round3Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro/round3.go#L17>)
+
+Round3Bcast contains values that will be broadcast to other participants\.
+
+```go
+type Round3Bcast = v1.ShareVerifier
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/dkg/gennaro/participant.go b/pkg/dkg/gennaro/participant.go
new file mode 100644
index 00000000..76af0701
--- /dev/null
+++ b/pkg/dkg/gennaro/participant.go
@@ -0,0 +1,96 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+// Participant is a DKG player that contains information needed to perform DKG rounds
+// and yield a secret key share and public key when finished
+type Participant struct {
+	round                  int
+	curve                  elliptic.Curve
+	scalar                 curves.EcScalar
+	otherParticipantShares map[uint32]*dkgParticipantData
+	id                     uint32
+	skShare                *curves.Element
+	verificationKey        *v1.ShareVerifier
+	feldman                *v1.Feldman
+	pedersen               *v1.Pedersen
+	pedersenResult         *v1.PedersenResult
+}
+
+// NewParticipant creates a participant ready to perform a DKG
+// `id` is the integer value identifier for this participant
+// `threshold` is the minimum bound for the secret sharing scheme
+// `generator` is the blinding factor generator used by pedersen's verifiable secret sharing
+// `otherParticipants` is the integer value identifiers for the other participants
+// `id` and `otherParticipants` must be the set of integers 1,2,....,n
+func NewParticipant(id, threshold uint32, generator *curves.EcPoint, scalar curves.EcScalar, otherParticipants ...uint32) (*Participant, error) {
+	if generator == nil || len(otherParticipants) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+	err := validIds(append(otherParticipants, id))
+	if err != nil {
+		return nil, err
+	}
+
+	limit := uint32(len(otherParticipants)) + 1
+	feldman, err := v1.NewFeldman(threshold, limit, generator.Curve)
+	if err != nil {
+		return nil, err
+	}
+	pedersen, err := v1.NewPedersen(threshold, limit, generator)
+	if err != nil {
+		return nil, err
+	}
+
+	otherParticipantShares := make(map[uint32]*dkgParticipantData, len(otherParticipants))
+	for _, id := range otherParticipants {
+		otherParticipantShares[id] = &dkgParticipantData{
+			Id: id,
+		}
+	}
+
+	return &Participant{
+		id:                     id,
+		round:                  1,
+		curve:                  generator.Curve,
+		scalar:                 scalar,
+		feldman:                feldman,
+		pedersen:               pedersen,
+		otherParticipantShares: otherParticipantShares,
+	}, nil
+}
+
+// Determines if the SSIDs are exactly the values 1..n.
+func validIds(ids []uint32) error {
+	// Index
+	idMap := make(map[uint32]bool, len(ids))
+	for _, id := range ids {
+		idMap[id] = true
+	}
+	// Check
+	for i := 1; i <= len(ids); i++ {
+		if ok := idMap[uint32(i)]; !ok {
+			return fmt.Errorf("the ID list %v is invalid. Values must be 1,2,..,n.", ids)
+		}
+	}
+	return nil
+}
+
+type dkgParticipantData struct {
+	Id        uint32
+	Share     *v1.ShamirShare
+	Verifiers []*v1.ShareVerifier
+}
diff --git a/pkg/dkg/gennaro/participant_test.go b/pkg/dkg/gennaro/participant_test.go
new file mode 100644
index 00000000..684a0ab3
--- /dev/null
+++ b/pkg/dkg/gennaro/participant_test.go
@@ -0,0 +1,47 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+var testGenerator, _ = curves.NewScalarBaseMult(btcec.S256(), big.NewInt(3333))
+
+func TestNewParticipantWorks(t *testing.T) {
+	p, err := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	require.NoError(t, err)
+	require.NotNil(t, p)
+	require.Equal(t, p.id, uint32(1))
+	require.Equal(t, p.round, 1)
+	require.Equal(t, p.curve, btcec.S256())
+	require.NotNil(t, p.pedersen)
+	require.NotNil(t, p.feldman)
+	require.Nil(t, p.pedersenResult)
+	require.NotNil(t, p.otherParticipantShares)
+	require.NotNil(t, p.scalar)
+	_, ok := p.otherParticipantShares[2]
+	require.True(t, ok)
+}
+
+func TestNewParticipantBadInputs(t *testing.T) {
+	_, err := NewParticipant(0, 0, nil, nil)
+	require.Error(t, err)
+	require.Equal(t, err, internal.ErrNilArguments)
+	_, err = NewParticipant(1, 2, nil, nil)
+	require.Error(t, err)
+	require.Equal(t, err, internal.ErrNilArguments)
+	_, err = NewParticipant(1, 2, testGenerator, nil)
+	require.Error(t, err)
+	require.Equal(t, err, internal.ErrNilArguments)
+}
diff --git a/pkg/dkg/gennaro/round1.go b/pkg/dkg/gennaro/round1.go
new file mode 100644
index 00000000..96a54972
--- /dev/null
+++ b/pkg/dkg/gennaro/round1.go
@@ -0,0 +1,80 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round1Bcast are the values that are broadcast to all other participants
+// after round1 completes
+type Round1Bcast = []*v1.ShareVerifier
+
+// Round1P2PSend are the values that are sent to individual participants based
+// on the id
+type Round1P2PSend = map[uint32]*Round1P2PSendPacket
+
+// Round1P2PSendPacket are the shares generated from the secret for a specific participant
+type Round1P2PSendPacket struct {
+	SecretShare   *v1.ShamirShare
+	BlindingShare *v1.ShamirShare
+}
+
+// Round1 computes the first round for the DKG
+// `secret` can be nil
+// NOTE: if `secret` is nil, a new secret is generated which creates a new key
+// if `secret` is set, then this performs key resharing aka proactive secret sharing update
+func (dp *Participant) Round1(secret []byte) (Round1Bcast, Round1P2PSend, error) {
+	if dp.round != 1 {
+		return nil, nil, internal.ErrInvalidRound
+	}
+
+	if secret == nil {
+		// 1. x $← Zq∗
+		s, err := dp.scalar.Random()
+		if err != nil {
+			return nil, nil, err
+		}
+		secret = s.Bytes()
+	} else {
+		s := new(big.Int).SetBytes(secret)
+		if !dp.scalar.IsValid(s) {
+			return nil, nil, fmt.Errorf("invalid secret value")
+		}
+		if s.Cmp(core.Zero) == 0 {
+			return nil, nil, internal.ErrZeroValue
+		}
+	}
+
+	var err error
+	// 2. {X1,...,Xt},{R1,...,Rt},{x1,...,xn},{r1,...,rn}= PedersenFeldmanShare(E,Q,x,t,{p1,...,pn})
+	dp.pedersenResult, err = dp.pedersen.Split(secret)
+
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 4. P2PSend x_j,r_j to participant p_j in {p_1,...,p_n}_{i != j}
+	p2pSend := make(Round1P2PSend, len(dp.otherParticipantShares))
+	for id := range dp.otherParticipantShares {
+		p2pSend[id] = &Round1P2PSendPacket{
+			SecretShare:   dp.pedersenResult.SecretShares[id-1],
+			BlindingShare: dp.pedersenResult.BlindingShares[id-1],
+		}
+	}
+
+	// Update internal state
+	dp.round = 2
+
+	// 3. EchoBroadcast {X_1,...,X_t} to all other participants.
+	return dp.pedersenResult.BlindedVerifiers, p2pSend, nil
+}
diff --git a/pkg/dkg/gennaro/round2.go b/pkg/dkg/gennaro/round2.go
new file mode 100644
index 00000000..ba474c53
--- /dev/null
+++ b/pkg/dkg/gennaro/round2.go
@@ -0,0 +1,91 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+type Round2Bcast = []*v1.ShareVerifier
+
+// Round2 computes the second round for Gennaro DKG
+// Algorithm 3 - Gennaro DKG Round 2
+// bcast contains all Round1 broadcast from other participants to this participant
+// p2p contains all Round1 P2P send message from other participants to this participant
+func (dp *Participant) Round2(bcast map[uint32]Round1Bcast, p2p map[uint32]*Round1P2PSendPacket) (Round2Bcast, error) {
+
+	// Check participant is not empty
+	if dp == nil || dp.curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Check participant has the correct dkg round number
+	if dp.round != 2 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Check the input is valid
+	if bcast == nil || p2p == nil || len(bcast) == 0 || len(p2p) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// 1. set sk = x_{ii}
+	sk := dp.pedersenResult.SecretShares[dp.id-1].Value
+
+	// 2. for j in 1,...,n
+	for id := range bcast {
+
+		// 3. if i = j continue
+		if id == dp.id {
+			continue
+		}
+
+		// Ensure a valid p2p entry exists
+		if p2p[id] == nil {
+			return nil, fmt.Errorf("missing p2p packet for id=%v", id)
+		}
+
+		// 4. If PedersenVerify(E, Q, x_ji, r_ji, {X_ji,...,X_jt}) = false, abort
+		xji := p2p[id].SecretShare
+		rji := p2p[id].BlindingShare
+		bvs := bcast[id]
+		if ok, err := dp.pedersen.Verify(xji, rji, bvs); !ok {
+			if err != nil {
+				return nil, err
+			} else {
+				return nil, fmt.Errorf("invalid share for participant id=%v", id)
+			}
+		}
+
+		// Store other participants' shares xji for usage in round 3
+		dp.otherParticipantShares[id].Share = p2p[id].SecretShare
+
+		// 5. sk = (sk+xji) mod q
+		// NOTE: we use the EcScalar class to add instead of
+		// just using big.Int Add and Mod
+		// because Ed25519 will fail with the big.Int Add and Mod
+		// and Ed25519 uses different little endian vs big endian
+		// in big.Int
+		t1 := sk.BigInt()
+		t2 := xji.Value.BigInt()
+		r := dp.scalar.Add(t1, t2)
+
+		sk = sk.Field().NewElement(r)
+	}
+
+	// Update internal state
+	dp.round = 3
+
+	// 7. Store ski as participant i's secret key share
+	dp.skShare = sk
+
+	// 6. EchoBroadcast {R_1,...,R_t} to all other participants.
+	return dp.pedersenResult.Verifiers, nil
+}
diff --git a/pkg/dkg/gennaro/round3.go b/pkg/dkg/gennaro/round3.go
new file mode 100644
index 00000000..02b30748
--- /dev/null
+++ b/pkg/dkg/gennaro/round3.go
@@ -0,0 +1,89 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+// Round3Bcast contains values that will be broadcast to other participants.
+type Round3Bcast = v1.ShareVerifier
+
+// Round3 computes the third round for Gennaro DKG
+// Algorithm 4 - Gennaro DKG Round 3
+// bcast contains all Round2 broadcast from other participants to this participant.
+func (dp *Participant) Round3(bcast map[uint32]Round2Bcast) (*Round3Bcast, *v1.ShamirShare, error) {
+	// Check participant is not empty
+	if dp == nil || dp.curve == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+
+	// Check participant has the correct dkg round number
+	if dp.round != 3 {
+		return nil, nil, internal.ErrInvalidRound
+	}
+
+	// Check the input is valid
+	if len(bcast) == 0 {
+		return nil, nil, internal.ErrNilArguments
+	}
+
+	// 1. SetBigInt Pk = R_i1
+	Pk := dp.pedersenResult.Verifiers[0]
+
+	// 2. for j in 1,...,n
+	for id := range bcast {
+		// 3. if i = j continue
+		if id == dp.id {
+			continue
+		}
+
+		// 4. If FeldmanVerify(E, xji, {R_j1,...,R_jt}) = false; abort
+		xji := dp.otherParticipantShares[id].Share
+		vs := bcast[id]
+		if ok, err := dp.feldman.Verify(xji, vs); !ok {
+			if err != nil {
+				return nil, nil, err
+			} else {
+				return nil, nil, fmt.Errorf("invalid share for participant #{id}")
+			}
+		}
+
+		// Store the feldman verifiers for round 4
+		dp.otherParticipantShares[id].Verifiers = vs
+
+		// 5. Pk = Pk+R_j1
+		temp, err := Pk.Add(bcast[id][0])
+		if err != nil {
+			return nil, nil, fmt.Errorf("error in computing Pk+R_j1")
+		} //nolint:errcheck
+		Pk = temp
+	}
+
+	// This is a sanity check to make sure nothing went wrong
+	// when computing the public key
+	if !Pk.IsOnCurve() || Pk.IsIdentity() {
+		return nil, nil, fmt.Errorf("invalid public key")
+	}
+
+	// 6. Store Pk as the public verification key
+	dp.verificationKey = Pk
+
+	// Update internal state
+	dp.round = 4
+
+	skShare := v1.ShamirShare{
+		Identifier: dp.id,
+		Value:      dp.skShare,
+	}
+
+	// Output Pk as the public verification key
+	return Pk, &skShare, nil
+}
diff --git a/pkg/dkg/gennaro/round4.go b/pkg/dkg/gennaro/round4.go
new file mode 100644
index 00000000..1133cee0
--- /dev/null
+++ b/pkg/dkg/gennaro/round4.go
@@ -0,0 +1,76 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round4 computes the public shares used by tECDSA during signing
+// that are converted to additive shares once the signing participants
+// are known. This function is idempotent
+func (dp *Participant) Round4() (map[uint32]*curves.EcPoint, error) {
+	// Check participant is not empty
+	if dp == nil || dp.curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Check participant has the correct dkg round number
+	if dp.round != 4 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	n := len(dp.otherParticipantShares) + 1 //+1 to include self
+	// Wj's
+	publicShares := make(map[uint32]*curves.EcPoint, n)
+
+	// 1. R = {{R1,...,Rt},{Rij,...,Rit}i!=j}
+	r := make(map[uint32][]*v1.ShareVerifier, n)
+	r[dp.id] = dp.pedersenResult.Verifiers
+	for j := range dp.otherParticipantShares {
+		r[j] = dp.otherParticipantShares[j].Verifiers
+	}
+
+	// 2. for j in 1,...,n
+	for j, v := range r {
+		// 3. Wj = Pk
+		publicShares[j] = &curves.EcPoint{
+			Curve: dp.verificationKey.Curve,
+			X:     new(big.Int).Set(dp.verificationKey.X),
+			Y:     new(big.Int).Set(dp.verificationKey.Y),
+		}
+
+		// 4. for k in 1,...,t
+		for k := 0; k < len(dp.pedersenResult.Verifiers); k++ {
+			// 5. ck = pj * k mod q
+			pj := big.NewInt(int64(j))
+			ck, err := core.Mul(pj, big.NewInt(int64(k+1)), dp.curve.Params().N)
+			if err != nil {
+				return nil, err
+			}
+
+			// 6a. t = ck * Rj
+			t, err := v[k].ScalarMult(ck)
+			if err != nil {
+				return nil, err
+			}
+
+			// 6b. Wj = Wj + t
+			publicShares[j], err = publicShares[j].Add(t)
+			if err != nil {
+				return nil, err
+			}
+		}
+	}
+
+	return publicShares, nil
+}
diff --git a/pkg/dkg/gennaro/rounds_test.go b/pkg/dkg/gennaro/rounds_test.go
new file mode 100644
index 00000000..bfa955fd
--- /dev/null
+++ b/pkg/dkg/gennaro/rounds_test.go
@@ -0,0 +1,381 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestParticipantRound1Works(t *testing.T) {
+	p1, err := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	require.NoError(t, err)
+	bcast, p2psend, err := p1.Round1(nil)
+	require.NoError(t, err)
+	require.NotNil(t, bcast)
+	require.NotNil(t, p2psend)
+	require.Equal(t, len(p2psend), 1)
+	require.Equal(t, len(bcast), 2)
+	require.NotNil(t, p1.pedersenResult)
+	require.Equal(t, p1.round, 2)
+	_, ok := p2psend[2]
+	require.True(t, ok)
+}
+
+func TestParticipantRound1RepeatCall(t *testing.T) {
+	p1, err := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	require.NoError(t, err)
+	_, _, err = p1.Round1(nil)
+	require.NoError(t, err)
+	_, _, err = p1.Round1(nil)
+	require.Error(t, err)
+}
+
+func TestParticipantRound1BadSecret(t *testing.T) {
+	p1, err := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	require.NoError(t, err)
+	// secret == 0
+	secret := []byte{0}
+	_, _, err = p1.Round1(secret)
+	require.Error(t, err)
+	// secret too big
+	secret = []byte{7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7}
+	_, _, err = p1.Round1(secret)
+	require.Error(t, err)
+}
+
+func PrepareRound2Input(t *testing.T) (*Participant, *Participant, Round1Bcast, Round1Bcast, Round1P2PSend) {
+	// Prepare round 1 output of 2 participants
+	p1, err := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	require.NoError(t, err)
+	require.Equal(t, p1.otherParticipantShares[2].Id, uint32(2))
+	p2, err := NewParticipant(2, 2, testGenerator, curves.NewK256Scalar(), 1)
+	require.NoError(t, err)
+	require.Equal(t, p2.otherParticipantShares[1].Id, uint32(1))
+	bcast1, _, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	return p1, p2, bcast1, bcast2, p2psend2
+}
+
+// Test Gennaro DKG round2 works
+func TestParticipantRound2Works(t *testing.T) {
+	// Prepare Dkg Round 1 output
+	p1, _, bcast1, bcast2, p2psend2 := PrepareRound2Input(t)
+	// Actual Test
+	require.NotNil(t, bcast1)
+	require.NotNil(t, bcast2)
+	require.NotNil(t, p2psend2[1])
+	bcast := make(map[uint32]Round1Bcast)
+	p2p := make(map[uint32]*Round1P2PSendPacket)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	round2Out, err := p1.Round2(bcast, p2p)
+	require.NoError(t, err)
+	require.NotNil(t, round2Out)
+	require.Equal(t, len(round2Out), 2)
+	require.NotNil(t, p1.skShare)
+	require.Equal(t, p1.round, 3)
+	require.NotNil(t, p1.otherParticipantShares)
+}
+
+// Test Gennaro DKG round 2 repeat call
+func TestParticipantRound2RepeatCall(t *testing.T) {
+	// Prepare Dkg Round 1 output
+	p1, _, bcast1, bcast2, p2psend2 := PrepareRound2Input(t)
+	// Actual Test
+	require.NotNil(t, bcast1)
+	require.NotNil(t, bcast2)
+	require.NotNil(t, p2psend2[1])
+	bcast := make(map[uint32]Round1Bcast)
+	p2p := make(map[uint32]*Round1P2PSendPacket)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	_, err := p1.Round2(bcast, p2p)
+	require.NoError(t, err)
+	_, err = p1.Round2(bcast, p2p)
+	require.Error(t, err)
+}
+
+// Test Gennaro Dkg Round 2 Bad Input
+func TestParticipantRound2BadInput(t *testing.T) {
+	// Prepare Dkg Round 1 output
+	p1, _, _, _, _ := PrepareRound2Input(t)
+	bcast := make(map[uint32]Round1Bcast)
+	p2p := make(map[uint32]*Round1P2PSendPacket)
+
+	// Test empty bcast and p2p
+	_, err := p1.Round2(bcast, p2p)
+	require.Error(t, err)
+
+	// Test nil bcast and p2p
+	p1, _, _, _, _ = PrepareRound2Input(t)
+	_, err = p1.Round2(nil, nil)
+	require.Error(t, err)
+
+	// Test tampered input bcast and p2p
+	p1, _, bcast1, bcast2, p2psend2 := PrepareRound2Input(t)
+	bcast = make(map[uint32]Round1Bcast)
+	p2p = make(map[uint32]*Round1P2PSendPacket)
+
+	// Tamper bcast1 and p2psend2 by doubling their value
+	bcast1[1].Y = bcast1[1].Y.Add(bcast1[1].Y, bcast1[1].Y)
+	p2psend2[1].SecretShare.Value = p2psend2[1].SecretShare.Value.Add(p2psend2[1].SecretShare.Value)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p[2] = p2psend2[1]
+	_, err = p1.Round2(bcast, p2p)
+	require.Error(t, err)
+}
+
+func PrepareRound3Input(t *testing.T) (*Participant, *Participant, map[uint32]Round2Bcast) {
+	p1, _ := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	p2, _ := NewParticipant(2, 2, testGenerator, curves.NewK256Scalar(), 1)
+	bcast1, p2psend1, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	bcast := make(map[uint32]Round1Bcast)
+	p2p1 := make(map[uint32]*Round1P2PSendPacket)
+	p2p2 := make(map[uint32]*Round1P2PSendPacket)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p1[2] = p2psend2[1]
+	p2p2[1] = p2psend1[2]
+	round2Out1, _ := p1.Round2(bcast, p2p1)
+	round2Out2, _ := p2.Round2(bcast, p2p2)
+	round3Input := make(map[uint32]Round2Bcast)
+	round3Input[1] = round2Out1
+	round3Input[2] = round2Out2
+	return p1, p2, round3Input
+}
+
+// Test Gennaro Dkg Round 3 Works
+func TestParticipantRound3Works(t *testing.T) {
+	// Prepare Gennaro Dkg Round 3 Input
+	p1, p2, round3Input := PrepareRound3Input(t)
+
+	// Actual Test
+	round3Out1, _, err := p1.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out1)
+	round3Out2, _, err := p2.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out2)
+	require.Equal(t, p1.round, 4)
+	require.Equal(t, p2.round, 4)
+	require.Equal(t, p1.verificationKey, p2.verificationKey)
+
+	// Test if shares recombine properly
+	s, _ := v1.NewShamir(2, 2, curves.NewField(btcec.S256().N))
+	sk, err := s.Combine(&v1.ShamirShare{Identifier: p1.id, Value: p1.skShare},
+		&v1.ShamirShare{Identifier: p2.id, Value: p2.skShare})
+	require.NoError(t, err)
+
+	// Test verification keys are G * sk
+	x, y := btcec.S256().ScalarBaseMult(sk)
+	tmp := &curves.EcPoint{
+		Curve: btcec.S256(),
+		X:     x,
+		Y:     y,
+	}
+	assert.True(t, tmp.Equals(p1.verificationKey))
+	assert.True(t, tmp.Equals(p2.verificationKey))
+}
+
+// Test Gennaro Dkg Round3 Repeat Call
+func TestParticipantRound3RepeatCall(t *testing.T) {
+	// Prepare Round 3 Input
+	p1, _, round3Input := PrepareRound3Input(t)
+
+	// Actual Test
+	_, _, err := p1.Round3(round3Input)
+	require.NoError(t, err)
+	_, _, err = p1.Round3(round3Input)
+	require.Error(t, err)
+}
+
+// Test Gennaro DKG Round 3 Bad Input
+func TestParticipantRound3BadInput(t *testing.T) {
+	// Test empty round 3 input
+	p1, _, _ := PrepareRound3Input(t)
+	emptyInput := make(map[uint32]Round2Bcast)
+	_, _, err := p1.Round3(emptyInput)
+	require.Error(t, err)
+
+	// Test nil round 3 input
+	p1, _, _ = PrepareRound3Input(t)
+	_, _, err = p1.Round3(nil)
+	require.Error(t, err)
+
+	// Test tampered round 3 input
+	p1, _, round3Input := PrepareRound3Input(t)
+	// Tamper participant2's broadcast
+	round3Input[2][0], _ = round3Input[2][0].Add(round3Input[2][1])
+	_, _, err = p1.Round3(round3Input)
+	require.Error(t, err)
+}
+
+// Test Gennaro Dkg Round 4 Works
+func TestParticipantRound4Works(t *testing.T) {
+	// Prepare Gennaro Dkg Round 3 Input
+	p1, p2, round3Input := PrepareRound3Input(t)
+	round3Out1, _, err := p1.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out1)
+	round3Out2, _, err := p2.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out2)
+
+	// Actual test
+	publicShares1, err := p1.Round4()
+	require.NoError(t, err)
+	require.NotNil(t, publicShares1)
+	publicShares2, err := p2.Round4()
+	require.NoError(t, err)
+	require.NotNil(t, publicShares2)
+
+	require.Equal(t, publicShares1, publicShares2)
+}
+
+// Test Gennaro Dkg Round 4 Works
+func TestParticipantRound4RepeatCall(t *testing.T) {
+	// Prepare Gennaro Dkg Round 3 Input
+	p1, p2, round3Input := PrepareRound3Input(t)
+	round3Out1, _, err := p1.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out1)
+	round3Out2, _, err := p2.Round3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out2)
+
+	// Actual test
+	publicShares1, err := p1.Round4()
+	require.NoError(t, err)
+	require.NotNil(t, publicShares1)
+	publicShares2, err := p1.Round4()
+	require.NoError(t, err)
+	require.NotNil(t, publicShares2)
+
+	require.Equal(t, publicShares1, publicShares2)
+}
+
+// Test all Gennaro DKG rounds
+func TestAllGennaroDkgRounds(t *testing.T) {
+	// Initiate two participants
+	p1, _ := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	p2, _ := NewParticipant(2, 2, testGenerator, curves.NewK256Scalar(), 1)
+
+	// Running round 1
+	bcast1, p2psend1, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	bcast := make(map[uint32]Round1Bcast)
+	p2p1 := make(map[uint32]*Round1P2PSendPacket)
+	p2p2 := make(map[uint32]*Round1P2PSendPacket)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p1[2] = p2psend2[1]
+	p2p2[1] = p2psend1[2]
+
+	// Running round 2
+	round2Out1, _ := p1.Round2(bcast, p2p1)
+	round2Out2, _ := p2.Round2(bcast, p2p2)
+	round3Input := make(map[uint32]Round2Bcast)
+	round3Input[1] = round2Out1
+	round3Input[2] = round2Out2
+
+	// Running round 3
+	round3Out1, _, _ := p1.Round3(round3Input)
+	round3Out2, _, _ := p2.Round3(round3Input)
+	require.NotNil(t, round3Out1)
+	require.NotNil(t, round3Out2)
+
+	// Running round 4
+	publicShares1, _ := p1.Round4()
+	publicShares2, _ := p2.Round4()
+
+	// Test output of all rounds
+	require.Equal(t, publicShares1, publicShares2)
+	s, _ := v1.NewShamir(2, 2, curves.NewField(btcec.S256().N))
+	sk, err := s.Combine(&v1.ShamirShare{Identifier: p1.id, Value: p1.skShare},
+		&v1.ShamirShare{Identifier: p2.id, Value: p2.skShare})
+	require.NoError(t, err)
+
+	x, y := btcec.S256().ScalarBaseMult(sk)
+	tmp := &curves.EcPoint{
+		Curve: btcec.S256(),
+		X:     x,
+		Y:     y,
+	}
+	require.True(t, tmp.Equals(p1.verificationKey))
+	require.True(t, tmp.Equals(p2.verificationKey))
+}
+
+// Ensure correct functioning when input is missing
+func TestParticipant2BadInput(t *testing.T) {
+	//
+	// Setup
+	//
+	p1, _ := NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 2)
+	p2, _ := NewParticipant(2, 2, testGenerator, curves.NewK256Scalar(), 1)
+	bcast1, _, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	bcast := make(map[uint32]Round1Bcast)
+	p2p1 := make(map[uint32]*Round1P2PSendPacket)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	// Exclude p2p 2>1
+	p2p1[4] = p2psend2[1]
+
+	// Run round 2
+	_, err := p1.Round2(bcast, p2p1)
+	assert.Error(t, err)
+}
+
+func TestValidIDs(t *testing.T) {
+	err := fmt.Errorf("")
+	tests := []struct {
+		name     string
+		in       []uint32
+		expected error
+	}{
+		{"positive-1,2", []uint32{1, 2}, nil},
+		{"positive-2,1", []uint32{2, 1}, nil},
+		{"positive-1-10", []uint32{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, nil},
+		{"positive-1-10-random", []uint32{10, 9, 6, 5, 3, 2, 8, 7, 1, 4}, nil},
+		{"negative-1,3", []uint32{1, 3}, err},
+		{"negative-1-10-missing-5", []uint32{10, 9, 6, 3, 2, 8, 7, 1, 4}, err},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			err := validIds(test.in)
+			if test.expected == nil {
+				assert.NoError(t, err)
+			} else {
+				assert.Error(t, err)
+			}
+		})
+	}
+}
+
+// Test newParticipant with arbitrary IDs
+func TestParticipantArbitraryIds(t *testing.T) {
+	_, err := NewParticipant(3, 2, testGenerator, curves.NewK256Scalar(), 4)
+	assert.Error(t, err)
+	_, err = NewParticipant(0, 2, testGenerator, curves.NewK256Scalar(), 1)
+	assert.Error(t, err)
+	_, err = NewParticipant(2, 2, testGenerator, curves.NewK256Scalar(), 2, 3, 5)
+	assert.Error(t, err)
+	_, err = NewParticipant(1, 2, testGenerator, curves.NewK256Scalar(), 4)
+	assert.Error(t, err)
+}
diff --git a/pkg/dkg/gennaro2p/README.md b/pkg/dkg/gennaro2p/README.md
new file mode 100755
index 00000000..e049e65f
--- /dev/null
+++ b/pkg/dkg/gennaro2p/README.md
@@ -0,0 +1,96 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# gennaro2p
+
+```go
+import "github.com/coinbase/kryptology/pkg/dkg/gennaro2p"
+```
+
+Wraps dkg/genarro and specializes it for the 2\-party case\. Simpler API\, no distinction between broadcast and peer messages\, and only counterparty messages are used as round inputs since self\-inputs are always ignored\.
+
+## Index
+
+- [type DkgResult](<#type-dkgresult>)
+- [type Participant](<#type-participant>)
+  - [func NewParticipant(id, counterPartyId uint32, blind *curves.EcPoint, scalar curves.EcScalar, curve elliptic.Curve) (*Participant, error)](<#func-newparticipant>)
+  - [func (p *Participant) Finalize(msg *Round2Message) (*DkgResult, error)](<#func-participant-finalize>)
+  - [func (p *Participant) Round1(secret []byte) (*Round1Message, error)](<#func-participant-round1>)
+  - [func (p *Participant) Round2(msg *Round1Message) (*Round2Message, error)](<#func-participant-round2>)
+- [type Round1Message](<#type-round1message>)
+- [type Round2Message](<#type-round2message>)
+
+
+## type [DkgResult](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L44-L48>)
+
+```go
+type DkgResult struct {
+    PublicKey    *curves.EcPoint
+    SecretShare  *v1.ShamirShare
+    PublicShares map[uint32]*curves.EcPoint
+}
+```
+
+## type [Participant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L26-L31>)
+
+Participant is a DKG player that contains information needed to perform DKG rounds and yield a secret key share and public key when finished
+
+```go
+type Participant struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewParticipant](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L54-L55>)
+
+```go
+func NewParticipant(id, counterPartyId uint32, blind *curves.EcPoint, scalar curves.EcScalar, curve elliptic.Curve) (*Participant, error)
+```
+
+NewParticipant creates a participant ready to perform a DKG blind must be a generator and must be synchronized between counterparties\. The first participant can set it to \`nil\` and a secure blinding factor will be generated\.
+
+### func \(\*Participant\) [Finalize](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L126>)
+
+```go
+func (p *Participant) Finalize(msg *Round2Message) (*DkgResult, error)
+```
+
+Completes the DKG using the counterparty's output from round 2\.
+
+### func \(\*Participant\) [Round1](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L83>)
+
+```go
+func (p *Participant) Round1(secret []byte) (*Round1Message, error)
+```
+
+Runs DKG round 1\. If \`secret\` is nil\, shares of a new\, random signing key are generated\. Otherwise\, the existing secret shares will be refreshed but the privkey and pubkey will remain unchanged\.
+
+### func \(\*Participant\) [Round2](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L106>)
+
+```go
+func (p *Participant) Round2(msg *Round1Message) (*Round2Message, error)
+```
+
+Runs DKG round 2 using the counterparty's output from round 1\.
+
+## type [Round1Message](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L33-L38>)
+
+```go
+type Round1Message struct {
+    Verifiers     []*v1.ShareVerifier
+    SecretShare   *v1.ShamirShare
+    BlindingShare *v1.ShamirShare
+    Blind         *curves.EcPoint
+}
+```
+
+## type [Round2Message](<https://github.com/coinbase/kryptology/blob/master/pkg/dkg/gennaro2p/genarro2p.go#L40-L42>)
+
+```go
+type Round2Message struct {
+    Verifiers []*v1.ShareVerifier
+}
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/dkg/gennaro2p/genarro2p.go b/pkg/dkg/gennaro2p/genarro2p.go
new file mode 100644
index 00000000..881b94ad
--- /dev/null
+++ b/pkg/dkg/gennaro2p/genarro2p.go
@@ -0,0 +1,148 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Wraps dkg/genarro and specializes it for the 2-party case. Simpler API, no
+// distinction between broadcast and peer messages, and only counterparty messages are
+// used as round inputs since self-inputs are always ignored.
+package gennaro2p
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"github.com/coinbase/kryptology/pkg/dkg/gennaro"
+	"github.com/pkg/errors"
+)
+
+const threshold = 2
+
+// Participant is a DKG player that contains information needed to perform DKG rounds
+// and yield a secret key share and public key when finished
+type Participant struct {
+	id             uint32
+	counterPartyId uint32
+	embedded       *gennaro.Participant
+	blind          *curves.EcPoint
+}
+
+type Round1Message struct {
+	Verifiers     []*v1.ShareVerifier
+	SecretShare   *v1.ShamirShare
+	BlindingShare *v1.ShamirShare
+	Blind         *curves.EcPoint
+}
+
+type Round2Message struct {
+	Verifiers []*v1.ShareVerifier
+}
+
+type DkgResult struct {
+	PublicKey    *curves.EcPoint
+	SecretShare  *v1.ShamirShare
+	PublicShares map[uint32]*curves.EcPoint
+}
+
+// NewParticipant creates a participant ready to perform a DKG
+// blind must be a generator and must be synchronized between counterparties.
+// The first participant can set it to `nil` and a secure blinding factor will be
+// generated.
+func NewParticipant(id, counterPartyId uint32, blind *curves.EcPoint,
+	scalar curves.EcScalar, curve elliptic.Curve) (*Participant, error) {
+	// Generate blinding value, if required
+	var err error
+	if blind == nil {
+		blind, err = newBlind(scalar, curve)
+		if err != nil {
+			return nil, errors.Wrap(err, "generating fresh blinding generator")
+		}
+	}
+	p, err := gennaro.NewParticipant(id, threshold, blind, scalar, counterPartyId)
+	if err != nil {
+		return nil, errors.Wrap(err, "created genarro.Participant")
+	}
+	return &Participant{id, counterPartyId, p, blind}, nil
+}
+
+// Creates a random blinding factor (as a generator) required for pedersen's VSS
+func newBlind(curveScalar curves.EcScalar, curve elliptic.Curve) (*curves.EcPoint, error) {
+	rScalar, err := curveScalar.Random()
+	if err != nil {
+		return nil, errors.Wrap(err, "generating blinding scalar")
+	}
+	return curves.NewScalarBaseMult(curve, rScalar)
+}
+
+// Runs DKG round 1. If `secret` is nil, shares of a new, random signing key are generated.
+// Otherwise, the existing secret shares will be refreshed but the privkey and pubkey
+// will remain unchanged.
+func (p *Participant) Round1(secret []byte) (*Round1Message, error) {
+	// Run round 1
+	bcast, p2p, err := p.embedded.Round1(secret)
+	if err != nil {
+		return nil, errors.Wrap(err, "calling embedded.Round1()")
+	}
+
+	// Ensure the map has the expected entry so there's no SIGSEGV when we
+	// repackage it
+	if p2p[p.counterPartyId] == nil {
+		return nil, fmt.Errorf("round1 response for p2p[%v] is nil", p.counterPartyId)
+	}
+
+	// Package response
+	return &Round1Message{
+		bcast,
+		p2p[p.counterPartyId].SecretShare,
+		p2p[p.counterPartyId].BlindingShare,
+		p.blind,
+	}, nil
+}
+
+// Runs DKG round 2 using the counterparty's output from round 1.
+func (p *Participant) Round2(msg *Round1Message) (*Round2Message, error) {
+	// Run round 2
+	bcast, err := p.embedded.Round2(
+		map[uint32]gennaro.Round1Bcast{
+			p.counterPartyId: msg.Verifiers,
+		},
+		map[uint32]*gennaro.Round1P2PSendPacket{
+			p.counterPartyId: {
+				SecretShare:   msg.SecretShare,
+				BlindingShare: msg.BlindingShare,
+			}})
+	if err != nil {
+		return nil, errors.Wrap(err, "calling embedded.Round2()")
+	}
+
+	// Package response
+	return &Round2Message{bcast}, nil
+}
+
+// Completes the DKG using the counterparty's output from round 2.
+func (p *Participant) Finalize(msg *Round2Message) (*DkgResult, error) {
+	// Run round 3
+	pk, share, err := p.embedded.Round3(
+		map[uint32]gennaro.Round2Bcast{
+			p.counterPartyId: msg.Verifiers,
+		})
+	if err != nil {
+		return nil, errors.Wrap(err, "calling embedded.Round3()")
+	}
+
+	// Compute public shares
+	pubShares, err := p.embedded.Round4()
+	if err != nil {
+		return nil, errors.Wrap(err, "calling embedded.Roun4()")
+	}
+
+	// Package response
+	return &DkgResult{
+		PublicKey:    pk,
+		SecretShare:  share,
+		PublicShares: pubShares,
+	}, nil
+}
diff --git a/pkg/dkg/gennaro2p/genarro2p_test.go b/pkg/dkg/gennaro2p/genarro2p_test.go
new file mode 100644
index 00000000..1d23f687
--- /dev/null
+++ b/pkg/dkg/gennaro2p/genarro2p_test.go
@@ -0,0 +1,181 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package gennaro2p
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"reflect"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	curveScalar = curves.NewK256Scalar()
+	curve       = btcec.S256()
+)
+
+const (
+	clientId = 1
+	serverId = 2
+)
+
+// Benchmark full DKG including blind selection and setup
+func BenchmarkDkg(b *testing.B) {
+	if testing.Short() {
+		b.Skip("skipping test in short mode.")
+	}
+
+	for i := 0; i < b.N; i++ {
+		_, _, err := dkg()
+		assert.NoError(b, err)
+	}
+}
+
+// Run a DKG and reports the client/server results
+func dkg() (*DkgResult, *DkgResult, error) {
+	// Create client/server
+	blind, _ := newBlind(curveScalar, curve)
+
+	client, err := NewParticipant(clientId, serverId, blind, curveScalar, curve)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	server, err := NewParticipant(serverId, clientId, blind, curveScalar, curve)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// R1
+	clientR1, err := client.Round1(nil)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	serverR1, err := server.Round1(nil)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// R2
+	clientR2, err := client.Round2(serverR1)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	serverR2, err := server.Round2(clientR1)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Finalize
+	clientResult, err := client.Finalize(serverR2)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	serverResult, err := server.Finalize(clientR2)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	return clientResult, serverResult, nil
+}
+
+// Run a full DKG and verify the absence of errors and valid results
+func TestDkg(t *testing.T) {
+	// Setup and ensure no errors
+	clientResult, serverResult, err := dkg()
+	require.NoError(t, err)
+	require.NotNil(t, clientResult)
+	require.NotNil(t, serverResult)
+
+	// Now run tests
+	t.Run("produce the same public key", func(t *testing.T) {
+		assert.Equal(t, clientResult.PublicKey, serverResult.PublicKey)
+	})
+	t.Run("produce identical public shares", func(t *testing.T) {
+		assert.True(t, reflect.DeepEqual(clientResult.PublicShares, serverResult.PublicShares))
+	})
+	t.Run("produce distinct secret shares", func(t *testing.T) {
+		assert.NotEqual(t, clientResult.SecretShare, serverResult.SecretShare)
+	})
+	t.Run("produce distinct secret shares", func(t *testing.T) {
+		assert.NotEqual(t, clientResult.SecretShare, serverResult.SecretShare)
+	})
+	t.Run("shares sum to expected public key", func(t *testing.T) {
+		pubkey, err := reconstructPubkey(
+			clientResult.SecretShare,
+			serverResult.SecretShare,
+			curve)
+		require.NoError(t, err)
+		assert.Equal(t, serverResult.PublicKey, pubkey)
+	})
+}
+
+// Reconstruct the pubkey from 2 shares
+func reconstructPubkey(s1, s2 *v1.ShamirShare, curve elliptic.Curve) (*curves.EcPoint, error) {
+	s, err := v1.NewShamir(2, 2, s1.Value.Field())
+	if err != nil {
+		return nil, err
+	}
+
+	sk, err := s.Combine(s1, s2)
+	if err != nil {
+		return nil, err
+	}
+
+	x, y := curve.ScalarBaseMult(sk)
+	return &curves.EcPoint{
+		Curve: curve,
+		X:     x,
+		Y:     y,
+	}, nil
+}
+
+// Test blind generator helper function produces a value on the expected curve
+func TestNewBlindOnCurve(t *testing.T) {
+	const n = 1024
+	for i := 0; i < n; i++ {
+		b, err := newBlind(curveScalar, curve)
+		require.NoError(t, err)
+		require.NotNil(t, b)
+
+		// Valid point?
+		assert.True(t, b.IsOnCurve() && b.IsValid())
+		assert.True(t, b.IsValid())
+		assert.False(t, b.IsIdentity())
+		assert.False(t, b.IsBasePoint())
+	}
+}
+
+func TestNewBlindProvidesDistinctPoints(t *testing.T) {
+	const n = 1024
+	seen := make(map[string]bool, n)
+	// seen := make(map[core.EcPoint]bool, n)
+
+	for i := 0; i < n; i++ {
+		b, err := newBlind(curveScalar, curve)
+		require.NoError(t, err)
+
+		// serialize so the point is hashable
+		txt := fmt.Sprintf("%#v", b)
+
+		// We shouldn't see the same point twice
+		ok := seen[txt]
+		assert.False(t, ok)
+
+		// store
+		seen[txt] = true
+	}
+}
diff --git a/pkg/paillier/README.md b/pkg/paillier/README.md
new file mode 100755
index 00000000..03b1c69d
--- /dev/null
+++ b/pkg/paillier/README.md
@@ -0,0 +1,403 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# paillier
+
+```go
+import "github.com/coinbase/kryptology/pkg/paillier"
+```
+
+Package paillier contains Paillier's cryptosystem \(1999\) \[P99\]\. Public\-Key Cryptosystems Based on Composite Degree Residuosity Class\. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf All routines here from pseudocode §2\.5\. Fig 1: The Paillier Cryptosystem\.
+
+This module provides APIs for:
+
+\- generating a safe keypair\, \- encryption and decryption\, \- adding two encrypted values\, Enc\(a\) and Enc\(b\)\, and obtaining Enc\(a \+ b\)\, and \- multiplying a plain value\, a\, and an encrypted value Enc\(b\)\, and obtaining Enc\(a \* b\)\.
+
+The encrypted values are represented as big\.Int and are serializable\. This module also provides JSON serialization for the PublicKey and the SecretKey\.
+
+<details><summary>Example (Encrypt Decrypt)</summary>
+<p>
+
+```go
+{
+
+	if testing.Short() {
+
+		fmt.Println("Succeeded in encrypting and decrypting the input message: Hello World!")
+		return
+	}
+	hexMessage := hex.EncodeToString([]byte("Hello World!"))
+	mappedMessage, ok := new(big.Int).SetString(hexMessage, 16)
+	if !ok {
+		panic("Error mapping message to scalar point.")
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	cipher, _, err := pub.Encrypt(mappedMessage)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	decrypted, err := sec.Decrypt(cipher)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+
+	decoded := string(decrypted.Bytes())
+	fmt.Println("Succeeded in encrypting and decrypting the input message:", decoded)
+
+}
+```
+
+#### Output
+
+```
+Succeeded in encrypting and decrypting the input message: Hello World!
+```
+
+</p>
+</details>
+
+<details><summary>Example (Homomorphic Addition)</summary>
+<p>
+
+```go
+{
+
+	if testing.Short() {
+
+		fmt.Println("Encrypting 123 and 456 separately.")
+		fmt.Println("Adding their encrypted versions together.")
+		fmt.Println("Succeeded in decrypting 579")
+		return
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	msg1 := tt.B10("123")
+	msg2 := tt.B10("456")
+	fmt.Printf("Encrypting %s and %s separately.\n", msg1, msg2)
+
+	cipher1, _, err := pub.Encrypt(msg1)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+	cipher2, _, err := pub.Encrypt(msg2)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	fmt.Println("Adding their encrypted versions together.")
+	cipher3, err := pub.Add(cipher1, cipher2)
+	if err != nil {
+		log.Fatalf("Error in adding the two ciphertexts: %v", err)
+	}
+	decrypted3, err := sec.Decrypt(cipher3)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+	fmt.Println("Succeeded in decrypting", decrypted3)
+
+}
+```
+
+#### Output
+
+```
+Encrypting 123 and 456 separately.
+Adding their encrypted versions together.
+Succeeded in decrypting 579
+```
+
+</p>
+</details>
+
+<details><summary>Example (Homomorphic Multiplication)</summary>
+<p>
+
+```go
+{
+
+	if testing.Short() {
+
+		fmt.Println("Encrypting 10.")
+		fmt.Println("Multiplying plain 5 with the encrypted 10.")
+		fmt.Println("Succeeded in decrypting 50.")
+		return
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	msg1 := tt.B10("10")
+	msg2 := tt.B10("5")
+	fmt.Printf("Encrypting %s.\n", msg1)
+
+	cipher1, _, err := pub.Encrypt(msg1)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	fmt.Printf("Multiplying plain %s with the encrypted %s.\n", msg2, msg1)
+	cipher3, err := pub.Mul(msg2, cipher1)
+	if err != nil {
+		log.Fatalf("Error in adding the two ciphertexts: %v", err)
+	}
+	decrypted3, err := sec.Decrypt(cipher3)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+	fmt.Printf("Succeeded in decrypting %s.\n", decrypted3)
+
+}
+```
+
+#### Output
+
+```
+Encrypting 10.
+Multiplying plain 5 with the encrypted 10.
+Succeeded in decrypting 50.
+```
+
+</p>
+</details>
+
+## Index
+
+- [Constants](<#constants>)
+- [func NewKeys() (*PublicKey, *SecretKey, error)](<#func-newkeys>)
+- [type Ciphertext](<#type-ciphertext>)
+- [type PsfProof](<#type-psfproof>)
+  - [func (p PsfProof) Verify(psf *PsfVerifyParams) error](<#func-psfproof-verify>)
+- [type PsfProofParams](<#type-psfproofparams>)
+  - [func (p *PsfProofParams) Prove() (PsfProof, error)](<#func-psfproofparams-prove>)
+- [type PsfVerifyParams](<#type-psfverifyparams>)
+- [type PublicKey](<#type-publickey>)
+  - [func NewPubkey(n *big.Int) *PublicKey](<#func-newpubkey>)
+  - [func (pk *PublicKey) Add(c, d Ciphertext) (Ciphertext, error)](<#func-publickey-add>)
+  - [func (pk *PublicKey) Encrypt(msg *big.Int) (Ciphertext, *big.Int, error)](<#func-publickey-encrypt>)
+  - [func (pk PublicKey) MarshalJSON() ([]byte, error)](<#func-publickey-marshaljson>)
+  - [func (pk *PublicKey) Mul(a *big.Int, c Ciphertext) (Ciphertext, error)](<#func-publickey-mul>)
+  - [func (pk *PublicKey) UnmarshalJSON(bytes []byte) error](<#func-publickey-unmarshaljson>)
+- [type PublicKeyJson](<#type-publickeyjson>)
+- [type SecretKey](<#type-secretkey>)
+  - [func NewSecretKey(p, q *big.Int) (*SecretKey, error)](<#func-newsecretkey>)
+  - [func (sk *SecretKey) Decrypt(c Ciphertext) (*big.Int, error)](<#func-secretkey-decrypt>)
+  - [func (sk SecretKey) MarshalJSON() ([]byte, error)](<#func-secretkey-marshaljson>)
+  - [func (sk *SecretKey) UnmarshalJSON(bytes []byte) error](<#func-secretkey-unmarshaljson>)
+- [type SecretKeyJson](<#type-secretkeyjson>)
+
+
+## Constants
+
+PaillierPrimeBits is the number of bits used to generate Paillier Safe Primes\.
+
+```go
+const PaillierPrimeBits = 1024
+```
+
+\[spec\] 10\.2 and ProvePSF\, VerifyPSF fig\.15
+
+```go
+const PsfProofLength = 13
+```
+
+## func [NewKeys](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L73>)
+
+```go
+func NewKeys() (*PublicKey, *SecretKey, error)
+```
+
+NewKeys generates Paillier keys with \`bits\` sized safe primes\.
+
+## type [Ciphertext](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L65>)
+
+Ciphertext in Pailler's cryptosystem: a value $c \\in Z\_\{N²\}$ \.
+
+```go
+type Ciphertext *big.Int
+```
+
+## type [PsfProof](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/psf.go#L40>)
+
+PsfProof is a slice of 13 big\.Int's that prove that a Paillier modulus is square\-free
+
+```go
+type PsfProof []*big.Int
+```
+
+### func \(PsfProof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/psf.go#L97>)
+
+```go
+func (p PsfProof) Verify(psf *PsfVerifyParams) error
+```
+
+Verify that a Paillier modulus is square\-free \[spec\] §10\.fig 15
+
+## type [PsfProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/psf.go#L24-L29>)
+
+PsfProofParams contains the inputs to ProvePSF
+
+```go
+type PsfProofParams struct {
+    Curve     elliptic.Curve
+    SecretKey *SecretKey
+    Pi        uint32
+    Y         *curves.EcPoint
+}
+```
+
+### func \(\*PsfProofParams\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/psf.go#L44>)
+
+```go
+func (p *PsfProofParams) Prove() (PsfProof, error)
+```
+
+Prove that a Paillier modulus is square\-free \[spec\] §10\.fig 15
+
+## type [PsfVerifyParams](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/psf.go#L32-L37>)
+
+PsfVerifyParams contains the inputs to VerifyPSF
+
+```go
+type PsfVerifyParams struct {
+    Curve     elliptic.Curve
+    PublicKey *PublicKey
+    Pi        uint32
+    Y         *curves.EcPoint
+}
+```
+
+## type [PublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L37-L40>)
+
+PublicKey is a Paillier public key: N = P\*Q; for safe primes P\,Q\.
+
+```go
+type PublicKey struct {
+    N   *big.Int // N = PQ
+    N2  *big.Int // N² computed and cached to prevent re-computation.
+}
+```
+
+### func [NewPubkey](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L209>)
+
+```go
+func NewPubkey(n *big.Int) *PublicKey
+```
+
+NewPubkey initializes a Paillier public key with a given n\.
+
+### func \(\*PublicKey\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L218>)
+
+```go
+func (pk *PublicKey) Add(c, d Ciphertext) (Ciphertext, error)
+```
+
+Add combines two Paillier ciphertexts\.
+
+### func \(\*PublicKey\) [Encrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L272>)
+
+```go
+func (pk *PublicKey) Encrypt(msg *big.Int) (Ciphertext, *big.Int, error)
+```
+
+Encrypt produces a ciphertext on input message\.
+
+### func \(PublicKey\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L148>)
+
+```go
+func (pk PublicKey) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON converts the public key into json format\.
+
+### func \(\*PublicKey\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L246>)
+
+```go
+func (pk *PublicKey) Mul(a *big.Int, c Ciphertext) (Ciphertext, error)
+```
+
+Mul is equivalent to adding two Paillier exponents\.
+
+### func \(\*PublicKey\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L154>)
+
+```go
+func (pk *PublicKey) UnmarshalJSON(bytes []byte) error
+```
+
+UnmarshalJSON converts the json data into this public key\.
+
+## type [PublicKeyJson](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L45-L47>)
+
+PublicKeyJson encapsulates the data that is serialized to JSON\. It is used internally and not for external use\. Public so other pieces can use for serialization\.
+
+```go
+type PublicKeyJson struct {
+    N *big.Int
+}
+```
+
+## type [SecretKey](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L50-L55>)
+
+SecretKey is a Paillier secret key\.
+
+```go
+type SecretKey struct {
+    PublicKey
+    Lambda  *big.Int // lcm(P - 1, Q - 1)
+    Totient *big.Int // Euler's totient: (P - 1) * (Q - 1)
+    U       *big.Int // L((N + 1)^λ(N) mod N²)−1 mod N
+}
+```
+
+### func [NewSecretKey](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L112>)
+
+```go
+func NewSecretKey(p, q *big.Int) (*SecretKey, error)
+```
+
+NewSecretKey computes intermediate values based on safe primes p\, q\.
+
+### func \(\*SecretKey\) [Decrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L320>)
+
+```go
+func (sk *SecretKey) Decrypt(c Ciphertext) (*big.Int, error)
+```
+
+Decrypt is the reverse operation of Encrypt\.
+
+### func \(SecretKey\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L350>)
+
+```go
+func (sk SecretKey) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON converts the secret key into json format\.
+
+### func \(\*SecretKey\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L361>)
+
+```go
+func (sk *SecretKey) UnmarshalJSON(bytes []byte) error
+```
+
+UnmarshalJSON converts the json data into this secret key\.
+
+## type [SecretKeyJson](<https://github.com/coinbase/kryptology/blob/master/pkg/paillier/paillier.go#L60-L62>)
+
+SecretKeyJson encapsulates the data that is serialized to JSON\. It is used internally and not for external use\. Public so other pieces can use for serialization\.
+
+```go
+type SecretKeyJson struct {
+    N, Lambda, Totient, U *big.Int
+}
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/paillier/paillier.go b/pkg/paillier/paillier.go
new file mode 100644
index 00000000..6796a0aa
--- /dev/null
+++ b/pkg/paillier/paillier.go
@@ -0,0 +1,374 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Package paillier contains Paillier's cryptosystem (1999) [P99].
+// Public-Key Cryptosystems Based on Composite Degree Residuosity Class.
+// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf
+// All routines here from pseudocode §2.5. Fig 1: The Paillier Cryptosystem.
+//
+// This module provides APIs for:
+//
+//  - generating a safe keypair,
+//  - encryption and decryption,
+//  - adding two encrypted values, Enc(a) and Enc(b), and obtaining Enc(a + b), and
+//  - multiplying a plain value, a, and an encrypted value Enc(b), and obtaining Enc(a * b).
+//
+// The encrypted values are represented as big.Int and are serializable. This module also provides
+// JSON serialization for the PublicKey and the SecretKey.
+package paillier
+
+import (
+	"encoding/json"
+	"fmt"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// PaillierPrimeBits is the number of bits used to generate Paillier Safe Primes.
+const PaillierPrimeBits = 1024
+
+type (
+	// PublicKey is a Paillier public key: N = P*Q; for safe primes P,Q.
+	PublicKey struct {
+		N  *big.Int // N = PQ
+		N2 *big.Int // N² computed and cached to prevent re-computation.
+	}
+
+	// PublicKeyJson encapsulates the data that is serialized to JSON.
+	// It is used internally and not for external use. Public so other pieces
+	// can use for serialization.
+	PublicKeyJson struct {
+		N *big.Int
+	}
+
+	// SecretKey is a Paillier secret key.
+	SecretKey struct {
+		PublicKey
+		Lambda  *big.Int // lcm(P - 1, Q - 1)
+		Totient *big.Int // Euler's totient: (P - 1) * (Q - 1)
+		U       *big.Int // L((N + 1)^λ(N) mod N²)−1 mod N
+	}
+
+	// SecretKeyJson encapsulates the data that is serialized to JSON.
+	// It is used internally and not for external use. Public so other pieces
+	// can use for serialization.
+	SecretKeyJson struct {
+		N, Lambda, Totient, U *big.Int
+	}
+
+	// Ciphertext in Pailler's cryptosystem: a value $c \in Z_{N²}$ .
+	Ciphertext *big.Int
+)
+
+var (
+	two = big.NewInt(2) // The odd prime
+)
+
+// NewKeys generates Paillier keys with `bits` sized safe primes.
+func NewKeys() (*PublicKey, *SecretKey, error) {
+	return keyGenerator(core.GenerateSafePrime, PaillierPrimeBits)
+}
+
+// keyGenerator generates Paillier keys with `bits` sized safe primes using function
+// `genSafePrime` to generate the safe primes.
+func keyGenerator(genSafePrime func(uint) (*big.Int, error), bits uint) (*PublicKey, *SecretKey, error) {
+	values := make(chan *big.Int, 2)
+	errors := make(chan error, 2)
+
+	var p, q *big.Int
+
+	for p == q {
+		for range []int{1, 2} {
+			go func() {
+				value, err := genSafePrime(bits)
+				values <- value
+				errors <- err
+			}()
+		}
+
+		for _, err := range []error{<-errors, <-errors} {
+			if err != nil {
+				return nil, nil, err
+			}
+		}
+
+		p, q = <-values, <-values
+	}
+
+	// Assemble the secret/public key pair.
+	sk, err := NewSecretKey(p, q)
+	if err != nil {
+		return nil, nil, err
+	}
+	return &sk.PublicKey, sk, nil
+}
+
+// NewSecretKey computes intermediate values based on safe primes p, q.
+func NewSecretKey(p, q *big.Int) (*SecretKey, error) {
+	if p == nil || q == nil {
+		return nil, internal.ErrNilArguments
+	}
+	// Pre-compute necessary values.
+	pm1 := new(big.Int).Sub(p, core.One) // P - 1
+	qm1 := new(big.Int).Sub(q, core.One) // Q - 1
+	n := new(big.Int).Mul(p, q)          // N = PQ
+	nn := new(big.Int).Mul(n, n)         // N²
+	lambda, err := lcm(pm1, qm1)         // λ(N) = lcm(P-1, Q-1)
+	if err != nil {
+		// Code coverage note: lcm returns error only if the inputs are nil, which can never happen here.
+		return nil, err
+	}
+	totient := new(big.Int).Mul(pm1, qm1) // 𝝋(N) = (P-1)(Q-1)
+	pk := PublicKey{
+		N:  n,
+		N2: nn,
+	}
+
+	// (N+1)^λ(N) mod N²
+	t := new(big.Int).Add(n, core.One)
+	t.Exp(t, lambda, nn)
+
+	// L((N+1)^λ(N) mod N²)
+	u, err := pk.l(t)
+	if err != nil {
+		return nil, err
+	}
+	// L((N+1)^λ(N) mod N²)^-1 mod N
+	u.ModInverse(u, n)
+
+	return &SecretKey{pk, lambda, totient, u}, nil
+}
+
+// MarshalJSON converts the public key into json format.
+func (pk PublicKey) MarshalJSON() ([]byte, error) {
+	data := PublicKeyJson{pk.N}
+	return json.Marshal(data)
+}
+
+// UnmarshalJSON converts the json data into this public key.
+func (pk *PublicKey) UnmarshalJSON(bytes []byte) error {
+	data := new(PublicKeyJson)
+	if err := json.Unmarshal(bytes, data); err != nil {
+		return err
+	}
+	if data.N == nil {
+		return nil
+	}
+	pk.N = data.N
+	pk.N2 = new(big.Int).Mul(data.N, data.N)
+	return nil
+}
+
+// lcm calculates the least common multiple.
+func lcm(x, y *big.Int) (*big.Int, error) {
+	if x == nil || y == nil {
+		return nil, internal.ErrNilArguments
+	}
+	gcd := new(big.Int).GCD(nil, nil, x, y)
+	if core.ConstantTimeEq(gcd, core.Zero) {
+		return core.Zero, nil
+	}
+	// Compute least common multiple: https://en.wikipedia.org/wiki/Least_common_multiple#Calculation .
+	b := new(big.Int)
+	return b.Abs(b.Mul(b.Div(x, gcd), y)), nil
+}
+
+// l computes a residuosity class of n^2: (x - 1) / n.
+// Where it is the quotient x - 1 divided by n not modular multiplication of x - 1 times
+// the modular multiplicative inverse of n. The function name comes from [P99].
+func (pk *PublicKey) l(x *big.Int) (*big.Int, error) {
+	if x == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	if core.ConstantTimeEq(pk.N, core.Zero) {
+		return nil, internal.ErrNCannotBeZero
+	}
+
+	// Ensure x = 1 mod N
+	if !core.ConstantTimeEq(new(big.Int).Mod(x, pk.N), core.One) {
+		return nil, internal.ErrResidueOne
+	}
+
+	// Ensure x ∈ Z_N²
+	if err := core.In(x, pk.N2); err != nil {
+		return nil, err
+	}
+
+	// (x - 1) / n
+	b := new(big.Int).Sub(x, core.One)
+	return b.Div(b, pk.N), nil
+}
+
+// NewPubkey initializes a Paillier public key with a given n.
+func NewPubkey(n *big.Int) *PublicKey {
+	// BUG(arash): TODO: It will segfault if n is nil. Refactor to check for it.
+	return &PublicKey{
+		N:  n,
+		N2: new(big.Int).Mul(n, n), // Compute and cache N²
+	}
+}
+
+// Add combines two Paillier ciphertexts.
+func (pk *PublicKey) Add(c, d Ciphertext) (Ciphertext, error) {
+	if c == nil || d == nil {
+		return nil, internal.ErrNilArguments
+	}
+	// Ensure c,d ∈ Z_N²
+	cErr := core.In(c, pk.N2)
+	dErr := core.In(d, pk.N2)
+	// Constant time error check
+	var err error
+	if cErr != nil {
+		err = cErr
+	}
+	if dErr != nil {
+		err = dErr
+	}
+	if err != nil {
+		return nil, err
+	}
+
+	ctxt, err := core.Mul(c, d, pk.N2)
+	if err != nil {
+		// Code coverage note: core.Mul returns error only if the inputs are nil, which can never happen here.
+		return nil, err
+	}
+	return ctxt, nil
+}
+
+// Mul is equivalent to adding two Paillier exponents.
+func (pk *PublicKey) Mul(a *big.Int, c Ciphertext) (Ciphertext, error) {
+	if a == nil || c == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Ensure a ∈ Z_N
+	aErr := core.In(a, pk.N)
+	// Ensure c ∈ Z_N²
+	cErr := core.In(c, pk.N2)
+
+	var err error
+
+	// Constant time error check
+	if aErr != nil {
+		err = aErr
+	}
+	if cErr != nil {
+		err = cErr
+	}
+	if err != nil {
+		return nil, err
+	}
+	return new(big.Int).Exp(c, a, pk.N2), nil
+}
+
+// Encrypt produces a ciphertext on input message.
+func (pk *PublicKey) Encrypt(msg *big.Int) (Ciphertext, *big.Int, error) {
+	// generate a nonce: r \in Z**_N
+	r, err := core.Rand(pk.N)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Generate and return the ciphertext
+	ct, err := pk.encrypt(msg, r)
+	return ct, r, err
+}
+
+// encrypt produces a ciphertext on input a message and nonce.
+func (pk *PublicKey) encrypt(msg, r *big.Int) (Ciphertext, error) {
+	if msg == nil || r == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Ensure msg ∈ Z_N
+	if err := core.In(msg, pk.N); err != nil {
+		return nil, err
+	}
+
+	// Ensure r ∈ Z^*_N: we use the method proved in docs/[EL20]
+	// ensure r ∈ Z^_N-{0}
+	if err := core.In(r, pk.N); err != nil {
+		return nil, err
+	}
+	if core.ConstantTimeEq(r, core.Zero) {
+		return nil, fmt.Errorf("r cannot be 0")
+	}
+
+	// Compute the ciphertext components: ɑ, β
+	// ɑ = (N+1)^m (mod N²)
+	ɑ := new(big.Int).Add(pk.N, core.One)
+	ɑ.Exp(ɑ, msg, pk.N2)
+	β := new(big.Int).Exp(r, pk.N, pk.N2) // β = r^N (mod N²)
+
+	// ciphertext = ɑ*β = (N+1)^m * r^N  (mod N²)
+	c, err := core.Mul(ɑ, β, pk.N2)
+	if err != nil {
+		// Code coverage note: core.Mul returns error only if the inputs are nil, which can never happen here.
+		return nil, err
+	}
+	return c, nil
+}
+
+// Decrypt is the reverse operation of Encrypt.
+func (sk *SecretKey) Decrypt(c Ciphertext) (*big.Int, error) {
+	if c == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Ensure C ∈ Z_N²
+	if err := core.In(c, sk.N2); err != nil {
+		return nil, err
+	}
+
+	// Compute the msg in components
+	// ɑ ≡ c^{λ(N)}		mod N²
+	ɑ := new(big.Int).Exp(c, sk.Lambda, sk.N2)
+
+	// l = L(ɑ, N)
+	ell, err := sk.l(ɑ)
+	if err != nil {
+		return nil, err
+	}
+
+	// Compute the msg
+	// m ≡ lu = L(ɑ)*u = L(c^{λ(N)})*u	mod N
+	m, err := core.Mul(ell, sk.U, sk.N)
+	if err != nil {
+		return nil, err
+	}
+	return m, nil
+}
+
+// MarshalJSON converts the secret key into json format.
+func (sk SecretKey) MarshalJSON() ([]byte, error) {
+	data := SecretKeyJson{
+		sk.N,
+		sk.Lambda,
+		sk.Totient,
+		sk.U,
+	}
+	return json.Marshal(data)
+}
+
+// UnmarshalJSON converts the json data into this secret key.
+func (sk *SecretKey) UnmarshalJSON(bytes []byte) error {
+	data := new(SecretKeyJson)
+	if err := json.Unmarshal(bytes, data); err != nil {
+		return err
+	}
+	if data.N != nil {
+		sk.N = data.N
+		sk.N2 = new(big.Int).Mul(data.N, data.N)
+	}
+	sk.U = data.U
+	sk.Totient = data.Totient
+	sk.Lambda = data.Lambda
+	return nil
+}
diff --git a/pkg/paillier/paillier_test.go b/pkg/paillier/paillier_test.go
new file mode 100644
index 00000000..2e060a8b
--- /dev/null
+++ b/pkg/paillier/paillier_test.go
@@ -0,0 +1,1067 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package paillier
+
+import (
+	"encoding/hex"
+	"errors"
+	"fmt"
+	"log"
+	"math/big"
+	"testing"
+
+	tt "github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+
+	"github.com/stretchr/testify/assert"
+)
+
+var (
+	x         = tt.B10("7146643783615963513942641287213372249533955323510461217840179896547799100626220786140425637990097431")
+	y         = tt.B10("1747698065194620177681258504464368264357359841192790848951902311522815739310792522712583635858354245")
+	N         = tt.B10("85832751158419329546684678412285185885848111422509523329716452068504806021136687603399722116388773253")
+	NminusOne = new(big.Int).Sub(N, crypto.One)
+	NplusOne  = new(big.Int).Add(N, crypto.One)
+	hundoN    = new(big.Int).Mul(N, big.NewInt(100))
+
+	NN         = new(big.Int).Mul(N, N)
+	NNminusOne = new(big.Int).Sub(NN, crypto.One)
+	NNplusOne  = new(big.Int).Add(NN, crypto.One)
+)
+
+func Example_encryptDecrypt() {
+	// Skip this example if -short parameter is passed.
+	if testing.Short() {
+		// Printing the expected output so that the test succeeds.
+		fmt.Println("Succeeded in encrypting and decrypting the input message: Hello World!")
+		return
+	}
+	hexMessage := hex.EncodeToString([]byte("Hello World!"))
+	mappedMessage, ok := new(big.Int).SetString(hexMessage, 16)
+	if !ok {
+		panic("Error mapping message to scalar point.")
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	// Ignoring the random value that was generated internally by `Encrypt`.
+	cipher, _, err := pub.Encrypt(mappedMessage)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	// Now decrypt using the secret key.
+	decrypted, err := sec.Decrypt(cipher)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+
+	decoded := string(decrypted.Bytes())
+	fmt.Println("Succeeded in encrypting and decrypting the input message:", decoded)
+
+	// Output:
+	// Succeeded in encrypting and decrypting the input message: Hello World!
+}
+
+func Example_homomorphicAddition() {
+	// Skip this example if -short parameter is passed.
+	if testing.Short() {
+		// Printing the expected output so that the test succeeds.
+		fmt.Println("Encrypting 123 and 456 separately.")
+		fmt.Println("Adding their encrypted versions together.")
+		fmt.Println("Succeeded in decrypting 579")
+		return
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	msg1 := tt.B10("123")
+	msg2 := tt.B10("456")
+	fmt.Printf("Encrypting %s and %s separately.\n", msg1, msg2)
+
+	cipher1, _, err := pub.Encrypt(msg1)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+	cipher2, _, err := pub.Encrypt(msg2)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	fmt.Println("Adding their encrypted versions together.")
+	cipher3, err := pub.Add(cipher1, cipher2)
+	if err != nil {
+		log.Fatalf("Error in adding the two ciphertexts: %v", err)
+	}
+	decrypted3, err := sec.Decrypt(cipher3)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+	fmt.Println("Succeeded in decrypting", decrypted3)
+
+	// Output:
+	// Encrypting 123 and 456 separately.
+	// Adding their encrypted versions together.
+	// Succeeded in decrypting 579
+}
+
+func Example_homomorphicMultiplication() {
+	// Skip this example if -short parameter is passed.
+	if testing.Short() {
+		// Printing the expected output so that the test succeeds.
+		fmt.Println("Encrypting 10.")
+		fmt.Println("Multiplying plain 5 with the encrypted 10.")
+		fmt.Println("Succeeded in decrypting 50.")
+		return
+	}
+	pub, sec, err := NewKeys()
+	if err != nil {
+		log.Fatalf("Error in generating keypair: %v", err)
+	}
+
+	msg1 := tt.B10("10")
+	msg2 := tt.B10("5")
+	fmt.Printf("Encrypting %s.\n", msg1)
+
+	cipher1, _, err := pub.Encrypt(msg1)
+	if err != nil {
+		log.Fatalf("Error in Encrypting the message: %v", err)
+	}
+
+	fmt.Printf("Multiplying plain %s with the encrypted %s.\n", msg2, msg1)
+	cipher3, err := pub.Mul(msg2, cipher1)
+	if err != nil {
+		log.Fatalf("Error in adding the two ciphertexts: %v", err)
+	}
+	decrypted3, err := sec.Decrypt(cipher3)
+	if err != nil {
+		log.Fatalf("Error in Decrypting the ciphertext: %v", err)
+	}
+	fmt.Printf("Succeeded in decrypting %s.\n", decrypted3)
+
+	// Output:
+	// Encrypting 10.
+	// Multiplying plain 5 with the encrypted 10.
+	// Succeeded in decrypting 50.
+}
+
+func TestGenerateSafePrimes(t *testing.T) {
+	if testing.Short() {
+		t.Skip("Skipping TestGenerateSafePrimes")
+	}
+	p, err := crypto.GenerateSafePrime(32)
+	if err != nil {
+		t.Errorf("GenerateSafePrime failed: %v", err)
+	}
+	if !p.ProbablyPrime(8) {
+		t.Errorf("GenerateSafePrime didn't return a prime number: %v", p)
+	}
+	p, err = crypto.GenerateSafePrime(3)
+	if err != nil {
+		t.Errorf("GenerateSafePrime failed: %v", err)
+	}
+	if !p.ProbablyPrime(8) {
+		t.Errorf("GenerateSafePrime didn't return a prime number: %v", p)
+	}
+}
+
+func TestGenerateSafePrimesLong(t *testing.T) {
+	if testing.Short() {
+		t.Skip("Skipping TestGenerateSafePrimesLong")
+	}
+	p, err := crypto.GenerateSafePrime(1024)
+	if err != nil {
+		t.Errorf("GenerateSafePrime failed: %v", err)
+	}
+	if !p.ProbablyPrime(8) {
+		t.Errorf("GenerateSafePrime didn't return a prime number: %v", p)
+	}
+	if p.BitLen() != 1024 {
+		t.Errorf("GenerateSafePrime didn't return a prime number with the exact bits")
+	}
+}
+
+func TestGenerateSafePrimesTooLow(t *testing.T) {
+	_, err := crypto.GenerateSafePrime(2)
+	tt.AssertSomeError(t, err)
+}
+
+type lcmTest struct {
+	x        *big.Int
+	y        *big.Int
+	err      error
+	expected *big.Int
+}
+
+func runTestLcm(t *testing.T, testArgs []lcmTest) {
+	for _, arg := range testArgs {
+		a, err := lcm(arg.x, arg.y)
+		if err != nil && arg.err == nil {
+			t.Errorf("lcm failed: %v", err)
+		}
+		if a == nil && arg.expected != nil || a.Cmp(arg.expected) != 0 {
+			t.Errorf("lcm failed. Expected %v, found: %v", arg.expected, a)
+		}
+	}
+}
+
+func TestLcm(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x:        big.NewInt(4),
+			y:        big.NewInt(6),
+			err:      nil,
+			expected: big.NewInt(12),
+		},
+		{
+			x:        big.NewInt(10),
+			y:        big.NewInt(22),
+			err:      nil,
+			expected: big.NewInt(110),
+		},
+		{
+			x:        big.NewInt(1),
+			y:        big.NewInt(3),
+			err:      nil,
+			expected: big.NewInt(3),
+		},
+		{
+			x:        big.NewInt(5),
+			y:        big.NewInt(7),
+			err:      nil,
+			expected: big.NewInt(35),
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLcmCommutative(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x:        big.NewInt(11),
+			y:        big.NewInt(7),
+			err:      nil,
+			expected: big.NewInt(77),
+		},
+		{
+			x:        big.NewInt(7),
+			y:        big.NewInt(11),
+			err:      nil,
+			expected: big.NewInt(77),
+		},
+		{
+			x:        big.NewInt(13),
+			y:        big.NewInt(23),
+			err:      nil,
+			expected: big.NewInt(299),
+		},
+		{
+			x:        big.NewInt(23),
+			y:        big.NewInt(13),
+			err:      nil,
+			expected: big.NewInt(299),
+		},
+		{
+			x:        big.NewInt(-23),
+			y:        big.NewInt(17),
+			err:      nil,
+			expected: big.NewInt(391),
+		},
+		{
+			x:        big.NewInt(23),
+			y:        big.NewInt(-17),
+			err:      nil,
+			expected: big.NewInt(391),
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLcmNegNums(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x:        big.NewInt(-5),
+			y:        big.NewInt(-7),
+			err:      nil,
+			expected: big.NewInt(35),
+		},
+		{
+			x:        big.NewInt(-5),
+			y:        big.NewInt(7),
+			err:      nil,
+			expected: big.NewInt(35),
+		},
+		{
+			x:        big.NewInt(3),
+			y:        big.NewInt(-11),
+			err:      nil,
+			expected: big.NewInt(33),
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLcmNil(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x:        nil,
+			y:        big.NewInt(1),
+			err:      errors.New("arguments cannot be nil"),
+			expected: nil,
+		},
+		{
+			x:        big.NewInt(1),
+			y:        nil,
+			err:      errors.New("arguments cannot be nil"),
+			expected: nil,
+		},
+		{
+			x:        nil,
+			y:        nil,
+			err:      errors.New("arguments cannot be nil"),
+			expected: nil,
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLcmZero(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x:        big.NewInt(0),
+			y:        big.NewInt(1),
+			err:      nil,
+			expected: big.NewInt(0),
+		},
+		{
+			x:        big.NewInt(0),
+			y:        big.NewInt(0),
+			err:      nil,
+			expected: big.NewInt(0),
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLcmBigPrimes(t *testing.T) {
+	x := new(big.Int)
+	y := new(big.Int)
+	// Generated by OpenSSL
+	x.SetString("133788347333574532510542341875219452703250094560184213896952738579939377079849213618116996737030817731544214409221015150233522821287955673536671953914660520267670984696713816508768479853621956967492030516224494353641551367310541202655075859386716364585825364092974073148178887544704793573033779774765431460367", 10)
+	y.SetString("121400263190232595456200749546561304956161672968687911935494950378721768184159069938532869288284686583150658925255722159156454219960265942696166947144912738151554579878178746701374346180640493532962639632666540478486867810588884360492830920363713588684509182704981665082591486786717530494254613085570321507623", 10)
+	expected := new(big.Int)
+	expected.SetString("16241940578082201531943448855852277578391761356628379864603641922876623601321625229339135653813019543205064366507109899018615521640687222340376734033815591736764469510811142260074144789284382858541066390183237904579674336717818949214144339382239132186500111594251680147962383065732964214151653795512167674648653475620307856642151695559944756719719799945193072239010815330021803557074201060705849949820706127488164694762724694756011467249889383401729777382247223470577114290663770295230883950621358271613200219512401437571399087878832070221157976750549142719310423012055140771277730139053532825828483343855582012877641", 10)
+
+	x2 := new(big.Int)
+	x2.SetString("133788347333574532510542341875219452703250094560184213896952738579939377079849213618116996737030817731544214409221015150233522821287955673536671953914660520267670984696713816508768479853621956967492030516224494353641551367310541202655075859386716364585825364092974073148178887544704793573033779774765431460367", 10)
+
+	x3 := new(big.Int)
+	y3 := new(big.Int)
+	x3.SetString("199624032515728289045241179631920514454939035695180729995055822158745789192452713406851424173447485774951354235728394322982696160719973464933778580097775959312681723073700577658531340015313241640799019163953248377211698591166024389845418771351325354733438115315318038016037617205770677410860231617155107859183", 10)
+	y3.SetString("142249905617339142091532152811520246816977809135348639617427185924289265672711180486386239769195440660717504105473521478033326628103915862155595134226885191558983128407247227273401068113332266238311624168954823649558019882800072911119616964386221647824743035538953625688976296691147616508925455607033114354959", 10)
+	expected2 := new(big.Int)
+	expected2.SetString("28396499784314989096609919418127345447157066075586506422680304338142086939236798450800279134642308338458035596559017626154823247809313781525454242216477721507296693149109832139024597927259443182893280359146077724553052468871051438675286719817790943900280362711254811533504902741179161752948522341835287769530110541739921633871308290020066875307078092554117637608375242902999872137629980200197702760214658136789637368191031173973090138816890631056194895911511193868568337270184231814553242352572122713100022187023932306383784997785740075483768764231396924369937421906728046753885386778340930941242102624489916449738497", 10)
+	testArgs := []lcmTest{
+		{
+			x, y, nil, expected,
+		},
+		{
+			x:        x2,
+			y:        big.NewInt(1),
+			err:      nil,
+			expected: x2,
+		},
+		{
+			x:        x3,
+			y:        y3,
+			err:      nil,
+			expected: expected2,
+		},
+	}
+	runTestLcm(t, testArgs)
+}
+
+func TestLKnownCases(t *testing.T) {
+	// test multiples of 5 for L
+	pk := NewPubkey(big.NewInt(5))
+	tests := []struct {
+		in, expected *big.Int
+	}{
+		{big.NewInt(6), big.NewInt(1)},
+		{big.NewInt(11), big.NewInt(2)},
+		{big.NewInt(16), big.NewInt(3)},
+		{big.NewInt(21), big.NewInt(4)},
+	}
+
+	for _, test := range tests {
+		r, err := pk.l(test.in)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, r, test.expected)
+	}
+}
+
+func TestLFailureCases(t *testing.T) {
+	pk := NewPubkey(big.NewInt(5))
+	tests := []*big.Int{
+		pk.N,                // u = N should fail
+		big.NewInt(25),      // u = NN should fail
+		big.NewInt(51),      // u > NN should fail
+		big.NewInt(9),       // u ≢ 1 (mod 5) should fail
+		big.NewInt(12),      // u ≢ 1 (mod 5) should fail
+		big.NewInt(22),      // u ≢ 1 (mod 5) should fail
+		big.NewInt(-1),      // negative N should fail
+		big.NewInt(-100000), // negative N should fail
+		nil,                 // nil should fail
+	}
+
+	for _, test := range tests {
+		_, err := pk.l(test)
+		tt.AssertSomeError(t, err)
+	}
+}
+
+type keygenTest struct {
+	bits                        uint
+	p, q, n, lambda, totient, u *big.Int
+}
+
+func TestKeyGen(t *testing.T) {
+	testValues := []*keygenTest{
+		// Small values
+		{
+			bits:    32,
+			p:       tt.B10("4294967387"),
+			q:       tt.B10("8589936203"),
+			n:       tt.B10("36893495848295611561"),
+			lambda:  tt.B10("18446747917705353986"),
+			totient: tt.B10("36893495835410707972"),
+			u:       tt.B10("30227647593197281524"),
+		},
+		{
+			bits:    32,
+			p:       tt.B10("2404778303"),
+			q:       tt.B10("2907092159"),
+			n:       tt.B10("6990912148784626177"),
+			lambda:  tt.B10("3495456071736377858"),
+			totient: tt.B10("6990912143472755716"),
+			u:       tt.B10("3614931622846492468"),
+		},
+		// Moderate values
+		{
+			bits:    128,
+			p:       tt.B10("505119856506205319276795183398241487263"),
+			q:       tt.B10("205972782400928578615836152187141707579"),
+			n:       tt.B10("104040942290540895974307747626520134740467527950099359068592315888198399066277"),
+			lambda:  tt.B10("52020471145270447987153873813260067369878217655596112585349842276306507935718"),
+			totient: tt.B10("104040942290540895974307747626520134739756435311192225170699684552613015871436"),
+			u:       tt.B10("95814396947082822381619843641016289162443592153179788942685091512428172029465"),
+		},
+		{
+			bits:    128,
+			p:       tt.B10("335833617445150372903755348587631934583"),
+			q:       tt.B10("275426149345634030797050866270209482803"),
+			n:       tt.B10("92497360073732512809517386349687056338889420300408887876944500444198759476149"),
+			lambda:  tt.B10("46248680036866256404758693174843528169139080266809051736621847114670459029382"),
+			totient: tt.B10("92497360073732512809517386349687056338278160533618103473243694229340918058764"),
+			u:       tt.B10("37541288371367874015853812738289992945377756025517882548300075720005348319216"),
+		},
+		{
+			bits:    256,
+			p:       tt.B10("115645895734860215235155088728394909334688633450524492586690742412129345961183"),
+			q:       tt.B10("94298418052417649431120534110853375174108454456092458684756344618179781451887"),
+			n:       tt.B10("10905225022052151768592443014939079805820716955892154646109970627753805040740378163517568530133182652794506558827042053659527293884287341299235199284102321"),
+			totient: tt.B10("10905225022052151768592443014939079805820716955892154646109970627753805040740168219203781252268516377171667310542533256571620676933015894212204890156689252"),
+			lambda:  tt.B10("5452612511026075884296221507469539902910358477946077323054985313876902520370084109601890626134258188585833655271266628285810338466507947106102445078344626"),
+			u:       tt.B10("169122108559803116345465577435019987080055058605295565203286696962456365170552011215103788832323625338104327792007096903690940420144823974727816140829004"),
+		},
+		{
+			bits:    384,
+			p:       tt.B10("36006692832910486705531921197379033634897461505036495703751117530881437756504623602114452424392242359949564580091963"),
+			q:       tt.B10("36321876854655342367765793082986061200135195654801162378979445503936881469720608843798409137541849432902150243071007"),
+			n:       tt.B10("1307830663020375807860069772466605443871885822612939940958802361999351292929784401772312287232210036471265772358253561264090635848856642357599288411446282200143037556882504679979558002244844355483553171478292766242112114935599016741"),
+			totient: tt.B10("1307830663020375807860069772466605443871885822612939940958802361999351292929784401772312287232210036471265772358253488935520948283027569059885008046351447167485877719224421949416523183925618130251107258616730832150319263220775853772"),
+			lambda:  tt.B10("653915331510187903930034886233302721935942911306469970479401180999675646464892200886156143616105018235632886179126744467760474141513784529942504023175723583742938859612210974708261591962809065125553629308365416075159631610387926886"),
+			u:       tt.B10("715317338270237792745674161133027331913306953524485480270742409164181533024685207574377116318911340995248759257081568534206599002649096879000033274962046481163095418392051555090184840289513260640923181142724977346034839256290483076"),
+		},
+		// Large values
+		{
+			bits:    512,
+			p:       tt.B10("13334877681824046536664719753000692481615243060546695171749157112026072862294410162436291925578885141357927002155461724765584886877402066038258074266638227"),
+			q:       tt.B10("12122745362522189816168535264551355768089283231069686330301128627041958196835868405970767150401427191976786435200511843851744213149595052566013030642866907"),
+			n:       tt.B10("161655326577133109177725996877941503037044267143093183990772875721980297379977570900477874093780897364088511586139843445141992295002878403748750051858500001631307112890860155944955185080369964944108396477646372269079498823545159135772467319334869864305928043113234061678778620562861360302446649667820279453889"),
+			totient: tt.B10("161655326577133109177725996877941503037044267143093183990772875721980297379977570900477874093780897364088511586139843445141992295002878403748750051858499976173684068544623803111700167528321715239582104861264870218793759755514100005493898912275793883993594708399796705705210003233761333305328045396715369948756"),
+			lambda:  tt.B10("80827663288566554588862998438970751518522133571546591995386437860990148689988785450238937046890448682044255793069921722570996147501439201874375025929249988086842034272311901555850083764160857619791052430632435109396879877757050002746949456137896941996797354199898352852605001616880666652664022698357684974378"),
+			u:       tt.B10("143261270242335180420072816055839865064298362037063587448317467367577401621254503191376775173811231300545030557865973916661565869494495913728327166081853904903334058396967815592631415604767903602152339275761555997082956433277741333963496039496540726125762611561934388357363014028934069272035911913194424272603"),
+		},
+		{
+			bits:    768,
+			p:       tt.B10("1346090925391135119143470623782502005582449208798686393499686094146720873293257316154858443761764176763426496081748327594475673914483978883075080616518148610864446133054517784818794038700373924492201179029136162262578223994386497407"),
+			q:       tt.B10("1267888740317619255987103204389173685200460862251480292534873171503916906509928280188817985770625788023592223617980306560361856737457586891910981446078699966027435065022526191471061668427090194699255004927681350300606724099539148139"),
+			n:       tt.B10("1706693527747144711594288434414073474898396319145231571914859473075446769444443882426378206783148798161228984036593560566511416432995440677335990047411064284625144780381208381275798262584775575885562112174608693614583699626181565327188316266582808161080083810509077419565819105286361318424233748287133200189491965280880943430756926385486914657888021988499576975592342792662208243895780558951878131107691067112167457219510292850345325644694079605526537816712375573"),
+			totient: tt.B10("1706693527747144711594288434414073474898396319145231571914859473075446769444443882426378206783148798161228984036593560566511416432995440677335990047411064284625144780381208381275798262584775575885562112174608693614583699626181565324574336600874053785949509982337401728782909034236194632389674482636495420386306368937204513898366961598468194958159387833662046323650777017676146181298931982059996933030647090822311750092046173658889141687876567042341589722786730028"),
+			lambda:  tt.B10("853346763873572355797144217207036737449198159572615785957429736537723384722221941213189103391574399080614492018296780283255708216497720338667995023705532142312572390190604190637899131292387787942781056087304346807291849813090782662287168300437026892974754991168700864391454517118097316194837241318247710193153184468602256949183480799234097479079693916831023161825388508838073090649465991029998466515323545411155875046023086829444570843938283521170794861393365014"),
+			u:       tt.B10("779879106968621551612916279464123438735012661607976871766884426257741506106933684516528094230394847057111517560275304735511075756729605155799199673159820709716869729022492405360829062001458468008371167876032343417620981083465124988041616116692784740773729428828021798152577117895496702246006365934433098458747623402795759758566365836593488130254049427800131843438461226605279227891251815575333006410913379796415963477224332006612563517643916428864744112156376520"),
+		},
+		{
+			bits:    1024,
+			p:       tt.B10("323048346478810234804346724288317979049543453886657577003300101860710127877799870550562838407667268404599358826513829060160504303395418566677040422188661745067470888457815635033321184439746580337024906877384167362567610372271431186610013379997212856608697550064099211785613236213633622219571487990672693003787"),
+			q:       tt.B10("289955956844872723713267618282085026937397801221604643862282902289352466511076698253093993268863225914839327563609168378629851975959785812001060859728689670901677697805606458924299545852498153652948060776824445669854015488773545309215892532182626763404124068861635361632889336491051975303142403383113070034867"),
+			n:       tt.B10("93669792410417391755898616958812213604373878875285824927431988118477734285768665211145268050244414695456141707631724902135831803247956851156058161652431398586664582925077157366114568914615913189006980440640666538921106871639116459047133240204886962593927223154881396777466153081835208630039047664120224812531738646998208894219436266840478325951526823776791414200683451217351791095609379048292074062880637329062218371522375097661526583290635879391529194601725476785472157424230313351359992497803391595095260449578824637692631790170131436072668730121222036510650215208397389118631464109460927478825133780143983053041329"),
+			lambda:  tt.B10("46834896205208695877949308479406106802186939437642912463715994059238867142884332605572634025122207347728070853815862451067915901623978425578029080826215699293332291462538578683057284457307956594503490220320333269460553435819558229523566620102443481296963611577440698388733076540917604315019523832060112406265562821347442605630459326248953961472769941260841575989908934106600864250610251239744208615602053417371389842566126050111368113505640337506425546659904062684751504418983445628701185883755573430552643740962308012330105082154543229788421412104521098445318696794735827272606480768378120940651209944385098645001338"),
+			totient: tt.B10("93669792410417391755898616958812213604373878875285824927431988118477734285768665211145268050244414695456141707631724902135831803247956851156058161652431398586664582925077157366114568914615913189006980440640666538921106871639116459047133240204886962593927223154881396777466153081835208630039047664120224812531125642694885211260918652497907922945539882521683151979817868213201728501220502479488417231204106834742779685132252100222736227011280675012851093319808125369503008837966891257402371767511146861105287481924616024660210164309086459576842824209042196890637393589471654545212961536756241881302419888770197290002676"),
+			u:       tt.B10("38135949745652485811937226692116929429180649272477224483199257365577156885532690396567815884583937557608568699362433418166707048319324785327166624071125908609604488150973723257324029836008236113484260165701873141666619439620722921574373345283540196413007597899672199365492304562415424130214337263020773327553873482407654450455061737687873828877767689823341811598685374044652873284145859288532695538432223451947587392094598520855737584462011917578978549967062842845942828735580257392245879142299251014137170130879720213249399499545177941592508341271051010776972469394170182828098805388982944454017008931873419560331115"),
+		},
+	}
+
+	for _, test := range testValues {
+		idx := 0
+		safePrimes := []*big.Int{test.p, test.q}
+		f := func(bits uint) (*big.Int, error) {
+			r := safePrimes[idx]
+			idx = (idx + 1) % 2
+			return r, nil
+		}
+
+		pub, sec, err := keyGenerator(f, test.bits)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, pub.N, test.n)
+		tt.AssertBigIntEq(t, sec.Totient, test.totient)
+		tt.AssertBigIntEq(t, sec.Lambda, test.lambda)
+		tt.AssertBigIntEq(t, sec.U, test.u)
+	}
+}
+
+func TestKeyGeneratorErrorConditions(t *testing.T) {
+	// Should fail if a safe prime cannot be generated.
+	f := func(bits uint) (*big.Int, error) {
+		return nil, fmt.Errorf("safeprime error")
+	}
+	_, _, err := keyGenerator(f, 1)
+	tt.AssertError(t, err, "safeprime error")
+
+	// Should fail if a gcd of p and q is zero.
+	val := int64(0)
+	oneF := func(bits uint) (*big.Int, error) {
+		b := big.NewInt(val)
+		val += 1
+		return b, nil
+	}
+	_, _, err = keyGenerator(oneF, 1)
+	tt.AssertError(t, err, "N cannot be 0")
+}
+
+func TestKeyGenSameInput(t *testing.T) {
+	p := tt.B10("4294967387")
+	q := tt.B10("8589936203")
+	idx := 0
+	safePrimes := []*big.Int{p, q}
+	f := func(bits uint) (*big.Int, error) {
+		r := safePrimes[idx]
+		idx = (idx + 1) % 2
+		return r, nil
+	}
+	pub1, sec1, err := keyGenerator(f, 32)
+	tt.AssertNoError(t, err)
+	pub2, sec2, err := keyGenerator(f, 32)
+	tt.AssertNoError(t, err)
+	tt.AssertBigIntEq(t, pub1.N, pub2.N)
+	tt.AssertBigIntEq(t, sec1.Lambda, sec2.Lambda)
+	tt.AssertBigIntEq(t, sec1.Totient, sec2.Totient)
+	tt.AssertBigIntEq(t, sec1.U, sec2.U)
+}
+
+func TestNewKeysDistinct(t *testing.T) {
+	if testing.Short() {
+		t.Skip("Skipping TestNewKeys")
+	}
+	pub1, sec1, err := NewKeys()
+	tt.AssertNoError(t, err)
+	pub2, sec2, err := NewKeys()
+	tt.AssertNoError(t, err)
+	// Ensure two fresh keys are distinct
+	tt.AssertBigIntNe(t, pub1.N, pub2.N)
+	tt.AssertBigIntNe(t, sec1.Totient, sec2.Totient)
+	tt.AssertBigIntNe(t, sec1.Lambda, sec2.Lambda)
+	tt.AssertBigIntNe(t, sec1.U, sec2.U)
+}
+
+// Tests the restrictions on input values for paillier.Add
+func TestAddErrorConditions(t *testing.T) {
+	pk := NewPubkey(N)
+
+	var tests = []struct {
+		x, y         *big.Int
+		expectedPass bool
+	}{
+		// Good: 0 ≤ x,y < N²
+		{crypto.Zero, crypto.One, true},
+		{NminusOne, big.NewInt(1024), true}, // N-1, 1024
+		{NplusOne, hundoN, true},            // N+1, 100N
+		{crypto.One, NNminusOne, true},      // one, N²-1
+
+		// Bad
+		{big.NewInt(-1), crypto.One, false},       // Negative values
+		{crypto.One, big.NewInt(-1), false},       // Negative values
+		{big.NewInt(-1000000), crypto.One, false}, // Negative values
+		{crypto.One, big.NewInt(-9993654), false}, // Negative values
+
+		{nil, crypto.One, false}, // x nil
+		{crypto.One, nil, false}, // y nil
+
+		{NNplusOne, crypto.One, false},                // N²+1
+		{NNplusOne, NNplusOne, false},                 // both bad
+		{crypto.One, NNplusOne, false},                // N²+1
+		{new(big.Int).Add(NN, NN), crypto.One, false}, // 2N²
+		{crypto.One, new(big.Int).Add(NN, NN), false}, // 2N²
+		{NN, crypto.One, false},                       // = N²
+		{crypto.One, NN, false},                       // = N²
+
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		_, err := pk.Add(test.x, test.y)
+		if test.expectedPass {
+			tt.AssertNoError(t, err)
+		} else {
+			tt.AssertSomeError(t, err)
+		}
+	}
+
+}
+
+// Tests for paillier addition with known answers
+func TestAdd(t *testing.T) {
+	z9 := NewPubkey(big.NewInt(3))
+	pk := NewPubkey(N)
+
+	// Pre-compute values for testing
+	NplusOne := NplusOne
+	// z = 2N+1
+	z := new(big.Int).Add(N, N)
+	z.Add(z, crypto.One)
+
+	var tests = []struct {
+		pk             *PublicKey
+		x, y, expected *big.Int
+	}{
+		// Small number tests: Z_9
+		{z9, big.NewInt(0), big.NewInt(1), big.NewInt(0)},
+		{z9, big.NewInt(1), big.NewInt(5), big.NewInt(5)},
+		{z9, big.NewInt(2), big.NewInt(2), big.NewInt(4)},
+		{z9, big.NewInt(5), big.NewInt(2), big.NewInt(1)},
+		{z9, big.NewInt(6), big.NewInt(8), big.NewInt(3)},
+		{z9, big.NewInt(7), big.NewInt(7), big.NewInt(4)},
+		{z9, big.NewInt(2), big.NewInt(4), big.NewInt(8)},
+		{z9, big.NewInt(8), big.NewInt(8), big.NewInt(1)},
+		{z9, big.NewInt(8), big.NewInt(2), big.NewInt(7)},
+
+		// large number tests: Z_N²
+		{pk, N, crypto.Zero, crypto.Zero},
+		{pk, N, N, crypto.Zero}, // N² ≡ 0 (N²)
+		{pk, crypto.Zero, NplusOne, crypto.Zero},
+		{pk, NplusOne, NplusOne, z}, // (N+1)² = N² + 2N + 1 ≡ 2N + 1 (N²)
+		{pk, tt.B10("11659564086467828628"), tt.B10("57089538512338875950"), tt.B10("665639132951488346363609789106750696600")},
+	}
+	// All the tests!
+	for _, test := range tests {
+		actual, err := test.pk.Add(test.x, test.y)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// Tests the restrictions on input values for paillier.Mul
+func TestMulErrorConditions(t *testing.T) {
+	pk := NewPubkey(N)
+
+	var tests = []struct {
+		x, y         *big.Int
+		expectedPass bool
+	}{
+		// Good
+		{crypto.Zero, crypto.One, true},     // 0 ≤ x,y < N
+		{NminusOne, big.NewInt(1024), true}, // 0 ≤ x,y < N
+		{NminusOne, hundoN, true},           // N-1 < N; 100N < N²
+		{crypto.One, NNminusOne, true},      // 1 < N; N²-1 < N
+
+		// Bad
+		{big.NewInt(-1), crypto.One, false},       // Negative value x
+		{big.NewInt(-1000000), crypto.One, false}, // Negative values x
+		{crypto.One, big.NewInt(-9993654), false}, // Negative values y
+		{crypto.One, big.NewInt(-1), false},       // Negative value y
+		{big.NewInt(-1), big.NewInt(-1), false},   // Negative values both
+
+		{NplusOne, crypto.One, false},                 // x > N; y ok
+		{NplusOne, NNplusOne, false},                  // both x,y bad
+		{crypto.One, NNplusOne, false},                // y bad
+		{new(big.Int).Add(NN, NN), crypto.One, false}, // x really bad
+		{crypto.One, new(big.Int).Add(NN, NN), false}, // y bad
+		{N, crypto.One, false},                        // x boundary condition
+		{crypto.One, NN, false},                       // y boundary condition
+		{nil, crypto.One, false},                      // x nil
+		{crypto.One, nil, false},                      // y nil
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		_, err := pk.Mul(test.x, test.y)
+		if test.expectedPass {
+			tt.AssertNoError(t, err)
+		} else {
+			tt.AssertSomeError(t, err)
+		}
+	}
+}
+
+// Tests for paillier multiplication with known answers
+func TestMul(t *testing.T) {
+	z25 := NewPubkey(big.NewInt(5))
+	pk := NewPubkey(N)
+
+	// Compute: ɑ ≡ -2N -1  (N²)
+	alpha, err := crypto.Mul(N, big.NewInt(-2), NN)
+	assert.Nil(t, err)
+	alpha.Add(alpha, crypto.One)
+
+	var tests = []struct {
+		pk *PublicKey
+		// Note: these values are in reverse-order from the order passed in as args
+		c, a, expected *big.Int
+	}{
+		// Small number tests: Z_{25}
+		{z25, big.NewInt(1), big.NewInt(0), big.NewInt(1)},
+		{z25, big.NewInt(5), big.NewInt(1), big.NewInt(5)},
+		{z25, big.NewInt(2), big.NewInt(2), big.NewInt(4)},
+		{z25, big.NewInt(2), big.NewInt(1), big.NewInt(2)},
+		{z25, big.NewInt(8), big.NewInt(4), big.NewInt(21)},
+		{z25, big.NewInt(7), big.NewInt(3), big.NewInt(18)},
+		{z25, big.NewInt(6), big.NewInt(0), big.NewInt(1)},
+		{z25, big.NewInt(4), big.NewInt(3), big.NewInt(14)},
+		{z25, big.NewInt(8), big.NewInt(1), big.NewInt(8)},
+		{z25, big.NewInt(2), big.NewInt(2), big.NewInt(4)},
+
+		// large number tests
+		{pk, x, crypto.Zero, crypto.One},          // x^0 = 1
+		{pk, y, crypto.One, y},                    // y^1 = 1
+		{pk, crypto.Zero, NminusOne, crypto.Zero}, // 0^{N-1} = 0
+		{pk, NminusOne, two, alpha},               // (N-1)² = N² - 2N - 1 ≡ -2N -1 (N²)
+
+		// large number test: WorlframAlpha test case
+		{NewPubkey(tt.B10("66563913295148834609789506")),
+			tt.B10("11659564086467828628"),
+			tt.B10("57089538512338875950"),
+			tt.B10("1487259371808822575685230766372478858208831958946972")},
+	}
+	// All the tests!
+	for _, test := range tests {
+		actual, err := test.pk.Mul(test.a, test.c)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// encrypt() is provided a nonce and must be deterministic
+func TestLittleEncryptDeterministic(t *testing.T) {
+	pk := NewPubkey(N)
+	r, err := crypto.Rand(pk.N)
+	tt.AssertNoError(t, err)
+
+	msg, _ := crypto.Rand(pk.N)
+
+	// Encrypt the same msg/nonce multiple times
+	a0, err := pk.encrypt(msg, r)
+	tt.AssertNoError(t, err)
+
+	a1, err := pk.encrypt(msg, r)
+	tt.AssertNoError(t, err)
+
+	a2, err := pk.encrypt(msg, r)
+	tt.AssertNoError(t, err)
+
+	// ❄️ == bad; confirm results are identical
+	tt.AssertBigIntEq(t, a0, a1)
+	tt.AssertBigIntEq(t, a0, a2)
+}
+
+// Tests the restrictions on input values for paillier.Encrypt
+func TestEncryptErrorConditions(t *testing.T) {
+	pk := NewPubkey(N)
+
+	var tests = []struct {
+		msg, r       *big.Int
+		expectedPass bool
+	}{
+		// Good
+		{crypto.Zero, crypto.One, true}, // 0 ≤ m,r < N
+		{crypto.One, NminusOne, true},   // 0 ≤ m,r < N
+		{NminusOne, two, true},          // 0 ≤ m,r < N
+
+		// Bad
+		{crypto.Zero, crypto.Zero, false},         // r cannot be 0
+		{big.NewInt(-1), crypto.One, false},       // Negative value m
+		{big.NewInt(-1000000), crypto.One, false}, // Negative value r
+		{big.NewInt(-1), big.NewInt(-1), false},   // Negative values both
+		{nil, crypto.One, false},                  // m nil
+		{crypto.One, nil, false},                  // r nil
+		{nil, nil, false},                         // both nil
+		{N, crypto.One, false},                    // m == N
+		{crypto.One, N, false},                    // r == N
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		_, err := pk.encrypt(test.msg, test.r)
+		if test.expectedPass {
+			tt.AssertNoError(t, err)
+		} else {
+			tt.AssertSomeError(t, err)
+		}
+	}
+
+	// Fail if N is nil
+	pk = &PublicKey{N: nil, N2: nil}
+	_, _, err := pk.Encrypt(crypto.One)
+	tt.AssertError(t, err, "arguments cannot be nil")
+}
+
+// Tests that each invocation of Encrypt() produces a distinct output
+func TestEncryptIsRandomized(t *testing.T) {
+	pk := NewPubkey(N)
+	msg := crypto.One
+
+	// Encrypt the same msg multiple times
+	a0, _, err := pk.Encrypt(msg)
+	tt.AssertNoError(t, err)
+
+	a1, _, err := pk.Encrypt(msg)
+	tt.AssertNoError(t, err)
+
+	a2, _, err := pk.Encrypt(msg)
+	tt.AssertNoError(t, err)
+
+	// ❄️ ❄️ ❄️
+	tt.AssertBigIntNe(t, a0, a1)
+	tt.AssertBigIntNe(t, a0, a2)
+}
+
+// Small number tests of Encrypt()
+func TestEncryptKnownAnswers(t *testing.T) {
+	// N=3, NN=9
+	z9 := NewPubkey(big.NewInt(3))
+
+	var tests = []struct {
+		m, r, expected *big.Int // m,r inputs
+	}{
+		// All operations below mod 9
+		{big.NewInt(1), big.NewInt(1), big.NewInt(4)}, // c = (3+1)^1 * (1^3) = 4*1 = 4
+		{big.NewInt(0), big.NewInt(1), big.NewInt(1)}, // c = (3+1)^0 * 1^3 = 1
+		{big.NewInt(2), big.NewInt(2), big.NewInt(2)}, // c = (3+1)^2 * 2^3 = 16*8 ≡ -7 ≡ 2
+		{big.NewInt(1), big.NewInt(2), big.NewInt(5)}, // c = (3+1)^1 * 2^3 = 4*8 ≡ 5
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		actual, err := z9.encrypt(test.m, test.r)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// Encrypt should succeed over a range of arbitrary, valid messages
+func TestEncryptSucceeds(t *testing.T) {
+	pk := NewPubkey(N)
+	iterations := 100
+	for i := 0; i < iterations; i++ {
+		msg, _ := crypto.Rand(pk.N)
+		c, r, err := pk.Encrypt(msg)
+		tt.AssertNoError(t, err)
+		tt.AssertNotNil(t, c, r)
+	}
+}
+
+// Tests the restrictions on input values for paillier.Decrypt
+func TestDecryptErrorConditions(t *testing.T) {
+	pk := NewPubkey(N)
+	// A fake secret key, but good enough to test parameter validation
+	sk := &SecretKey{*pk, NplusOne, NplusOne, NplusOne}
+
+	var tests = []struct {
+		c            *big.Int
+		expectedPass bool
+	}{
+		// Good: c ∈ Z_N²
+		// TODO: Fix when L() param restrictions settled
+		// {crypto.Zero, true},
+		// {crypto.One, true},
+		// {N, true},
+		// {NplusOne, true},
+		// {hundoN, true},
+		// {NNminusOne, true},
+
+		// Bad
+		{big.NewInt(-1), false},       // Negative
+		{big.NewInt(-1000000), false}, // Negative
+		{NN, false},                   // c = N²
+		{NNplusOne, false},            // c > N²
+		{nil, false},                  // nil
+	}
+
+	// All the tests!
+	for _, test := range tests {
+		_, err := sk.Decrypt(test.c)
+		if test.expectedPass {
+			tt.AssertNoError(t, err)
+		} else {
+			tt.AssertSomeError(t, err)
+		}
+	}
+
+	// nil values in the SecretKey
+	sk = &SecretKey{
+		PublicKey: PublicKey{N: big.NewInt(100), N2: big.NewInt(10000)},
+		Lambda:    big.NewInt(200),
+		Totient:   nil,
+		U:         nil,
+	}
+	_, err := sk.Decrypt(crypto.One)
+	tt.AssertSomeError(t, err)
+
+	// N = 0 is pub key
+	sk = &SecretKey{
+		PublicKey: PublicKey{N: big.NewInt(0), N2: big.NewInt(10000)},
+		Lambda:    big.NewInt(200),
+		Totient:   nil,
+		U:         nil,
+	}
+	_, err = sk.Decrypt(crypto.One)
+	tt.AssertError(t, err, "N cannot be 0")
+}
+
+// Decrypt·Encrypt is the identity function
+func TestEncryptDecryptRoundTrip(t *testing.T) {
+	// Pre-computed safe primes
+	p := tt.B10("133788347333574532510542341875219452703250094560184213896952738579939377079849213618116996737030817731544214409221015150233522821287955673536671953914660520267670984696713816508768479853621956967492030516224494353641551367310541202655075859386716364585825364092974073148178887544704793573033779774765431460367")
+	q := tt.B10("121400263190232595456200749546561304956161672968687911935494950378721768184159069938532869288284686583150658925255722159156454219960265942696166947144912738151554579878178746701374346180640493532962639632666540478486867810588884360492830920363713588684509182704981665082591486786717530494254613085570321507623")
+	n := tt.B10("16241940578082201531943448855852277578391761356628379864603641922876623601321625229339135653813019543205064366507109899018615521640687222340376734033815591736764469510811142260074144789284382858541066390183237904579674336717818949214144339382239132186500111594251680147962383065732964214151653795512167674648653475620307856642151695559944756719719799945193072239010815330021803557074201060705849949820706127488164694762724694756011467249889383401729777382247223470577114290663770295230883950621358271613200219512401437571399087878832070221157976750549142719310423012055140771277730139053532825828483343855582012877641")
+	nMinusOne := new(big.Int).Sub(n, crypto.One)
+	// Artbitrary value < 2^1024
+	x := tt.B10("20317113632585528798845062224869200275863225217624919914930609441107430244099181911960782321973293974573717329695193847701610218076524443400374940131739854056496412361090757880543495337916419061120521895395069964501013582917510846097488944684808895337780780147474736309539340360589608026856645992290890400384")
+
+	// Create sk, pk for testing
+	sk, err := NewSecretKey(p, q)
+	tt.AssertNoError(t, err)
+	pk := NewPubkey(n)
+
+	// Valid msgs ∈ Z_N
+	msgs := []*big.Int{
+		crypto.Zero,
+		crypto.One,
+		nMinusOne,
+		x,
+	}
+
+	// All the tests!
+	for _, m := range msgs {
+		// Encrypt,validate
+		c, _, err := pk.Encrypt(m)
+		tt.AssertNoError(t, err)
+		tt.AssertNotNil(t, c)
+
+		// Decrypt-validate
+		actual, err := sk.Decrypt(c)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, m, actual)
+	}
+}
+
+func TestSerializePublicKeyWorks(t *testing.T) {
+	n := tt.B10("16241940578082201531943448855852277578391761356628379864603641922876623601321625229339135653813019543205064366507109899018615521640687222340376734033815591736764469510811142260074144789284382858541066390183237904579674336717818949214144339382239132186500111594251680147962383065732964214151653795512167674648653475620307856642151695559944756719719799945193072239010815330021803557074201060705849949820706127488164694762724694756011467249889383401729777382247223470577114290663770295230883950621358271613200219512401437571399087878832070221157976750549142719310423012055140771277730139053532825828483343855582012877641")
+	pk := NewPubkey(n)
+
+	data, err := pk.MarshalJSON()
+	assert.NoError(t, err)
+
+	pk2 := new(PublicKey)
+	assert.NoError(t, pk2.UnmarshalJSON(data))
+	assert.Equal(t, pk2, pk)
+	assert.NoError(t, pk2.UnmarshalJSON([]byte(`{"N":1251}`)))
+}
+
+func TestSerializePublicKeyIgnoreFields(t *testing.T) {
+	tests := [][]byte{
+		[]byte(`{}`),
+		[]byte(`{"a":null}`),
+		[]byte(`{"n":null}`),
+		[]byte(`{"N":null}`),
+	}
+	pk := new(PublicKey)
+	for _, test := range tests {
+		assert.NoError(t, pk.UnmarshalJSON(test))
+	}
+}
+
+func TestSerializeSecretKeyWorks(t *testing.T) {
+	p := tt.B10("133788347333574532510542341875219452703250094560184213896952738579939377079849213618116996737030817731544214409221015150233522821287955673536671953914660520267670984696713816508768479853621956967492030516224494353641551367310541202655075859386716364585825364092974073148178887544704793573033779774765431460367")
+	q := tt.B10("121400263190232595456200749546561304956161672968687911935494950378721768184159069938532869288284686583150658925255722159156454219960265942696166947144912738151554579878178746701374346180640493532962639632666540478486867810588884360492830920363713588684509182704981665082591486786717530494254613085570321507623")
+	sk, err := NewSecretKey(p, q)
+	assert.NoError(t, err)
+
+	data, err := sk.MarshalJSON()
+	assert.NoError(t, err)
+	sk2 := new(SecretKey)
+	assert.NoError(t, sk2.UnmarshalJSON(data))
+	assert.Equal(t, sk2, sk)
+	assert.NoError(t, sk2.UnmarshalJSON([]byte(`{"N":2,"Totient":1,"U":1,"Lambda":1}`)))
+}
+
+func TestSerializeSecretKeyIgnoreFields(t *testing.T) {
+	tests := [][]byte{
+		[]byte(`{}`),
+		[]byte(`{"a":null}`),
+		[]byte(`{"n":null}`),
+		[]byte(`{"N":null}`),
+		[]byte(`{"N":null,"U":1}`),
+	}
+	sk := new(SecretKey)
+	for _, test := range tests {
+		assert.NoError(t, sk.UnmarshalJSON(test))
+	}
+}
+
+func TestSerializationErrorConditions(t *testing.T) {
+	pk := new(PublicKey)
+	tt.AssertSomeError(t, pk.UnmarshalJSON([]byte(`invalid`)))
+
+	sk := new(SecretKey)
+	tt.AssertSomeError(t, sk.UnmarshalJSON([]byte(`invalid`)))
+}
+
+func TestNewSecretKeyErrorConditions(t *testing.T) {
+	testArgs := []lcmTest{
+		{
+			x: nil,
+			y: big.NewInt(1),
+		},
+		{
+			x: big.NewInt(1),
+			y: nil,
+		},
+		{
+			x: nil,
+			y: nil,
+		},
+	}
+	for _, arg := range testArgs {
+		_, err := NewSecretKey(arg.x, arg.y)
+		tt.AssertError(t, err, "arguments cannot be nil")
+	}
+}
diff --git a/pkg/paillier/psf.go b/pkg/paillier/psf.go
new file mode 100644
index 00000000..7e27fa54
--- /dev/null
+++ b/pkg/paillier/psf.go
@@ -0,0 +1,222 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+// This file contains proofs that Paillier moduli are square-free: [spec] fig 15
+
+package paillier
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+)
+
+// [spec] 10.2 and ProvePSF, VerifyPSF fig.15
+const PsfProofLength = 13
+
+// PsfProofParams contains the inputs to ProvePSF
+type PsfProofParams struct {
+	Curve     elliptic.Curve
+	SecretKey *SecretKey
+	Pi        uint32
+	Y         *curves.EcPoint
+}
+
+// PsfVerifyParams contains the inputs to VerifyPSF
+type PsfVerifyParams struct {
+	Curve     elliptic.Curve
+	PublicKey *PublicKey
+	Pi        uint32
+	Y         *curves.EcPoint
+}
+
+// PsfProof is a slice of 13 big.Int's that prove that a Paillier modulus is square-free
+type PsfProof []*big.Int
+
+// Prove that a Paillier modulus is square-free
+// [spec] §10.fig 15
+func (p *PsfProofParams) Prove() (PsfProof, error) {
+	// Verify that params are sane
+	if p.Curve == nil ||
+		p.SecretKey == nil ||
+		p.Pi == 0 ||
+		p.Y == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// 1. ell = 13
+	// Note this is set above as PsfProofLength
+
+	// 2. M = N^{-1} mod \phi(N)
+	M, err := crypto.Inv(p.SecretKey.N, p.SecretKey.Totient)
+	if err != nil {
+		return nil, err
+	}
+
+	// 3. [x_1, ..., x_ell] <- GenerateChallenges(g,q,y,Pi,ell)
+	// NOTE: spec doesn't include N, but it's an oversight--should be part of the
+	// commitment
+	x, err := generateChallenges(p.Curve.Params(), p.SecretKey.N, p.Pi, p.Y)
+	if err != nil {
+		return nil, err
+	}
+	if len(x) != PsfProofLength {
+		return nil, fmt.Errorf("Challenges array is not correct length: want=%v got=%v", PsfProofLength, len(x))
+	}
+
+	// 4. For i = [1, ... \ell]
+	// NOTE: typo in spec: says j = ... but uses subscript i in loop
+	proof := make([]*big.Int, PsfProofLength)
+	for i, xj := range x {
+		// 5. Compute y_i = x_i^M mod N
+		// NOTE: the pseudocode shows mod phi(N) which is incorrect
+		// it should be mod N otherwise the reverse in Verify
+		// will fail. Using phi(N) puts M in the wrong group.
+		yi, err := crypto.Exp(xj, M, p.SecretKey.N)
+		if err != nil {
+			return nil, err
+		}
+
+		// 6. Set \Pi = [y_1, ..., y_\ell]
+		// NOTE: typo in spec: says y_t not y_\ell
+		proof[i] = yi
+	}
+
+	// 7. return \Pi
+	return proof, nil
+}
+
+// Verify that a Paillier modulus is square-free
+// [spec] §10.fig 15
+func (p PsfProof) Verify(psf *PsfVerifyParams) error {
+	// Verify that params are sane
+	if psf == nil ||
+		psf.Curve == nil ||
+		psf.PublicKey == nil ||
+		psf.Pi == 0 ||
+		psf.Y == nil {
+		return internal.ErrNilArguments
+	}
+
+	// 1. ell = 13
+	// Note this is set above as PsfProofLength
+
+	// 2. t = 1000
+	// NOTE not used anywhere
+
+	// 3. if q|N return false
+	if new(big.Int).Mod(psf.PublicKey.N, psf.Curve.Params().N).Cmp(crypto.Zero) == 0 {
+		return fmt.Errorf("paillier public key is a multiple of the curve subgroup")
+	}
+
+	// 4. [x_1, ..., x_ell] <- GenerateChallenges(g,q,y,Pi,ell)
+	// NOTE: spec doesn't include N, but it's an oversight--should be part of the
+	// commitment
+	x, err := generateChallenges(psf.Curve.Params(), psf.PublicKey.N, psf.Pi, psf.Y)
+	if err != nil {
+		return err
+	}
+	if len(x) != PsfProofLength {
+		return fmt.Errorf("challenges array is not correct length: want=%v got=%v", PsfProofLength, len(x))
+	}
+
+	// 5. for j in [1,...,l]
+	for j, xj := range x {
+		// 6. yj^N != x mod N return false
+		// NOTE: pseudocode uses i when loop uses j
+		lhs, err := crypto.Exp(p[j], psf.PublicKey.N, psf.PublicKey.N)
+		if err != nil {
+			return err
+		}
+		if lhs.Cmp(xj) != 0 {
+			return fmt.Errorf("not equal at %d", j)
+		}
+	}
+
+	return nil
+}
+
+// generateChallenges computes `l` deterministic numbers as
+// challenges for PsfProof which proves that the Paillier modulus is square free
+// [spec] fig.15 GenerateChallenges
+func generateChallenges(params *elliptic.CurveParams, N *big.Int, pi uint32, y *curves.EcPoint) ([]*big.Int, error) {
+	if params == nil ||
+		y == nil ||
+		pi == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// 1. Set b = |N| // bit length of N
+	b := N.BitLen()
+
+	// a modulus that is too small turns this function into an infinite loop
+	// need at least a byte to guarantee termination
+	if b < 8 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// 2. h = output bit-length of fiat-shamir hash
+	// See util.fiatShamir which uses sha256
+	// So the output bit-length is 256 bits
+	const h int = 256
+
+	// 3. Compute s = ⌈b/h⌉ // number of hash outputs required to obtain b bits
+	// i.e. the number of times we have to call fs-shamir to get the same bits as
+	// `b`. Compute ceil as ceilVal = (a+b-1) / b
+	s := int64((b + h - 1) / h)
+
+	// 4. j = 0
+	j := int64(0)
+
+	// 5. m = 0
+	m := big.NewInt(0)
+
+	x := make([]*big.Int, PsfProofLength)
+
+	Pi := new(big.Int).SetUint64(uint64(pi))
+	// 6. while j ≤ l
+	for j < PsfProofLength {
+
+		bij := big.NewInt(j)
+		var ej []byte
+
+		// 7. for k = [1,...,s]
+		for k := int64(1); k <= s; k++ {
+			bik := big.NewInt(k)
+
+			// 8. Compute e_jk = FS-HASH(g, q, y, p_i, j, k, m)
+			res, err := crypto.FiatShamir(params.Gx, params.Gy, params.N, y.X, y.Y, Pi, bij, bik, m)
+			if err != nil {
+				return nil, err
+			}
+			// 9. Set x_j = eJ1 || ... || eJs
+			// Pseudocode says to concatenate outside this loop
+			// however, we just concatenate the bytes now instead of storing as temporary
+			// variables
+			ej = append(ej, res...)
+		}
+		// 10. Truncate ej to b bits
+		xj := new(big.Int).SetBytes(ej[:b/8])
+
+		// 11. if x_j < Z_N* i.e. 0 < x_j and x_j < N
+		if xj.Cmp(crypto.Zero) == 1 && xj.Cmp(N) == -1 {
+			x[j] = xj
+
+			// 12 j = j + 1
+			j++
+			// 13 m = 0
+			m = big.NewInt(0)
+			// 14 else
+		} else {
+			// 15. Set m = m + 1
+			m.Add(m, crypto.One)
+		}
+	}
+	return x, nil
+}
diff --git a/pkg/paillier/psf_test.go b/pkg/paillier/psf_test.go
new file mode 100644
index 00000000..bc04bb79
--- /dev/null
+++ b/pkg/paillier/psf_test.go
@@ -0,0 +1,285 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package paillier
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	curves2 "github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+var testPrimes = []*big.Int{
+	internal.B10("186141419611617071752010179586510154515933389116254425631491755419216243670159714804545944298892950871169229878325987039840135057969555324774918895952900547869933648175107076399993833724447909579697857041081987997463765989497319509683575289675966710007879762972723174353568113668226442698275449371212397561567"),
+	internal.B10("94210786053667323206442523040419729883258172350738703980637961803118626748668924192069593010365236618255120977661397310932923345291377692570649198560048403943687994859423283474169530971418656709749020402756179383990602363122039939937953514870699284906666247063852187255623958659551404494107714695311474384687"),
+	internal.B10("130291226847076770981564372061529572170236135412763130013877155698259035960569046218348763182598589633420963942796327547969527085797839549642610021986391589746295634536750785366034581957858065740296991986002552598751827526181747791647357767502200771965093659353354985289411489453223546075843993686648576029043"),
+	internal.B10("172938910323633442195852028319756134734590277522945546987913328782597284762767185925315797321999389252040294991952361905020940252121762387957669654615602135429944435719699091344247805645764550860505536884031064967454028383404046221898300153428182409080298694828920944094158777327533157774919783417586902830043"),
+	internal.B10("135841191929788643010555393808775051922265083622266098277752143441294911675705272940799534437169053045878247274810449617960047255023823301284034559807472662111224710158898548617194658983006262996831617082584649612602010680423107108651221824216065228161009680618243402116924511141821829055830713600437589058643"),
+	internal.B10("179677777376220950493907657233669314916823596507009854134559513388779535023958212632715646194917807302098015450071151245496651913873851032302340489007561121851068326577148680474495447007833318066335149850926605897908761267606415610900931306044455332084757793630487163583451178807470499389106913845684353833379"),
+	internal.B10("62649985409697862206708027961094957171873130708493280862148817115812710388878279240372941307490519941098268192630359164091992515623574326498710952492586770923230983753287493884398990474917756375654842939939940915963324175552421981212594421823752854754541693709434365609636589761589816398869727328798680335583"),
+	internal.B10("196576931859098680370388202020086631604584490828609819764890020064880575503817891126703473215983239396058738287255240835101797315137072822716923594188151190460588551553676484461393180135097616711975997391550414447010491794087888246885960280296709672609456539741162207414899687167396008233995214434586323322859"),
+	internal.B10("271336420864746369701165973306090650688066226258594853124089876839120277465060891854507381090238664515950686049792387028144049076707224579184820539700879884119579186284072404459682082855184644444282438298561112002507411996589407330801765394106772460665497195944412067027079123717579308322520985921886949051399"),
+	internal.B10("147653127360336844448178027222853805809444645720500374788954343695331927468524513989671450440433430392339037667457657655958027740671071573403925974795764987870476118984896439440386146680643457835633462311776946902713168513155240275028008685964121441954481847113848701823211862974120297600518927026940189810103"),
+	internal.B10("61539010433774119199101441060312213379096965116494840834113311373246794436251480454630309900106802555812462300777026043563820643373439814989443964169335227347638731691284339678436222951965582264570176875078394338903074717434072995072121221264531723385013005031614327462206339323414428493321384497439106152163"),
+	internal.B10("311771090987243597109711542316907830756641693311804000593662622484722315782429237915515708860530841821213561483232298821623675096481796856960171671330638042763441430256097782130268494276848432981045602236986861083392706904041234926428759947857376161689191720483868111001987710383245853931937989224732484206639"),
+	internal.B10("348545239501897032367950520763624245702184225360238826931782856428685149253861325854706825698843098817604431561258712026020688621010635185480321876001016614912927680387840531641703966894322797491484955817022624047355473480912508041252361257911175397626575812830091471419378132244146077774966527307225203863239"),
+	internal.B10("167562983031509383478485987630533113343120902430985961468758712448125734458812918541051012669749885569679178971612428577288632429606851871845164719448590160530844833425628143996971699662729056519326776907622035340086832629206691942750594912221135787534670122007438859975313187460872690748138136170080913902203"),
+	internal.B10("151715609132228776595716500435665208768897792993205818803431003524953811539898459230192282642811956896879836518212758893685104146944932088195466999437630114129887975508715417094019351746027667352287673763064246395392591213231796089814648654152625331299642171758052545451706130433176935280325874961374276589763"),
+	internal.B10("281712498774102170277967098381151873986368736986748325672760355775943894718315925237789122870763991635031524237638254080973752419302437870447849091185409669906909828874532209010547976564209374430136988588219470076527433259993640332285914706329187116209118972038509278879237122949265824264856530096167843589043"),
+	internal.B10("86882427063713590116032012033991745733440719961931885774819345297872782432110706546175706398857226544896860987721577779470479838062106788873559026307646871133570915480684987993282364698928926188640576189281202695899665555602891606955025957497645420156315890379148794822782242384167644977894987285630058930123"),
+	internal.B10("83303406464212917441403726886711948278716398972782717472384580707071541544369912289531948826578557956123897261910116726555850408667234850301141318443154703778225305104540324875867615851047711871915209458107086347063530255813116254895432804373554367035028329996279513893337862177371103671113527972705508417219"),
+	internal.B10("290829612093510969863838578444630131194824970528125429399090307997156531200557462531776190769158191441614466855963164356672434851525764502180873524299787560160992955274777477308009367164212073773611071813219472273292916120276721541591451163160398750751633065097434700462944540404208636130411713202759646572187"),
+	internal.B10("48881643615473281990659967689574873112454227417010573158578046287415357392674453353386274403945930212163960526780980360358370255117866064326375672959460785974850231208253282115124348836379470403659096433419030132737534978624170609788431758477453270578400762995584298785082853409573009591146163658067217132999"),
+	internal.B10("47818664065019136841944639898604168570191742429107462510943153778085167306149797958497736138014922106778177497683417470713996340979203175236987691632152128071256018368891463388744514315997309312144264057334961479235114340091423812710466596081259537323405527816634204224641066174554915788023121121924554823463"),
+	internal.B10("229695065817346126758526483359337260282925372883465036895664320607569899180246065431164369223444026964554195802821338287119074827091354255558249504915527499047398698041873875019622138440848556549357174461846992529556315682586788137744896985847052668283284231628825924370859640129811142861116994552829398428647"),
+	internal.B10("100501115016957347491693508757253443864758446032047524096020585354104983606736759639044367167134409576092528219013168507381959241052976704837620234061351712684500077849808223040972825725745511581504906610633548112115513604053190610668096089811015493012026572475283305559529666099836493252485826156659750294903"),
+	internal.B10("164941338210872461448879529698900150056451305424623398039343691654768566536491493438826728710972441042226712374570117138883019423322602098706113298908005378303473844839971995715847918643285222217768344335264383514921181158565529236124115589719970140511822410990649549555047928093673140752570788415674868532299"),
+	internal.B10("277037199251333188171108034082127252450960810846571117481542098050121457972964006392527344163695411986229107011168411232117984760439307440561490229321182283823299859836750264962218540927582605520434969388646847458788766216835350519741512353041653865564337457599778511921159510170311560556844284028160928114623"),
+	internal.B10("194450633495795999995837828580097111229016136925345956148788562473415774074431957758705067019578300241653926511426134047652491974620284426575921711048247821582093564387999309993254763749991516361193554847964638949731507356038181346481870018202492098453036116472375750355687853028597643560794156133662678349939"),
+	internal.B10("351287943170075259292767465687447861777186026969543801283411356809391771346213158326614410370157474105344692424346410925411240089238093158848815209147605381454294661108047095253146499393310219242924552687094316959878415907497273176683394122976929775532753961555304244867490393116346360677109958055297215711587"),
+	internal.B10("329970582937843908299463472795994928703202360293919677760100619380642134736439176597341134222679061949935544692834943628667398294307004076774417457697130314341974849843695836050603685013468031012892094273233016929045028941716224648802422408386216033754532303003405690778077639489173685122357063674177077611499"),
+	internal.B10("67751546105580063387575764356375682499165422473383503143930633584920975946879807021875353514236996076344028719391905234977223693643926924731304657199486141030504275775023186923364159168130612275534168246529309247449138607249407760246378829338068736888203134857601657561860157938495777271164458736576560502603"),
+	internal.B10("276043923868350639738966705196129285523536747369492013710841410915407411458158268634302674024358477700030814139419613881758439643092328709376796555454484423864587139181985503560495790018232370315219082876142282958894264284344738294415199758590186234114829175455336589153989920707778566032047921277945163061363"),
+	internal.B10("62028909880050184794454820320289487394141550306616974968340908736543032782344593292214952852576535830823991093496498970213686040280098908204236051130358424961175634703281821899530101130244725435470475135483879784963475148975313832483400747421265545413510460046067002322131902159892876739088034507063542087523"),
+	internal.B10("321804071508183671133831207712462079740282619152225438240259877528712344129467977098976100894625335474509551113902455258582802291330071887726188174124352664849954838358973904505681968878957681630941310372231688127901147200937955329324769631743029415035218057960201863908173045670622969475867077447909836936523"),
+	internal.B10("52495647838749571441531580865340679598533348873590977282663145916368795913408897399822291638579504238082829052094508345857857144973446573810004060341650816108578548997792700057865473467391946766537119012441105169305106247003867011741811274367120479722991749924616247396514197345075177297436299446651331187067"),
+	internal.B10("118753381771703394804894143450628876988609300829627946826004421079000316402854210786451078221445575185505001470635997217855372731401976507648597119694813440063429052266569380936671291883364036649087788968029662592370202444662489071262833666489940296758935970249316300642591963940296755031586580445184253416139"),
+}
+
+func TestGenerateChallengesWorks(t *testing.T) {
+	curves := []elliptic.Curve{btcec.S256(), elliptic.P256()}
+	for _, curve := range curves {
+		// dummy secret based on curve
+		y, _ := curves2.NewScalarBaseMult(curve, big.NewInt(3))
+
+		for i := 0; i < 5; i++ {
+			for j := 0; j < 5; j++ {
+				// Compute N from test primes
+				skN := new(big.Int).Mul(testPrimes[i], testPrimes[j])
+				x, err := generateChallenges(curve.Params(), skN, uint32(i+1), y)
+
+				assert.NoError(t, err)
+				for _, xj := range x {
+					assert.NotNil(t, xj)
+					assert.Greater(t, xj.Cmp(crypto.Zero), 0)
+					assert.Equal(t, xj.Cmp(skN), -1)
+				}
+			}
+		}
+	}
+}
+
+// tests whether the hash function can still produce valid challenges
+// even when the modulus is smaller than the hash output
+func TestGenerateChallengesPrimeN(t *testing.T) {
+	curves := []elliptic.Curve{btcec.S256(), elliptic.P256()}
+	n := []*big.Int{
+		internal.B10("680564733841876926926749214863536724007"),
+		internal.B10("1234345830644315716128223123383371693999"),
+		internal.B10("358070498390900219760227294443948492156530525739357363711230524749453568134007"),
+		internal.B10("409819537231165473932776844223512813127760876374228481246566335070809195677439"),
+		internal.B10("336327054820888403283842064345570507895192245801107954728200717775133442039527"),
+		internal.B10("353526063197730551176241127281213353808518592628930654494044427064787696719527"),
+	}
+
+	for _, curve := range curves {
+		// dummy secret based on curve
+		y, _ := curves2.NewScalarBaseMult(curve, big.NewInt(3))
+		for i := 0; i < 5; i++ {
+			for j := 0; j < 5; j++ {
+				x, err := generateChallenges(curve.Params(), n[i], uint32(j+1), y)
+
+				assert.NoError(t, err)
+				for _, xj := range x {
+					assert.NotNil(t, xj)
+					assert.Greater(t, xj.Cmp(crypto.Zero), 0)
+				}
+			}
+		}
+	}
+}
+
+func TestGenerateChallengesNilInputs(t *testing.T) {
+	y, _ := curves2.NewScalarBaseMult(elliptic.P256(), big.NewInt(1))
+
+	_, err := generateChallenges(nil, nil, 0, nil)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), nil, 0, nil)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), big.NewInt(0), 0, nil)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), big.NewInt(1), 1, nil)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), big.NewInt(1), 1, y)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), big.NewInt(1), 1, y)
+	assert.Error(t, err)
+	_, err = generateChallenges(elliptic.P256().Params(), big.NewInt(255), 1, y)
+	assert.NoError(t, err)
+}
+
+func TestPsfProofParams_Prove(t *testing.T) {
+	// RSA primes for testing
+	sk, _ := NewSecretKey(
+		// 75-digit random primes from Wolfram-Alpha
+		internal.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687"),
+		internal.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779"))
+	smallSk, _ := NewSecretKey(big.NewInt(13), big.NewInt(11))
+
+	// Some points for testing
+	k := internal.B10("270988338908697209412444309907441365656383309727758604622908325428179708750")
+	Qp256, _ := curves2.NewScalarBaseMult(elliptic.P256(), k)
+	Qs256, _ := curves2.NewScalarBaseMult(btcec.S256(), k)
+	pi := uint32(4)
+
+	tests := []struct {
+		name              string
+		in                *PsfProofParams
+		expectedError     error
+		expectedResultLen int
+	}{
+		// Positive tests
+		{"positive: p256, small numbers",
+			&PsfProofParams{elliptic.P256(), smallSk, 1001, Qp256},
+			nil,
+			PsfProofLength,
+		},
+		{"positive: p256, large numbers",
+			&PsfProofParams{elliptic.P256(), sk, pi, Qp256},
+			nil,
+			PsfProofLength,
+		},
+		{"positive: s256, large numbers",
+			&PsfProofParams{btcec.S256(), sk, pi, Qs256},
+			nil,
+			PsfProofLength,
+		},
+
+		// Nil params
+		{"negative: ",
+			&PsfProofParams{btcec.S256(),
+				sk,
+				pi,
+				Qs256},
+			nil,
+			PsfProofLength,
+		},
+		{"negative: proof params are nil",
+			&PsfProofParams{nil,
+				sk,
+				pi,
+				Qs256},
+			internal.ErrNilArguments,
+			0,
+		},
+		{"negative: SecretKey is nil",
+			&PsfProofParams{btcec.S256(),
+				nil,
+				pi,
+				Qs256},
+			internal.ErrNilArguments,
+			0,
+		},
+		{"negative: y is nil",
+			&PsfProofParams{btcec.S256(),
+				sk,
+				0,
+				Qs256},
+			internal.ErrNilArguments,
+			0,
+		},
+		{"negative: Pi is nil",
+			&PsfProofParams{btcec.S256(),
+				sk,
+				pi,
+				nil},
+			internal.ErrNilArguments,
+			0},
+	}
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			// test
+			result, err := test.in.Prove()
+
+			// Verify the results are as expected
+			assert.Equal(t, test.expectedError, err)
+			assert.Len(t, result, test.expectedResultLen)
+		})
+	}
+
+}
+
+// Test that Range2Proof can be marshaled and unmarshaled correctly
+func TestPsfProof_MarshalJSON(t *testing.T) {
+	// Generate some proof
+	sk, _ := NewSecretKey(
+		internal.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687"),
+		internal.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779"))
+	Q, _ := curves2.NewScalarBaseMult(elliptic.P256(),
+		internal.B10("270988338908697209412444309907441365656383309727758604622908325428179708750"))
+	params := &PsfProofParams{
+		elliptic.P256(), sk,
+		1,
+		Q,
+	}
+	proof, err := params.Prove()
+	require.NoError(t, err)
+	require.NotNil(t, proof)
+
+	// Marshal
+	testJSON, err := json.Marshal(proof)
+	require.NoError(t, err)
+	require.NotNil(t, testJSON)
+
+	var unmarshaled PsfProof
+	err = json.Unmarshal(testJSON, &unmarshaled)
+	require.NoError(t, err)
+
+	// Test for equality
+	assert.Len(t, ([]*big.Int)(unmarshaled), len(([]*big.Int)(proof)))
+	for i := range proof {
+		internal.AssertBigIntEq(t, proof[i], unmarshaled[i])
+	}
+}
+
+// Tests for Verify
+// prove/verify round trip works
+// modifying any parameter causes verify to fail
+func TestPsfProofWorks(t *testing.T) {
+	// RSA primes for testing
+	sk, _ := NewSecretKey(
+		// 75-digit random primes from Wolfram-Alpha
+		internal.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687"),
+		internal.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779"))
+
+	// Some points for testing
+	k := internal.B10("270988338908697209412444309907441365656383309727758604622908325428179708750")
+	Qp256, _ := curves2.NewScalarBaseMult(elliptic.P256(), k)
+	pi := uint32(2)
+
+	proveParams := &PsfProofParams{
+		Curve:     elliptic.P256(),
+		SecretKey: sk,
+		Pi:        pi,
+		Y:         Qp256,
+	}
+	proof, _ := proveParams.Prove()
+	verifyParams := &PsfVerifyParams{
+		Curve:     elliptic.P256(),
+		PublicKey: &sk.PublicKey,
+		Pi:        pi,
+		Y:         Qp256,
+	}
+	assert.NoError(t, proof.Verify(verifyParams))
+}
diff --git a/pkg/sharing/README.md b/pkg/sharing/README.md
new file mode 100755
index 00000000..7561f059
--- /dev/null
+++ b/pkg/sharing/README.md
@@ -0,0 +1,248 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# sharing
+
+```go
+import "github.com/coinbase/kryptology/pkg/sharing"
+```
+
+## Index
+
+- [type Feldman](<#type-feldman>)
+  - [func NewFeldman(threshold, limit uint32, curve *curves.Curve) (*Feldman, error)](<#func-newfeldman>)
+  - [func (f Feldman) Combine(shares ...*ShamirShare) (curves.Scalar, error)](<#func-feldman-combine>)
+  - [func (f Feldman) CombinePoints(shares ...*ShamirShare) (curves.Point, error)](<#func-feldman-combinepoints>)
+  - [func (f Feldman) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)](<#func-feldman-lagrangecoeffs>)
+  - [func (f Feldman) Split(secret curves.Scalar, reader io.Reader) (*FeldmanVerifier, []*ShamirShare, error)](<#func-feldman-split>)
+- [type FeldmanVerifier](<#type-feldmanverifier>)
+  - [func (v FeldmanVerifier) Verify(share *ShamirShare) error](<#func-feldmanverifier-verify>)
+- [type Pedersen](<#type-pedersen>)
+  - [func NewPedersen(threshold, limit uint32, generator curves.Point) (*Pedersen, error)](<#func-newpedersen>)
+  - [func (pd Pedersen) Combine(shares ...*ShamirShare) (curves.Scalar, error)](<#func-pedersen-combine>)
+  - [func (pd Pedersen) CombinePoints(shares ...*ShamirShare) (curves.Point, error)](<#func-pedersen-combinepoints>)
+  - [func (pd Pedersen) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)](<#func-pedersen-lagrangecoeffs>)
+  - [func (pd Pedersen) Split(secret curves.Scalar, reader io.Reader) (*PedersenResult, error)](<#func-pedersen-split>)
+- [type PedersenResult](<#type-pedersenresult>)
+- [type PedersenVerifier](<#type-pedersenverifier>)
+  - [func (pv PedersenVerifier) Verify(share, blindShare *ShamirShare) error](<#func-pedersenverifier-verify>)
+- [type Polynomial](<#type-polynomial>)
+  - [func (p Polynomial) Evaluate(x curves.Scalar) curves.Scalar](<#func-polynomial-evaluate>)
+  - [func (p *Polynomial) Init(intercept curves.Scalar, degree uint32, reader io.Reader) *Polynomial](<#func-polynomial-init>)
+- [type Shamir](<#type-shamir>)
+  - [func NewShamir(threshold, limit uint32, curve *curves.Curve) (*Shamir, error)](<#func-newshamir>)
+  - [func (s Shamir) Combine(shares ...*ShamirShare) (curves.Scalar, error)](<#func-shamir-combine>)
+  - [func (s Shamir) CombinePoints(shares ...*ShamirShare) (curves.Point, error)](<#func-shamir-combinepoints>)
+  - [func (s Shamir) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)](<#func-shamir-lagrangecoeffs>)
+  - [func (s Shamir) Split(secret curves.Scalar, reader io.Reader) ([]*ShamirShare, error)](<#func-shamir-split>)
+- [type ShamirShare](<#type-shamirshare>)
+  - [func (ss ShamirShare) Bytes() []byte](<#func-shamirshare-bytes>)
+  - [func (ss ShamirShare) Validate(curve *curves.Curve) error](<#func-shamirshare-validate>)
+
+
+## type [Feldman](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L43-L46>)
+
+```go
+type Feldman struct {
+    Threshold, Limit uint32
+    Curve            *curves.Curve
+}
+```
+
+### func [NewFeldman](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L48>)
+
+```go
+func NewFeldman(threshold, limit uint32, curve *curves.Curve) (*Feldman, error)
+```
+
+### func \(Feldman\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L91>)
+
+```go
+func (f Feldman) Combine(shares ...*ShamirShare) (curves.Scalar, error)
+```
+
+### func \(Feldman\) [CombinePoints](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L100>)
+
+```go
+func (f Feldman) CombinePoints(shares ...*ShamirShare) (curves.Point, error)
+```
+
+### func \(Feldman\) [LagrangeCoeffs](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L82>)
+
+```go
+func (f Feldman) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)
+```
+
+### func \(Feldman\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L64>)
+
+```go
+func (f Feldman) Split(secret curves.Scalar, reader io.Reader) (*FeldmanVerifier, []*ShamirShare, error)
+```
+
+## type [FeldmanVerifier](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L15-L17>)
+
+```go
+type FeldmanVerifier struct {
+    Commitments []curves.Point
+}
+```
+
+### func \(FeldmanVerifier\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/feldman.go#L19>)
+
+```go
+func (v FeldmanVerifier) Verify(share *ShamirShare) error
+```
+
+## type [Pedersen](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L16-L20>)
+
+Pedersen Verifiable Secret Sharing Scheme
+
+```go
+type Pedersen struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewPedersen](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L67>)
+
+```go
+func NewPedersen(threshold, limit uint32, generator curves.Point) (*Pedersen, error)
+```
+
+NewPedersen creates a new pedersen VSS
+
+### func \(Pedersen\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L131>)
+
+```go
+func (pd Pedersen) Combine(shares ...*ShamirShare) (curves.Scalar, error)
+```
+
+### func \(Pedersen\) [CombinePoints](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L140>)
+
+```go
+func (pd Pedersen) CombinePoints(shares ...*ShamirShare) (curves.Point, error)
+```
+
+### func \(Pedersen\) [LagrangeCoeffs](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L122>)
+
+```go
+func (pd Pedersen) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)
+```
+
+### func \(Pedersen\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L91>)
+
+```go
+func (pd Pedersen) Split(secret curves.Scalar, reader io.Reader) (*PedersenResult, error)
+```
+
+Split creates the verifiers\, blinding and shares
+
+## type [PedersenResult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L59-L64>)
+
+PedersenResult contains all the data from calling Split
+
+```go
+type PedersenResult struct {
+    Blinding                     curves.Scalar
+    BlindingShares, SecretShares []*ShamirShare
+    FeldmanVerifier              *FeldmanVerifier
+    PedersenVerifier             *PedersenVerifier
+}
+```
+
+## type [PedersenVerifier](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L22-L25>)
+
+```go
+type PedersenVerifier struct {
+    Generator   curves.Point
+    Commitments []curves.Point
+}
+```
+
+### func \(PedersenVerifier\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/pedersen.go#L27>)
+
+```go
+func (pv PedersenVerifier) Verify(share, blindShare *ShamirShare) error
+```
+
+## type [Polynomial](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/polynomial.go#L14-L16>)
+
+```go
+type Polynomial struct {
+    Coefficients []curves.Scalar
+}
+```
+
+### func \(Polynomial\) [Evaluate](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/polynomial.go#L27>)
+
+```go
+func (p Polynomial) Evaluate(x curves.Scalar) curves.Scalar
+```
+
+### func \(\*Polynomial\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/polynomial.go#L18>)
+
+```go
+func (p *Polynomial) Init(intercept curves.Scalar, degree uint32, reader io.Reader) *Polynomial
+```
+
+## type [Shamir](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L41-L44>)
+
+```go
+type Shamir struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewShamir](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L46>)
+
+```go
+func NewShamir(threshold, limit uint32, curve *curves.Curve) (*Shamir, error)
+```
+
+### func \(Shamir\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L109>)
+
+```go
+func (s Shamir) Combine(shares ...*ShamirShare) (curves.Scalar, error)
+```
+
+### func \(Shamir\) [CombinePoints](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L135>)
+
+```go
+func (s Shamir) CombinePoints(shares ...*ShamirShare) (curves.Point, error)
+```
+
+### func \(Shamir\) [LagrangeCoeffs](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L83>)
+
+```go
+func (s Shamir) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error)
+```
+
+### func \(Shamir\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L62>)
+
+```go
+func (s Shamir) Split(secret curves.Scalar, reader io.Reader) ([]*ShamirShare, error)
+```
+
+## type [ShamirShare](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L16-L19>)
+
+```go
+type ShamirShare struct {
+    Id    uint32 `json:"identifier"`
+    Value []byte `json:"value"`
+}
+```
+
+### func \(ShamirShare\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L35>)
+
+```go
+func (ss ShamirShare) Bytes() []byte
+```
+
+### func \(ShamirShare\) [Validate](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/shamir.go#L21>)
+
+```go
+func (ss ShamirShare) Validate(curve *curves.Curve) error
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/sharing/ed25519_feldman_test.go b/pkg/sharing/ed25519_feldman_test.go
new file mode 100644
index 00000000..caf69d1a
--- /dev/null
+++ b/pkg/sharing/ed25519_feldman_test.go
@@ -0,0 +1,131 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	crand "crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+var testCurve = curves.ED25519()
+
+func TestEd25519FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, testCurve)
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, testCurve)
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, testCurve)
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split(testCurve.NewScalar(), crand.Reader)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Id:    1,
+			Value: testCurve.Scalar.New(3).Bytes(),
+		},
+		{
+			Id:    1,
+			Value: testCurve.Scalar.New(3).Bytes(),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Id:    0,
+			Value: testCurve.Scalar.New(3).Bytes(),
+		},
+		{
+			Id:    2,
+			Value: testCurve.Scalar.New(3).Bytes(),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Id:    4,
+		Value: testCurve.Scalar.New(3).Bytes(),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := testCurve.Scalar.Hash([]byte("test"))
+	verifiers, shares, err := scheme.Split(secret, crand.Reader)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		err = verifiers.Verify(s)
+		assert.Nil(t, err)
+	}
+	secret2, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret2, secret)
+}
+
+func TestEd25519FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, testCurve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := testCurve.Scalar.Hash([]byte("test"))
+	verifiers, shares, err := scheme.Split(secret, crand.Reader)
+	for _, s := range shares {
+		err = verifiers.Verify(s)
+		assert.Nil(t, err)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/feldman.go b/pkg/sharing/feldman.go
new file mode 100644
index 00000000..63522459
--- /dev/null
+++ b/pkg/sharing/feldman.go
@@ -0,0 +1,107 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+type FeldmanVerifier struct {
+	Commitments []curves.Point
+}
+
+func (v FeldmanVerifier) Verify(share *ShamirShare) error {
+	curve := curves.GetCurveByName(v.Commitments[0].CurveName())
+	err := share.Validate(curve)
+	if err != nil {
+		return err
+	}
+	x := curve.Scalar.New(int(share.Id))
+	i := curve.Scalar.One()
+	rhs := v.Commitments[0]
+
+	for j := 1; j < len(v.Commitments); j++ {
+		i = i.Mul(x)
+		rhs = rhs.Add(v.Commitments[j].Mul(i))
+	}
+	sc, _ := curve.Scalar.SetBytes(share.Value)
+	lhs := v.Commitments[0].Generator().Mul(sc)
+
+	if lhs.Equal(rhs) {
+		return nil
+	} else {
+		return fmt.Errorf("not equal")
+	}
+}
+
+type Feldman struct {
+	Threshold, Limit uint32
+	Curve            *curves.Curve
+}
+
+func NewFeldman(threshold, limit uint32, curve *curves.Curve) (*Feldman, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold cannot be less than 2")
+	}
+	if limit > 255 {
+		return nil, fmt.Errorf("cannot exceed 255 shares")
+	}
+	if curve == nil {
+		return nil, fmt.Errorf("invalid curve")
+	}
+	return &Feldman{threshold, limit, curve}, nil
+}
+
+func (f Feldman) Split(secret curves.Scalar, reader io.Reader) (*FeldmanVerifier, []*ShamirShare, error) {
+	if secret.IsZero() {
+		return nil, nil, fmt.Errorf("invalid secret")
+	}
+	shamir := &Shamir{
+		threshold: f.Threshold,
+		limit:     f.Limit,
+		curve:     f.Curve,
+	}
+	shares, poly := shamir.getPolyAndShares(secret, reader)
+	verifier := new(FeldmanVerifier)
+	verifier.Commitments = make([]curves.Point, f.Threshold)
+	for i := range verifier.Commitments {
+		verifier.Commitments[i] = f.Curve.ScalarBaseMult(poly.Coefficients[i])
+	}
+	return verifier, shares, nil
+}
+
+func (f Feldman) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error) {
+	shamir := &Shamir{
+		threshold: f.Threshold,
+		limit:     f.Limit,
+		curve:     f.Curve,
+	}
+	return shamir.LagrangeCoeffs(shares)
+}
+
+func (f Feldman) Combine(shares ...*ShamirShare) (curves.Scalar, error) {
+	shamir := &Shamir{
+		threshold: f.Threshold,
+		limit:     f.Limit,
+		curve:     f.Curve,
+	}
+	return shamir.Combine(shares...)
+}
+
+func (f Feldman) CombinePoints(shares ...*ShamirShare) (curves.Point, error) {
+	shamir := &Shamir{
+		threshold: f.Threshold,
+		limit:     f.Limit,
+		curve:     f.Curve,
+	}
+	return shamir.CombinePoints(shares...)
+}
diff --git a/pkg/sharing/pedersen.go b/pkg/sharing/pedersen.go
new file mode 100644
index 00000000..fbcd72af
--- /dev/null
+++ b/pkg/sharing/pedersen.go
@@ -0,0 +1,147 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+// Pedersen Verifiable Secret Sharing Scheme
+type Pedersen struct {
+	threshold, limit uint32
+	curve            *curves.Curve
+	generator        curves.Point
+}
+
+type PedersenVerifier struct {
+	Generator   curves.Point
+	Commitments []curves.Point
+}
+
+func (pv PedersenVerifier) Verify(share, blindShare *ShamirShare) error {
+	curve := curves.GetCurveByName(pv.Generator.CurveName())
+	if err := share.Validate(curve); err != nil {
+		return err
+	}
+	if err := blindShare.Validate(curve); err != nil {
+		return err
+	}
+
+	x := curve.Scalar.New(int(share.Id))
+	i := curve.Scalar.One()
+	rhs := pv.Commitments[0]
+
+	for j := 1; j < len(pv.Commitments); j++ {
+		i = i.Mul(x)
+		rhs = rhs.Add(pv.Commitments[j].Mul(i))
+	}
+
+	sc, _ := curve.Scalar.SetBytes(share.Value)
+	bsc, _ := curve.Scalar.SetBytes(blindShare.Value)
+	g := pv.Commitments[0].Generator().Mul(sc)
+	h := pv.Generator.Mul(bsc)
+	lhs := g.Add(h)
+
+	if lhs.Equal(rhs) {
+		return nil
+	} else {
+		return fmt.Errorf("not equal")
+	}
+}
+
+// PedersenResult contains all the data from calling Split
+type PedersenResult struct {
+	Blinding                     curves.Scalar
+	BlindingShares, SecretShares []*ShamirShare
+	FeldmanVerifier              *FeldmanVerifier
+	PedersenVerifier             *PedersenVerifier
+}
+
+// NewPedersen creates a new pedersen VSS
+func NewPedersen(threshold, limit uint32, generator curves.Point) (*Pedersen, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold cannot be less than 2")
+	}
+	if limit > 255 {
+		return nil, fmt.Errorf("cannot exceed 255 shares")
+	}
+	curve := curves.GetCurveByName(generator.CurveName())
+	if curve == nil {
+		return nil, fmt.Errorf("invalid curve")
+	}
+	if generator == nil {
+		return nil, fmt.Errorf("invalid generator")
+	}
+	if !generator.IsOnCurve() || generator.IsIdentity() {
+		return nil, fmt.Errorf("invalid generator")
+	}
+	return &Pedersen{threshold, limit, curve, generator}, nil
+}
+
+// Split creates the verifiers, blinding and shares
+func (pd Pedersen) Split(secret curves.Scalar, reader io.Reader) (*PedersenResult, error) {
+	// generate a random blinding factor
+	blinding := pd.curve.Scalar.Random(reader)
+
+	shamir := Shamir{pd.threshold, pd.limit, pd.curve}
+	// split the secret into shares
+	shares, poly := shamir.getPolyAndShares(secret, reader)
+
+	// split the blinding into shares
+	blindingShares, polyBlinding := shamir.getPolyAndShares(blinding, reader)
+
+	// Generate the verifiable commitments to the polynomial for the shares
+	blindedverifiers := make([]curves.Point, pd.threshold)
+	verifiers := make([]curves.Point, pd.threshold)
+
+	// ({p0 * G + b0 * H}, ...,{pt * G + bt * H})
+	for i, c := range poly.Coefficients {
+		s := pd.curve.ScalarBaseMult(c)
+		b := pd.generator.Mul(polyBlinding.Coefficients[i])
+		bv := s.Add(b)
+		blindedverifiers[i] = bv
+		verifiers[i] = s
+	}
+	verifier1 := &FeldmanVerifier{Commitments: verifiers}
+	verifier2 := &PedersenVerifier{Commitments: blindedverifiers, Generator: pd.generator}
+
+	return &PedersenResult{
+		blinding, blindingShares, shares, verifier1, verifier2,
+	}, nil
+}
+
+func (pd Pedersen) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error) {
+	shamir := &Shamir{
+		threshold: pd.threshold,
+		limit:     pd.limit,
+		curve:     pd.curve,
+	}
+	return shamir.LagrangeCoeffs(shares)
+}
+
+func (pd Pedersen) Combine(shares ...*ShamirShare) (curves.Scalar, error) {
+	shamir := &Shamir{
+		threshold: pd.threshold,
+		limit:     pd.limit,
+		curve:     pd.curve,
+	}
+	return shamir.Combine(shares...)
+}
+
+func (pd Pedersen) CombinePoints(shares ...*ShamirShare) (curves.Point, error) {
+	shamir := &Shamir{
+		threshold: pd.threshold,
+		limit:     pd.limit,
+		curve:     pd.curve,
+	}
+	return shamir.CombinePoints(shares...)
+}
diff --git a/pkg/sharing/polynomial.go b/pkg/sharing/polynomial.go
new file mode 100644
index 00000000..cd34da8b
--- /dev/null
+++ b/pkg/sharing/polynomial.go
@@ -0,0 +1,34 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+type Polynomial struct {
+	Coefficients []curves.Scalar
+}
+
+func (p *Polynomial) Init(intercept curves.Scalar, degree uint32, reader io.Reader) *Polynomial {
+	p.Coefficients = make([]curves.Scalar, degree)
+	p.Coefficients[0] = intercept.Clone()
+	for i := 1; i < int(degree); i++ {
+		p.Coefficients[i] = intercept.Random(reader)
+	}
+	return p
+}
+
+func (p Polynomial) Evaluate(x curves.Scalar) curves.Scalar {
+	degree := len(p.Coefficients) - 1
+	out := p.Coefficients[degree].Clone()
+	for i := degree - 1; i >= 0; i-- {
+		out = out.Mul(x).Add(p.Coefficients[i])
+	}
+	return out
+}
diff --git a/pkg/sharing/polynomial_test.go b/pkg/sharing/polynomial_test.go
new file mode 100644
index 00000000..07b75dd5
--- /dev/null
+++ b/pkg/sharing/polynomial_test.go
@@ -0,0 +1,31 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	crand "crypto/rand"
+	curves "github.com/coinbase/kryptology/pkg/core/curves"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestNewPoly(t *testing.T) {
+	curve := curves.BLS12381G1()
+	secret := curve.NewScalar().Hash([]byte("test"))
+
+	poly := new(Polynomial).Init(secret, 4, crand.Reader)
+	assert.NotNil(t, poly)
+
+	assert.Equal(t, poly.Coefficients[0], secret)
+}
diff --git a/pkg/sharing/shamir.go b/pkg/sharing/shamir.go
new file mode 100644
index 00000000..5788f6fb
--- /dev/null
+++ b/pkg/sharing/shamir.go
@@ -0,0 +1,200 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+type ShamirShare struct {
+	Id    uint32 `json:"identifier"`
+	Value []byte `json:"value"`
+}
+
+func (ss ShamirShare) Validate(curve *curves.Curve) error {
+	if ss.Id == 0 {
+		return fmt.Errorf("invalid identifier")
+	}
+	sc, err := curve.Scalar.SetBytes(ss.Value)
+	if err != nil {
+		return err
+	}
+	if sc.IsZero() {
+		return fmt.Errorf("invalid share")
+	}
+	return nil
+}
+
+func (ss ShamirShare) Bytes() []byte {
+	var id [4]byte
+	binary.BigEndian.PutUint32(id[:], ss.Id)
+	return append(id[:], ss.Value...)
+}
+
+type Shamir struct {
+	threshold, limit uint32
+	curve            *curves.Curve
+}
+
+func NewShamir(threshold, limit uint32, curve *curves.Curve) (*Shamir, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold cannot be less than 2")
+	}
+	if limit > 255 {
+		return nil, fmt.Errorf("cannot exceed 255 shares")
+	}
+	if curve == nil {
+		return nil, fmt.Errorf("invalid curve")
+	}
+	return &Shamir{threshold, limit, curve}, nil
+}
+
+func (s Shamir) Split(secret curves.Scalar, reader io.Reader) ([]*ShamirShare, error) {
+	if secret.IsZero() {
+		return nil, fmt.Errorf("invalid secret")
+	}
+	shares, _ := s.getPolyAndShares(secret, reader)
+	return shares, nil
+}
+
+func (s Shamir) getPolyAndShares(secret curves.Scalar, reader io.Reader) ([]*ShamirShare, *Polynomial) {
+	poly := new(Polynomial).Init(secret, s.threshold, reader)
+	shares := make([]*ShamirShare, s.limit)
+	for i := range shares {
+		x := s.curve.Scalar.New(i + 1)
+		shares[i] = &ShamirShare{
+			Id:    uint32(i + 1),
+			Value: poly.Evaluate(x).Bytes(),
+		}
+	}
+	return shares, poly
+}
+
+func (s Shamir) LagrangeCoeffs(shares map[uint32]*ShamirShare) (map[uint32]curves.Scalar, error) {
+	xs := make(map[uint32]curves.Scalar, len(shares))
+	for i, xi := range shares {
+		xs[i] = s.curve.Scalar.New(int(xi.Id))
+	}
+
+	result := make(map[uint32]curves.Scalar, len(shares))
+	for i, xi := range xs {
+		num := s.curve.Scalar.One()
+		den := s.curve.Scalar.One()
+		for j, xj := range xs {
+			if i == j {
+				continue
+			}
+
+			num = num.Mul(xj)
+			den = den.Mul(xj.Sub(xi))
+		}
+		if den.IsZero() {
+			return nil, fmt.Errorf("divide by zero")
+		}
+		result[i] = num.Div(den)
+	}
+	return result, nil
+}
+
+func (s Shamir) Combine(shares ...*ShamirShare) (curves.Scalar, error) {
+	if len(shares) < int(s.threshold) {
+		return nil, fmt.Errorf("invalid number of shares")
+	}
+	dups := make(map[uint32]bool, len(shares))
+	xs := make([]curves.Scalar, len(shares))
+	ys := make([]curves.Scalar, len(shares))
+
+	for i, share := range shares {
+		err := share.Validate(s.curve)
+		if err != nil {
+			return nil, err
+		}
+		if share.Id > s.limit {
+			return nil, fmt.Errorf("invalid share identifier")
+		}
+		if _, in := dups[share.Id]; in {
+			return nil, fmt.Errorf("duplicate share")
+		}
+		dups[share.Id] = true
+		ys[i], _ = s.curve.Scalar.SetBytes(share.Value)
+		xs[i] = s.curve.Scalar.New(int(share.Id))
+	}
+	return s.interpolate(xs, ys)
+}
+
+func (s Shamir) CombinePoints(shares ...*ShamirShare) (curves.Point, error) {
+	if len(shares) < int(s.threshold) {
+		return nil, fmt.Errorf("invalid number of shares")
+	}
+	dups := make(map[uint32]bool, len(shares))
+	xs := make([]curves.Scalar, len(shares))
+	ys := make([]curves.Point, len(shares))
+
+	for i, share := range shares {
+		err := share.Validate(s.curve)
+		if err != nil {
+			return nil, err
+		}
+		if share.Id > s.limit {
+			return nil, fmt.Errorf("invalid share identifier")
+		}
+		if _, in := dups[share.Id]; in {
+			return nil, fmt.Errorf("duplicate share")
+		}
+		dups[share.Id] = true
+		sc, _ := s.curve.Scalar.SetBytes(share.Value)
+		ys[i] = s.curve.ScalarBaseMult(sc)
+		xs[i] = s.curve.Scalar.New(int(share.Id))
+	}
+	return s.interpolatePoint(xs, ys)
+}
+
+func (s Shamir) interpolate(xs, ys []curves.Scalar) (curves.Scalar, error) {
+	result := s.curve.Scalar.Zero()
+	for i, xi := range xs {
+		num := s.curve.Scalar.One()
+		den := s.curve.Scalar.One()
+		for j, xj := range xs {
+			if i == j {
+				continue
+			}
+			num = num.Mul(xj)
+			den = den.Mul(xj.Sub(xi))
+		}
+		if den.IsZero() {
+			return nil, fmt.Errorf("divide by zero")
+		}
+		result = result.Add(ys[i].Mul(num.Div(den)))
+	}
+	return result, nil
+}
+
+func (s Shamir) interpolatePoint(xs []curves.Scalar, ys []curves.Point) (curves.Point, error) {
+	result := s.curve.NewIdentityPoint()
+	for i, xi := range xs {
+		num := s.curve.Scalar.One()
+		den := s.curve.Scalar.One()
+		for j, xj := range xs {
+			if i == j {
+				continue
+			}
+			num = num.Mul(xj)
+			den = den.Mul(xj.Sub(xi))
+		}
+		if den.IsZero() {
+			return nil, fmt.Errorf("divide by zero")
+		}
+		result = result.Add(ys[i].Mul(num.Div(den)))
+	}
+	return result, nil
+}
diff --git a/pkg/sharing/shamir_test.go b/pkg/sharing/shamir_test.go
new file mode 100644
index 00000000..53626228
--- /dev/null
+++ b/pkg/sharing/shamir_test.go
@@ -0,0 +1,182 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package sharing
+
+import (
+	"bytes"
+	crand "crypto/rand"
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestShamirSplitInvalidArgs(t *testing.T) {
+	curve := curves.ED25519()
+	_, err := NewShamir(0, 0, curve)
+	assert.NotNil(t, err)
+	_, err = NewShamir(3, 2, curve)
+	assert.NotNil(t, err)
+	_, err = NewShamir(1, 10, curve)
+	assert.NotNil(t, err)
+	scheme, err := NewShamir(2, 3, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Split(curve.NewScalar(), crand.Reader)
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineNoShares(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(2, 3, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineDuplicateShare(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(2, 3, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Id:    1,
+			Value: curve.NewScalar().New(3).Bytes(),
+		},
+		{
+			Id:    1,
+			Value: curve.NewScalar().New(3).Bytes(),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineBadIdentifier(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(2, 3, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Id:    0,
+			Value: curve.NewScalar().New(3).Bytes(),
+		},
+		{
+			Id:    2,
+			Value: curve.NewScalar().New(3).Bytes(),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Id:    4,
+		Value: curve.NewScalar().New(3).Bytes(),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineSingle(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(2, 3, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	shares, err := scheme.Split(curve.NewScalar().Hash([]byte("test")), crand.Reader)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, curve.NewScalar().Hash([]byte("test")))
+}
+
+// Test ComputeL function to compute Lagrange coefficients.
+func TestShamirComputeL(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(2, 2, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	secret := curve.Scalar.Hash([]byte("test"))
+	shares, err := scheme.Split(secret, crand.Reader)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	lCoeffs, err := scheme.LagrangeCoeffs(map[uint32]*ShamirShare{1: shares[0], 2: shares[1]})
+	assert.Nil(t, err)
+	assert.NotNil(t, lCoeffs)
+
+	// Checking we can reconstruct the same secret using Lagrange coefficients.
+	result := curve.NewScalar()
+	for _, r := range shares {
+		rc, _ := curve.Scalar.SetBytes(r.Value)
+		result = result.Add(rc.Mul(lCoeffs[r.Id]))
+	}
+	assert.Equal(t, result.Bytes(), secret.Bytes())
+}
+
+func TestShamirAllCombinations(t *testing.T) {
+	curve := curves.ED25519()
+	scheme, err := NewShamir(3, 5, curve)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := curve.Scalar.Hash([]byte("test"))
+	shares, err := scheme.Split(secret, crand.Reader)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
+
+// Ensures that ShamirShare's un/marshal successfully.
+func TestMarshalJsonRoundTrip(t *testing.T) {
+	curve := curves.ED25519()
+	shares := []ShamirShare{
+		{0, curve.Scalar.New(300).Bytes()},
+		{2, curve.Scalar.New(300000).Bytes()},
+		{20, curve.Scalar.New(12812798).Bytes()},
+		{31, curve.Scalar.New(17).Bytes()},
+		{57, curve.Scalar.New(5066680).Bytes()},
+		{128, curve.Scalar.New(3005).Bytes()},
+		{19, curve.Scalar.New(317).Bytes()},
+		{7, curve.Scalar.New(323).Bytes()},
+		{222, curve.NewScalar().New(-1).Bytes()},
+	}
+	// Run all the tests!
+	for _, in := range shares {
+		input, err := json.Marshal(in)
+		require.NoError(t, err)
+		require.NotNil(t, input)
+
+		// Unmarshal and test
+		out := &ShamirShare{}
+		//out.Value = curve.NewScalar()
+		err = json.Unmarshal(input, &out)
+		require.NoError(t, err)
+		assert.Equal(t, in.Id, out.Id)
+		assert.Equal(t, bytes.Compare(in.Value, out.Value), 0)
+	}
+}
diff --git a/pkg/sharing/v1/README.md b/pkg/sharing/v1/README.md
new file mode 100644
index 00000000..1f4ef640
--- /dev/null
+++ b/pkg/sharing/v1/README.md
@@ -0,0 +1,477 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# v1
+
+```go
+import "github.com/coinbase/kryptology/pkg/sharing/v1"
+```
+
+## Index
+
+- [func K256GeneratorFromHashedBytes(bytes []byte) (x, y *big.Int, err error)](<#func-k256generatorfromhashedbytes>)
+- [type Bls12381G1Curve](<#type-bls12381g1curve>)
+  - [func Bls12381G1() *Bls12381G1Curve](<#func-bls12381g1>)
+  - [func Bls12381G2() *Bls12381G1Curve](<#func-bls12381g2>)
+  - [func (curve *Bls12381G1Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)](<#func-bls12381g1curve-add>)
+  - [func (curve *Bls12381G1Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error)](<#func-bls12381g1curve-compressedbytesfrombigints>)
+  - [func (curve *Bls12381G1Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)](<#func-bls12381g1curve-double>)
+  - [func (curve *Bls12381G1Curve) Hash(msg []byte) (*big.Int, *big.Int)](<#func-bls12381g1curve-hash>)
+  - [func (curve *Bls12381G1Curve) IsOnCurve(x, y *big.Int) bool](<#func-bls12381g1curve-isoncurve>)
+  - [func (curve *Bls12381G1Curve) Params() *elliptic.CurveParams](<#func-bls12381g1curve-params>)
+  - [func (curve *Bls12381G1Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)](<#func-bls12381g1curve-scalarbasemult>)
+  - [func (curve *Bls12381G1Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)](<#func-bls12381g1curve-scalarmult>)
+- [type Bls12381G2Curve](<#type-bls12381g2curve>)
+  - [func (curve *Bls12381G2Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)](<#func-bls12381g2curve-add>)
+  - [func (curve *Bls12381G2Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error)](<#func-bls12381g2curve-compressedbytesfrombigints>)
+  - [func (curve *Bls12381G2Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)](<#func-bls12381g2curve-double>)
+  - [func (curve *Bls12381G2Curve) Hash(msg []byte) (*big.Int, *big.Int)](<#func-bls12381g2curve-hash>)
+  - [func (curve *Bls12381G2Curve) IsOnCurve(x, y *big.Int) bool](<#func-bls12381g2curve-isoncurve>)
+  - [func (curve *Bls12381G2Curve) Params() *elliptic.CurveParams](<#func-bls12381g2curve-params>)
+  - [func (curve *Bls12381G2Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)](<#func-bls12381g2curve-scalarbasemult>)
+  - [func (curve *Bls12381G2Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)](<#func-bls12381g2curve-scalarmult>)
+- [type Ed25519Curve](<#type-ed25519curve>)
+  - [func Ed25519() *Ed25519Curve](<#func-ed25519>)
+  - [func (curve *Ed25519Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)](<#func-ed25519curve-add>)
+  - [func (curve *Ed25519Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)](<#func-ed25519curve-double>)
+  - [func (curve *Ed25519Curve) Hash(msg []byte) (*big.Int, *big.Int)](<#func-ed25519curve-hash>)
+  - [func (curve *Ed25519Curve) IsOnCurve(x, y *big.Int) bool](<#func-ed25519curve-isoncurve>)
+  - [func (curve *Ed25519Curve) Neg(Bx, By *big.Int) (*big.Int, *big.Int)](<#func-ed25519curve-neg>)
+  - [func (curve *Ed25519Curve) Params() *elliptic.CurveParams](<#func-ed25519curve-params>)
+  - [func (curve *Ed25519Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)](<#func-ed25519curve-scalarbasemult>)
+  - [func (curve *Ed25519Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)](<#func-ed25519curve-scalarmult>)
+- [type Feldman](<#type-feldman>)
+  - [func NewFeldman(threshold, limit uint32, curve elliptic.Curve) (*Feldman, error)](<#func-newfeldman>)
+  - [func (f Feldman) Combine(shares ...*ShamirShare) ([]byte, error)](<#func-feldman-combine>)
+  - [func (f Feldman) Split(secret []byte) ([]*ShareVerifier, []*ShamirShare, error)](<#func-feldman-split>)
+  - [func (f Feldman) Verify(share *ShamirShare, verifiers []*ShareVerifier) (bool, error)](<#func-feldman-verify>)
+- [type FeldmanResult](<#type-feldmanresult>)
+- [type Pedersen](<#type-pedersen>)
+  - [func NewPedersen(threshold, limit uint32, generator *curves.EcPoint) (*Pedersen, error)](<#func-newpedersen>)
+  - [func (pd Pedersen) Combine(shares ...*ShamirShare) ([]byte, error)](<#func-pedersen-combine>)
+  - [func (pd Pedersen) Split(secret []byte) (*PedersenResult, error)](<#func-pedersen-split>)
+  - [func (pd Pedersen) Verify(share *ShamirShare, blinding *ShamirShare, blindedverifiers []*ShareVerifier) (bool, error)](<#func-pedersen-verify>)
+- [type PedersenResult](<#type-pedersenresult>)
+- [type Shamir](<#type-shamir>)
+  - [func NewShamir(threshold, limit int, field *curves.Field) (*Shamir, error)](<#func-newshamir>)
+  - [func (s *Shamir) Combine(shares ...*ShamirShare) ([]byte, error)](<#func-shamir-combine>)
+  - [func (s Shamir) ComputeL(shares ...*ShamirShare) ([]*curves.Element, error)](<#func-shamir-computel>)
+  - [func (s *Shamir) GetSharesAndPolynomial(secret []byte) ([]*ShamirShare, *polynomial, error)](<#func-shamir-getsharesandpolynomial>)
+  - [func (s *Shamir) Interpolate(xCoordinates, yCoordinates []*curves.Element) (*curves.Element, error)](<#func-shamir-interpolate>)
+  - [func (s *Shamir) Split(secret []byte) ([]*ShamirShare, error)](<#func-shamir-split>)
+- [type ShamirShare](<#type-shamirshare>)
+  - [func NewShamirShare(x uint32, y []byte, f *curves.Field) *ShamirShare](<#func-newshamirshare>)
+  - [func (s ShamirShare) Add(other *ShamirShare) *ShamirShare](<#func-shamirshare-add>)
+  - [func (s ShamirShare) Bytes() []byte](<#func-shamirshare-bytes>)
+- [type ShareVerifier](<#type-shareverifier>)
+
+
+## func [K256GeneratorFromHashedBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L168>)
+
+```go
+func K256GeneratorFromHashedBytes(bytes []byte) (x, y *big.Int, err error)
+```
+
+K256GeneratorFromHashedBytes computes a generator whose discrete log is unknown from a bytes sequence
+
+## type [Bls12381G1Curve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L25-L27>)
+
+```go
+type Bls12381G1Curve struct {
+    *elliptic.CurveParams
+}
+```
+
+### func [Bls12381G1](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L40>)
+
+```go
+func Bls12381G1() *Bls12381G1Curve
+```
+
+### func [Bls12381G2](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L40>)
+
+```go
+func Bls12381G2() *Bls12381G1Curve
+```
+
+### func \(\*Bls12381G1Curve\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L81>)
+
+```go
+func (curve *Bls12381G1Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G1Curve\) [CompressedBytesFromBigInts](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L137>)
+
+```go
+func (curve *Bls12381G1Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error)
+```
+
+CompressedBytesFromBigInts takes x and y coordinates and converts them to the BLS compressed point form
+
+### func \(\*Bls12381G1Curve\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L95>)
+
+```go
+func (curve *Bls12381G1Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G1Curve\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L128>)
+
+```go
+func (curve *Bls12381G1Curve) Hash(msg []byte) (*big.Int, *big.Int)
+```
+
+Hash an arbitrary byte sequence to a G1 point according to the hash\-to\-curve standard
+
+### func \(\*Bls12381G1Curve\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L76>)
+
+```go
+func (curve *Bls12381G1Curve) IsOnCurve(x, y *big.Int) bool
+```
+
+### func \(\*Bls12381G1Curve\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L72>)
+
+```go
+func (curve *Bls12381G1Curve) Params() *elliptic.CurveParams
+```
+
+### func \(\*Bls12381G1Curve\) [ScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L117>)
+
+```go
+func (curve *Bls12381G1Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G1Curve\) [ScalarMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g1curve.go#L104>)
+
+```go
+func (curve *Bls12381G1Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)
+```
+
+## type [Bls12381G2Curve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L25-L27>)
+
+```go
+type Bls12381G2Curve struct {
+    *elliptic.CurveParams
+}
+```
+
+### func \(\*Bls12381G2Curve\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L81>)
+
+```go
+func (curve *Bls12381G2Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G2Curve\) [CompressedBytesFromBigInts](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L137>)
+
+```go
+func (curve *Bls12381G2Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error)
+```
+
+CompressedBytesFromBigInts takes x and y coordinates and converts them to the BLS compressed point form
+
+### func \(\*Bls12381G2Curve\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L95>)
+
+```go
+func (curve *Bls12381G2Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G2Curve\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L128>)
+
+```go
+func (curve *Bls12381G2Curve) Hash(msg []byte) (*big.Int, *big.Int)
+```
+
+Hash an arbitrary byte sequence to a G1 point according to the hash\-to\-curve standard
+
+### func \(\*Bls12381G2Curve\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L76>)
+
+```go
+func (curve *Bls12381G2Curve) IsOnCurve(x, y *big.Int) bool
+```
+
+### func \(\*Bls12381G2Curve\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L72>)
+
+```go
+func (curve *Bls12381G2Curve) Params() *elliptic.CurveParams
+```
+
+### func \(\*Bls12381G2Curve\) [ScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L117>)
+
+```go
+func (curve *Bls12381G2Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
+```
+
+### func \(\*Bls12381G2Curve\) [ScalarMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/bls12381g2curve.go#L104>)
+
+```go
+func (curve *Bls12381G2Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)
+```
+
+## type [Ed25519Curve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L22-L24>)
+
+```go
+type Ed25519Curve struct {
+    *elliptic.CurveParams
+}
+```
+
+### func [Ed25519](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L37>)
+
+```go
+func Ed25519() *Ed25519Curve
+```
+
+### func \(\*Ed25519Curve\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L53>)
+
+```go
+func (curve *Ed25519Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Ed25519Curve\) [Double](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L76>)
+
+```go
+func (curve *Ed25519Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Ed25519Curve\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L133>)
+
+```go
+func (curve *Ed25519Curve) Hash(msg []byte) (*big.Int, *big.Int)
+```
+
+### func \(\*Ed25519Curve\) [IsOnCurve](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L46>)
+
+```go
+func (curve *Ed25519Curve) IsOnCurve(x, y *big.Int) bool
+```
+
+### func \(\*Ed25519Curve\) [Neg](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L118>)
+
+```go
+func (curve *Ed25519Curve) Neg(Bx, By *big.Int) (*big.Int, *big.Int)
+```
+
+### func \(\*Ed25519Curve\) [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L42>)
+
+```go
+func (curve *Ed25519Curve) Params() *elliptic.CurveParams
+```
+
+### func \(\*Ed25519Curve\) [ScalarBaseMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L104>)
+
+```go
+func (curve *Ed25519Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)
+```
+
+### func \(\*Ed25519Curve\) [ScalarMult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/ed25519curve.go#L86>)
+
+```go
+func (curve *Ed25519Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)
+```
+
+## type [Feldman](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L17-L20>)
+
+Feldman Verifiable Secret Sharing Scheme
+
+```go
+type Feldman struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewFeldman](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L28>)
+
+```go
+func NewFeldman(threshold, limit uint32, curve elliptic.Curve) (*Feldman, error)
+```
+
+### func \(Feldman\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L59>)
+
+```go
+func (f Feldman) Combine(shares ...*ShamirShare) ([]byte, error)
+```
+
+### func \(Feldman\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L40>)
+
+```go
+func (f Feldman) Split(secret []byte) ([]*ShareVerifier, []*ShamirShare, error)
+```
+
+### func \(Feldman\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L66>)
+
+```go
+func (f Feldman) Verify(share *ShamirShare, verifiers []*ShareVerifier) (bool, error)
+```
+
+Verify checks a share for validity
+
+## type [FeldmanResult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/feldman.go#L23-L26>)
+
+FeldmanResult contains all the data from calling Split
+
+```go
+type FeldmanResult struct {
+    SecretShares []*ShamirShare
+    Verifiers    []*ShareVerifier
+}
+```
+
+## type [Pedersen](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L20-L23>)
+
+Pedersen Verifiable Secret Sharing Scheme
+
+```go
+type Pedersen struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewPedersen](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L34>)
+
+```go
+func NewPedersen(threshold, limit uint32, generator *curves.EcPoint) (*Pedersen, error)
+```
+
+NewPedersen creates a new pedersen VSS
+
+### func \(Pedersen\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L109>)
+
+```go
+func (pd Pedersen) Combine(shares ...*ShamirShare) ([]byte, error)
+```
+
+Combine recreates the original secret from the shares
+
+### func \(Pedersen\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L58>)
+
+```go
+func (pd Pedersen) Split(secret []byte) (*PedersenResult, error)
+```
+
+Split creates the verifiers\, blinding and shares
+
+### func \(Pedersen\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L116>)
+
+```go
+func (pd Pedersen) Verify(share *ShamirShare, blinding *ShamirShare, blindedverifiers []*ShareVerifier) (bool, error)
+```
+
+Verify checks a share for validity
+
+## type [PedersenResult](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/pedersen.go#L26-L31>)
+
+PedersenResult contains all the data from calling Split
+
+```go
+type PedersenResult struct {
+    Blinding                     *big.Int
+    BlindingShares, SecretShares []*ShamirShare
+    BlindedVerifiers             []*ShareVerifier
+    Verifiers                    []*ShareVerifier
+}
+```
+
+## type [Shamir](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L51-L54>)
+
+Shamir is the Shamir secret sharing scheme
+
+```go
+type Shamir struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewShamir](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L57>)
+
+```go
+func NewShamir(threshold, limit int, field *curves.Field) (*Shamir, error)
+```
+
+NewShamir creates a Shamir secret sharing scheme
+
+### func \(\*Shamir\) [Combine](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L77>)
+
+```go
+func (s *Shamir) Combine(shares ...*ShamirShare) ([]byte, error)
+```
+
+Combine takes any number of shares and tries to combine them into the original secret
+
+### func \(Shamir\) [ComputeL](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L171>)
+
+```go
+func (s Shamir) ComputeL(shares ...*ShamirShare) ([]*curves.Element, error)
+```
+
+ComputeL is a function that computes all Lagrange coefficients\. This function is particularly needed in FROST tSchnorr signature\.
+
+### func \(\*Shamir\) [GetSharesAndPolynomial](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L110>)
+
+```go
+func (s *Shamir) GetSharesAndPolynomial(secret []byte) ([]*ShamirShare, *polynomial, error)
+```
+
+getSharesAndPolynomial returns the shares for the specified secret and the polynomial used to create the shares
+
+### func \(\*Shamir\) [Interpolate](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L138>)
+
+```go
+func (s *Shamir) Interpolate(xCoordinates, yCoordinates []*curves.Element) (*curves.Element, error)
+```
+
+interpolate calculates the lagrange interpolation
+
+### func \(\*Shamir\) [Split](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L71>)
+
+```go
+func (s *Shamir) Split(secret []byte) ([]*ShamirShare, error)
+```
+
+Split takes a secret and splits it into multiple shares that requires threshold to reconstruct
+
+## type [ShamirShare](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L17-L22>)
+
+ShamirShare is the data from splitting a secret
+
+```go
+type ShamirShare struct {
+    // x-coordinate
+    Identifier uint32 `json:"identifier"`
+    // y-coordinate
+    Value *curves.Element `json:"value"`
+}
+```
+
+### func [NewShamirShare](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L25>)
+
+```go
+func NewShamirShare(x uint32, y []byte, f *curves.Field) *ShamirShare
+```
+
+NewShamirShare creates a ShamirShare given the Identifier\, value\, and Field for the value
+
+### func \(ShamirShare\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L42>)
+
+```go
+func (s ShamirShare) Add(other *ShamirShare) *ShamirShare
+```
+
+Add returns the sum of two Shamir shares
+
+### func \(ShamirShare\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/shamir.go#L34>)
+
+```go
+func (s ShamirShare) Bytes() []byte
+```
+
+Bytes returns the representation of the share in bytes with the identifier as the first 4 bytes
+
+## type [ShareVerifier](<https://github.com/coinbase/kryptology/blob/master/pkg/sharing/v1/common.go#L14>)
+
+ShareVerifier is used to verify secret shares from Feldman or Pedersen VSS
+
+```go
+type ShareVerifier = kryptology.EcPoint
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/sharing/v1/bls12381g1_feldman_test.go b/pkg/sharing/v1/bls12381g1_feldman_test.go
new file mode 100644
index 00000000..063e0732
--- /dev/null
+++ b/pkg/sharing/v1/bls12381g1_feldman_test.go
@@ -0,0 +1,140 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+var (
+	modulus, _ = new(big.Int).SetString(
+		"1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
+		16,
+	)
+	field = curves.NewField(modulus)
+)
+
+func TestBls12381G1FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, Bls12381G1())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, Bls12381G1())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, Bls12381G1())
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, _, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G1FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G1FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G1FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G1FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	verifiers, shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestBls12381G1FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, Bls12381G1())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	verifiers, shares, err := scheme.Split(secret)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/bls12381g1curve.go b/pkg/sharing/v1/bls12381g1curve.go
new file mode 100644
index 00000000..17cda14a
--- /dev/null
+++ b/pkg/sharing/v1/bls12381g1curve.go
@@ -0,0 +1,143 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"crypto/sha256"
+	"math/big"
+	"sync"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+const g1pointSize = 48
+
+var bls12381g1Initonce sync.Once
+var bls12381g1 Bls12381G1Curve
+
+var g1 = bls12381.NewG1()
+
+type Bls12381G1Curve struct {
+	*elliptic.CurveParams
+}
+
+func bls12381g1InitAll() {
+	bls12381g1.CurveParams = new(elliptic.CurveParams)
+	bls12381g1.P, _ = new(big.Int).SetString("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", 16)
+	bls12381g1.N = g1.Q()
+	bls12381g1.B, _ = new(big.Int).SetString("0bbc3efc5008a26a0e1c8c3fad0059c051ac582950405194dd595f13570725ce8c22631a7918fd8ebaac93d50ce72271", 16)
+	bls12381g1.Gx, _ = new(big.Int).SetString("120177419e0bfb75edce6ecc21dbf440f0ae6acdf3d0e747154f95c7143ba1c17817fc679976fff55cb38790fd530c16", 16)
+	bls12381g1.Gy, _ = new(big.Int).SetString("0bbc3efc5008a26a0e1c8c3fad0059c051ac582950405194dd595f13570725ce8c22631a7918fd8ebaac93d50ce72271", 16)
+	bls12381g1.BitSize = 381
+	bls12381g1.Name = "Bls12381G1"
+}
+
+func Bls12381G1() *Bls12381G1Curve {
+	bls12381g1Initonce.Do(bls12381g1InitAll)
+	return &bls12381g1
+}
+
+func bigIntCoordsToPointG1(x, y *big.Int, pointSize int) (*bls12381.PointG1, error) {
+	arr := make([]byte, pointSize*2)
+	mid := pointSize
+	// Use big-endian format copy from the back
+	b := x.Bytes()
+	i := mid - 1
+	for j := len(b) - 1; j >= 0; j-- {
+		arr[i] = b[j]
+		i--
+	}
+
+	b = y.Bytes()
+	i = len(arr) - 1
+	for j := len(b) - 1; j >= 0; j-- {
+		arr[i] = b[j]
+		i--
+	}
+	return g1.FromUncompressed(arr)
+}
+
+func pointG1ToBigIntCoords(p *bls12381.PointG1, pointSize int) (*big.Int, *big.Int) {
+	b, _ := g1.ToUncompressed(p)
+	x := new(big.Int).SetBytes(b[:pointSize])
+	y := new(big.Int).SetBytes(b[pointSize:])
+	return x, y
+}
+
+func (curve *Bls12381G1Curve) Params() *elliptic.CurveParams {
+	return curve.CurveParams
+}
+
+func (curve *Bls12381G1Curve) IsOnCurve(x, y *big.Int) bool {
+	_, err := bigIntCoordsToPointG1(x, y, g1pointSize)
+	return err == nil
+}
+
+func (curve *Bls12381G1Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	p1, err := bigIntCoordsToPointG1(x1, y1, g1pointSize)
+	if err != nil {
+		panic(err)
+	}
+	p2, err := bigIntCoordsToPointG1(x2, y2, g1pointSize)
+	if err != nil {
+		panic(err)
+	}
+	g1.Add(p1, p1, p2)
+
+	return pointG1ToBigIntCoords(p1, g1pointSize)
+}
+
+func (curve *Bls12381G1Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	p, err := bigIntCoordsToPointG1(x1, y1, g1pointSize)
+	if err != nil {
+		panic(err)
+	}
+	g1.Double(p, p)
+	return pointG1ToBigIntCoords(p, g1pointSize)
+}
+
+func (curve *Bls12381G1Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	p, err := bigIntCoordsToPointG1(Bx, By, g1pointSize)
+	if err != nil {
+		panic(err)
+	}
+	s := new(big.Int).SetBytes(k)
+	g1.MulScalar(p, p, s)
+	if !g1.InCorrectSubgroup(p) {
+		panic("point is not in correct subgroup")
+	}
+	return pointG1ToBigIntCoords(p, g1pointSize)
+}
+
+func (curve *Bls12381G1Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	s := new(big.Int).SetBytes(k)
+	p := g1.New()
+	g1.MulScalar(p, g1.One(), s)
+	if !g1.InCorrectSubgroup(p) {
+		panic("point is not in correct subgroup")
+	}
+	return pointG1ToBigIntCoords(p, g1pointSize)
+}
+
+// Hash an arbitrary byte sequence to a G1 point according to the hash-to-curve standard
+func (curve *Bls12381G1Curve) Hash(msg []byte) (*big.Int, *big.Int) {
+	p, err := g1.HashToCurve(sha256.New, msg, []byte("BLS12381G1_XMD:SHA-256_SSWU_RO_"))
+	if err != nil {
+		panic(err)
+	}
+	return pointG1ToBigIntCoords(p, g1pointSize)
+}
+
+// CompressedBytesFromBigInts takes x and y coordinates and converts them to the BLS compressed point form
+func (curve *Bls12381G1Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error) {
+	p, err := bigIntCoordsToPointG1(x, y, g1pointSize)
+	if err != nil {
+		return nil, err
+	}
+	return g1.ToCompressed(p), nil
+}
diff --git a/pkg/sharing/v1/bls12381g2_feldman_test.go b/pkg/sharing/v1/bls12381g2_feldman_test.go
new file mode 100644
index 00000000..875f503a
--- /dev/null
+++ b/pkg/sharing/v1/bls12381g2_feldman_test.go
@@ -0,0 +1,131 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestBls12381G2FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, Bls12381G2())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, Bls12381G2())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, Bls12381G2())
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, _, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G2FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G2FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G2FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestBls12381G2FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	verifiers, shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestBls12381G2FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, Bls12381G2())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	verifiers, shares, err := scheme.Split(secret)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/bls12381g2curve.go b/pkg/sharing/v1/bls12381g2curve.go
new file mode 100644
index 00000000..2127da0f
--- /dev/null
+++ b/pkg/sharing/v1/bls12381g2curve.go
@@ -0,0 +1,143 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"crypto/sha256"
+	"math/big"
+	"sync"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+const g2pointSize = 96
+
+var bls12381g2Initonce sync.Once
+var bls12381g2 Bls12381G2Curve
+
+var g2 = bls12381.NewG2()
+
+type Bls12381G2Curve struct {
+	*elliptic.CurveParams
+}
+
+func bls12381g2InitAll() {
+	bls12381g2.CurveParams = new(elliptic.CurveParams)
+	bls12381g2.P, _ = new(big.Int).SetString("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", 16)
+	bls12381g2.N = g1.Q()
+	bls12381g2.B, _ = new(big.Int).SetString("0bbc3efc5008a26a0e1c8c3fad0059c051ac582950405194dd595f13570725ce8c22631a7918fd8ebaac93d50ce72271", 16)
+	bls12381g2.Gx, _ = new(big.Int).SetString("120177419e0bfb75edce6ecc21dbf440f0ae6acdf3d0e747154f95c7143ba1c17817fc679976fff55cb38790fd530c16", 16)
+	bls12381g2.Gy, _ = new(big.Int).SetString("0bbc3efc5008a26a0e1c8c3fad0059c051ac582950405194dd595f13570725ce8c22631a7918fd8ebaac93d50ce72271", 16)
+	bls12381g2.BitSize = 381
+	bls12381g2.Name = "Bls12381G1"
+}
+
+func Bls12381G2() *Bls12381G1Curve {
+	bls12381g2Initonce.Do(bls12381g2InitAll)
+	return &bls12381g1
+}
+
+func bigIntCoordsToPointG2(x, y *big.Int, pointSize int) (*bls12381.PointG2, error) {
+	arr := make([]byte, pointSize*2)
+	mid := pointSize
+	// Use big-endian format copy from the back
+	b := x.Bytes()
+	i := mid - 1
+	for j := len(b) - 1; j >= 0; j-- {
+		arr[i] = b[j]
+		i--
+	}
+
+	b = y.Bytes()
+	i = len(arr) - 1
+	for j := len(b) - 1; j >= 0; j-- {
+		arr[i] = b[j]
+		i--
+	}
+	return g2.FromUncompressed(arr)
+}
+
+func pointG2ToBigIntCoords(p *bls12381.PointG2, pointSize int) (*big.Int, *big.Int) {
+	b, _ := g2.ToUncompressed(p)
+	x := new(big.Int).SetBytes(b[:pointSize])
+	y := new(big.Int).SetBytes(b[pointSize:])
+	return x, y
+}
+
+func (curve *Bls12381G2Curve) Params() *elliptic.CurveParams {
+	return curve.CurveParams
+}
+
+func (curve *Bls12381G2Curve) IsOnCurve(x, y *big.Int) bool {
+	_, err := bigIntCoordsToPointG2(x, y, g2pointSize)
+	return err == nil
+}
+
+func (curve *Bls12381G2Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	p1, err := bigIntCoordsToPointG2(x1, y1, g2pointSize)
+	if err != nil {
+		panic(err)
+	}
+	p2, err := bigIntCoordsToPointG2(x2, y2, g2pointSize)
+	if err != nil {
+		panic(err)
+	}
+	g2.Add(p1, p1, p2)
+
+	return pointG2ToBigIntCoords(p1, g2pointSize)
+}
+
+func (curve *Bls12381G2Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	p, err := bigIntCoordsToPointG2(x1, y1, g2pointSize)
+	if err != nil {
+		panic(err)
+	}
+	g2.Double(p, p)
+	return pointG2ToBigIntCoords(p, g2pointSize)
+}
+
+func (curve *Bls12381G2Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	p, err := bigIntCoordsToPointG2(Bx, By, g2pointSize)
+	if err != nil {
+		panic(err)
+	}
+	s := new(big.Int).SetBytes(k)
+	g2.MulScalar(p, p, s)
+	if !g2.InCorrectSubgroup(p) {
+		panic("point is not in correct subgroup")
+	}
+	return pointG2ToBigIntCoords(p, g2pointSize)
+}
+
+func (curve *Bls12381G2Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	s := new(big.Int).SetBytes(k)
+	p := g2.New()
+	g2.MulScalar(p, g2.One(), s)
+	if !g2.InCorrectSubgroup(p) {
+		panic("point is not in correct subgroup")
+	}
+	return pointG2ToBigIntCoords(p, g2pointSize)
+}
+
+// Hash an arbitrary byte sequence to a G1 point according to the hash-to-curve standard
+func (curve *Bls12381G2Curve) Hash(msg []byte) (*big.Int, *big.Int) {
+	p, err := g2.HashToCurve(sha256.New, msg, []byte("BLS12381G2_XMD:SHA-256_SSWU_RO_"))
+	if err != nil {
+		panic(err)
+	}
+	return pointG2ToBigIntCoords(p, g2pointSize)
+}
+
+// CompressedBytesFromBigInts takes x and y coordinates and converts them to the BLS compressed point form
+func (curve *Bls12381G2Curve) CompressedBytesFromBigInts(x, y *big.Int) ([]byte, error) {
+	p, err := bigIntCoordsToPointG2(x, y, g2pointSize)
+	if err != nil {
+		return nil, err
+	}
+	return g2.ToCompressed(p), nil
+}
diff --git a/pkg/sharing/v1/common.go b/pkg/sharing/v1/common.go
new file mode 100644
index 00000000..57a24387
--- /dev/null
+++ b/pkg/sharing/v1/common.go
@@ -0,0 +1,14 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	kryptology "github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// ShareVerifier is used to verify secret shares from Feldman or Pedersen VSS
+type ShareVerifier = kryptology.EcPoint
diff --git a/pkg/sharing/v1/ed25519_feldman_test.go b/pkg/sharing/v1/ed25519_feldman_test.go
new file mode 100644
index 00000000..58b0aa5e
--- /dev/null
+++ b/pkg/sharing/v1/ed25519_feldman_test.go
@@ -0,0 +1,131 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestEd25519FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, Ed25519())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, Ed25519())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, Ed25519())
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, _, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	verifiers, shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestEd25519FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, Ed25519())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	verifiers, shares, err := scheme.Split(secret)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/ed25519_pedersen_test.go b/pkg/sharing/v1/ed25519_pedersen_test.go
new file mode 100644
index 00000000..182a2cfa
--- /dev/null
+++ b/pkg/sharing/v1/ed25519_pedersen_test.go
@@ -0,0 +1,153 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/sha512"
+	core "github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"filippo.io/edwards25519"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/stretchr/testify/assert"
+)
+
+var (
+	ed25519BasePoint    = &core.EcPoint{Curve: Ed25519(), X: Ed25519().Gx, Y: Ed25519().Gy}
+	testPointEd25519, _ = core.NewScalarBaseMult(Ed25519(), big.NewInt(2222))
+)
+
+func TestEd25519PedersenSplitInvalidArgs(t *testing.T) {
+	_, err := NewPedersen(0, 0, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(3, 2, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(1, 10, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(2, 3, nil)
+	assert.NotNil(t, err)
+	scheme, err := NewPedersen(2, 3, ed25519BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	// test that split doesn't work on secrets bigger than the modulus
+	_, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestEd25519PedersenCombineNoShares(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, ed25519BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestEd25519PedersenCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, ed25519BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestEd25519PedersenCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, ed25519BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.Error(t, err)
+}
+
+func TestEd25519PedersenCombineSingle(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, testPointEd25519)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	hBytes := sha512.Sum512([]byte("test"))
+	var arr [32]byte
+	copy(arr[:], hBytes[:])
+	sc, err := edwards25519.NewScalar().SetBytesWithClamping(arr[:])
+	assert.Nil(t, err)
+	result, err := scheme.Split(internal.ReverseScalarBytes(sc.Bytes()))
+	assert.Nil(t, err)
+	assert.NotNil(t, result)
+	for i, s := range result.SecretShares {
+		ok, err := scheme.Verify(s, result.BlindingShares[i], result.BlindedVerifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(result.SecretShares...)
+	assert.Nil(t, err)
+	assert.Equal(t, internal.ReverseScalarBytes(secret), sc.Bytes())
+}
+
+func TestEd25519PedersenAllCombinations(t *testing.T) {
+	scheme, err := NewPedersen(3, 5, testPointEd25519)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	result, err := scheme.Split(secret)
+	for i, s := range result.SecretShares {
+		ok, err := scheme.Verify(s, result.BlindingShares[i], result.BlindedVerifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, result)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(result.SecretShares[i], result.SecretShares[j], result.SecretShares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+
+				bSecret, err := scheme.Combine(result.BlindingShares[i], result.BlindingShares[j], result.BlindingShares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, bSecret)
+				assert.Equal(t, bSecret, result.Blinding.Bytes())
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/ed25519curve.go b/pkg/sharing/v1/ed25519curve.go
new file mode 100644
index 00000000..cbbe579c
--- /dev/null
+++ b/pkg/sharing/v1/ed25519curve.go
@@ -0,0 +1,140 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"sync"
+
+	ed "filippo.io/edwards25519"
+	"github.com/coinbase/kryptology/internal"
+)
+
+var ed25519Initonce sync.Once
+var ed25519 Ed25519Curve
+
+type Ed25519Curve struct {
+	*elliptic.CurveParams
+}
+
+func ed25519InitAll() {
+	// taken from https://datatracker.ietf.org/doc/html/rfc8032
+	ed25519.CurveParams = new(elliptic.CurveParams)
+	ed25519.P, _ = new(big.Int).SetString("7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED", 16)
+	ed25519.N, _ = new(big.Int).SetString("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16)
+	ed25519.Gx = new(big.Int)
+	ed25519.Gy = new(big.Int).SetBytes(ed.NewGeneratorPoint().Bytes())
+	ed25519.BitSize = 255
+	ed25519.Name = "ed25519"
+}
+
+func Ed25519() *Ed25519Curve {
+	ed25519Initonce.Do(ed25519InitAll)
+	return &ed25519
+}
+
+func (curve *Ed25519Curve) Params() *elliptic.CurveParams {
+	return curve.CurveParams
+}
+
+func (curve *Ed25519Curve) IsOnCurve(x, y *big.Int) bool {
+	// ignore the x value since Ed25519 is canonical 32 bytes of y according to RFC 8032
+	// Set bytes returns an error if not a valid point
+	_, err := internal.BigInt2Ed25519Point(y)
+	return err == nil
+}
+
+func (curve *Ed25519Curve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int) {
+	var p1, p2 *ed.Point
+	var err error
+	if y1.Cmp(big.NewInt(0)) == 0 {
+		p1 = ed.NewIdentityPoint()
+	} else {
+		p1, err = internal.BigInt2Ed25519Point(y1)
+	}
+	if err != nil {
+		panic(err)
+	}
+	if y2.Cmp(big.NewInt(0)) == 0 {
+		p2 = ed.NewIdentityPoint()
+	} else {
+		p2, err = internal.BigInt2Ed25519Point(y2)
+	}
+	if err != nil {
+		panic(err)
+	}
+	p1.Add(p1, p2)
+	return new(big.Int), new(big.Int).SetBytes(p1.Bytes())
+}
+
+func (curve *Ed25519Curve) Double(x1, y1 *big.Int) (*big.Int, *big.Int) {
+	p, err := internal.BigInt2Ed25519Point(y1)
+	if err != nil {
+		panic(err)
+	}
+	p1, _ := internal.BigInt2Ed25519Point(y1)
+	p.Add(p, p1)
+	return new(big.Int), new(big.Int).SetBytes(p.Bytes())
+}
+
+func (curve *Ed25519Curve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int) {
+	p, err := internal.BigInt2Ed25519Point(By)
+	if err != nil {
+		panic(err)
+	}
+	s, err := internal.BigInt2Ed25519Scalar(new(big.Int).SetBytes(k))
+	if err != nil {
+		var t [64]byte
+		copy(t[:], internal.ReverseScalarBytes(k))
+		s, err = ed.NewScalar().SetUniformBytes(t[:])
+		if err != nil {
+			panic(err)
+		}
+	}
+	p.ScalarMult(s, p)
+	return new(big.Int), new(big.Int).SetBytes(p.Bytes())
+}
+
+func (curve *Ed25519Curve) ScalarBaseMult(k []byte) (*big.Int, *big.Int) {
+	s, err := internal.BigInt2Ed25519Scalar(new(big.Int).SetBytes(k))
+	if err != nil {
+		var t [64]byte
+		copy(t[:], internal.ReverseScalarBytes(k))
+		s, err = ed.NewScalar().SetUniformBytes(t[:])
+		if err != nil {
+			panic(err)
+		}
+	}
+	p := ed.NewIdentityPoint().ScalarBaseMult(s)
+	return new(big.Int), new(big.Int).SetBytes(p.Bytes())
+}
+
+func (curve *Ed25519Curve) Neg(Bx, By *big.Int) (*big.Int, *big.Int) {
+	var p1 *ed.Point
+	var err error
+	if By.Cmp(big.NewInt(0)) == 0 {
+		p1 = ed.NewIdentityPoint()
+	} else {
+		p1, err = internal.BigInt2Ed25519Point(By)
+		if err != nil {
+			panic(err)
+		}
+	}
+	p1.Negate(p1)
+	return new(big.Int), new(big.Int).SetBytes(p1.Bytes())
+}
+
+func (curve *Ed25519Curve) Hash(msg []byte) (*big.Int, *big.Int) {
+	data := new(curves.PointEd25519).Hash(msg).ToAffineCompressed()
+	pt, err := ed.NewIdentityPoint().SetBytes(data)
+	if err != nil {
+		panic(err)
+	}
+	return new(big.Int), new(big.Int).SetBytes(internal.ReverseScalarBytes(pt.Bytes()))
+}
diff --git a/pkg/sharing/v1/ed25519curve_test.go b/pkg/sharing/v1/ed25519curve_test.go
new file mode 100644
index 00000000..cf60fc27
--- /dev/null
+++ b/pkg/sharing/v1/ed25519curve_test.go
@@ -0,0 +1,26 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestEd25519ScalarMult(t *testing.T) {
+	// These values were caught during testing where this combination
+	// yields leading zeros in which big.Int chops.
+	// This test makes sure that this case is correctly handled
+	y := new(big.Int).SetBytes([]byte{37, 228, 49, 105, 78, 97, 108, 221, 63, 25, 125, 212, 108, 189, 247, 169, 52, 86, 150, 97, 93, 199, 212, 254, 122, 98, 189, 7, 97, 14, 78, 12})
+	x := new(big.Int).SetInt64(4)
+	curve := Ed25519()
+	require.True(t, curve.IsOnCurve(nil, y))
+	_, newY := curve.ScalarMult(nil, y, x.Bytes())
+	require.True(t, curve.IsOnCurve(nil, newY))
+}
diff --git a/pkg/sharing/v1/feldman.go b/pkg/sharing/v1/feldman.go
new file mode 100644
index 00000000..df596bdf
--- /dev/null
+++ b/pkg/sharing/v1/feldman.go
@@ -0,0 +1,106 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Feldman Verifiable Secret Sharing Scheme
+type Feldman struct {
+	threshold, limit uint32
+	curve            elliptic.Curve
+}
+
+// FeldmanResult contains all the data from calling Split
+type FeldmanResult struct {
+	SecretShares []*ShamirShare
+	Verifiers    []*ShareVerifier
+}
+
+func NewFeldman(threshold, limit uint32, curve elliptic.Curve) (*Feldman, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+	return &Feldman{
+		threshold, limit, curve,
+	}, nil
+}
+
+func (f Feldman) Split(secret []byte) ([]*ShareVerifier, []*ShamirShare, error) {
+	field := curves.NewField(f.curve.Params().N)
+	shamir := Shamir{f.threshold, f.limit, field}
+	shares, poly, err := shamir.GetSharesAndPolynomial(secret)
+	if err != nil {
+		return nil, nil, err
+	}
+	// Generate the verifiable commitments to the polynomial for the shares
+	verifiers := make([]*ShareVerifier, len(poly.Coefficients))
+	for i, c := range poly.Coefficients {
+		v, err := curves.NewScalarBaseMult(f.curve, c.Value)
+		if err != nil {
+			return nil, nil, err
+		}
+		verifiers[i] = v
+	}
+	return verifiers, shares, nil
+}
+
+func (f Feldman) Combine(shares ...*ShamirShare) ([]byte, error) {
+	field := curves.NewField(f.curve.Params().N)
+	shamir := Shamir{f.threshold, f.limit, field}
+	return shamir.Combine(shares...)
+}
+
+// Verify checks a share for validity
+func (f Feldman) Verify(share *ShamirShare, verifiers []*ShareVerifier) (bool, error) {
+	if len(verifiers) < int(f.threshold) {
+		return false, fmt.Errorf("not enough verifiers to check")
+	}
+	field := curves.NewField(f.curve.Params().N)
+
+	xBytes := make([]byte, 4)
+	binary.BigEndian.PutUint32(xBytes, share.Identifier)
+	x := field.ElementFromBytes(xBytes)
+
+	i := share.Value.Modulus.One()
+
+	// c_0
+	rhs := verifiers[0]
+
+	// Compute the sum of products
+	// c_0 * c_1^i * c_2^{i^2} * c_3^{i^3} ... c_t^{i_t}
+	for j := 1; j < len(verifiers); j++ {
+		// i *= x
+		i = i.Mul(x)
+
+		c, err := verifiers[j].ScalarMult(i.Value)
+		if err != nil {
+			return false, err
+		}
+
+		// ... * c_j^{i^j}
+		rhs, err = rhs.Add(c)
+		if err != nil {
+			return false, err
+		}
+	}
+
+	lhs, err := curves.NewScalarBaseMult(f.curve, share.Value.Value)
+	if err != nil {
+		return false, err
+	}
+
+	// Check if lhs == rhs
+	return lhs.Equals(rhs), nil
+}
diff --git a/pkg/sharing/v1/k256_feldman_test.go b/pkg/sharing/v1/k256_feldman_test.go
new file mode 100644
index 00000000..ed7d4029
--- /dev/null
+++ b/pkg/sharing/v1/k256_feldman_test.go
@@ -0,0 +1,132 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestK256FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, btcec.S256())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, btcec.S256())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, btcec.S256())
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, _, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestK256FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestK256FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestK256FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestK256FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	verifiers, shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestK256FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, btcec.S256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	verifiers, shares, err := scheme.Split(secret)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/k256_pedersen_test.go b/pkg/sharing/v1/k256_pedersen_test.go
new file mode 100644
index 00000000..11bb32ca
--- /dev/null
+++ b/pkg/sharing/v1/k256_pedersen_test.go
@@ -0,0 +1,155 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	core "github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	k256BasePoint    = &core.EcPoint{Curve: btcec.S256(), X: btcec.S256().Gx, Y: btcec.S256().Gy}
+	testPointK256, _ = core.NewScalarBaseMult(btcec.S256(), big.NewInt(2222))
+)
+
+func TestK256PedersenSplitInvalidArgs(t *testing.T) {
+	_, err := NewPedersen(0, 0, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(3, 2, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(1, 10, nil)
+	assert.NotNil(t, err)
+	_, err = NewPedersen(2, 3, nil)
+	assert.NotNil(t, err)
+	scheme, err := NewPedersen(2, 3, k256BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	// test that split doesn't work on secrets bigger than the modulus
+	_, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestK256PedersenCombineNoShares(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, k256BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestK256PedersenCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, k256BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestK256PedersenCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, k256BasePoint)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.Error(t, err)
+}
+
+func TestK256GeneratorFromHashedBytes(t *testing.T) {
+	x, y, err := K256GeneratorFromHashedBytes([]byte("Fair is foul, and foul is fair: Hover through the fog and filthy air."))
+	require.NoError(t, err)
+	require.NotNil(t, x)
+	require.NotNil(t, y)
+	require.True(t, btcec.S256().IsOnCurve(x, y))
+}
+
+func TestK256PedersenCombineSingle(t *testing.T) {
+	scheme, err := NewPedersen(2, 3, testPointK256)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	result, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, result)
+	for i, s := range result.SecretShares {
+		ok, err := scheme.Verify(s, result.BlindingShares[i], result.BlindedVerifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(result.SecretShares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestK256PedersenAllCombinations(t *testing.T) {
+	scheme, err := NewPedersen(3, 5, testPointK256)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	result, err := scheme.Split(secret)
+	for i, s := range result.SecretShares {
+		ok, err := scheme.Verify(s, result.BlindingShares[i], result.BlindedVerifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, result)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(result.SecretShares[i], result.SecretShares[j], result.SecretShares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+
+				bSecret, err := scheme.Combine(result.BlindingShares[i], result.BlindingShares[j], result.BlindingShares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, bSecret)
+				assert.Equal(t, bSecret, result.Blinding.Bytes())
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/p256_feldman_test.go b/pkg/sharing/v1/p256_feldman_test.go
new file mode 100644
index 00000000..2d81638d
--- /dev/null
+++ b/pkg/sharing/v1/p256_feldman_test.go
@@ -0,0 +1,132 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestP256FeldmanSplitInvalidArgs(t *testing.T) {
+	_, err := NewFeldman(0, 0, elliptic.P256())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(3, 2, elliptic.P256())
+	assert.NotNil(t, err)
+	_, err = NewFeldman(1, 10, elliptic.P256())
+	assert.NotNil(t, err)
+	scheme, err := NewFeldman(2, 3, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, _, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, _, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestP256FeldmanCombineNoShares(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestP256FeldmanCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestP256FeldmanCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestP256FeldmanCombineSingle(t *testing.T) {
+	scheme, err := NewFeldman(2, 3, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	verifiers, shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+func TestP256FeldmanAllCombinations(t *testing.T) {
+	scheme, err := NewFeldman(3, 5, elliptic.P256())
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	verifiers, shares, err := scheme.Split(secret)
+	for _, s := range shares {
+		ok, err := scheme.Verify(s, verifiers)
+		assert.Nil(t, err)
+		assert.True(t, ok)
+	}
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
diff --git a/pkg/sharing/v1/pedersen.go b/pkg/sharing/v1/pedersen.go
new file mode 100644
index 00000000..a8e8801c
--- /dev/null
+++ b/pkg/sharing/v1/pedersen.go
@@ -0,0 +1,175 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	crand "crypto/rand"
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+// Pedersen Verifiable Secret Sharing Scheme
+type Pedersen struct {
+	threshold, limit uint32
+	generator        *curves.EcPoint
+}
+
+// PedersenResult contains all the data from calling Split
+type PedersenResult struct {
+	Blinding                     *big.Int
+	BlindingShares, SecretShares []*ShamirShare
+	BlindedVerifiers             []*ShareVerifier
+	Verifiers                    []*ShareVerifier
+}
+
+// NewPedersen creates a new pedersen VSS
+func NewPedersen(threshold, limit uint32, generator *curves.EcPoint) (*Pedersen, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+
+	if generator == nil {
+		return nil, internal.ErrNilArguments
+	}
+	if generator.IsIdentity() {
+		return nil, fmt.Errorf("generator point cannot be at infinity")
+	}
+	if !generator.IsOnCurve() {
+		return nil, fmt.Errorf("generator point must be on the curve")
+	}
+
+	return &Pedersen{
+		threshold, limit, generator,
+	}, nil
+}
+
+// Split creates the verifiers, blinding and shares
+func (pd Pedersen) Split(secret []byte) (*PedersenResult, error) {
+	// generate a random blinding factor
+	blinding, err := crand.Int(crand.Reader, pd.generator.Curve.Params().N)
+
+	if err != nil {
+		return nil, err
+	}
+
+	field := curves.NewField(pd.generator.Curve.Params().N)
+	shamir := Shamir{pd.threshold, pd.limit, field}
+	// split the secret into shares
+	shares, polySecret, err := shamir.GetSharesAndPolynomial(secret)
+	if err != nil {
+		return nil, err
+	}
+
+	// split the blinding into shares
+	blindingShares, polyBlinding, err := shamir.GetSharesAndPolynomial(blinding.Bytes())
+	if err != nil {
+		return nil, err
+	}
+
+	// Generate the verifiable commitments to the polynomial for the shares
+	blindedverifiers := make([]*ShareVerifier, pd.threshold)
+	verifiers := make([]*ShareVerifier, pd.threshold)
+
+	// ({p0 * G + b0 * H}, ...,{pt * G + bt * H})
+	for i, c := range polySecret.Coefficients {
+		s, err := curves.NewScalarBaseMult(pd.generator.Curve, c.Value)
+		if err != nil {
+			return nil, err
+		}
+		b, err := pd.generator.ScalarMult(polyBlinding.Coefficients[i].Value)
+		if err != nil {
+			return nil, err
+		}
+
+		bv, err := s.Add(b)
+		if err != nil {
+			return nil, err
+		}
+
+		blindedverifiers[i] = bv
+		verifiers[i] = s
+	}
+	return &PedersenResult{
+		blinding, blindingShares, shares, blindedverifiers, verifiers,
+	}, nil
+}
+
+// Combine recreates the original secret from the shares
+func (pd Pedersen) Combine(shares ...*ShamirShare) ([]byte, error) {
+	field := curves.NewField(pd.generator.Curve.Params().N)
+	shamir := Shamir{pd.threshold, pd.limit, field}
+	return shamir.Combine(shares...)
+}
+
+// Verify checks a share for validity
+func (pd Pedersen) Verify(share *ShamirShare, blinding *ShamirShare, blindedverifiers []*ShareVerifier) (bool, error) {
+	if len(blindedverifiers) < int(pd.threshold) {
+		return false, fmt.Errorf("not enough blindedverifiers to check")
+	}
+	field := curves.NewField(pd.generator.Curve.Params().N)
+
+	xBytes := make([]byte, 4)
+	binary.BigEndian.PutUint32(xBytes, share.Identifier)
+	x := field.ElementFromBytes(xBytes)
+
+	i := share.Value.Modulus.One()
+
+	// c_0
+	rhs := blindedverifiers[0]
+
+	// Compute the sum of products
+	// c_0 * c_1^i * c_2^{i^2} * c_3^{i^3} ... c_t^{i_t}
+	for j := 1; j < len(blindedverifiers); j++ {
+		// i *= x
+		i = i.Mul(x)
+
+		c, err := blindedverifiers[j].ScalarMult(i.Value)
+		if err != nil {
+			return false, err
+		}
+
+		// ... * c_j^{i^j}
+		rhs, err = rhs.Add(c)
+		if err != nil {
+			return false, err
+		}
+	}
+
+	lhs, err := curves.NewScalarBaseMult(pd.generator.Curve, share.Value.Value)
+	if err != nil {
+		return false, err
+	}
+	tmp, err := pd.generator.ScalarMult(blinding.Value.Value)
+	if err != nil {
+		return false, err
+	}
+	lhs, err = lhs.Add(tmp)
+	if err != nil {
+		return false, err
+	}
+
+	// Check if lhs == rhs
+	return lhs.Equals(rhs), nil
+}
+
+// K256GeneratorFromHashedBytes computes a generator whose discrete log is unknown
+// from a bytes sequence
+func K256GeneratorFromHashedBytes(bytes []byte) (x, y *big.Int, err error) {
+	pt := new(curves.PointK256).Hash(bytes)
+	p, _ := pt.(*curves.PointK256)
+	x = p.X()
+	y = p.Y()
+	err = nil
+	return
+}
diff --git a/pkg/sharing/v1/polynomial.go b/pkg/sharing/v1/polynomial.go
new file mode 100644
index 00000000..4dcada40
--- /dev/null
+++ b/pkg/sharing/v1/polynomial.go
@@ -0,0 +1,49 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+type polynomial struct {
+	Coefficients []*curves.Element
+}
+
+// newPoly creates a random polynomial of the given degree but with the provided intercept value
+func newPoly(intercept *curves.Element, degree uint32) (polynomial, error) {
+	p := polynomial{
+		Coefficients: make([]*curves.Element, degree),
+	}
+
+	// Intercept is the value to be split
+	p.Coefficients[0] = intercept
+
+	// random coefficients
+	for i := uint32(1); i < degree; i++ {
+		c, err := intercept.Field().RandomElement(nil)
+		if err != nil {
+			return p, err
+		}
+		p.Coefficients[i] = c
+	}
+
+	return p, nil
+}
+
+// evaluate returns the value of the polynomial for the given x
+func (p polynomial) evaluate(x *curves.Element) *curves.Element {
+	// Compute the polynomial value using Horner's Method
+
+	degree := len(p.Coefficients) - 1
+	result := p.Coefficients[degree].Clone()
+	for i := degree - 1; i >= 0; i-- {
+		result = result.Mul(x).Add(p.Coefficients[i])
+	}
+
+	return result
+}
diff --git a/pkg/sharing/v1/polynomial_test.go b/pkg/sharing/v1/polynomial_test.go
new file mode 100644
index 00000000..5a3aa0d1
--- /dev/null
+++ b/pkg/sharing/v1/polynomial_test.go
@@ -0,0 +1,29 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestNewPoly(t *testing.T) {
+	secret := field.ElementFromBytes([]byte("test"))
+
+	poly, err := newPoly(secret, 4)
+	assert.Nil(t, err)
+	assert.NotNil(t, poly)
+
+	assert.Equal(t, poly.Coefficients[0], secret)
+}
diff --git a/pkg/sharing/v1/shamir.go b/pkg/sharing/v1/shamir.go
new file mode 100644
index 00000000..e65893e7
--- /dev/null
+++ b/pkg/sharing/v1/shamir.go
@@ -0,0 +1,211 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+)
+
+// ShamirShare is the data from splitting a secret
+type ShamirShare struct {
+	// x-coordinate
+	Identifier uint32 `json:"identifier"`
+	// y-coordinate
+	Value *curves.Element `json:"value"`
+}
+
+// NewShamirShare creates a ShamirShare given the Identifier, value, and Field for the value
+func NewShamirShare(x uint32, y []byte, f *curves.Field) *ShamirShare {
+	return &ShamirShare{
+		Identifier: x,
+		Value:      f.ElementFromBytes(y),
+	}
+}
+
+// Bytes returns the representation of the share in bytes with the identifier as the first
+// 4 bytes
+func (s ShamirShare) Bytes() []byte {
+	a := make([]byte, 4)
+	binary.BigEndian.PutUint32(a, s.Identifier)
+	a = append(a, s.Value.Bytes()...)
+	return a
+}
+
+// Add returns the sum of two Shamir shares
+func (s ShamirShare) Add(other *ShamirShare) *ShamirShare {
+	if s.Identifier != other.Identifier {
+		panic("identifiers must match for valid addition")
+	}
+	newSecret := s.Value.Add(other.Value)
+	return NewShamirShare(s.Identifier, newSecret.Bytes(), s.Value.Field())
+}
+
+// Shamir is the Shamir secret sharing scheme
+type Shamir struct {
+	threshold, limit uint32
+	field            *curves.Field
+}
+
+// NewShamir creates a Shamir secret sharing scheme
+func NewShamir(threshold, limit int, field *curves.Field) (*Shamir, error) {
+	if limit < threshold {
+		return nil, fmt.Errorf("limit cannot be less than threshold")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+	return &Shamir{
+		uint32(threshold), uint32(limit), field,
+	}, nil
+}
+
+// Split takes a secret and splits it into multiple shares that requires
+// threshold to reconstruct
+func (s *Shamir) Split(secret []byte) ([]*ShamirShare, error) {
+	shares, _, err := s.GetSharesAndPolynomial(secret)
+	return shares, err
+}
+
+// Combine takes any number of shares and tries to combine them into the original secret
+func (s *Shamir) Combine(shares ...*ShamirShare) ([]byte, error) {
+	if len(shares) < int(s.threshold) {
+		return nil, fmt.Errorf("not enough shares to combine")
+	}
+
+	dups := make(map[uint32]bool)
+	xCoordinates := make([]*curves.Element, s.threshold)
+	yCoordinates := make([]*curves.Element, s.threshold)
+
+	for i := 0; i < int(s.threshold); i++ {
+		r := shares[i]
+		if r.Identifier > s.limit || r.Identifier < 1 {
+			return nil, fmt.Errorf("invalid share identifier")
+		}
+		if _, ok := dups[r.Identifier]; ok {
+			return nil, fmt.Errorf("duplicate shares cannot be used")
+		}
+
+		xBytes := make([]byte, 4)
+		binary.BigEndian.PutUint32(xBytes, r.Identifier)
+		xCoordinates[i] = s.field.ElementFromBytes(xBytes)
+		yCoordinates[i] = r.Value
+	}
+
+	secret, err := s.Interpolate(xCoordinates, yCoordinates)
+	if err != nil {
+		return nil, err
+	}
+	return secret.Bytes(), nil
+}
+
+// getSharesAndPolynomial returns the shares for the specified secret and the polynomial
+// used to create the shares
+func (s *Shamir) GetSharesAndPolynomial(secret []byte) ([]*ShamirShare, *polynomial, error) {
+	if len(secret) == 0 {
+		return nil, nil, fmt.Errorf("cannot split an empty secret")
+	}
+	intSecret := new(big.Int).SetBytes(secret)
+	if !s.field.IsValid(intSecret) {
+		return nil, nil, fmt.Errorf("secret is too large")
+	}
+
+	elemSecret := s.field.NewElement(intSecret)
+	poly, err := newPoly(elemSecret, s.threshold)
+	if err != nil {
+		return nil, nil, fmt.Errorf("failed to generate polynomial: %v", err)
+	}
+
+	shares := make([]*ShamirShare, s.limit)
+	for i := uint32(0); i < s.limit; i++ {
+		x := s.field.NewElement(big.NewInt(int64(i + 1)))
+		y := poly.evaluate(x)
+		shares[i] = &ShamirShare{
+			Identifier: i + 1,
+			Value:      y,
+		}
+	}
+	return shares, &poly, nil
+}
+
+// interpolate calculates the lagrange interpolation
+func (s *Shamir) Interpolate(xCoordinates, yCoordinates []*curves.Element) (*curves.Element, error) {
+	if len(xCoordinates) < int(s.threshold) ||
+		len(yCoordinates) < int(s.threshold) {
+		return nil, fmt.Errorf("not enough points")
+	}
+
+	zero := xCoordinates[0].Field().Zero()
+	result := yCoordinates[0].Field().Zero()
+
+	for i := 0; i < int(s.threshold); i++ {
+		basis := xCoordinates[0].Field().One()
+		for j := 0; j < int(s.threshold); j++ {
+			if i == j {
+				continue
+			}
+
+			// x_m - x_j
+			denom := xCoordinates[j].Sub(xCoordinates[i])
+			if denom.IsEqual(zero) {
+				return nil, fmt.Errorf("invalid x coordinates")
+			}
+			// x_m / x_m - x_j
+			basis = basis.Mul(xCoordinates[j].Div(denom))
+		}
+
+		result = result.Add(yCoordinates[i].Mul(basis))
+	}
+
+	return result, nil
+}
+
+// ComputeL is a function that computes all Lagrange coefficients.
+// This function is particularly needed in FROST tSchnorr signature.
+func (s Shamir) ComputeL(shares ...*ShamirShare) ([]*curves.Element, error) {
+	if len(shares) < int(s.threshold) {
+		return nil, fmt.Errorf("Not enough shares to compute Lagrange coefficients")
+	}
+	dups := make(map[uint32]bool)
+	xCoordinates := make([]*curves.Element, s.threshold)
+	for i := 0; i < int(s.threshold); i++ {
+		r := shares[i]
+		if r.Identifier > s.limit || r.Identifier < 1 {
+			return nil, fmt.Errorf("ComputeL: invalid share identifier")
+		}
+		if _, ok := dups[r.Identifier]; ok {
+			return nil, fmt.Errorf("ComputeL: duplicate shares cannot be used")
+		}
+
+		xBytes := make([]byte, 4)
+		binary.BigEndian.PutUint32(xBytes, r.Identifier)
+		xCoordinates[i] = s.field.ElementFromBytes(xBytes)
+	}
+
+	zero := xCoordinates[0].Field().Zero()
+	result := make([]*curves.Element, s.threshold)
+
+	for i := 0; i < int(s.threshold); i++ {
+		basis := xCoordinates[0].Field().One()
+		for j := 0; j < int(s.threshold); j++ {
+			if i == j {
+				continue
+			}
+			// x_m - x_j
+			denom := xCoordinates[j].Sub(xCoordinates[i])
+			if denom.IsEqual(zero) {
+				return nil, fmt.Errorf("invalid x coordinates")
+			}
+			// x_m / x_m - x_j
+			basis = basis.Mul(xCoordinates[j].Div(denom))
+		}
+		result[i] = basis
+	}
+	return result, nil
+}
diff --git a/pkg/sharing/v1/shamir_test.go b/pkg/sharing/v1/shamir_test.go
new file mode 100644
index 00000000..1cf894d0
--- /dev/null
+++ b/pkg/sharing/v1/shamir_test.go
@@ -0,0 +1,205 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package v1
+
+import (
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestShamirSplitInvalidArgs(t *testing.T) {
+	_, err := NewShamir(0, 0, field)
+	assert.NotNil(t, err)
+	_, err = NewShamir(3, 2, field)
+	assert.NotNil(t, err)
+	_, err = NewShamir(1, 10, field)
+	assert.NotNil(t, err)
+	scheme, err := NewShamir(2, 3, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Split([]byte{})
+	assert.NotNil(t, err)
+	_, err = scheme.Split([]byte{0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65, 0x65})
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineNoShares(t *testing.T) {
+	scheme, err := NewShamir(2, 3, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine()
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineDuplicateShare(t *testing.T) {
+	scheme, err := NewShamir(2, 3, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	_, err = scheme.Combine([]*ShamirShare{
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 1,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}...)
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineBadIdentifier(t *testing.T) {
+	scheme, err := NewShamir(2, 3, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	shares := []*ShamirShare{
+		{
+			Identifier: 0,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+		{
+			Identifier: 2,
+			Value:      field.NewElement(big.NewInt(3)),
+		},
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+	shares[0] = &ShamirShare{
+		Identifier: 4,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	_, err = scheme.Combine(shares...)
+	assert.NotNil(t, err)
+}
+
+func TestShamirCombineSingle(t *testing.T) {
+	scheme, err := NewShamir(2, 3, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	shares, err := scheme.Split([]byte("test"))
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	secret, err := scheme.Combine(shares...)
+	assert.Nil(t, err)
+	assert.Equal(t, secret, []byte("test"))
+}
+
+// Test ComputeL function to compute Lagrange coefficients.
+func TestShamirComputeL(t *testing.T) {
+	scheme, err := NewShamir(2, 2, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+	secret := []byte("test")
+	shares, err := scheme.Split(secret)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	lCoeffs, err := scheme.ComputeL(shares[0], shares[1])
+	assert.Nil(t, err)
+	assert.NotNil(t, lCoeffs)
+
+	// Checking we can reconstruct the same secret using Lagrange coefficients.
+	inputShares := [2]*ShamirShare{shares[0], shares[1]}
+	yCoordinates := make([]*curves.Element, 2)
+	for i := 0; i < 2; i++ {
+		r := inputShares[i]
+		yCoordinates[i] = r.Value
+	}
+	result := yCoordinates[0].Field().Zero()
+	for i := 0; i < 2; i++ {
+		result = result.Add(yCoordinates[i].Mul(lCoeffs[i]))
+	}
+	assert.Equal(t, result.Bytes(), secret)
+}
+
+func TestShamirAllCombinations(t *testing.T) {
+	scheme, err := NewShamir(3, 5, field)
+	assert.Nil(t, err)
+	assert.NotNil(t, scheme)
+
+	secret := []byte("test")
+	shares, err := scheme.Split(secret)
+	assert.Nil(t, err)
+	assert.NotNil(t, shares)
+	// There are 5*4*3 possible combinations
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if i == j {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if i == k || j == k {
+					continue
+				}
+
+				rSecret, err := scheme.Combine(shares[i], shares[j], shares[k])
+				assert.Nil(t, err)
+				assert.NotNil(t, rSecret)
+				assert.Equal(t, rSecret, secret)
+			}
+		}
+	}
+}
+
+// Ensures that ShamirShare's un/marshal successfully.
+func TestMarshalJsonRoundTrip(t *testing.T) {
+	oneBelowModulus := new(big.Int).Sub(modulus, big.NewInt(1))
+	shares := []ShamirShare{
+		{0, field.NewElement(big.NewInt(300))},
+		{2, field.NewElement(big.NewInt(300000))},
+		{20, field.NewElement(big.NewInt(12812798))},
+		{31, field.NewElement(big.NewInt(17))},
+		{57, field.NewElement(big.NewInt(5066680))},
+		{128, field.NewElement(big.NewInt(3005))},
+		{19, field.NewElement(big.NewInt(317))},
+		{7, field.NewElement(big.NewInt(323))},
+		{222, field.NewElement(oneBelowModulus)},
+	}
+	// Run all the tests!
+	for _, in := range shares {
+		bytes, err := json.Marshal(in)
+		require.NoError(t, err)
+		require.NotNil(t, bytes)
+
+		// Unmarshal and test
+		out := &ShamirShare{}
+		err = json.Unmarshal(bytes, &out)
+		require.NoError(t, err)
+		assert.Equal(t, in.Identifier, out.Identifier)
+		assert.Equal(t, in.Value.Value.Bytes(), out.Value.Value.Bytes())
+	}
+}
+
+func TestSharesAdd(t *testing.T) {
+	finiteField := curves.NewField(big.NewInt(7))
+	one := NewShamirShare(0, []byte{0x01}, finiteField)
+	two := NewShamirShare(0, []byte{0x02}, finiteField)
+
+	// basic addition
+	sum := one.Add(two)
+	assert.Equal(t, uint32(0), sum.Identifier)
+	assert.Equal(t, []byte{0x03}, sum.Value.Bytes())
+
+	// addition is performed within the globalField
+	sum = two.Add(NewShamirShare(0, []byte{0x06}, finiteField))
+	assert.Equal(t, uint32(0), sum.Identifier)
+	assert.Equal(t, []byte{0x01}, sum.Value.Bytes())
+}
+
+func TestSharesAdd_errors(t *testing.T) {
+	finiteField := curves.NewField(big.NewInt(7))
+	one := NewShamirShare(0, []byte{0x01}, finiteField)
+	two := NewShamirShare(1, []byte{0x02}, finiteField)
+	assert.PanicsWithValue(t, "identifiers must match for valid addition", func() {
+		one.Add(two)
+	})
+}
diff --git a/pkg/signatures/bbs/README.md b/pkg/signatures/bbs/README.md
new file mode 100755
index 00000000..75f23c04
--- /dev/null
+++ b/pkg/signatures/bbs/README.md
@@ -0,0 +1,386 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# bbs
+
+```go
+import "github.com/coinbase/kryptology/pkg/signatures/bbs"
+```
+
+## Index
+
+- [func NewKeys(curve *curves.PairingCurve) (*PublicKey, *SecretKey, error)](<#func-newkeys>)
+- [type BlindSignature](<#type-blindsignature>)
+  - [func (sig *BlindSignature) Init(curve *curves.PairingCurve) *BlindSignature](<#func-blindsignature-init>)
+  - [func (sig BlindSignature) MarshalBinary() ([]byte, error)](<#func-blindsignature-marshalbinary>)
+  - [func (sig BlindSignature) ToUnblinded(blinder common.SignatureBlinding) *Signature](<#func-blindsignature-tounblinded>)
+  - [func (sig *BlindSignature) UnmarshalBinary(data []byte) error](<#func-blindsignature-unmarshalbinary>)
+- [type BlindSignatureContext](<#type-blindsignaturecontext>)
+  - [func NewBlindSignatureContext(curve *curves.PairingCurve, msgs map[int]curves.Scalar, generators *MessageGenerators, nonce common.Nonce, reader io.Reader) (*BlindSignatureContext, common.SignatureBlinding, error)](<#func-newblindsignaturecontext>)
+  - [func (bsc *BlindSignatureContext) Init(curve *curves.PairingCurve) *BlindSignatureContext](<#func-blindsignaturecontext-init>)
+  - [func (bsc BlindSignatureContext) MarshalBinary() ([]byte, error)](<#func-blindsignaturecontext-marshalbinary>)
+  - [func (bsc BlindSignatureContext) ToBlindSignature(msgs map[int]curves.Scalar, sk *SecretKey, generators *MessageGenerators, nonce common.Nonce) (*BlindSignature, error)](<#func-blindsignaturecontext-toblindsignature>)
+  - [func (bsc *BlindSignatureContext) UnmarshalBinary(in []byte) error](<#func-blindsignaturecontext-unmarshalbinary>)
+  - [func (bsc BlindSignatureContext) Verify(knownMsgs []int, generators *MessageGenerators, nonce common.Nonce) error](<#func-blindsignaturecontext-verify>)
+- [type MessageGenerators](<#type-messagegenerators>)
+  - [func (msgg MessageGenerators) Get(i int) curves.PairingPoint](<#func-messagegenerators-get>)
+  - [func (msgg *MessageGenerators) Init(w *PublicKey, length int) *MessageGenerators](<#func-messagegenerators-init>)
+- [type PokSignature](<#type-poksignature>)
+  - [func NewPokSignature(sig *Signature, generators *MessageGenerators, msgs []common.ProofMessage, reader io.Reader) (*PokSignature, error)](<#func-newpoksignature>)
+  - [func (pok *PokSignature) GenerateProof(challenge curves.Scalar) (*PokSignatureProof, error)](<#func-poksignature-generateproof>)
+  - [func (pok *PokSignature) GetChallengeContribution(transcript *merlin.Transcript)](<#func-poksignature-getchallengecontribution>)
+- [type PokSignatureProof](<#type-poksignatureproof>)
+  - [func (pok PokSignatureProof) GetChallengeContribution(generators *MessageGenerators, revealedMessages map[int]curves.Scalar, challenge common.Challenge, transcript *merlin.Transcript)](<#func-poksignatureproof-getchallengecontribution>)
+  - [func (pok *PokSignatureProof) Init(curve *curves.PairingCurve) *PokSignatureProof](<#func-poksignatureproof-init>)
+  - [func (pok *PokSignatureProof) MarshalBinary() ([]byte, error)](<#func-poksignatureproof-marshalbinary>)
+  - [func (pok *PokSignatureProof) UnmarshalBinary(in []byte) error](<#func-poksignatureproof-unmarshalbinary>)
+  - [func (pok PokSignatureProof) Verify(revealedMsgs map[int]curves.Scalar, pk *PublicKey, generators *MessageGenerators, nonce common.Nonce, challenge common.Challenge, transcript *merlin.Transcript) bool](<#func-poksignatureproof-verify>)
+  - [func (pok PokSignatureProof) VerifySigPok(pk *PublicKey) bool](<#func-poksignatureproof-verifysigpok>)
+- [type PublicKey](<#type-publickey>)
+  - [func (pk *PublicKey) Init(curve *curves.PairingCurve) *PublicKey](<#func-publickey-init>)
+  - [func (pk PublicKey) MarshalBinary() ([]byte, error)](<#func-publickey-marshalbinary>)
+  - [func (pk *PublicKey) UnmarshalBinary(in []byte) error](<#func-publickey-unmarshalbinary>)
+  - [func (pk PublicKey) Verify(signature *Signature, generators *MessageGenerators, msgs []curves.Scalar) error](<#func-publickey-verify>)
+- [type SecretKey](<#type-secretkey>)
+  - [func NewSecretKey(curve *curves.PairingCurve) (*SecretKey, error)](<#func-newsecretkey>)
+  - [func (sk *SecretKey) Init(curve *curves.PairingCurve) *SecretKey](<#func-secretkey-init>)
+  - [func (sk SecretKey) MarshalBinary() ([]byte, error)](<#func-secretkey-marshalbinary>)
+  - [func (sk *SecretKey) PublicKey() *PublicKey](<#func-secretkey-publickey>)
+  - [func (sk *SecretKey) Sign(generators *MessageGenerators, msgs []curves.Scalar) (*Signature, error)](<#func-secretkey-sign>)
+  - [func (sk *SecretKey) UnmarshalBinary(in []byte) error](<#func-secretkey-unmarshalbinary>)
+- [type Signature](<#type-signature>)
+  - [func (sig *Signature) Init(curve *curves.PairingCurve) *Signature](<#func-signature-init>)
+  - [func (sig Signature) MarshalBinary() ([]byte, error)](<#func-signature-marshalbinary>)
+  - [func (sig *Signature) UnmarshalBinary(data []byte) error](<#func-signature-unmarshalbinary>)
+
+
+## func [NewKeys](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L73>)
+
+```go
+func NewKeys(curve *curves.PairingCurve) (*PublicKey, *SecretKey, error)
+```
+
+## type [BlindSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature.go#L22-L25>)
+
+BlindSignature is a BBS\+ blind signature structurally identical to \`Signature\` but is used to help avoid misuse and confusion\.
+
+1 or more message have been hidden by the potential signature holder so the signer only knows a subset of the messages to be signed
+
+```go
+type BlindSignature struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*BlindSignature\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature.go#L29>)
+
+```go
+func (sig *BlindSignature) Init(curve *curves.PairingCurve) *BlindSignature
+```
+
+Init creates an empty signature to a specific curve which should be followed by UnmarshalBinary
+
+### func \(BlindSignature\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature.go#L36>)
+
+```go
+func (sig BlindSignature) MarshalBinary() ([]byte, error)
+```
+
+### func \(BlindSignature\) [ToUnblinded](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature.go#L67>)
+
+```go
+func (sig BlindSignature) ToUnblinded(blinder common.SignatureBlinding) *Signature
+```
+
+### func \(\*BlindSignature\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature.go#L42>)
+
+```go
+func (sig *BlindSignature) UnmarshalBinary(data []byte) error
+```
+
+## type [BlindSignatureContext](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L27-L34>)
+
+BlindSignatureContext contains the data used for computing a blind signature and verifying proof of hidden messages from a future signature holder\. A potential holder commits to messages that the signer will not know during the signing process rendering them hidden\, but requires the holder to prove knowledge of those messages so a malicious party doesn't add just random data from anywhere\.
+
+```go
+type BlindSignatureContext struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewBlindSignatureContext](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L43>)
+
+```go
+func NewBlindSignatureContext(curve *curves.PairingCurve, msgs map[int]curves.Scalar, generators *MessageGenerators, nonce common.Nonce, reader io.Reader) (*BlindSignatureContext, common.SignatureBlinding, error)
+```
+
+NewBlindSignatureContext creates the data needed to send to a signer to complete a blinded signature \`msgs\` is an index to message map where the index corresponds to the index in \`generators\` msgs are hidden from the signer but can also be empty if no messages are hidden but a blind signature is still desired because the signer should have no knowledge of the signature
+
+### func \(\*BlindSignatureContext\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L106>)
+
+```go
+func (bsc *BlindSignatureContext) Init(curve *curves.PairingCurve) *BlindSignatureContext
+```
+
+### func \(BlindSignatureContext\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L116>)
+
+```go
+func (bsc BlindSignatureContext) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary store the generators as a sequence of bytes where each point is compressed\. Needs \(N \+ 1\) \* ScalarSize \+ PointSize
+
+### func \(BlindSignatureContext\) [ToBlindSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L197>)
+
+```go
+func (bsc BlindSignatureContext) ToBlindSignature(msgs map[int]curves.Scalar, sk *SecretKey, generators *MessageGenerators, nonce common.Nonce) (*BlindSignature, error)
+```
+
+ToBlindSignature converts a blind signature where msgs are known to the signer \`msgs\` is an index to message map where the index corresponds to the index in \`generators\`
+
+### func \(\*BlindSignatureContext\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L124>)
+
+```go
+func (bsc *BlindSignatureContext) UnmarshalBinary(in []byte) error
+```
+
+### func \(BlindSignatureContext\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/blind_signature_context.go#L158>)
+
+```go
+func (bsc BlindSignatureContext) Verify(knownMsgs []int, generators *MessageGenerators, nonce common.Nonce) error
+```
+
+Verify validates a proof of hidden messages
+
+## type [MessageGenerators](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/message_generators.go#L28-L33>)
+
+MessageGenerators are used to sign a vector of commitments for a BBS\+ signature\. These must be the same generators used by sign\, verify\, prove\, and open
+
+These are generated in a deterministic manner\. By using MessageGenerators in this way\, the generators do not need to be stored alongside the public key and the same key can be used to sign an arbitrary number of messages Generators are created by computing H\_i = H\_G1\(W || I2OSP\(0\, 4\) || I2OSP\(0\, 1\) || I2OSP\(length\, 4\)\) where I2OSP means Integer to Octet Stream Primitive and I2OSP represents an integer in a statically sized byte array\. \`W\` is the BBS\+ public key\. Internally we store the 201 byte state since the only value that changes is the index
+
+```go
+type MessageGenerators struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(MessageGenerators\) [Get](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/message_generators.go#L54>)
+
+```go
+func (msgg MessageGenerators) Get(i int) curves.PairingPoint
+```
+
+### func \(\*MessageGenerators\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/message_generators.go#L36>)
+
+```go
+func (msgg *MessageGenerators) Init(w *PublicKey, length int) *MessageGenerators
+```
+
+Init set the message generators to the default state
+
+## type [PokSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature.go#L21-L33>)
+
+PokSignature a\.k\.a\. Proof of Knowledge of a Signature is used by the prover to convince a verifier that they possess a valid signature and can selectively disclose a set of signed messages
+
+```go
+type PokSignature struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewPokSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature.go#L36-L39>)
+
+```go
+func NewPokSignature(sig *Signature, generators *MessageGenerators, msgs []common.ProofMessage, reader io.Reader) (*PokSignature, error)
+```
+
+NewPokSignature creates the initial proof data before a Fiat\-Shamir calculation
+
+### func \(\*PokSignature\) [GenerateProof](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature.go#L141>)
+
+```go
+func (pok *PokSignature) GenerateProof(challenge curves.Scalar) (*PokSignatureProof, error)
+```
+
+GenerateProof converts the blinding factors and secrets into Schnorr proofs
+
+### func \(\*PokSignature\) [GetChallengeContribution](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature.go#L132>)
+
+```go
+func (pok *PokSignature) GetChallengeContribution(transcript *merlin.Transcript)
+```
+
+GetChallengeContribution returns the bytes that should be added to a sigma protocol transcript for generating the challenge
+
+## type [PokSignatureProof](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L19-L22>)
+
+PokSignatureProof is the actual proof sent from a prover to a verifier that contains a proof of knowledge of a signature and the selective disclosure proof
+
+```go
+type PokSignatureProof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(PokSignatureProof\) [GetChallengeContribution](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L114-L119>)
+
+```go
+func (pok PokSignatureProof) GetChallengeContribution(generators *MessageGenerators, revealedMessages map[int]curves.Scalar, challenge common.Challenge, transcript *merlin.Transcript)
+```
+
+GetChallengeContribution converts the committed values to bytes for the Fiat\-Shamir challenge
+
+### func \(\*PokSignatureProof\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L26>)
+
+```go
+func (pok *PokSignatureProof) Init(curve *curves.PairingCurve) *PokSignatureProof
+```
+
+Init creates an empty proof to a specific curve which should be followed by UnmarshalBinary
+
+### func \(\*PokSignatureProof\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L38>)
+
+```go
+func (pok *PokSignatureProof) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PokSignatureProof\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L50>)
+
+```go
+func (pok *PokSignatureProof) UnmarshalBinary(in []byte) error
+```
+
+### func \(PokSignatureProof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L184-L191>)
+
+```go
+func (pok PokSignatureProof) Verify(revealedMsgs map[int]curves.Scalar, pk *PublicKey, generators *MessageGenerators, nonce common.Nonce, challenge common.Challenge, transcript *merlin.Transcript) bool
+```
+
+Verify checks a signature proof of knowledge and selective disclosure proof
+
+### func \(PokSignatureProof\) [VerifySigPok](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/pok_signature_proof.go#L176>)
+
+```go
+func (pok PokSignatureProof) VerifySigPok(pk *PublicKey) bool
+```
+
+VerifySigPok only validates the signature proof\, the selective disclosure proof is checked by verifying pok\.challenge == computedChallenge
+
+## type [PublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/public_key.go#L15-L17>)
+
+PublicKey is a BBS\+ verification key
+
+```go
+type PublicKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*PublicKey\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/public_key.go#L19>)
+
+```go
+func (pk *PublicKey) Init(curve *curves.PairingCurve) *PublicKey
+```
+
+### func \(PublicKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/public_key.go#L24>)
+
+```go
+func (pk PublicKey) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*PublicKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/public_key.go#L28>)
+
+```go
+func (pk *PublicKey) UnmarshalBinary(in []byte) error
+```
+
+### func \(PublicKey\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/public_key.go#L38>)
+
+```go
+func (pk PublicKey) Verify(signature *Signature, generators *MessageGenerators, msgs []curves.Scalar) error
+```
+
+Verify checks a signature where all messages are known to the verifier
+
+## type [SecretKey](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L20-L22>)
+
+SecretKey is a BBS\+ signing key
+
+```go
+type SecretKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewSecretKey](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L24>)
+
+```go
+func NewSecretKey(curve *curves.PairingCurve) (*SecretKey, error)
+```
+
+### func \(\*SecretKey\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L81>)
+
+```go
+func (sk *SecretKey) Init(curve *curves.PairingCurve) *SecretKey
+```
+
+### func \(SecretKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L86>)
+
+```go
+func (sk SecretKey) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*SecretKey\) [PublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L130>)
+
+```go
+func (sk *SecretKey) PublicKey() *PublicKey
+```
+
+PublicKey returns the corresponding public key
+
+### func \(\*SecretKey\) [Sign](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L100>)
+
+```go
+func (sk *SecretKey) Sign(generators *MessageGenerators, msgs []curves.Scalar) (*Signature, error)
+```
+
+Sign generates a new signature where all messages are known to the signer
+
+### func \(\*SecretKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/secret_key.go#L90>)
+
+```go
+func (sk *SecretKey) UnmarshalBinary(in []byte) error
+```
+
+## type [Signature](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/signature.go#L17-L20>)
+
+Signature is a BBS\+ signature as described in 4\.3 in \<https://eprint.iacr.org/2016/663.pdf\>
+
+```go
+type Signature struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*Signature\) [Init](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/signature.go#L24>)
+
+```go
+func (sig *Signature) Init(curve *curves.PairingCurve) *Signature
+```
+
+Init creates an empty signature to a specific curve which should be followed by UnmarshalBinary or Create
+
+### func \(Signature\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/signature.go#L31>)
+
+```go
+func (sig Signature) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*Signature\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/bbs/signature.go#L37>)
+
+```go
+func (sig *Signature) UnmarshalBinary(data []byte) error
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/signatures/bbs/blind_signature.go b/pkg/signatures/bbs/blind_signature.go
new file mode 100644
index 00000000..78815916
--- /dev/null
+++ b/pkg/signatures/bbs/blind_signature.go
@@ -0,0 +1,73 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/signatures/common"
+)
+
+// BlindSignature is a BBS+ blind signature
+// structurally identical to `Signature` but
+// is used to help avoid misuse and confusion.
+//
+// 1 or more message have been hidden by the
+// potential signature holder so the signer
+// only knows a subset of the messages to be signed
+type BlindSignature struct {
+	a    curves.PairingPoint
+	e, s curves.Scalar
+}
+
+// Init creates an empty signature to a specific curve
+// which should be followed by UnmarshalBinary
+func (sig *BlindSignature) Init(curve *curves.PairingCurve) *BlindSignature {
+	sig.a = curve.NewG1IdentityPoint()
+	sig.e = curve.NewScalar()
+	sig.s = curve.NewScalar()
+	return sig
+}
+
+func (sig BlindSignature) MarshalBinary() ([]byte, error) {
+	out := append(sig.a.ToAffineCompressed(), sig.e.Bytes()...)
+	out = append(out, sig.s.Bytes()...)
+	return out, nil
+}
+
+func (sig *BlindSignature) UnmarshalBinary(data []byte) error {
+	pointLength := len(sig.a.ToAffineCompressed())
+	scalarLength := len(sig.s.Bytes())
+	expectedLength := pointLength + scalarLength*2
+	if len(data) != expectedLength {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	a, err := sig.a.FromAffineCompressed(data[:pointLength])
+	if err != nil {
+		return err
+	}
+	e, err := sig.e.SetBytes(data[pointLength:(pointLength + scalarLength)])
+	if err != nil {
+		return err
+	}
+	s, err := sig.s.SetBytes(data[(pointLength + scalarLength):])
+	if err != nil {
+		return err
+	}
+	sig.a = a.(curves.PairingPoint)
+	sig.e = e
+	sig.s = s
+	return nil
+}
+
+func (sig BlindSignature) ToUnblinded(blinder common.SignatureBlinding) *Signature {
+	return &Signature{
+		a: sig.a,
+		e: sig.e,
+		s: sig.s.Add(blinder),
+	}
+}
diff --git a/pkg/signatures/bbs/blind_signature_context.go b/pkg/signatures/bbs/blind_signature_context.go
new file mode 100644
index 00000000..de00a0bc
--- /dev/null
+++ b/pkg/signatures/bbs/blind_signature_context.go
@@ -0,0 +1,253 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/signatures/common"
+	"github.com/gtank/merlin"
+	"golang.org/x/crypto/sha3"
+	"io"
+	"sort"
+)
+
+// BlindSignatureContext contains the data used for computing
+// a blind signature and verifying proof of hidden messages from
+// a future signature holder. A potential holder commits to messages
+// that the signer will not know during the signing process
+// rendering them hidden, but requires the holder to
+// prove knowledge of those messages so a malicious party
+// doesn't add just random data from anywhere.
+type BlindSignatureContext struct {
+	// The blinded signature commitment
+	commitment common.Commitment
+	// The challenge hash for the Fiat-Shamir heuristic
+	challenge curves.Scalar
+	// The proofs of hidden messages.
+	proofs []curves.Scalar
+}
+
+// NewBlindSignatureContext creates the data needed to
+// send to a signer to complete a blinded signature
+// `msgs` is an index to message map where the index
+// corresponds to the index in `generators`
+// msgs are hidden from the signer but can also be empty
+// if no messages are hidden but a blind signature is still desired
+// because the signer should have no knowledge of the signature
+func NewBlindSignatureContext(curve *curves.PairingCurve, msgs map[int]curves.Scalar, generators *MessageGenerators, nonce common.Nonce, reader io.Reader) (*BlindSignatureContext, common.SignatureBlinding, error) {
+	if curve == nil || generators == nil || nonce == nil || reader == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+	points := make([]curves.Point, 0)
+	secrets := make([]curves.Scalar, 0)
+
+	committing := common.NewProofCommittedBuilder(&curves.Curve{
+		Scalar: curve.Scalar,
+		Point:  curve.Scalar.Point().(curves.PairingPoint).OtherGroup(),
+		Name:   curve.Name,
+	})
+
+	// C = h0^blinding_factor*h_i^m_i.....
+	for i, m := range msgs {
+		if i > generators.length || i < 0 {
+			return nil, nil, fmt.Errorf("invalid index")
+		}
+		secrets = append(secrets, m)
+		pt := generators.Get(i + 1)
+		points = append(points, pt)
+		err := committing.CommitRandom(pt, reader)
+		if err != nil {
+			return nil, nil, err
+		}
+	}
+	blinding, ok := curve.Scalar.Random(reader).(common.SignatureBlinding)
+	if !ok {
+		return nil, nil, fmt.Errorf("unable to create signature blinding")
+	}
+	secrets = append(secrets, blinding)
+
+	h0 := generators.Get(0)
+	points = append(points, h0)
+	err := committing.CommitRandom(h0, reader)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Create a random commitment, compute challenges and response.
+	// The proof of knowledge consists of a commitment and responses
+	// Holder and signer engage in a proof of knowledge for `commitment`
+	commitment := curve.Scalar.Point().(curves.PairingPoint).OtherGroup().SumOfProducts(points, secrets)
+	transcript := merlin.NewTranscript("new blind signature")
+	transcript.AppendMessage([]byte("random commitment"), committing.GetChallengeContribution())
+	transcript.AppendMessage([]byte("blind commitment"), commitment.ToAffineCompressed())
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	okm := transcript.ExtractBytes([]byte("blind signature context challenge"), 64)
+	challenge, err := curve.Scalar.SetBytesWide(okm)
+	if err != nil {
+		return nil, nil, err
+	}
+	proofs, err := committing.GenerateProof(challenge, secrets)
+	if err != nil {
+		return nil, nil, err
+	}
+	return &BlindSignatureContext{
+		commitment: commitment,
+		challenge:  challenge,
+		proofs:     proofs,
+	}, blinding, nil
+}
+
+func (bsc *BlindSignatureContext) Init(curve *curves.PairingCurve) *BlindSignatureContext {
+	bsc.challenge = curve.NewScalar()
+	bsc.commitment = curve.Scalar.Point().(curves.PairingPoint).OtherGroup()
+	bsc.proofs = make([]curves.Scalar, 0)
+	return bsc
+}
+
+// MarshalBinary store the generators as a sequence of bytes
+// where each point is compressed.
+// Needs (N + 1) * ScalarSize + PointSize
+func (bsc BlindSignatureContext) MarshalBinary() ([]byte, error) {
+	buffer := append(bsc.commitment.ToAffineCompressed(), bsc.challenge.Bytes()...)
+	for _, p := range bsc.proofs {
+		buffer = append(buffer, p.Bytes()...)
+	}
+	return buffer, nil
+}
+
+func (bsc *BlindSignatureContext) UnmarshalBinary(in []byte) error {
+	scSize := len(bsc.challenge.Bytes())
+	ptSize := len(bsc.commitment.ToAffineCompressed())
+	if len(in) < scSize*2+ptSize {
+		return fmt.Errorf("insufficient number of bytes")
+	}
+
+	if (len(in)-ptSize)%scSize != 0 {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	commitment, err := bsc.commitment.FromAffineCompressed(in[:ptSize])
+	if err != nil {
+		return err
+	}
+	challenge, err := bsc.challenge.SetBytes(in[ptSize:(ptSize + scSize)])
+	if err != nil {
+		return err
+	}
+
+	nProofs := ((len(in) - ptSize) / scSize) - 1
+	proofs := make([]curves.Scalar, nProofs)
+	for i := 0; i < nProofs; i++ {
+		proofs[i], err = bsc.challenge.SetBytes(in[(ptSize + (i+1)*scSize):(ptSize + (i+2)*scSize)])
+		if err != nil {
+			return err
+		}
+	}
+	bsc.commitment = commitment
+	bsc.challenge = challenge
+	bsc.proofs = proofs
+	return nil
+}
+
+// Verify validates a proof of hidden messages
+func (bsc BlindSignatureContext) Verify(knownMsgs []int, generators *MessageGenerators, nonce common.Nonce) error {
+	known := make(map[int]bool, len(knownMsgs))
+	for _, i := range knownMsgs {
+		if i > generators.length {
+			return fmt.Errorf("invalid message index")
+		}
+		known[i] = true
+	}
+
+	points := make([]curves.Point, 0)
+	for i := 0; i < generators.length; i++ {
+		if _, contains := known[i]; !contains {
+			points = append(points, generators.Get(i+1))
+		}
+	}
+	points = append(points, generators.Get(0), bsc.commitment)
+	scalars := append(bsc.proofs, bsc.challenge.Neg())
+
+	commitment := points[0].SumOfProducts(points, scalars)
+	transcript := merlin.NewTranscript("new blind signature")
+	transcript.AppendMessage([]byte("random commitment"), commitment.ToAffineCompressed())
+	transcript.AppendMessage([]byte("blind commitment"), bsc.commitment.ToAffineCompressed())
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	okm := transcript.ExtractBytes([]byte("blind signature context challenge"), 64)
+	challenge, err := bsc.challenge.SetBytesWide(okm)
+	if err != nil {
+		return err
+	}
+
+	if challenge.Cmp(bsc.challenge) != 0 {
+		return fmt.Errorf("invalid proof")
+	}
+	return nil
+}
+
+// ToBlindSignature converts a blind signature where
+// msgs are known to the signer
+// `msgs` is an index to message map where the index
+// corresponds to the index in `generators`
+func (bsc BlindSignatureContext) ToBlindSignature(msgs map[int]curves.Scalar, sk *SecretKey, generators *MessageGenerators, nonce common.Nonce) (*BlindSignature, error) {
+	if sk == nil || generators == nil || nonce == nil {
+		return nil, internal.ErrNilArguments
+	}
+	if sk.value.IsZero() {
+		return nil, fmt.Errorf("invalid secret key")
+	}
+	tv1 := make([]int, 0, len(msgs))
+	for i := range msgs {
+		if i > generators.length {
+			return nil, fmt.Errorf("not enough message generators")
+		}
+		tv1 = append(tv1, i)
+	}
+	sort.Ints(tv1)
+	signingMsgs := make([]curves.Scalar, len(msgs))
+	for i, index := range tv1 {
+		signingMsgs[i] = msgs[index]
+	}
+	err := bsc.Verify(tv1, generators, nonce)
+	if err != nil {
+		return nil, err
+	}
+
+	drbg := sha3.NewShake256()
+	_, _ = drbg.Write(sk.value.Bytes())
+	addDeterministicNonceData(generators, signingMsgs, drbg)
+	// Should yield non-zero values for `e` and `s`, very small likelihood of being zero
+	e := getNonZeroScalar(sk.value, drbg)
+	s := getNonZeroScalar(sk.value, drbg)
+
+	exp, err := e.Add(sk.value).Invert()
+	if err != nil {
+		return nil, err
+	}
+	// B = g1+h_0^s+h_1^m_1...
+	points := make([]curves.Point, len(msgs)+3)
+	scalars := make([]curves.Scalar, len(msgs)+3)
+	points[0] = bsc.commitment
+	points[1] = bsc.commitment.Generator()
+	points[2] = generators.Get(0)
+	scalars[0] = sk.value.One()
+	scalars[1] = sk.value.One()
+	scalars[2] = s
+	i := 3
+	for idx, m := range msgs {
+		points[i] = generators.Get(idx + 1)
+		scalars[i] = m
+		i++
+	}
+	b := bsc.commitment.SumOfProducts(points, scalars)
+	return &BlindSignature{
+		a: b.Mul(exp).(curves.PairingPoint),
+		e: e,
+		s: s,
+	}, nil
+}
diff --git a/pkg/signatures/bbs/blind_signature_context_test.go b/pkg/signatures/bbs/blind_signature_context_test.go
new file mode 100644
index 00000000..d4080e2f
--- /dev/null
+++ b/pkg/signatures/bbs/blind_signature_context_test.go
@@ -0,0 +1,94 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	crand "crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/assert"
+	"testing"
+)
+
+func TestBlindSignatureContext(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	assert.NotNil(t, pk)
+	assert.NotNil(t, sk)
+
+	generators := new(MessageGenerators).Init(pk, 4)
+	nonce := curve.Scalar.Random(crand.Reader)
+	msgs := make(map[int]curves.Scalar, 1)
+	msgs[0] = curve.Scalar.Hash([]byte("identifier"))
+
+	ctx, blinding, err := NewBlindSignatureContext(curve, msgs, generators, nonce, crand.Reader)
+	assert.NoError(t, err)
+	assert.NotNil(t, blinding)
+	assert.False(t, blinding.IsZero())
+	assert.NotNil(t, ctx)
+	assert.False(t, ctx.commitment.IsIdentity())
+	assert.False(t, ctx.challenge.IsZero())
+	for _, p := range ctx.proofs {
+		assert.False(t, p.IsZero())
+	}
+
+	delete(msgs, 0)
+	msgs[1] = curve.Scalar.Hash([]byte("firstname"))
+	msgs[2] = curve.Scalar.Hash([]byte("lastname"))
+	msgs[3] = curve.Scalar.Hash([]byte("age"))
+	blindSig, err := ctx.ToBlindSignature(msgs, sk, generators, nonce)
+	assert.NoError(t, err)
+	assert.NotNil(t, blindSig)
+	assert.False(t, blindSig.a.IsIdentity())
+	assert.False(t, blindSig.e.IsZero())
+	assert.False(t, blindSig.s.IsZero())
+	sig := blindSig.ToUnblinded(blinding)
+	msgs[0] = curve.Scalar.Hash([]byte("identifier"))
+	var sigMsgs [4]curves.Scalar
+	for i := 0; i < 4; i++ {
+		sigMsgs[i] = msgs[i]
+	}
+	err = pk.Verify(sig, generators, sigMsgs[:])
+	assert.NoError(t, err)
+}
+
+func TestBlindSignatureContextMarshalBinary(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	assert.NotNil(t, pk)
+	assert.NotNil(t, sk)
+
+	generators := new(MessageGenerators).Init(pk, 4)
+	nonce := curve.Scalar.Random(crand.Reader)
+	msgs := make(map[int]curves.Scalar, 1)
+	msgs[0] = curve.Scalar.Hash([]byte("identifier"))
+
+	ctx, blinding, err := NewBlindSignatureContext(curve, msgs, generators, nonce, crand.Reader)
+	assert.NoError(t, err)
+	assert.NotNil(t, blinding)
+	assert.False(t, blinding.IsZero())
+	assert.NotNil(t, ctx)
+	assert.False(t, ctx.commitment.IsIdentity())
+	assert.False(t, ctx.challenge.IsZero())
+	for _, p := range ctx.proofs {
+		assert.False(t, p.IsZero())
+	}
+
+	data, err := ctx.MarshalBinary()
+	assert.NoError(t, err)
+	assert.NotNil(t, data)
+	ctx2 := new(BlindSignatureContext).Init(curve)
+	err = ctx2.UnmarshalBinary(data)
+	assert.NoError(t, err)
+	assert.Equal(t, ctx.challenge.Cmp(ctx2.challenge), 0)
+	assert.True(t, ctx.commitment.Equal(ctx2.commitment))
+	assert.Equal(t, len(ctx.proofs), len(ctx2.proofs))
+	for i, p := range ctx.proofs {
+		assert.Equal(t, p.Cmp(ctx2.proofs[i]), 0)
+	}
+}
diff --git a/pkg/signatures/bbs/doc.go b/pkg/signatures/bbs/doc.go
new file mode 100644
index 00000000..be10cdc1
--- /dev/null
+++ b/pkg/signatures/bbs/doc.go
@@ -0,0 +1,7 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
diff --git a/pkg/signatures/bbs/message_generators.go b/pkg/signatures/bbs/message_generators.go
new file mode 100644
index 00000000..0eed992c
--- /dev/null
+++ b/pkg/signatures/bbs/message_generators.go
@@ -0,0 +1,67 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// MessageGenerators are used to sign a vector of commitments for
+// a BBS+ signature. These must be the same generators used by
+// sign, verify, prove, and open
+//
+// These are generated in a deterministic manner. By using
+// MessageGenerators in this way, the generators do not need to be
+// stored alongside the public key and the same key can be used to sign
+// an arbitrary number of messages
+// Generators are created by computing
+// H_i = H_G1(W || I2OSP(0, 4) || I2OSP(0, 1) || I2OSP(length, 4))
+// where I2OSP means Integer to Octet Stream Primitive and
+// I2OSP represents an integer in a statically sized byte array.
+// `W` is the BBS+ public key.
+// Internally we store the 201 byte state since the only value that changes
+// is the index
+type MessageGenerators struct {
+	// Blinding factor generator, stored, so we know what points to return in `Get`
+	h0     curves.PairingPoint
+	length int
+	state  [201]byte
+}
+
+// Init set the message generators to the default state
+func (msgg *MessageGenerators) Init(w *PublicKey, length int) *MessageGenerators {
+	if length < 0 {
+		return nil
+	}
+	msgg.length = length
+	for i := range msgg.state {
+		msgg.state[i] = 0
+	}
+	copy(msgg.state[:192], w.value.ToAffineUncompressed())
+	msgg.state[197] = byte(length >> 24)
+	msgg.state[198] = byte(length >> 16)
+	msgg.state[199] = byte(length >> 8)
+	msgg.state[200] = byte(length)
+	msgg.h0 = w.value.OtherGroup().Hash(msgg.state[:]).(curves.PairingPoint)
+
+	return msgg
+}
+
+func (msgg MessageGenerators) Get(i int) curves.PairingPoint {
+	if i <= 0 {
+		return msgg.h0
+	}
+	if i > msgg.length {
+		return nil
+	}
+	state := msgg.state
+	state[193] = byte(i >> 24)
+	state[194] = byte(i >> 16)
+	state[195] = byte(i >> 8)
+	state[196] = byte(i)
+	return msgg.h0.Hash(msgg.state[:]).(curves.PairingPoint)
+}
diff --git a/pkg/signatures/bbs/pok_signature.go b/pkg/signatures/bbs/pok_signature.go
new file mode 100644
index 00000000..d632c829
--- /dev/null
+++ b/pkg/signatures/bbs/pok_signature.go
@@ -0,0 +1,157 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/signatures/common"
+	"github.com/gtank/merlin"
+	"io"
+)
+
+// PokSignature a.k.a. Proof of Knowledge of a Signature
+// is used by the prover to convince a verifier
+// that they possess a valid signature and
+// can selectively disclose a set of signed messages
+type PokSignature struct {
+	// These values correspond to values with the same name
+	// as section 4.5 in <https://eprint.iacr.org/2016/663.pdf>
+	aPrime, aBar, d curves.PairingPoint
+	// proof1 for proving signature
+	// proof2 for selective disclosure
+	proof1, proof2 *common.ProofCommittedBuilder
+	// secrets1 for proving signature
+	// secrets2 for proving relation
+	// g1 * h1^m1 * h2^m2.... for all disclosed messages
+	// m_i == d^r3 * h_0^{-s_prime} * h1^-m1 * h2^-m2.... for all undisclosed messages m_i
+	secrets1, secrets2 []curves.Scalar
+}
+
+// NewPokSignature creates the initial proof data before a Fiat-Shamir calculation
+func NewPokSignature(sig *Signature,
+	generators *MessageGenerators,
+	msgs []common.ProofMessage,
+	reader io.Reader) (*PokSignature, error) {
+
+	if len(msgs) != generators.length {
+		return nil, fmt.Errorf("mismatch messages and generators")
+	}
+
+	r1 := getNonZeroScalar(sig.s, reader)
+	r2 := getNonZeroScalar(sig.s, reader)
+	r3, err := r1.Invert()
+	if err != nil {
+		return nil, err
+	}
+
+	sigMsgs := make([]curves.Scalar, len(msgs))
+	for i, m := range msgs {
+		sigMsgs[i] = m.GetMessage()
+	}
+
+	b := computeB(sig.s, sigMsgs, generators)
+
+	aPrime, ok := sig.a.Mul(r1).(curves.PairingPoint)
+	if !ok {
+		return nil, fmt.Errorf("invalid point")
+	}
+	aBar, ok := b.Mul(r1).Sub(aPrime.Mul(sig.e)).(curves.PairingPoint)
+	if !ok {
+		return nil, fmt.Errorf("invalid point")
+	}
+	// d = b * r1 + h0 * r2
+	d, ok := aPrime.SumOfProducts([]curves.Point{b, generators.h0}, []curves.Scalar{r1, r2}).(curves.PairingPoint)
+	if !ok {
+		return nil, fmt.Errorf("invalid point")
+	}
+
+	// s' = s + r2r3
+	sPrime := sig.s.Add(r2.Mul(r3))
+
+	// For proving relation aBar - d = aPrime * -e + h0 * r2
+	curve := curves.Curve{
+		Scalar: sig.s.Zero(),
+		Point:  sig.a.Identity(),
+	}
+	proof1 := common.NewProofCommittedBuilder(&curve)
+	// For aPrime * -e
+	err = proof1.CommitRandom(aPrime, reader)
+	if err != nil {
+		return nil, err
+	}
+	err = proof1.CommitRandom(generators.h0, reader)
+	if err != nil {
+		return nil, err
+	}
+	secrets1 := []curves.Scalar{sig.e, r2}
+
+	// For selective disclosure
+	proof2 := common.NewProofCommittedBuilder(&curve)
+	// For d * -r3
+	err = proof2.CommitRandom(d.Neg(), reader)
+	if err != nil {
+		return nil, err
+	}
+	// For h0 * s'
+	err = proof2.CommitRandom(generators.h0, reader)
+	if err != nil {
+		return nil, err
+	}
+	secrets2 := make([]curves.Scalar, 0, len(msgs)+2)
+	secrets2 = append(secrets2, r3)
+	secrets2 = append(secrets2, sPrime)
+
+	for i, m := range msgs {
+		if m.IsHidden() {
+			err = proof2.Commit(generators.Get(i+1), m.GetBlinding(reader))
+			if err != nil {
+				return nil, err
+			}
+			secrets2 = append(secrets2, m.GetMessage())
+		}
+	}
+
+	return &PokSignature{
+		aPrime,
+		aBar,
+		d,
+		proof1,
+		proof2,
+		secrets1,
+		secrets2,
+	}, nil
+}
+
+// GetChallengeContribution returns the bytes that should be added to
+// a sigma protocol transcript for generating the challenge
+func (pok *PokSignature) GetChallengeContribution(transcript *merlin.Transcript) {
+	transcript.AppendMessage([]byte("A'"), pok.aPrime.ToAffineCompressed())
+	transcript.AppendMessage([]byte("Abar"), pok.aBar.ToAffineCompressed())
+	transcript.AppendMessage([]byte("D"), pok.d.ToAffineCompressed())
+	transcript.AppendMessage([]byte("Proof1"), pok.proof1.GetChallengeContribution())
+	transcript.AppendMessage([]byte("Proof2"), pok.proof2.GetChallengeContribution())
+}
+
+// GenerateProof converts the blinding factors and secrets into Schnorr proofs
+func (pok *PokSignature) GenerateProof(challenge curves.Scalar) (*PokSignatureProof, error) {
+	proof1, err := pok.proof1.GenerateProof(challenge, pok.secrets1)
+	if err != nil {
+		return nil, err
+	}
+	proof2, err := pok.proof2.GenerateProof(challenge, pok.secrets2)
+	if err != nil {
+		return nil, err
+	}
+	return &PokSignatureProof{
+		aPrime: pok.aPrime,
+		aBar:   pok.aBar,
+		d:      pok.d,
+		proof1: proof1,
+		proof2: proof2,
+	}, nil
+}
diff --git a/pkg/signatures/bbs/pok_signature_proof.go b/pkg/signatures/bbs/pok_signature_proof.go
new file mode 100644
index 00000000..3dc249c6
--- /dev/null
+++ b/pkg/signatures/bbs/pok_signature_proof.go
@@ -0,0 +1,200 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/signatures/common"
+	"github.com/gtank/merlin"
+)
+
+// PokSignatureProof is the actual proof sent from a prover
+// to a verifier that contains a proof of knowledge of a signature
+// and the selective disclosure proof
+type PokSignatureProof struct {
+	aPrime, aBar, d curves.PairingPoint
+	proof1, proof2  []curves.Scalar
+}
+
+// Init creates an empty proof to a specific curve
+// which should be followed by UnmarshalBinary
+func (pok *PokSignatureProof) Init(curve *curves.PairingCurve) *PokSignatureProof {
+	pok.aPrime = curve.Scalar.Point().(curves.PairingPoint).OtherGroup()
+	pok.aBar = pok.aPrime
+	pok.d = pok.aPrime
+	pok.proof1 = []curves.Scalar{
+		curve.Scalar.Zero(),
+		curve.Scalar.Zero(),
+	}
+	pok.proof2 = make([]curves.Scalar, 0)
+	return pok
+}
+
+func (pok *PokSignatureProof) MarshalBinary() ([]byte, error) {
+	data := append(pok.aPrime.ToAffineCompressed(), pok.aBar.ToAffineCompressed()...)
+	data = append(data, pok.d.ToAffineCompressed()...)
+	for _, p := range pok.proof1 {
+		data = append(data, p.Bytes()...)
+	}
+	for _, p := range pok.proof2 {
+		data = append(data, p.Bytes()...)
+	}
+	return data, nil
+}
+
+func (pok *PokSignatureProof) UnmarshalBinary(in []byte) error {
+	scSize := len(pok.proof1[0].Bytes())
+	ptSize := len(pok.aPrime.ToAffineCompressed())
+	minSize := scSize*4 + ptSize*3
+	inSize := len(in)
+	if inSize < minSize {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	if (inSize-ptSize)%scSize != 0 {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	secretCnt := ((inSize - ptSize*3) / scSize) - 2
+	offset := 0
+	end := ptSize
+
+	aPrime, err := pok.aPrime.FromAffineCompressed(in[offset:end])
+	if err != nil {
+		return err
+	}
+	offset = end
+	end += ptSize
+	aBar, err := pok.aBar.FromAffineCompressed(in[offset:end])
+	if err != nil {
+		return err
+	}
+	offset = end
+	end += ptSize
+	d, err := pok.d.FromAffineCompressed(in[offset:end])
+	if err != nil {
+		return err
+	}
+	offset = end
+	end += scSize
+	proof1i0, err := pok.proof1[0].SetBytes(in[offset:end])
+	if err != nil {
+		return err
+	}
+	offset = end
+	end += scSize
+	proof1i1, err := pok.proof1[1].SetBytes(in[offset:end])
+	if err != nil {
+		return err
+	}
+	proof2 := make([]curves.Scalar, secretCnt)
+	for i := 0; i < secretCnt; i++ {
+		offset = end
+		end += scSize
+		proof2[i], err = pok.proof1[0].SetBytes(in[offset:end])
+		if err != nil {
+			return err
+		}
+	}
+
+	pok.aPrime = aPrime.(curves.PairingPoint)
+	pok.aBar = aBar.(curves.PairingPoint)
+	pok.d = d.(curves.PairingPoint)
+	pok.proof1[0] = proof1i0
+	pok.proof1[1] = proof1i1
+	pok.proof2 = proof2
+	return nil
+}
+
+// GetChallengeContribution converts the committed values to bytes
+// for the Fiat-Shamir challenge
+func (pok PokSignatureProof) GetChallengeContribution(
+	generators *MessageGenerators,
+	revealedMessages map[int]curves.Scalar,
+	challenge common.Challenge,
+	transcript *merlin.Transcript,
+) {
+	transcript.AppendMessage([]byte("A'"), pok.aPrime.ToAffineCompressed())
+	transcript.AppendMessage([]byte("Abar"), pok.aBar.ToAffineCompressed())
+	transcript.AppendMessage([]byte("D"), pok.d.ToAffineCompressed())
+
+	proof1Points := []curves.Point{pok.aBar.Sub(pok.d), pok.aPrime, generators.h0}
+	proof1Scalars := []curves.Scalar{challenge, pok.proof1[0], pok.proof1[1]}
+	commitmentProof1 := pok.aPrime.SumOfProducts(proof1Points, proof1Scalars)
+	transcript.AppendMessage([]byte("Proof1"), commitmentProof1.ToAffineCompressed())
+
+	rPoints := make([]curves.Point, 1, len(revealedMessages)+1)
+	rScalars := make([]curves.Scalar, 1, len(revealedMessages)+1)
+
+	rPoints[0] = pok.aPrime.Generator()
+	rScalars[0] = pok.proof1[0].One()
+
+	for idx, msg := range revealedMessages {
+		rPoints = append(rPoints, generators.Get(idx+1))
+		rScalars = append(rScalars, msg)
+	}
+
+	r := pok.aPrime.SumOfProducts(rPoints, rScalars)
+
+	pts := 2 + generators.length - len(revealedMessages)
+	proof2Points := make([]curves.Point, 3, pts)
+	proof2Scalars := make([]curves.Scalar, 3, pts)
+
+	// R * c
+	proof2Points[0] = r
+	proof2Scalars[0] = challenge
+
+	// D * -r3Hat
+	proof2Points[1] = pok.d.Neg()
+	proof2Scalars[1] = pok.proof2[0]
+
+	// H0 * s'Hat
+	proof2Points[2] = generators.h0
+	proof2Scalars[2] = pok.proof2[1]
+
+	j := 2
+	for i := 0; i < generators.length; i++ {
+		if _, contains := revealedMessages[i]; contains {
+			continue
+		}
+		proof2Points = append(proof2Points, generators.Get(i+1))
+		proof2Scalars = append(proof2Scalars, pok.proof2[j])
+		j++
+	}
+	commitmentProof2 := r.SumOfProducts(proof2Points, proof2Scalars)
+
+	transcript.AppendMessage([]byte("Proof2"), commitmentProof2.ToAffineCompressed())
+}
+
+// VerifySigPok only validates the signature proof,
+// the selective disclosure proof is checked by
+// verifying
+// pok.challenge == computedChallenge
+func (pok PokSignatureProof) VerifySigPok(pk *PublicKey) bool {
+	return !pk.value.IsIdentity() &&
+		!pok.aPrime.IsIdentity() &&
+		!pok.aBar.IsIdentity() &&
+		pok.aPrime.MultiPairing(pok.aPrime, pk.value, pok.aBar, pk.value.Generator().Neg().(curves.PairingPoint)).IsOne()
+}
+
+// Verify checks a signature proof of knowledge and selective disclosure proof
+func (pok PokSignatureProof) Verify(
+	revealedMsgs map[int]curves.Scalar,
+	pk *PublicKey,
+	generators *MessageGenerators,
+	nonce common.Nonce,
+	challenge common.Challenge,
+	transcript *merlin.Transcript,
+) bool {
+	pok.GetChallengeContribution(generators, revealedMsgs, challenge, transcript)
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	okm := transcript.ExtractBytes([]byte("signature proof of knowledge"), 64)
+	vChallenge, err := pok.proof1[0].SetBytesWide(okm)
+	if err != nil {
+		return false
+	}
+	return pok.VerifySigPok(pk) && challenge.Cmp(vChallenge) == 0
+}
diff --git a/pkg/signatures/bbs/pok_signature_proof_test.go b/pkg/signatures/bbs/pok_signature_proof_test.go
new file mode 100644
index 00000000..03ae4f44
--- /dev/null
+++ b/pkg/signatures/bbs/pok_signature_proof_test.go
@@ -0,0 +1,163 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	crand "crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/signatures/common"
+	"github.com/gtank/merlin"
+	"github.com/stretchr/testify/assert"
+	"testing"
+)
+
+func TestPokSignatureProofWorks(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	assert.NotNil(t, sk)
+	assert.NotNil(t, pk)
+	assert.False(t, sk.value.IsZero())
+	assert.False(t, pk.value.IsIdentity())
+	_, ok := pk.value.(*curves.PointBls12381G2)
+	assert.True(t, ok)
+	generators := new(MessageGenerators).Init(pk, 4)
+	msgs := []curves.Scalar{
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+		curve.Scalar.New(5),
+	}
+
+	sig, err := sk.Sign(generators, msgs)
+	assert.NoError(t, err)
+	assert.NotNil(t, sig)
+	assert.False(t, sig.a.IsIdentity())
+	assert.False(t, sig.e.IsZero())
+	assert.False(t, sig.s.IsZero())
+
+	proofMsgs := []common.ProofMessage{
+		&common.ProofSpecificMessage{
+			Message: msgs[0],
+		},
+		&common.ProofSpecificMessage{
+			Message: msgs[1],
+		},
+		&common.RevealedMessage{
+			Message: msgs[2],
+		},
+		&common.RevealedMessage{
+			Message: msgs[3],
+		},
+	}
+
+	pok, err := NewPokSignature(sig, generators, proofMsgs, crand.Reader)
+	assert.NoError(t, err)
+	assert.NotNil(t, pok)
+	nonce := curve.Scalar.Random(crand.Reader)
+	transcript := merlin.NewTranscript("TestPokSignatureProofWorks")
+	pok.GetChallengeContribution(transcript)
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	okm := transcript.ExtractBytes([]byte("signature proof of knowledge"), 64)
+	challenge, err := curve.Scalar.SetBytesWide(okm)
+	assert.NoError(t, err)
+
+	pokSig, err := pok.GenerateProof(challenge)
+	assert.NoError(t, err)
+	assert.NotNil(t, pokSig)
+	assert.True(t, pokSig.VerifySigPok(pk))
+
+	revealedMsgs := map[int]curves.Scalar{
+		2: msgs[2],
+		3: msgs[3],
+	}
+	// Manual verify to show how when used in conjunction with other ZKPs
+	transcript = merlin.NewTranscript("TestPokSignatureProofWorks")
+	pokSig.GetChallengeContribution(generators, revealedMsgs, challenge, transcript)
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	okm = transcript.ExtractBytes([]byte("signature proof of knowledge"), 64)
+	vChallenge, err := curve.Scalar.SetBytesWide(okm)
+	assert.NoError(t, err)
+	assert.Equal(t, challenge.Cmp(vChallenge), 0)
+
+	// Use the all-inclusive method
+	transcript = merlin.NewTranscript("TestPokSignatureProofWorks")
+	assert.True(t, pokSig.Verify(revealedMsgs, pk, generators, nonce, challenge, transcript))
+}
+
+func TestPokSignatureProofMarshalBinary(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	assert.NotNil(t, sk)
+	assert.NotNil(t, pk)
+	assert.False(t, sk.value.IsZero())
+	assert.False(t, pk.value.IsIdentity())
+	_, ok := pk.value.(*curves.PointBls12381G2)
+	assert.True(t, ok)
+	generators := new(MessageGenerators).Init(pk, 4)
+	msgs := []curves.Scalar{
+		curve.Scalar.New(2),
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+		curve.Scalar.New(5),
+	}
+
+	sig, err := sk.Sign(generators, msgs)
+	assert.NoError(t, err)
+	assert.NotNil(t, sig)
+	assert.False(t, sig.a.IsIdentity())
+	assert.False(t, sig.e.IsZero())
+	assert.False(t, sig.s.IsZero())
+
+	proofMsgs := []common.ProofMessage{
+		&common.ProofSpecificMessage{
+			Message: msgs[0],
+		},
+		&common.ProofSpecificMessage{
+			Message: msgs[1],
+		},
+		&common.RevealedMessage{
+			Message: msgs[2],
+		},
+		&common.RevealedMessage{
+			Message: msgs[3],
+		},
+	}
+
+	pok, err := NewPokSignature(sig, generators, proofMsgs, crand.Reader)
+	assert.NoError(t, err)
+	assert.NotNil(t, pok)
+	nonce := curve.Scalar.Random(crand.Reader)
+	transcript := merlin.NewTranscript("TestPokSignatureProofMarshalBinary")
+	pok.GetChallengeContribution(transcript)
+	transcript.AppendMessage([]byte("nonce"), nonce.Bytes())
+	challenge, err := curve.Scalar.SetBytesWide(transcript.ExtractBytes([]byte("signature proof of knowledge"), 64))
+	assert.NoError(t, err)
+
+	pokSig, err := pok.GenerateProof(challenge)
+	assert.NoError(t, err)
+	assert.NotNil(t, pokSig)
+
+	data, err := pokSig.MarshalBinary()
+	assert.NoError(t, err)
+	assert.NotNil(t, data)
+	pokSig2 := new(PokSignatureProof).Init(curve)
+	err = pokSig2.UnmarshalBinary(data)
+	assert.NoError(t, err)
+	assert.True(t, pokSig.aPrime.Equal(pokSig2.aPrime))
+	assert.True(t, pokSig.aBar.Equal(pokSig2.aBar))
+	assert.True(t, pokSig.d.Equal(pokSig2.d))
+	assert.Equal(t, len(pokSig.proof1), len(pokSig2.proof1))
+	assert.Equal(t, len(pokSig.proof2), len(pokSig2.proof2))
+	for i, p := range pokSig.proof1 {
+		assert.Equal(t, p.Cmp(pokSig2.proof1[i]), 0)
+	}
+	for i, p := range pokSig.proof2 {
+		assert.Equal(t, p.Cmp(pokSig2.proof2[i]), 0)
+	}
+}
diff --git a/pkg/signatures/bbs/public_key.go b/pkg/signatures/bbs/public_key.go
new file mode 100644
index 00000000..b91a01ee
--- /dev/null
+++ b/pkg/signatures/bbs/public_key.go
@@ -0,0 +1,67 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// PublicKey is a BBS+ verification key
+type PublicKey struct {
+	value curves.PairingPoint
+}
+
+func (pk *PublicKey) Init(curve *curves.PairingCurve) *PublicKey {
+	pk.value = curve.NewG2IdentityPoint()
+	return pk
+}
+
+func (pk PublicKey) MarshalBinary() ([]byte, error) {
+	return pk.value.ToAffineCompressed(), nil
+}
+
+func (pk *PublicKey) UnmarshalBinary(in []byte) error {
+	value, err := pk.value.FromAffineCompressed(in)
+	if err != nil {
+		return err
+	}
+	pk.value = value.(curves.PairingPoint)
+	return nil
+}
+
+// Verify checks a signature where all messages are known to the verifier
+func (pk PublicKey) Verify(signature *Signature, generators *MessageGenerators, msgs []curves.Scalar) error {
+	if generators.length < len(msgs) {
+		return fmt.Errorf("not enough message generators")
+	}
+	if len(msgs) < 1 {
+		return fmt.Errorf("invalid messages")
+	}
+	// Identity Point will always return true which is not what we want
+	if pk.value.IsIdentity() {
+		return fmt.Errorf("invalid public key")
+	}
+	if signature.a.IsIdentity() {
+		return fmt.Errorf("invalid signature")
+	}
+	a, ok := pk.value.Generator().Mul(signature.e).Add(pk.value).(curves.PairingPoint)
+	if !ok {
+		return fmt.Errorf("not a valid point")
+	}
+	b, ok := computeB(signature.s, msgs, generators).Neg().(curves.PairingPoint)
+	if !ok {
+		return fmt.Errorf("not a valid point")
+	}
+
+	res := a.MultiPairing(signature.a, a, b, pk.value.Generator().(curves.PairingPoint))
+	if !res.IsOne() {
+		return fmt.Errorf("invalid result")
+	}
+
+	return nil
+}
diff --git a/pkg/signatures/bbs/secret_key.go b/pkg/signatures/bbs/secret_key.go
new file mode 100644
index 00000000..de23e975
--- /dev/null
+++ b/pkg/signatures/bbs/secret_key.go
@@ -0,0 +1,170 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	crand "crypto/rand"
+	"crypto/sha256"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"golang.org/x/crypto/hkdf"
+	"golang.org/x/crypto/sha3"
+	"io"
+)
+
+// SecretKey is a BBS+ signing key
+type SecretKey struct {
+	value curves.PairingScalar
+}
+
+func NewSecretKey(curve *curves.PairingCurve) (*SecretKey, error) {
+	// The salt used with generating secret keys
+	// See section 2.3 from https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04
+	const hkdfKeyGenSalt = "BLS-SIG-KEYGEN-SALT-"
+	const Size = 33
+	var ikm [Size]byte
+	cnt, err := crand.Read(ikm[:32])
+	if err != nil {
+		return nil, err
+	}
+	if cnt != Size-1 {
+		return nil, fmt.Errorf("unable to read sufficient random data")
+	}
+
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04#section-2.3
+	h := sha256.New()
+	n, err := h.Write([]byte(hkdfKeyGenSalt))
+	if err != nil {
+		return nil, err
+	}
+	if n != len(hkdfKeyGenSalt) {
+		return nil, fmt.Errorf("incorrect salt bytes written to be hashed")
+	}
+	salt := h.Sum(nil)
+
+	// Leaves key_info parameter as the default empty string
+	// and just adds parameter I2OSP(L, 2)
+	kdf := hkdf.New(sha256.New, ikm[:], salt, []byte{0, 48})
+	var okm [48]byte
+	read, err := kdf.Read(okm[:])
+	if err != nil {
+		return nil, err
+	}
+	if read != 48 {
+		return nil, fmt.Errorf("failed to create secret key")
+	}
+	v, err := curve.Scalar.SetBytesWide(okm[:])
+	if err != nil {
+		return nil, err
+	}
+	value, ok := v.(curves.PairingScalar)
+	if !ok {
+		return nil, fmt.Errorf("invalid scalar")
+	}
+	return &SecretKey{
+		value: value.SetPoint(curve.PointG2),
+	}, nil
+}
+
+func NewKeys(curve *curves.PairingCurve) (*PublicKey, *SecretKey, error) {
+	sk, err := NewSecretKey(curve)
+	if err != nil {
+		return nil, nil, err
+	}
+	return sk.PublicKey(), sk, nil
+}
+
+func (sk *SecretKey) Init(curve *curves.PairingCurve) *SecretKey {
+	sk.value = curve.NewScalar()
+	return sk
+}
+
+func (sk SecretKey) MarshalBinary() ([]byte, error) {
+	return sk.value.Bytes(), nil
+}
+
+func (sk *SecretKey) UnmarshalBinary(in []byte) error {
+	value, err := sk.value.SetBytes(in)
+	if err != nil {
+		return err
+	}
+	sk.value = value.(curves.PairingScalar)
+	return nil
+}
+
+// Sign generates a new signature where all messages are known to the signer
+func (sk *SecretKey) Sign(generators *MessageGenerators, msgs []curves.Scalar) (*Signature, error) {
+	if generators.length < len(msgs) {
+		return nil, fmt.Errorf("not enough message generators")
+	}
+	if len(msgs) < 1 {
+		return nil, fmt.Errorf("invalid messages")
+	}
+	if sk.value.IsZero() {
+		return nil, fmt.Errorf("invalid secret key")
+	}
+
+	drbg := sha3.NewShake256()
+	_, _ = drbg.Write(sk.value.Bytes())
+	addDeterministicNonceData(generators, msgs, drbg)
+	// Should yield non-zero values for `e` and `s`, very small likelihood of being zero
+	e := getNonZeroScalar(sk.value, drbg)
+	s := getNonZeroScalar(sk.value, drbg)
+	b := computeB(s, msgs, generators)
+	exp, err := e.Add(sk.value).Invert()
+	if err != nil {
+		return nil, err
+	}
+	return &Signature{
+		a: b.Mul(exp).(curves.PairingPoint),
+		e: e,
+		s: s,
+	}, nil
+}
+
+// PublicKey returns the corresponding public key
+func (sk *SecretKey) PublicKey() *PublicKey {
+	return &PublicKey{
+		value: sk.value.Point().Generator().Mul(sk.value).(curves.PairingPoint),
+	}
+}
+
+// computes g1 + s * h0 + msgs[0] * h[0] + msgs[1] * h[1] ...
+func computeB(s curves.Scalar, msgs []curves.Scalar, generators *MessageGenerators) curves.PairingPoint {
+	nMsgs := len(msgs)
+	points := make([]curves.Point, nMsgs+2)
+	points[1] = generators.Get(0)
+	points[0] = points[1].Generator()
+
+	scalars := make([]curves.Scalar, nMsgs+2)
+	scalars[0] = msgs[0].One()
+	scalars[1] = s
+	for i, m := range msgs {
+		points[i+2] = generators.Get(i + 1)
+		scalars[i+2] = m
+	}
+	pt := points[0].SumOfProducts(points, scalars)
+	return pt.(curves.PairingPoint)
+}
+
+func addDeterministicNonceData(generators *MessageGenerators, msgs []curves.Scalar, drbg io.Writer) {
+	for i := 0; i <= generators.length; i++ {
+		_, _ = drbg.Write(generators.Get(i).ToAffineUncompressed())
+	}
+	for _, m := range msgs {
+		_, _ = drbg.Write(m.Bytes())
+	}
+}
+
+func getNonZeroScalar(sc curves.Scalar, reader io.Reader) curves.Scalar {
+	// Should yield non-zero values for `e` and `s`, very small likelihood of being zero
+	e := sc.Random(reader)
+	for e.IsZero() {
+		e = sc.Random(reader)
+	}
+	return e
+}
diff --git a/pkg/signatures/bbs/signature.go b/pkg/signatures/bbs/signature.go
new file mode 100644
index 00000000..95e3052a
--- /dev/null
+++ b/pkg/signatures/bbs/signature.go
@@ -0,0 +1,60 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Signature is a BBS+ signature
+// as described in 4.3 in
+// <https://eprint.iacr.org/2016/663.pdf>
+type Signature struct {
+	a    curves.PairingPoint
+	e, s curves.Scalar
+}
+
+// Init creates an empty signature to a specific curve
+// which should be followed by UnmarshalBinary or Create
+func (sig *Signature) Init(curve *curves.PairingCurve) *Signature {
+	sig.a = curve.NewG1IdentityPoint()
+	sig.e = curve.NewScalar()
+	sig.s = curve.NewScalar()
+	return sig
+}
+
+func (sig Signature) MarshalBinary() ([]byte, error) {
+	out := append(sig.a.ToAffineCompressed(), sig.e.Bytes()...)
+	out = append(out, sig.s.Bytes()...)
+	return out, nil
+}
+
+func (sig *Signature) UnmarshalBinary(data []byte) error {
+	pointLength := len(sig.a.ToAffineCompressed())
+	scalarLength := len(sig.s.Bytes())
+	expectedLength := pointLength + scalarLength*2
+	if len(data) != expectedLength {
+		return fmt.Errorf("invalid byte sequence")
+	}
+	a, err := sig.a.FromAffineCompressed(data[:pointLength])
+	if err != nil {
+		return err
+	}
+	e, err := sig.e.SetBytes(data[pointLength:(pointLength + scalarLength)])
+	if err != nil {
+		return err
+	}
+	s, err := sig.s.SetBytes(data[(pointLength + scalarLength):])
+	if err != nil {
+		return err
+	}
+	sig.a = a.(curves.PairingPoint)
+	sig.e = e
+	sig.s = s
+	return nil
+}
diff --git a/pkg/signatures/bbs/signature_test.go b/pkg/signatures/bbs/signature_test.go
new file mode 100644
index 00000000..af71937f
--- /dev/null
+++ b/pkg/signatures/bbs/signature_test.go
@@ -0,0 +1,76 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package bbs
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/assert"
+	"testing"
+)
+
+func TestSignatureWorks(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	msgs := []curves.Scalar{
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+		curve.Scalar.New(5),
+		curve.Scalar.New(6),
+	}
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	generators := new(MessageGenerators).Init(pk, 4)
+
+	sig, err := sk.Sign(generators, msgs)
+	assert.NoError(t, err)
+	err = pk.Verify(sig, generators, msgs)
+	assert.NoError(t, err)
+}
+
+func TestSignatureIncorrectMessages(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	msgs := []curves.Scalar{
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+		curve.Scalar.New(5),
+		curve.Scalar.New(6),
+	}
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	generators := new(MessageGenerators).Init(pk, 4)
+
+	sig, err := sk.Sign(generators, msgs)
+	assert.NoError(t, err)
+	msgs[0] = curve.Scalar.New(7)
+	err = pk.Verify(sig, generators, msgs)
+	assert.Error(t, err)
+}
+
+func TestSignatureMarshalBinary(t *testing.T) {
+	curve := curves.BLS12381(&curves.PointBls12381G2{})
+	msgs := []curves.Scalar{
+		curve.Scalar.New(3),
+		curve.Scalar.New(4),
+		curve.Scalar.New(5),
+		curve.Scalar.New(6),
+	}
+	pk, sk, err := NewKeys(curve)
+	assert.NoError(t, err)
+	generators := new(MessageGenerators).Init(pk, 4)
+
+	sig, err := sk.Sign(generators, msgs)
+	assert.NoError(t, err)
+
+	data, err := sig.MarshalBinary()
+	assert.NoError(t, err)
+	assert.Equal(t, 112, len(data))
+	sig2 := new(Signature).Init(curve)
+	err = sig2.UnmarshalBinary(data)
+	assert.NoError(t, err)
+	assert.True(t, sig.a.Equal(sig2.a))
+	assert.Equal(t, sig.e.Cmp(sig2.e), 0)
+	assert.Equal(t, sig.s.Cmp(sig2.s), 0)
+}
diff --git a/pkg/signatures/bls/CHANGELOG b/pkg/signatures/bls/CHANGELOG
new file mode 100644
index 00000000..ea7e9729
--- /dev/null
+++ b/pkg/signatures/bls/CHANGELOG
@@ -0,0 +1,8 @@
+1.0.2
+    - Bring library into compliance with Draft V4 as shown in the [diff](https://www.ietf.org/rfcdiff?url1=draft-irtf-cfrg-bls-signature-03&url2=draft-irtf-cfrg-bls-signature-04)
+        - Hash `salt` before passing to HKDF
+1.0.1
+    - Bring library into compliance with Draft V3 as shown in the [diff](https://www.ietf.org/rfcdiff?url1=draft-irtf-cfrg-bls-signature-02&url2=draft-irtf-cfrg-bls-signature-03)
+    - Update README
+1.0.0
+    - Initial Release
diff --git a/pkg/signatures/bls/README.md b/pkg/signatures/bls/README.md
new file mode 100644
index 00000000..a02e1012
--- /dev/null
+++ b/pkg/signatures/bls/README.md
@@ -0,0 +1,112 @@
+# BLS Signatures
+
+An implementation of the Boneh-Lynn-Shacham (BLS) signatures according to the [standard](https://datatracker.ietf.org/doc/draft-irtf-cfrg-bls-signature/?include_text=1)
+on top of the Barreto-Lynn-Scott (BLS) 12-381 curve. The [BLS12-381 curve](https://github.com/zkcrypto/pairing/tree/master/src/bls12_381#serialization) provides roughly
+128-bits of security and BLS is a digital signature with aggregation properties.
+
+We have implemented all three signature schemes described in the [standard](https://datatracker.ietf.org/doc/draft-irtf-cfrg-bls-signature/?include_text=1)
+which are designed to handle rogue-key attacks differently. These three are:
+
+- **Basic** handles rogue key attacks by requiring all signed messages in an aggregate signature be distinct
+- **Message Augmentation** handles rogue key attacks by prepending the public key to the message during signing which ensures that all messages are distinct for different public keys.
+- **Proof of Possession** handles rogue key attacks by validating public keys in a separate step called a proof of possession. This allows for faster aggregate verification.
+
+Pairing-friendly curves have two generator-groups &#x1D53E;<sub>1</sub>, &#x1D53E;<sub>2</sub>. 
+Data in &#x1D53E;<sub>2</sub> is twice the size of &#x1D53E;<sub>1</sub> and operations are slower. 
+BLS signatures require signatures and public keys to be in opposite groups i.e. signatures in &#x1D53E;<sub>1</sub> and public keys in &#x1D53E;<sub>2</sub> or
+signatures in &#x1D53E;<sub>2</sub> and public keys in &#x1D53E;<sub>1</sub>. This means one of two things:
+
+- **Short public keys, long signatures**: Signatures are longer and slower to create, verify, and aggregate but public keys are small and fast to aggregate. Used when signing and verification operations not computed as often or for minimizing storage or bandwidth for public keys.
+- **Short signatures, long public keys**: Signatures are short and fast to create, verify, and aggregate but public keys are bigger and slower to aggregate. Used when signing and verification operations are computed often or for minimizing storage or bandwidth for signatures.
+
+This library supports both of these variants for all three signature schemes. The more widely deployed
+variant is short public keys, long signatures. We refer to this variant as `UsualBls`. The other variant,
+short signatures, long public keys, is named `TinyBls`.
+The naming convention follows Sig`SchemeType`[Vt] where **Vt** is short for variant. For example,
+
+- **Usual Bls Basic -> SigBasic**: Provides all the functions for the Basic signature scheme with signatures in &#x1D53E;<sub>2</sub> and public keys in &#x1D53E;<sub>1</sub>
+- **Tiny Bls Basic -> SigBasicVt**: Provides all the functions for the Basic signature scheme with signatures in &#x1D53E;<sub>1</sub> and public keys in &#x1D53E;<sub>2</sub>
+
+One final note, in cryptography, it is considered good practice to use domain separation values to limit attacks to specific contexts. The [standard](https://datatracker.ietf.org/doc/draft-irtf-cfrg-bls-signature/?include_text=1)
+recommends specific values for each scheme but this library also supports supplying custom domain separation values. For example, there are two functions for creating
+a BLS signing instance:
+
+- **NewSigBasic()** creates a Basic BLS signature using the recommended domain separation value.
+- **NewSigBasicWithDst(dst)** creates a Basic BLS signature using the parameter `dst` as the domain separation value such as in the [Eth2.0 Spec](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/phase0/validator.md#attestation-aggregation)
+
+Also implemented is Threshold BLS as described in section 3.2 of [B03](https://www.cc.gatech.edu/~aboldyre/papers/bold.pdf).
+
+- ThresholdKeygen(parts, threshold int) -> ([]*SecretKeyShare, error)
+- PartialSign(share *SecretKeyShare, msg []byte) -> *PartialSignature
+- CombineSigs(*PartialSignature...) -> *Signature
+
+## Security Considerations
+
+### Validating secret keys
+
+Low entropy secret keys are a problem since this means an attacker can more easily guess the value and now can impersonate the key holder.
+Secret keys are derived using trusted random number generators (TRNG). If the TRNG produces bad entropy
+the secret key will be weak. Secret keys are checked to be non-zero values. A zero value secret key
+not only fails the entropy test but also yields a public key that will validate any signature.
+
+[Malchemy](go/malchemy) is used to test the entropy of the secret keys. Malchemy runs
+5 entropy tests to validate secret keys. This library uses the BLS12-381 curve which has a bias
+in the modulus which causes malchemy to fail two tests: mean and &chi;<sup>2</sup>.
+These two tests do not account for this bias but does not mean the secret keys are not sufficiently random.
+The keys still pass the Shannon entropy, Monte Carlo Pi calculation, and Serial Correlation Coefficient tests.
+This is an acceptable pass rate.
+
+### Validating public keys
+
+Public keys are ensured to be valid. A valid public key means
+it represents a valid, non-identity elliptic curve point in the correct subgroup.
+Public keys that are the identity element mean any signature would pass a call to verify.
+
+### Validating signatures
+
+Generated signatures are ensured to be valid. A valid signature means
+it represents a valid, non-identity elliptic curve point in the correct subgroup.
+Signatures that are the identity element mean any signature would pass a call to verify.
+Verify checks signatures for non-identity elements in the correct subgroup before checking
+for a valid signature.
+
+### Mitigating Rogue Key Attacks
+
+A rogue key attacks can only happen to multisignature or aggregated signature.
+A rogue key attack is where at least one party produces a valid but malicious public key such that the multisignature requires less than the threshold to verify a signature.
+There are two ways to mitigate rogue key attacks: Guarantee all signed messages are unique or validate each public key before use. This library offers both solutions.
+
+## Comparison to other BLS implementations and integrations
+
+This library has been tested to be compatible with the following implementations
+by randomly generating millions of keys and signatures and importing and verifying
+between the two libraries.
+
+1. Ethereum's [py_ecc](https://github.com/ethereum/py_ecc)
+1. PhoreProject [Go BLS](https://github.com/phoreproject/bls)
+1. Herumi's [BLS](https://github.com/herumi/bls-eth-go-binary)
+1. Algorand's [Rust BLS Sig](https://crates.io/crates/bls_sigs_ref)
+1. Miracl's [Rust and Go BLS sig](https://github.com/miracl/core)
+
+The most common and high risk failures that can occur with library implementations
+are low entropy secret keys, malformed public keys, and invalid signature generation.
+
+Low entropy secret keys are a problem since this means an attacker can more easily guess
+the value and now can impersonate the key holder.
+
+Malformed public keys and signatures result in invalid addresses and no ability to withdraw funds.
+
+To check for these problems, We tested millions of keys/signatures (vs say thousands or hundreds) to prove that 
+
+1. The odds of producing an invalid key/signature is already theoretically low 2<sup>-255</sup>
+1. The results of running millions of checks shows that nothing bad happened in 10M attempts
+
+In other words, keys and signatures generated from these libraries can be consumed by this library
+and visa-versa.
+
+Some of the libraries, namely Algorand's and Miracl's implementations for hash to curve were either out of date
+or not compliant with the [IETF Spec](https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/).
+This meant that signatures generated by this library would not validate with Algorand or Miracl and visa-versa.
+However, public keys were found to be compatible in all libraries.
+
+This library is compliant with the latest version (10 as of this writing).
\ No newline at end of file
diff --git a/pkg/signatures/bls/bls_sig/lib.go b/pkg/signatures/bls/bls_sig/lib.go
new file mode 100644
index 00000000..82a2214d
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/lib.go
@@ -0,0 +1,187 @@
+package bls_sig
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"math/big"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+	"github.com/coinbase/kryptology/pkg/signatures/bls/finitefield"
+	"github.com/coinbase/kryptology/pkg/signatures/bls/shamir"
+	"golang.org/x/crypto/hkdf"
+)
+
+// Secret key in Fr
+const SecretKeySize = 32
+
+// Secret key share with identifier byte in Fr
+const SecretKeyShareSize = 33
+
+// The salt used with generating secret keys
+// See section 2.3 from https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+const hkdfKeyGenSalt = "BLS-SIG-KEYGEN-SALT-"
+
+var blsEngine = bls12381.NewEngine()
+
+// Represents a value mod r where r is the curve order or
+// order of the subgroups in G1 and G2
+type SecretKey struct {
+	value big.Int
+}
+
+func allRowsUnique(data [][]byte) bool {
+	seen := make(map[string]bool)
+	for _, row := range data {
+		m := string(row)
+		if _, ok := seen[m]; ok {
+			return false
+		}
+		seen[m] = true
+	}
+	return true
+}
+
+func generateRandBytes(count int) ([]byte, error) {
+	ikm := make([]byte, count)
+	cnt, err := rand.Read(ikm)
+	if err != nil {
+		return nil, err
+	}
+	if cnt != count {
+		return nil, fmt.Errorf("unable to read sufficient random data")
+	}
+	return ikm, nil
+}
+
+// Creates a new BLS secret key
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (sk SecretKey) Generate(ikm []byte) (*SecretKey, error) {
+	if len(ikm) < 32 {
+		return nil, fmt.Errorf("ikm is too short. Must be at least 32")
+	}
+
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-04#section-2.3
+	h := sha256.New()
+	n, err := h.Write([]byte(hkdfKeyGenSalt))
+	if err != nil {
+		return nil, err
+	}
+	if n != len(hkdfKeyGenSalt) {
+		return nil, fmt.Errorf("incorrect salt bytes written to be hashed")
+	}
+	salt := h.Sum(nil)
+
+	ikm = append(ikm, 0)
+	// Leaves key_info parameter as the default empty string
+	// and just adds parameter I2OSP(L, 2)
+	kdf := hkdf.New(sha256.New, ikm, salt, []byte{0, 48})
+	okm := make([]byte, 48)
+	read, err := kdf.Read(okm)
+	if err != nil {
+		return nil, err
+	}
+	if read != 48 {
+		return nil, fmt.Errorf("failed to create private key")
+	}
+	x := new(big.Int).SetBytes(okm)
+	v := new(big.Int).Mod(x, blsEngine.G1.Q())
+	return &SecretKey{value: *v}, nil
+}
+
+// Serialize a secret key to raw bytes
+func (sk SecretKey) MarshalBinary() ([]byte, error) {
+	bytes := sk.value.Bytes()
+	padding := make([]byte, SecretKeySize-len(bytes))
+	bytes = append(padding, bytes...)
+	return bytes, nil
+}
+
+// Deserialize a secret key from raw bytes
+// Cannot be zero. Must be 32 bytes and cannot be all zeroes.
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-2.3
+func (sk *SecretKey) UnmarshalBinary(data []byte) error {
+	if len(data) != SecretKeySize {
+		return fmt.Errorf("secret key must be %d bytes", SecretKeySize)
+	}
+	zeros := make([]byte, len(data))
+	if subtle.ConstantTimeCompare(data, zeros) == 1 {
+		return fmt.Errorf("secret key cannot be zero")
+	}
+	sk.value.SetBytes(data)
+	return nil
+}
+
+// SecretKeyShare is shamir share of a private key
+type SecretKeyShare struct {
+	value shamir.Share
+}
+
+// Serialize a secret key share to raw bytes
+func (sks SecretKeyShare) MarshalBinary() ([]byte, error) {
+	return sks.value.Bytes(), nil
+}
+
+// Deserialize a secret key share from raw bytes
+func (sks *SecretKeyShare) UnmarshalBinary(data []byte) error {
+	if len(data) != SecretKeyShareSize {
+		return fmt.Errorf("secret key share must be %d bytes", SecretKeyShareSize)
+	}
+
+	zeros := make([]byte, len(data))
+	if subtle.ConstantTimeCompare(data, zeros) == 1 {
+		return fmt.Errorf("secret key share cannot be zero")
+	}
+	q := blsEngine.G1.Q()
+	sks.value = *shamir.ShareFromBytes(data, finitefield.New(q))
+	return nil
+}
+
+// thresholdizeSecretKey splits a composite secret key such that
+// `threshold` partial signatures can be combined to form a composite signature
+func thresholdizeSecretKey(secretKey *SecretKey, threshold, total uint) ([]*SecretKeyShare, error) {
+	// Verify our parametes are acceptable.
+	if secretKey == nil {
+		return nil, fmt.Errorf("secret key is nil")
+	}
+	if threshold > total {
+		return nil, fmt.Errorf("threshold cannot be greater than the total")
+	}
+	if threshold == 0 {
+		return nil, fmt.Errorf("threshold cannot be zero")
+	}
+	if total <= 1 {
+		return nil, fmt.Errorf("total must be larger than 1")
+	}
+	if total > 255 || threshold > 255 {
+		return nil, fmt.Errorf("cannot have more than 255 shares")
+	}
+
+	// Marshal and split our secret key into shares
+	sk, err := secretKey.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	q := blsEngine.G1.Q()
+	shareSet, err := shamir.NewDealer(finitefield.New(q)).Split(sk, int(threshold), int(total))
+	if err != nil {
+		return nil, err
+	}
+	shares := shareSet.Shares
+
+	// Verify we got the expected number of shares
+	if uint(len(shares)) != total {
+		return nil, fmt.Errorf("shamir.NewDealer return %v != %v shares", len(shares), total)
+	}
+
+	// Package our shares
+	secrets := make([]*SecretKeyShare, len(shares))
+	for i, s := range shares {
+		sks := &SecretKeyShare{value: *s}
+		secrets[i] = sks
+	}
+
+	return secrets, nil
+}
diff --git a/pkg/signatures/bls/bls_sig/lib_test.go b/pkg/signatures/bls/bls_sig/lib_test.go
new file mode 100644
index 00000000..cdd8bee5
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/lib_test.go
@@ -0,0 +1,239 @@
+package bls_sig
+
+import (
+	"bytes"
+	"crypto/rand"
+	"encoding"
+	"math/big"
+	"testing"
+)
+
+func genSecretKey(t *testing.T) *SecretKey {
+	ikm := make([]byte, 32)
+	sk, err := new(SecretKey).Generate(ikm)
+	if err != nil {
+		t.Errorf("Couldn't generate secret key")
+	}
+	return sk
+}
+
+func genRandSecretKey(ikm []byte, t *testing.T) *SecretKey {
+	sk, err := new(SecretKey).Generate(ikm)
+	if err != nil {
+		t.Errorf("Couldn't generate secret key")
+	}
+	return sk
+}
+
+func genPublicKeyVt(sk *SecretKey, t *testing.T) *PublicKeyVt {
+	pk, err := sk.GetPublicKeyVt()
+	if err != nil {
+		t.Errorf("Expected GetPublicKeyVt to pass but failed: %v", err)
+	}
+	return pk
+}
+
+func genPublicKey(sk *SecretKey, t *testing.T) *PublicKey {
+	pk, err := sk.GetPublicKey()
+	if err != nil {
+		t.Errorf("GetPublicKey failed. Couldn't generate public key: %v", err)
+	}
+	return pk
+}
+
+func genSignature(sk *SecretKey, message []byte, t *testing.T) *Signature {
+	bls := NewSigPop()
+
+	sig, err := bls.Sign(sk, message)
+	if err != nil {
+		t.Errorf("createSignature couldn't sign message: %v", err)
+	}
+	return sig
+}
+
+func genSignatureVt(sk *SecretKey, message []byte, t *testing.T) *SignatureVt {
+	bls := NewSigPopVt()
+	sig, err := bls.Sign(sk, message)
+	if err != nil {
+		t.Errorf("createSignatureVt couldn't sign message: %v", err)
+	}
+	return sig
+}
+
+func readRand(ikm []byte, t *testing.T) {
+	n, err := rand.Read(ikm)
+	if err != nil || n < len(ikm) {
+		t.Errorf("Not enough data was read or an error occurred")
+	}
+}
+
+func assertSecretKeyGen(seed, expected []byte, t *testing.T) {
+	sk, err := new(SecretKey).Generate(seed)
+	if err != nil {
+		t.Errorf("Expected Generate to succeed but failed")
+	}
+	actual := sk.value.Bytes()
+	if len(actual) != len(expected) {
+		t.Errorf("Length of Generate output is incorrect. Expected 32, found: %v\n", len(actual))
+	}
+	if !bytes.Equal(actual, expected) {
+		t.Errorf("SecretKey was not as expected")
+	}
+}
+
+func marshalStruct(value encoding.BinaryMarshaler, t *testing.T) []byte {
+	out, err := value.MarshalBinary()
+	if err != nil {
+		t.Errorf("MarshalBinary failed: %v", err)
+	}
+	return out
+}
+
+func TestSecretKeyZeroBytes(t *testing.T) {
+	seed := []byte{}
+	_, err := new(SecretKey).Generate(seed)
+	if err == nil {
+		t.Errorf("Expected Generate to fail but succeeded")
+	}
+}
+
+func TestMarshalLeadingZeroes(t *testing.T) {
+	tests := []struct {
+		name string
+		in   []byte
+	}{
+		{"no leading zeroes", []byte{74, 53, 59, 227, 218, 192, 145, 160, 167, 230, 64, 98, 3, 114, 245, 225, 226, 228, 64, 23, 23, 193, 231, 156, 172, 111, 251, 168, 246, 144, 86, 4}},
+		{"one leading zero byte", []byte{00, 53, 59, 227, 218, 192, 145, 160, 167, 230, 64, 98, 3, 114, 245, 225, 226, 228, 64, 23, 23, 193, 231, 156, 172, 111, 251, 168, 246, 144, 86, 4}},
+		{"two leading zeroes", []byte{00, 00, 59, 227, 218, 192, 145, 160, 167, 230, 64, 98, 3, 114, 245, 225, 226, 228, 64, 23, 23, 193, 231, 156, 172, 111, 251, 168, 246, 144, 86, 4}},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		// Marshal
+		var k big.Int
+		k.SetBytes(test.in)
+		bytes, err := SecretKey{k}.MarshalBinary()
+		if err != nil {
+			t.Errorf("%v", err)
+			continue
+		}
+
+		// Test that marshal produces a values of the exected len
+		t.Run(test.name, func(t *testing.T) {
+			if len(bytes) != SecretKeySize {
+				t.Errorf("expected len=%v got len=%v", SecretKeySize, len(bytes))
+			}
+		})
+
+		// Test that we can also unmarhsal correctly
+		t.Run(test.name, func(t *testing.T) {
+			var actual SecretKey
+			err := actual.UnmarshalBinary(bytes)
+
+			// Test for error
+			if err != nil {
+				t.Errorf("%v", err)
+				return
+			}
+
+			// Test for correctness
+			if actual.value.Cmp(&k) != 0 {
+				t.Errorf("unmarshaled doens't match original value")
+			}
+		})
+	}
+}
+
+func TestSecretKey32Bytes(t *testing.T) {
+	seed := make([]byte, 32)
+	expected := []byte{77, 18, 154, 25, 223, 134, 160, 245, 52, 91, 173, 76, 198, 242, 73, 236, 42, 129, 156, 204, 51, 134, 137, 91, 235, 79, 125, 152, 179, 219, 98, 53}
+	assertSecretKeyGen(seed, expected, t)
+}
+
+func TestSecretKey128Bytes(t *testing.T) {
+	seed := make([]byte, 128)
+	expected := []byte{97, 207, 109, 96, 94, 90, 233, 215, 221, 207, 240, 139, 24, 209, 152, 170, 73, 209, 151, 241, 148, 176, 173, 92, 101, 48, 39, 175, 201, 219, 146, 168}
+	assertSecretKeyGen(seed, expected, t)
+}
+
+func TestRandomSecretKey(t *testing.T) {
+	seed := make([]byte, 48)
+	_, _ = rand.Read(seed)
+	_, err := new(SecretKey).Generate(seed)
+	if err != nil {
+		t.Errorf("Expected Generate to succeed but failed")
+	}
+}
+
+func TestSecretKeyToBytes(t *testing.T) {
+	sk := genSecretKey(t)
+	skBytes := marshalStruct(sk, t)
+	sk1 := new(SecretKey)
+	err := sk1.UnmarshalBinary(skBytes)
+	if err != nil {
+		t.Errorf("Expected UnmarshalBinary to pass but failed: %v", err)
+	}
+	for i, b := range sk1.value.Bytes() {
+		if skBytes[i] != b {
+			t.Errorf("Expected secret keys to be equal but are different at offset %d: %v != %v", i, skBytes[i], b)
+		}
+	}
+	sk2 := new(SecretKey)
+	err = sk2.UnmarshalBinary(skBytes)
+	if err != nil {
+		t.Errorf("Expected FromBytes to succeed but failed.")
+	}
+	if !bytes.Equal(marshalStruct(sk2, t), skBytes) {
+		t.Errorf("Expected secret keys to be equal but are different")
+	}
+}
+
+// Verifies that the thresholdize creates the expected number
+// of shares
+func TestThresholdizeSecretKeyCountsCorrect(t *testing.T) {
+	sk := &SecretKey{value: *big.NewInt(248631463258962596)}
+	tests := []struct {
+		key           *SecretKey
+		t, n          uint
+		expectedError bool
+	}{
+		// bad cases
+		{sk, 1, 1, true},     // n == 1
+		{sk, 1, 5, true},     // t == 1
+		{nil, 3, 5, true},    // sk nil
+		{sk, 101, 100, true}, // t> n
+		{sk, 0, 10, true},    // t == 0
+		{sk, 10, 256, true},  // n > 256
+
+		// good cases
+		{sk, 10, 10, false},   // t == n
+		{sk, 2, 10, false},    // boundary case for t
+		{sk, 9, 10, false},    // boundary case for t
+		{sk, 10, 255, false},  // boundary case for n
+		{sk, 254, 255, false}, // boundary case for t,n
+		{sk, 100, 200, false}, // arbitrary t,n values
+		{sk, 10, 20, false},   // arbitrary t,n values
+		{sk, 15, 200, false},  // arbitrary t,n values
+		{sk, 254, 255, false}, // boundary case
+		{sk, 255, 255, false}, // boundary case
+	}
+
+	// Run all the tests!
+	for _, test := range tests {
+		shares, err := thresholdizeSecretKey(test.key, test.t, test.n)
+
+		// Check for errors
+		if test.expectedError && err == nil {
+			t.Errorf("expected an error but received nil. t=%v, n=%v, sk=%v", test.t, test.n, sk)
+		}
+
+		// Check for errors
+		if !test.expectedError && err != nil {
+			t.Errorf("received unexpected error %v. t=%v, n=%v, sk=%v", err, test.t, test.n, sk)
+		}
+
+		// Check the share count == n
+		if !test.expectedError && test.n != uint(len(shares)) {
+			t.Errorf("expected len(shares) = %v != %v (n)", len(shares), test.n)
+		}
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/tiny_bls.go b/pkg/signatures/bls/bls_sig/tiny_bls.go
new file mode 100644
index 00000000..a61b88df
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/tiny_bls.go
@@ -0,0 +1,432 @@
+package bls_sig
+
+import (
+	"fmt"
+)
+
+const (
+	// Domain separation tag for basic signatures
+	// according to section 4.2.1 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignatureBasicVtDst = "BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_"
+	// Domain separation tag for basic signatures
+	// according to section 4.2.2 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignatureAugVtDst = "BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_AUG_"
+	// Domain separation tag for proof of possession signatures
+	// according to section 4.2.3 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignaturePopVtDst = "BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_POP_"
+	// Domain separation tag for proof of possession proofs
+	// according to section 4.2.3 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsPopProofVtDst = "BLS_POP_BLS12381G1_XMD:SHA-256_SSWU_RO_POP_"
+)
+
+type BlsSchemeVt interface {
+	Keygen() (*PublicKeyVt, *SecretKey, error)
+	KeygenWithSeed(ikm []byte) (*PublicKeyVt, *SecretKey, error)
+	Sign(sk *SecretKey, msg []byte) (*SignatureVt, error)
+	Verify(pk *PublicKeyVt, msg []byte, sig *SignatureVt) bool
+	AggregateVerify(pks []*PublicKeyVt, msgs [][]byte, sigs []*SignatureVt) bool
+}
+
+// generateKeysVt creates 32 bytes of random data to be fed to
+// generateKeysWithSeedVt
+func generateKeysVt() (*PublicKeyVt, *SecretKey, error) {
+	ikm, err := generateRandBytes(32)
+	if err != nil {
+		return nil, nil, err
+	}
+	return generateKeysWithSeedVt(ikm)
+}
+
+// generateKeysWithSeedVt generates a BLS key pair given input key material (ikm)
+func generateKeysWithSeedVt(ikm []byte) (*PublicKeyVt, *SecretKey, error) {
+	sk, err := new(SecretKey).Generate(ikm)
+	if err != nil {
+		return nil, nil, err
+	}
+	pk, err := sk.GetPublicKeyVt()
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, sk, nil
+}
+
+// thresholdGenerateKeys will generate random secret key shares and the corresponding public key
+func thresholdGenerateKeysVt(threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	pk, sk, err := generateKeysVt()
+	if err != nil {
+		return nil, nil, err
+	}
+	shares, err := thresholdizeSecretKey(sk, threshold, total)
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, shares, nil
+}
+
+// thresholdGenerateKeysWithSeed will generate random secret key shares and the corresponding public key
+// using the corresponding seed `ikm`
+func thresholdGenerateKeysWithSeedVt(ikm []byte, threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	pk, sk, err := generateKeysWithSeedVt(ikm)
+	if err != nil {
+		return nil, nil, err
+	}
+	shares, err := thresholdizeSecretKey(sk, threshold, total)
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, shares, nil
+}
+
+// SigBasic is minimal-pubkey-size scheme that doesn't support FastAggregateVerification.
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.1
+type SigBasicVt struct {
+	dst string
+}
+
+// Creates a new BLS basic signature scheme with the standard domain separation tag used for signatures.
+func NewSigBasicVt() *SigBasicVt {
+	return &SigBasicVt{dst: blsSignatureBasicVtDst}
+}
+
+// Creates a new BLS basic signature scheme with a custom domain separation tag used for signatures.
+func NewSigBasicVtWithDst(signDst string) *SigBasicVt {
+	return &SigBasicVt{dst: signDst}
+}
+
+// Creates a new BLS key pair
+func (b SigBasicVt) Keygen() (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysVt()
+}
+
+// Creates a new BLS key pair
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigBasicVt) KeygenWithSeed(ikm []byte) (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysWithSeedVt(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigBasicVt) ThresholdKeygen(threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysVt(threshold, total)
+}
+
+// ThresholdKeygenWithSeed generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures from input key material (ikm)
+func (b SigBasicVt) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeedVt(ikm, threshold, total)
+}
+
+// Computes a signature in G1 from sk, a secret key, and a message
+func (b SigBasicVt) Sign(sk *SecretKey, msg []byte) (*SignatureVt, error) {
+	return sk.createSignatureVt(msg, b.dst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigBasicVt) PartialSign(sks *SecretKeyShare, msg []byte) (*PartialSignatureVt, error) {
+	return sks.partialSignVt(msg, b.dst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigBasicVt) CombineSignatures(sigs ...*PartialSignatureVt) (*SignatureVt, error) {
+	return combineSigsVt(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+func (b SigBasicVt) Verify(pk *PublicKeyVt, msg []byte, sig *SignatureVt) (bool, error) {
+	return pk.verifySignatureVt(msg, sig, b.dst)
+}
+
+// The AggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// Each message must be different or this will return false.
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigBasicVt) AggregateVerify(pks []*PublicKeyVt, msgs [][]byte, sigs []*SignatureVt) (bool, error) {
+	if !allRowsUnique(msgs) {
+		return false, fmt.Errorf("all messages must be distinct")
+	}
+	asig, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, msgs, b.dst)
+}
+
+// SigAugVt is minimal-signature-size scheme that doesn't support FastAggregateVerification.
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.2
+type SigAugVt struct {
+	dst string
+}
+
+// Creates a new BLS message augmentation signature scheme with the standard domain separation tag used for signatures.
+func NewSigAugVt() *SigAugVt {
+	return &SigAugVt{dst: blsSignatureAugVtDst}
+}
+
+// Creates a new BLS message augmentation signature scheme with a custom domain separation tag used for signatures.
+func NewSigAugVtWithDst(signDst string) *SigAugVt {
+	return &SigAugVt{dst: signDst}
+}
+
+// Creates a new BLS key pair
+func (b SigAugVt) Keygen() (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysVt()
+}
+
+// Creates a new BLS secret key
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigAugVt) KeygenWithSeed(ikm []byte) (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysWithSeedVt(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigAugVt) ThresholdKeygen(threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysVt(threshold, total)
+}
+
+// ThresholdKeygenWithSeed generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigAugVt) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeedVt(ikm, threshold, total)
+}
+
+// Computes a signature in G1 from sk, a secret key, and a message
+// See section 3.2.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-02
+func (b SigAugVt) Sign(sk *SecretKey, msg []byte) (*SignatureVt, error) {
+	pk, err := sk.GetPublicKeyVt()
+	if err != nil {
+		return nil, err
+	}
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, fmt.Errorf("MarshalBinary failed")
+	}
+	bytes = append(bytes, msg...)
+	return sk.createSignatureVt(bytes, b.dst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigAugVt) PartialSign(sks *SecretKeyShare, pk *PublicKeyVt, msg []byte) (*PartialSignatureVt, error) {
+	if len(msg) == 0 {
+		return nil, fmt.Errorf("message cannot be empty or nil")
+	}
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, fmt.Errorf("MarshalBinary failed")
+	}
+	bytes = append(bytes, msg...)
+	return sks.partialSignVt(bytes, b.dst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigAugVt) CombineSignatures(sigs ...*PartialSignatureVt) (*SignatureVt, error) {
+	return combineSigsVt(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+// See section 3.2.2 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigAugVt) Verify(pk *PublicKeyVt, msg []byte, sig *SignatureVt) (bool, error) {
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return false, err
+	}
+	bytes = append(bytes, msg...)
+	return pk.verifySignatureVt(bytes, sig, b.dst)
+}
+
+// The aggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// See section 3.2.3 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigAugVt) AggregateVerify(pks []*PublicKeyVt, msgs [][]byte, sigs []*SignatureVt) (bool, error) {
+	if len(pks) != len(msgs) {
+		return false, fmt.Errorf("the number of public keys does not match the number of messages: %v != %v", len(pks), len(msgs))
+	}
+	data := make([][]byte, len(msgs))
+	for i, msg := range msgs {
+		bytes, err := pks[i].MarshalBinary()
+		if err != nil {
+			return false, err
+		}
+		data[i] = append(bytes, msg...)
+	}
+	asig, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, data, b.dst)
+}
+
+// SigEth2Vt supports signatures on Eth2.
+// Internally is an alias for SigPopVt
+type SigEth2Vt = SigPopVt
+
+// NewSigEth2Vt Creates a new BLS ETH2 signature scheme with the standard domain separation tag used for signatures.
+func NewSigEth2Vt() *SigEth2Vt {
+	return NewSigPopVt()
+}
+
+// SigPopVt is minimal-signature-size scheme that supports FastAggregateVerification
+// and requires using proofs of possession to mitigate rogue-key attacks
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.3
+type SigPopVt struct {
+	sigDst string
+	popDst string
+}
+
+// Creates a new BLS proof of possession signature scheme with the standard domain separation tag used for signatures.
+func NewSigPopVt() *SigPopVt {
+	return &SigPopVt{sigDst: blsSignaturePopVtDst, popDst: blsPopProofVtDst}
+}
+
+// Creates a new BLS message proof of possession signature scheme with a custom domain separation tag used for signatures.
+func NewSigPopVtWithDst(signDst, popDst string) (*SigPopVt, error) {
+	if signDst == popDst {
+		return nil, fmt.Errorf("domain separation tags cannot be equal")
+	}
+	return &SigPopVt{sigDst: signDst, popDst: popDst}, nil
+}
+
+// Creates a new BLS key pair
+func (b SigPopVt) Keygen() (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysVt()
+}
+
+// Creates a new BLS secret key
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigPopVt) KeygenWithSeed(ikm []byte) (*PublicKeyVt, *SecretKey, error) {
+	return generateKeysWithSeedVt(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigPopVt) ThresholdKeygen(threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysVt(threshold, total)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigPopVt) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKeyVt, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeedVt(ikm, threshold, total)
+}
+
+// Computes a signature in G1 from sk, a secret key, and a message
+// See section 2.6 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) Sign(sk *SecretKey, msg []byte) (*SignatureVt, error) {
+	return sk.createSignatureVt(msg, b.sigDst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigPopVt) PartialSign(sks *SecretKeyShare, msg []byte) (*PartialSignatureVt, error) {
+	return sks.partialSignVt(msg, b.sigDst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigPopVt) CombineSignatures(sigs ...*PartialSignatureVt) (*SignatureVt, error) {
+	return combineSigsVt(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+// See section 2.7 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) Verify(pk *PublicKeyVt, msg []byte, sig *SignatureVt) (bool, error) {
+	return pk.verifySignatureVt(msg, sig, b.sigDst)
+}
+
+// The aggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// Each message must be different or this will return false.
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-02
+func (b SigPopVt) AggregateVerify(pks []*PublicKeyVt, msgs [][]byte, sigs []*SignatureVt) (bool, error) {
+	if !allRowsUnique(msgs) {
+		return false, fmt.Errorf("all messages must be distinct")
+	}
+	asig, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, msgs, b.sigDst)
+}
+
+// Combine many signatures together to form a Multisignature.
+// Multisignatures can be created when multiple signers jointly
+// generate signatures over the same message.
+func (b SigPopVt) AggregateSignatures(sigs ...*SignatureVt) (*MultiSignatureVt, error) {
+	g1, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		return nil, err
+	}
+	return &MultiSignatureVt{value: g1.value}, nil
+}
+
+// Combine many public keys together to form a Multipublickey.
+// Multipublickeys are used to verify multisignatures.
+func (b SigPopVt) AggregatePublicKeys(pks ...*PublicKeyVt) (*MultiPublicKeyVt, error) {
+	g2, err := aggregatePublicKeysVt(pks...)
+	if err != nil {
+		return nil, err
+	}
+	return &MultiPublicKeyVt{value: g2.value}, nil
+}
+
+// Checks that a multisignature is valid for the message under the multi public key
+// Similar to FastAggregateVerify except the keys and signatures have already been
+// combined. See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-02
+func (b SigPopVt) VerifyMultiSignature(pk *MultiPublicKeyVt, msg []byte, sig *MultiSignatureVt) (bool, error) {
+	s := &SignatureVt{value: sig.value}
+	p := &PublicKeyVt{value: pk.value}
+	return p.verifySignatureVt(msg, s, b.sigDst)
+}
+
+// FastAggregateVerify verifies an aggregated signature over the same message under the given public keys.
+// See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) FastAggregateVerify(pks []*PublicKeyVt, msg []byte, asig *SignatureVt) (bool, error) {
+	apk, err := aggregatePublicKeysVt(pks...)
+	if err != nil {
+		return false, nil
+	}
+	return apk.verifySignatureVt(msg, asig, b.sigDst)
+}
+
+// FastAggregateVerifyConstituent verifies a list of signature over the same message under the given public keys.
+// See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) FastAggregateVerifyConstituent(pks []*PublicKeyVt, msg []byte, sigs []*SignatureVt) (bool, error) {
+	asig, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return b.FastAggregateVerify(pks, msg, asig)
+}
+
+// Create a proof of possession for the corresponding public key.
+// A proof of possession must be created for each public key to be used
+// in FastAggregateVerify or a Multipublickey to avoid rogue key attacks.
+// See section 3.3.2 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) PopProve(sk *SecretKey) (*ProofOfPossessionVt, error) {
+	return sk.createProofOfPossessionVt(b.popDst)
+}
+
+// verify a proof of possession for the corresponding public key is valid.
+// A proof of possession must be created for each public key to be used
+// in FastAggregateVerify or a Multipublickey to avoid rogue key attacks.
+// See section 3.3.3 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPopVt) PopVerify(pk *PublicKeyVt, pop1 *ProofOfPossessionVt) (bool, error) {
+	return pop1.verify(pk, b.popDst)
+}
diff --git a/pkg/signatures/bls/bls_sig/tiny_bls_sig.go b/pkg/signatures/bls/bls_sig/tiny_bls_sig.go
new file mode 100644
index 00000000..409985d8
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/tiny_bls_sig.go
@@ -0,0 +1,484 @@
+package bls_sig
+
+import (
+	"crypto/sha256"
+	"fmt"
+	"math/big"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+	"github.com/coinbase/kryptology/pkg/signatures/bls/finitefield"
+)
+
+// Implement BLS signatures on the BLS12-381 curve
+// according to https://crypto.standford.edu/~dabo/pubs/papers/BLSmultisig.html
+// and https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+// this file implements signatures in G1 and public keys in G2.
+// Public Keys and Signatures can be aggregated but the consumer
+// must use proofs of possession to defend against rogue-key attacks.
+
+const (
+	// Public key size in G2
+	PublicKeyVtSize = 96
+	// Signature size in G1
+	SignatureVtSize = 48
+	// Proof of Possession in G1
+	ProofOfPossessionVtSize = 48
+)
+
+// Represents a public key in G2
+type PublicKeyVt struct {
+	value bls12381.PointG2
+}
+
+// Serialize a public key to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pk *PublicKeyVt) MarshalBinary() ([]byte, error) {
+	return blsEngine.G2.ToCompressed(&pk.value), nil
+}
+
+// Deserialize a public key from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the public key
+// otherwise it will return an error
+func (pk *PublicKeyVt) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeyVtSize {
+		return fmt.Errorf("public key must be %d bytes", PublicKeySize)
+	}
+	p2, err := blsEngine.G2.FromCompressed(data)
+	if err != nil {
+		return err
+	}
+	if blsEngine.G2.IsZero(p2) {
+		return fmt.Errorf("public keys cannot be zero")
+	}
+	pk.value = *p2
+	return nil
+}
+
+// Represents a BLS signature in G1
+type SignatureVt struct {
+	value bls12381.PointG1
+}
+
+// Serialize a signature to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (sig *SignatureVt) MarshalBinary() ([]byte, error) {
+	return blsEngine.G1.ToCompressed(&sig.value), nil
+}
+
+func (sig *SignatureVt) verify(pk *PublicKeyVt, message []byte, signDstVt string) (bool, error) {
+	return pk.verifySignatureVt(message, sig, signDstVt)
+}
+
+// The AggregateVerify algorithm checks an aggregated signature over
+// several (PK, message) pairs.
+// The Signature is the output of aggregateSignaturesVt
+// Each message must be different or this will return false.
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (sig *SignatureVt) aggregateVerify(pks []*PublicKeyVt, msgs [][]byte, signDstVt string) (bool, error) {
+	return sig.coreAggregateVerify(pks, msgs, signDstVt)
+}
+
+func (sig *SignatureVt) coreAggregateVerify(pks []*PublicKeyVt, msgs [][]byte, signDstVt string) (bool, error) {
+	if len(pks) < 1 {
+		return false, fmt.Errorf("at least one key is required")
+	}
+	if len(msgs) < 1 {
+		return false, fmt.Errorf("at least one message is required")
+	}
+	if len(pks) != len(msgs) {
+		return false, fmt.Errorf("the number of public keys does not match the number of messages: %v != %v", len(pks), len(msgs))
+	}
+	if !blsEngine.G1.InCorrectSubgroup(&sig.value) {
+		return false, fmt.Errorf("signature is not in the correct subgroup")
+	}
+
+	engine := bls12381.NewEngine()
+	dst := []byte(signDstVt)
+	// e(H(m_1), pk_1)*...*e(H(m_N), pk_N) == e(s, g2)
+	// However, we use only one miller loop
+	// by doing the equivalent of
+	// e(H(m_1), pk_1)*...*e(H(m_N), pk_N) * e(s^-1, g2) == 1
+	for i, pk := range pks {
+		if pk == nil {
+			return false, fmt.Errorf("public key at %d is nil", i)
+		}
+		if engine.G2.IsZero(&pk.value) || !engine.G2.InCorrectSubgroup(&pk.value) {
+			return false, fmt.Errorf("public key at %d is not in the correct subgroup", i)
+		}
+		p1, err := engine.G1.HashToCurve(sha256.New, msgs[i], dst)
+		if err != nil {
+			return false, err
+		}
+		engine.AddPair(p1, &pk.value)
+	}
+	g2 := engine.G2.One()
+	engine.G2.Neg(g2, g2)
+	engine.AddPair(&sig.value, g2)
+	return engine.Check()
+}
+
+// Deserialize a signature from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (sig *SignatureVt) UnmarshalBinary(data []byte) error {
+	if len(data) != SignatureVtSize {
+		return fmt.Errorf("signature must be %d bytes", SignatureSize)
+	}
+	p1, err := blsEngine.G1.FromCompressed(data)
+	if err != nil {
+		return err
+	}
+	if blsEngine.G1.IsZero(p1) {
+		return fmt.Errorf("signatures cannot be zero")
+	}
+	sig.value = *p1
+	return nil
+}
+
+// Get the corresponding public key from a secret key
+// Verifies the public key is in the correct subgroup
+func (sk *SecretKey) GetPublicKeyVt() (*PublicKeyVt, error) {
+	result := blsEngine.G2.New()
+	blsEngine.G2.MulScalar(result, blsEngine.G2.One(), &sk.value)
+	if !blsEngine.G2.InCorrectSubgroup(result) || blsEngine.G2.IsZero(result) {
+		return nil, fmt.Errorf("point is not in correct subgroup")
+	}
+	return &PublicKeyVt{value: *result}, nil
+}
+
+// Compute a signature from a secret key and message
+// This signature is deterministic which protects against
+// attacks arising from signing with bad randomness like
+// the nonce reuse attack on ECDSA. `message` is
+// hashed to a point in G1 as described in to
+// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/?include_text=1
+// See Section 2.6 in https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+// nil message is not permitted but empty slice is allowed
+func (sk *SecretKey) createSignatureVt(message []byte, dstVt string) (*SignatureVt, error) {
+	if message == nil {
+		return nil, fmt.Errorf("message cannot be nil")
+	}
+	if sk.value.Cmp(big.NewInt(0)) == 0 {
+		return nil, fmt.Errorf("invalid secret key")
+	}
+	p1, err := blsEngine.G1.HashToCurve(sha256.New, message, []byte(dstVt))
+	if err != nil {
+		return nil, err
+	}
+	result := blsEngine.G1.New()
+	blsEngine.G1.MulScalar(result, p1, &sk.value)
+	if !blsEngine.G1.InCorrectSubgroup(result) {
+		return nil, fmt.Errorf("point is not in correct subgroup")
+	}
+	return &SignatureVt{value: *result}, nil
+}
+
+// Verify a signature is valid for the message under this public key.
+// See Section 2.7 in https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (pk PublicKeyVt) verifySignatureVt(message []byte, signature *SignatureVt, dstVt string) (bool, error) {
+	if signature == nil || message == nil || blsEngine.G2.IsZero(&pk.value) {
+		return false, fmt.Errorf("signature and message and public key cannot be nil or zero")
+	}
+	if blsEngine.G1.IsZero(&signature.value) || !blsEngine.G1.InCorrectSubgroup(&signature.value) {
+		return false, fmt.Errorf("signature is not in the correct subgroup")
+	}
+	engine := bls12381.NewEngine()
+
+	p1, err := engine.G1.HashToCurve(sha256.New, message, []byte(dstVt))
+	if err != nil {
+		return false, err
+	}
+	// e(H(m), pk) == e(s, g2)
+	// However, we can reduce the number of miller loops
+	// by doing the equivalent of
+	// e(H(m)^-1, pk) * e(s, g2) == 1
+	engine.AddPairInv(p1, &pk.value)
+	engine.AddPair(&signature.value, engine.G2.One())
+	return engine.Check()
+}
+
+// Combine public keys into one aggregated key
+func aggregatePublicKeysVt(pks ...*PublicKeyVt) (*PublicKeyVt, error) {
+	if len(pks) < 1 {
+		return nil, fmt.Errorf("at least one public key is required")
+	}
+	result := blsEngine.G2.New()
+	for i, k := range pks {
+		if k == nil {
+			return nil, fmt.Errorf("key at %d is nil, keys cannot be nil", i)
+		}
+		if !blsEngine.G2.InCorrectSubgroup(&k.value) {
+			return nil, fmt.Errorf("key at %d is not in the correct subgroup", i)
+		}
+		blsEngine.G2.Add(result, result, &k.value)
+	}
+	return &PublicKeyVt{value: *result}, nil
+}
+
+// Combine signatures into one aggregated signature
+func aggregateSignaturesVt(sigs ...*SignatureVt) (*SignatureVt, error) {
+	if len(sigs) < 1 {
+		return nil, fmt.Errorf("at least one signature is required")
+	}
+	result := blsEngine.G1.New()
+	for i, s := range sigs {
+		if s == nil {
+			return nil, fmt.Errorf("signature at %d is nil, signature cannot be nil", i)
+		}
+		if !blsEngine.G1.InCorrectSubgroup(&s.value) {
+			return nil, fmt.Errorf("signature at %d is not in the correct subgroup", i)
+		}
+		blsEngine.G1.Add(result, result, &s.value)
+	}
+	return &SignatureVt{value: *result}, nil
+}
+
+// A proof of possession scheme uses a separate public key validation
+// step, called a proof of possession, to defend against rogue key
+// attacks. This enables an optimization to aggregate signature
+// verification for the case that all signatures are on the same
+// message.
+type ProofOfPossessionVt struct {
+	value bls12381.PointG1
+}
+
+// Generates a proof-of-possession (PoP) for this secret key. The PoP signature should be verified before
+// before accepting any aggregate signatures related to the corresponding pubkey.
+func (sk *SecretKey) createProofOfPossessionVt(popDstVt string) (*ProofOfPossessionVt, error) {
+	pk, err := sk.GetPublicKeyVt()
+	if err != nil {
+		return nil, err
+	}
+	msg, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	sig, err := sk.createSignatureVt(msg, popDstVt)
+	if err != nil {
+		return nil, err
+	}
+	return &ProofOfPossessionVt{value: sig.value}, nil
+}
+
+// Serialize a proof of possession to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pop *ProofOfPossessionVt) MarshalBinary() ([]byte, error) {
+	return blsEngine.G1.ToCompressed(&pop.value), nil
+}
+
+// Deserialize a proof of possession from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (pop *ProofOfPossessionVt) UnmarshalBinary(data []byte) error {
+	p1 := new(SignatureVt)
+	err := p1.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	pop.value = p1.value
+	return nil
+}
+
+// Verifies that PoP is valid for this pubkey. In order to prevent rogue key attacks, a PoP must be validated
+// for each pubkey in an aggregated signature.
+func (pop *ProofOfPossessionVt) verify(pk *PublicKeyVt, popDstVt string) (bool, error) {
+	if pk == nil {
+		return false, fmt.Errorf("public key cannot be nil")
+	}
+	msg, err := pk.MarshalBinary()
+	if err != nil {
+		return false, err
+	}
+	return pk.verifySignatureVt(msg, &SignatureVt{value: pop.value}, popDstVt)
+}
+
+// Represents an MultiSignature in G1. A multisignature is used when multiple signatures
+// are calculated over the same message vs an aggregate signature where each message signed
+// is a unique.
+type MultiSignatureVt struct {
+	value bls12381.PointG1
+}
+
+// Serialize a multi-signature to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (sig *MultiSignatureVt) MarshalBinary() ([]byte, error) {
+	return blsEngine.G1.ToCompressed(&sig.value), nil
+}
+
+// Check a multisignature is valid for a multipublickey and a message
+func (sig *MultiSignatureVt) verify(pk *MultiPublicKeyVt, message []byte, signDstVt string) (bool, error) {
+	if pk == nil {
+		return false, fmt.Errorf("public key cannot be nil")
+	}
+	p := &PublicKeyVt{value: pk.value}
+	return p.verifySignatureVt(message, &SignatureVt{value: sig.value}, signDstVt)
+}
+
+// Deserialize a signature from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (sig *MultiSignatureVt) UnmarshalBinary(data []byte) error {
+	if len(data) != SignatureVtSize {
+		return fmt.Errorf("multi signature must be %v bytes", SignatureSize)
+	}
+	s1 := new(SignatureVt)
+	err := s1.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	sig.value = s1.value
+	return nil
+}
+
+// Represents accumulated multiple Public Keys in G2 for verifying a multisignature
+type MultiPublicKeyVt struct {
+	value bls12381.PointG2
+}
+
+// Serialize a public key to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pk *MultiPublicKeyVt) MarshalBinary() ([]byte, error) {
+	return blsEngine.G2.ToCompressed(&pk.value), nil
+}
+
+// Deserialize a public key from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the public key
+// otherwise it will return an error
+func (pk *MultiPublicKeyVt) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeyVtSize {
+		return fmt.Errorf("multi public key must be %v bytes", PublicKeySize)
+	}
+	p2 := new(PublicKeyVt)
+	err := p2.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	pk.value = p2.value
+	return nil
+}
+
+// Check a multisignature is valid for a multipublickey and a message
+func (pk *MultiPublicKeyVt) verify(message []byte, sig *MultiSignatureVt, signDstVt string) (bool, error) {
+	return sig.verify(pk, message, signDstVt)
+}
+
+// PartialSignatureVt represents threshold Gap Diffie-Hellman BLS signature
+// that can be combined with other partials to yield a completed BLS signature
+// See section 3.2 in <https://www.cc.gatech.edu/~aboldyre/papers/bold.pdf>
+type PartialSignatureVt struct {
+	identifier byte
+	signature  bls12381.PointG1
+}
+
+// partialSignVt creates a partial signature that can be combined with other partial signatures
+// to yield a complete signature
+func (sks *SecretKeyShare) partialSignVt(message []byte, signDst string) (*PartialSignatureVt, error) {
+	if len(message) == 0 {
+		return nil, fmt.Errorf("message cannot be empty or nil")
+	}
+	p1, err := blsEngine.G1.HashToCurve(sha256.New, message, []byte(signDst))
+	if err != nil {
+		return nil, err
+	}
+	result := blsEngine.G1.New()
+	blsEngine.G1.MulScalar(result, p1, sks.value.Secret.BigInt())
+	if !blsEngine.G1.InCorrectSubgroup(result) {
+		return nil, fmt.Errorf("point is not on correct subgroup")
+	}
+	return &PartialSignatureVt{identifier: sks.value.Identifier, signature: *result}, nil
+}
+
+// combineSigsVt gathers partial signatures and yields a complete signature
+func combineSigsVt(partials []*PartialSignatureVt) (*SignatureVt, error) {
+	if len(partials) < 2 {
+		return nil, fmt.Errorf("must have at least 2 partial signatures")
+	}
+	if len(partials) > 255 {
+		return nil, fmt.Errorf("unsupported to combine more than 255 signatures")
+	}
+	field := finitefield.New(blsEngine.G1.Q())
+	xVars, yVars, err := splitXYVt(field, partials)
+
+	if err != nil {
+		return nil, err
+	}
+
+	sTmp := blsEngine.G1.New()
+	sig := blsEngine.G1.New()
+
+	// Lagrange interpolation
+	x := field.Zero()
+	for i, xi := range xVars {
+		basis := field.One()
+
+		for j, xj := range xVars {
+			if i == j {
+				continue
+			}
+
+			num := x.Sub(xj)  // x - x_m
+			den := xi.Sub(xj) // x_j - x_m
+			if den.IsEqual(field.Zero()) {
+				return nil, fmt.Errorf("signatures cannot be recombined")
+			}
+			basis = basis.Mul(num.Div(den))
+		}
+		blsEngine.G1.MulScalar(sTmp, yVars[i], basis.BigInt())
+		blsEngine.G1.Add(sig, sig, sTmp)
+	}
+	if !blsEngine.G1.InCorrectSubgroup(sig) {
+		return nil, fmt.Errorf("signature is not in the correct subgroup")
+	}
+
+	return &SignatureVt{value: *sig}, nil
+}
+
+// Ensure no duplicates x values and convert x values to field elements
+func splitXYVt(field *finitefield.Field, partials []*PartialSignatureVt) ([]*finitefield.Element, []*bls12381.PointG1, error) {
+	x := make([]*finitefield.Element, len(partials))
+	y := make([]*bls12381.PointG1, len(partials))
+
+	dup := make(map[byte]bool)
+
+	for i, sp := range partials {
+		if sp == nil {
+			return nil, nil, fmt.Errorf("partial signature cannot be nil")
+		}
+		if _, exists := dup[sp.identifier]; exists {
+			return nil, nil, fmt.Errorf("duplicate signature included")
+		}
+		if !blsEngine.G1.InCorrectSubgroup(&sp.signature) {
+			return nil, nil, fmt.Errorf("signature is not in the correct subgroup")
+		}
+		dup[sp.identifier] = true
+		x[i] = field.ElementFromBytes([]byte{sp.identifier})
+		y[i] = &sp.signature
+	}
+	return x, y, nil
+}
diff --git a/pkg/signatures/bls/bls_sig/tiny_bls_sig_aug_test.go b/pkg/signatures/bls/bls_sig/tiny_bls_sig_aug_test.go
new file mode 100644
index 00000000..ca32d88b
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/tiny_bls_sig_aug_test.go
@@ -0,0 +1,378 @@
+package bls_sig
+
+import (
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+func generateAugSignatureG1(sk *SecretKey, msg []byte, t *testing.T) *SignatureVt {
+	bls := NewSigAugVt()
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Aug Sign failed")
+	}
+	return sig
+}
+
+func generateAugAggregateDataG1(t *testing.T) ([]*PublicKeyVt, []*SignatureVt, [][]byte) {
+	msgs := make([][]byte, numAggregateG1)
+	pks := make([]*PublicKeyVt, numAggregateG1)
+	sigs := make([]*SignatureVt, numAggregateG1)
+	ikm := make([]byte, 32)
+	bls := NewSigAugVt()
+
+	for i := 0; i < numAggregateG1; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Aug KeyGen failed")
+		}
+		msg := make([]byte, 20)
+		readRand(msg, t)
+		sig := generateAugSignatureG1(sk, msg, t)
+		msgs[i] = msg
+		sigs[i] = sig
+		pks[i] = pk
+	}
+	return pks, sigs, msgs
+}
+
+func TestAugKeyGenG1Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAugVt()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+}
+
+func TestAugKeyGenG1Fail(t *testing.T) {
+	ikm := make([]byte, 10)
+	readRand(ikm, t)
+	bls := NewSigAugVt()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Aug KeyGen succeeded when it should've failed")
+	}
+}
+
+func TestAugCustomDstG1(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAugVtWithDst("BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_AUG_TEST")
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug Custom Dst KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig, err := bls.Sign(sk, ikm)
+
+	if err != nil {
+		t.Errorf("Aug Custom Dst Sign failed")
+	}
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Aug Custom Dst Verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Aug Custom Dst Verify succeeded when it should've failed.")
+	}
+}
+
+func TestAugSigningG1(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAugVt()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig := generateAugSignatureG1(sk, ikm, t)
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Aug Verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Aug Verify succeeded when it should've failed.")
+	}
+}
+
+func TestAugAggregateVerifyG1Works(t *testing.T) {
+	pks, sigs, msgs := generateAugAggregateDataG1(t)
+	bls := NewSigAugVt()
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug AggregateVerify failed")
+	}
+}
+
+func TestAugAggregateVerifyG1BadPks(t *testing.T) {
+	bls := NewSigAugVt()
+	pks, sigs, msgs := generateAugAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug AggregateVerify failed")
+	}
+
+	pks[0] = pks[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug AggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g2 := bls12381.NewG2()
+	pkValue := g2.New()
+	pks[0] = &PublicKeyVt{value: *pkValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug AggregateVerify succeeded with zero byte public key it should've failed")
+	}
+
+	// Try with base generator
+	pkValue = g2.One()
+	pks[0] = &PublicKeyVt{value: *pkValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with the base generator public key it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG1BadSigs(t *testing.T) {
+	bls := NewSigAugVt()
+	pks, sigs, msgs := generateAugAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed")
+	}
+
+	sigs[0] = sigs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g1 := bls12381.NewG1()
+	sigValue := g1.New()
+	sigs[0] = &SignatureVt{value: *sigValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with zero byte signature it should've failed")
+	}
+
+	// Try with base generator
+	sigValue = g1.One()
+	sigs[0] = &SignatureVt{value: *sigValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with the base generator signature it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG1BadMsgs(t *testing.T) {
+	bls := NewSigAugVt()
+	pks, sigs, msgs := generateAugAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed")
+	}
+
+	// Test len(pks) != len(msgs)
+	if res, _ := bls.AggregateVerify(pks, msgs[0:8], sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+
+	msgs[0] = msgs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG1DupMsg(t *testing.T) {
+	bls := NewSigAugVt()
+
+	// Only two messages but repeated
+	messages := make([][]byte, numAggregateG1)
+	messages[0] = []byte("Yes")
+	messages[1] = []byte("No")
+	for i := 2; i < numAggregateG1; i++ {
+		messages[i] = messages[i%2]
+	}
+
+	pks := make([]*PublicKeyVt, numAggregateG1)
+	sigs := make([]*SignatureVt, numAggregateG1)
+
+	ikm := make([]byte, 32)
+	for i := 0; i < numAggregateG1; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Aug KeyGen failed")
+		}
+
+		sig := generateAugSignatureG1(sk, messages[i], t)
+		pks[i] = pk
+		sigs[i] = sig
+	}
+
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed for duplicate messages")
+	}
+}
+
+func TestBlsAugG1KeyGen(t *testing.T) {
+	bls := NewSigAugVt()
+	_, _, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+}
+
+func TestAugVtThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigAugVt()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(1, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestAugVtThresholdKeygen(t *testing.T) {
+	bls := NewSigAugVt()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+
+func TestAugPartialSignVt(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigAugVt()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], pk, msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], pk, msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestAugVtPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigAugVt()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignatureVt, total)
+	sigs2 := make([]*PartialSignatureVt, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], pk1, msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], pk2, msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
+
+func TestEmptyMessageAugPartialSignVt(t *testing.T) {
+	bls := NewSigAugVt()
+	pk, sks, err := bls.ThresholdKeygen(5, 6)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+
+	// Sign an empty message
+	_, err = bls.PartialSign(sks[0], pk, []byte{})
+	if err == nil {
+		t.Errorf("Expected partial sign to fail on empty message")
+	}
+}
+
+func TestNilMessageAugPartialSignVt(t *testing.T) {
+	bls := NewSigAugVt()
+	pk, sks, err := bls.ThresholdKeygen(5, 6)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+
+	// Sign nil message
+	_, err = bls.PartialSign(sks[0], pk, nil)
+	if err == nil {
+		t.Errorf("Expected partial signing to fail on nil message")
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/tiny_bls_sig_basic_test.go b/pkg/signatures/bls/bls_sig/tiny_bls_sig_basic_test.go
new file mode 100644
index 00000000..6979a5ee
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/tiny_bls_sig_basic_test.go
@@ -0,0 +1,373 @@
+package bls_sig
+
+import (
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+func generateBasicSignatureG1(sk *SecretKey, msg []byte, t *testing.T) *SignatureVt {
+	bls := NewSigBasicVt()
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Basic Sign failed")
+	}
+	return sig
+}
+
+func generateBasicAggregateDataG1(t *testing.T) ([]*PublicKeyVt, []*SignatureVt, [][]byte) {
+	msgs := make([][]byte, numAggregateG1)
+	pks := make([]*PublicKeyVt, numAggregateG1)
+	sigs := make([]*SignatureVt, numAggregateG1)
+	ikm := make([]byte, 32)
+	bls := NewSigBasicVt()
+
+	for i := 0; i < numAggregateG1; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Basic KeyGen failed")
+		}
+		msg := make([]byte, 20)
+		readRand(msg, t)
+		sig := generateBasicSignatureG1(sk, msg, t)
+		msgs[i] = msg
+		sigs[i] = sig
+		pks[i] = pk
+	}
+	return pks, sigs, msgs
+}
+
+func TestBasicKeyGenG1Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasicVt()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+}
+
+func TestBasicKeyGenG1Fail(t *testing.T) {
+	ikm := make([]byte, 10)
+	readRand(ikm, t)
+	bls := NewSigBasicVt()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Basic KeyGen succeeded when it should've failed")
+	}
+}
+
+func TestBasicCustomDstG1(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasicVtWithDst("BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_TEST")
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic Custom Dst KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig, err := bls.Sign(sk, ikm)
+
+	if err != nil {
+		t.Errorf("Basic Custom Dst Sign failed")
+	}
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Basic Custon Dst Verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Basic Custom Dst Verify succeeded when it should've failed.")
+	}
+}
+
+func TestBasicSigningG1(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasicVt()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig := generateBasicSignatureG1(sk, ikm, t)
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Basic Verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Basic Verify succeeded when it should've failed.")
+	}
+}
+
+func TestBasicSigningEmptyMessage(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	// Sign an empty message
+	_, err = bls.Sign(sk, []byte{})
+	if err != nil {
+		t.Errorf("Expected signing message to succeed: %v", err)
+	}
+}
+
+func TestBasicSigningNilMessage(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	// Sign nil message
+	_, err = bls.Sign(sk, nil)
+	if err == nil {
+		t.Errorf("Expected signing empty message to fail")
+	}
+}
+
+func TestBasicAggregateVerifyG1Works(t *testing.T) {
+	pks, sigs, msgs := generateBasicAggregateDataG1(t)
+	bls := NewSigBasicVt()
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic AggregateVerify failed")
+	}
+}
+
+func TestBasicAggregateVerifyG1BadPks(t *testing.T) {
+	bls := NewSigBasicVt()
+	pks, sigs, msgs := generateBasicAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic aggregateVerify failed")
+	}
+
+	pks[0] = pks[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g2 := bls12381.NewG2()
+	pkValue := g2.New()
+	pks[0] = &PublicKeyVt{value: *pkValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with zero byte public key it should've failed")
+	}
+
+	// Try with base generator
+	pkValue = g2.One()
+	pks[0] = &PublicKeyVt{value: *pkValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with the base generator public key it should've failed")
+	}
+}
+
+func TestBasicAggregateVerifyG1BadSigs(t *testing.T) {
+	bls := NewSigBasicVt()
+	pks, sigs, msgs := generateBasicAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic aggregateVerify failed")
+	}
+
+	sigs[0] = sigs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g1 := bls12381.NewG1()
+	sigValue := g1.New()
+	sigs[0] = &SignatureVt{value: *sigValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with zero byte signature it should've failed")
+	}
+
+	// Try with base generator
+	sigValue = g1.One()
+	sigs[0] = &SignatureVt{value: *sigValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with the base generator signature it should've failed")
+	}
+}
+
+func TestBasicAggregateVerifyG1BadMsgs(t *testing.T) {
+	bls := NewSigBasicVt()
+	pks, sigs, msgs := generateBasicAggregateDataG1(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic aggregateVerify failed")
+	}
+
+	msgs[0] = msgs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded when it should've failed")
+	}
+}
+
+func TestBasicVtThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(0, 1)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestBasicVtThresholdKeygen(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+
+func TestBasicPartialSignVt(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigBasicVt()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures succeeded when it should've failed")
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestBasicVtPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigBasicVt()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignatureVt, total)
+	sigs2 := make([]*PartialSignatureVt, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
+
+func TestIdentityPublicKeyVt(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+	msg := []byte{0, 0, 0, 0}
+	sig, _ := bls.Sign(sk, msg)
+	pk := PublicKeyVt{value: *bls12381.NewG2().Zero()}
+	if res, _ := bls.Verify(&pk, msg, sig); res {
+		t.Errorf("Verify succeeded when the public key is the identity.")
+	}
+}
+
+func TestThresholdSignTooHighAndLowVt(t *testing.T) {
+	bls := NewSigBasicVt()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	msg := make([]byte, 10)
+
+	ps, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("PartialSign failed: %v", err)
+	}
+
+	_, err = bls.CombineSignatures(ps)
+	if err == nil {
+		t.Errorf("CombinSignatures succeeded when it should've failed")
+	}
+
+	pss := make([]*PartialSignatureVt, 256)
+
+	_, err = bls.CombineSignatures(pss...)
+	if err == nil {
+		t.Errorf("CombinSignatures succeeded when it should've failed")
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/tiny_bls_sig_pop_test.go b/pkg/signatures/bls/bls_sig/tiny_bls_sig_pop_test.go
new file mode 100644
index 00000000..096953aa
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/tiny_bls_sig_pop_test.go
@@ -0,0 +1,841 @@
+package bls_sig
+
+import (
+	"bytes"
+	"math/big"
+	"math/rand"
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+const numAggregateG1 = 10
+
+func TestGetPublicKeyG2(t *testing.T) {
+	sk := genSecretKey(t)
+	pk := genPublicKeyVt(sk, t)
+	actual := marshalStruct(pk, t)
+	expected := []byte{175, 76, 33, 103, 184, 172, 12, 111, 24, 87, 84, 61, 243, 82, 99, 76, 131, 95, 171, 237, 145, 143, 7, 93, 205, 148, 104, 29, 153, 103, 187, 206, 112, 223, 252, 198, 102, 41, 38, 244, 228, 223, 102, 16, 216, 152, 231, 250, 7, 111, 90, 98, 194, 244, 101, 251, 69, 130, 11, 209, 41, 210, 133, 105, 217, 179, 190, 1, 6, 155, 135, 2, 168, 249, 253, 41, 59, 87, 8, 49, 231, 198, 142, 30, 186, 44, 175, 17, 198, 63, 210, 176, 237, 171, 11, 127}
+	if !bytes.Equal(actual, expected) {
+		t.Errorf("Expected GetPublicKeyVt to pass but failed.")
+	}
+}
+
+func testSignG1(message []byte, t *testing.T) {
+	sk := genSecretKey(t)
+	sig := genSignatureVt(sk, message, t)
+	pk := genPublicKeyVt(sk, t)
+
+	bls := NewSigPopVt()
+
+	if res, _ := bls.Verify(pk, message, sig); !res {
+		t.Errorf("createSignatureVt failed when it should've passed.")
+	}
+}
+
+func TestSignG1EmptyNilMessage(t *testing.T) {
+	sk := genSecretKey(t)
+	bls := NewSigPopVt()
+	sig, _ := bls.Sign(sk, nil)
+	pk := genPublicKeyVt(sk, t)
+
+	if res, _ := bls.Verify(pk, nil, sig); res {
+		t.Errorf("createSignature succeeded when it should've failed")
+	}
+
+	message := []byte{}
+	sig = genSignatureVt(sk, message, t)
+
+	if res, err := bls.Verify(pk, message, sig); !res {
+		t.Errorf("create and verify failed on empty message: %v", err)
+	}
+}
+
+func TestSignG1OneByteMessage(t *testing.T) {
+	message := []byte{1}
+	testSignG1(message, t)
+}
+
+func TestSignG1LargeMessage(t *testing.T) {
+	message := make([]byte, 1048576)
+	testSignG1(message, t)
+}
+
+func TestSignG1RandomMessage(t *testing.T) {
+	message := make([]byte, 65537)
+	readRand(message, t)
+	testSignG1(message, t)
+}
+
+func TestSignG1BadMessage(t *testing.T) {
+	message := make([]byte, 1024)
+	sk := genSecretKey(t)
+	sig := genSignatureVt(sk, message, t)
+	pk := genPublicKeyVt(sk, t)
+	message = []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
+
+	bls := NewSigPopVt()
+
+	if res, _ := bls.Verify(pk, message, sig); res {
+		t.Errorf("Expected signature to not verify")
+	}
+}
+
+func TestBadConversionsG1(t *testing.T) {
+	sk := genSecretKey(t)
+	message := []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
+	sig := genSignatureVt(sk, message, t)
+	pk := genPublicKeyVt(sk, t)
+
+	bls := NewSigPopVt()
+
+	if res, _ := bls.Verify(pk, message, sig); !res {
+		t.Errorf("Signature should be valid")
+	}
+	if res, _ := sig.verify(pk, message, blsSignaturePopVtDst); !res {
+		t.Errorf("Signature should be valid")
+	}
+
+	// Convert public key to signature in G2
+	sig2 := new(Signature)
+	err := sig2.UnmarshalBinary(marshalStruct(pk, t))
+	if err != nil {
+		t.Errorf("Should be able to convert to signature in G2")
+	}
+	pk2 := new(PublicKey)
+	err = pk2.UnmarshalBinary(marshalStruct(sig, t))
+	if err != nil {
+		t.Errorf("Should be able to convert to public key in G1")
+	}
+
+	res, _ := pk2.verifySignature(message, sig2, blsSignaturePopVtDst)
+	if res {
+		t.Errorf("The signature shouldn't verify")
+	}
+}
+
+func TestAggregatePublicKeysG2(t *testing.T) {
+	pks := []*PublicKeyVt{}
+	ikm := make([]byte, 32)
+	for i := 0; i < 20; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		pk := genPublicKeyVt(sk, t)
+		pks = append(pks, pk)
+	}
+	apk1, err := aggregatePublicKeysVt(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	rand.Seed(1234567890)
+	rand.Shuffle(len(pks), func(i, j int) { pks[i], pks[j] = pks[j], pks[i] })
+	apk2, err := aggregatePublicKeysVt(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(apk1, t), marshalStruct(apk2, t)) {
+		t.Errorf("Aggregated public keys should be equal")
+	}
+	rand.Shuffle(len(pks), func(i, j int) { pks[i], pks[j] = pks[j], pks[i] })
+	apk1, err = aggregatePublicKeysVt(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(apk1, t), marshalStruct(apk2, t)) {
+		t.Errorf("Aggregated public keys should be equal")
+	}
+}
+
+func TestAggregateSignaturesG1(t *testing.T) {
+	sigs := []*SignatureVt{}
+	ikm := make([]byte, 32)
+	for i := 0; i < 20; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		sig := genSignatureVt(sk, ikm, t)
+		sigs = append(sigs, sig)
+	}
+	asig1, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	rand.Seed(1234567890)
+	rand.Shuffle(len(sigs), func(i, j int) { sigs[i], sigs[j] = sigs[j], sigs[i] })
+	asig2, err := aggregateSignaturesVt(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(asig1, t), marshalStruct(asig2, t)) {
+		t.Errorf("Aggregated signatures should be equal")
+	}
+	rand.Shuffle(len(sigs), func(i, j int) { sigs[i], sigs[j] = sigs[j], sigs[i] })
+	asig1, err = aggregateSignaturesVt(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(asig1, t), marshalStruct(asig2, t)) {
+		t.Errorf("Aggregated signatures should be equal")
+	}
+}
+
+func initAggregatedTestValuesG1(messages [][]byte, t *testing.T) ([]*PublicKeyVt, []*SignatureVt) {
+	pks := []*PublicKeyVt{}
+	sigs := []*SignatureVt{}
+	ikm := make([]byte, 32)
+	for i := 0; i < numAggregateG1; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		sig := genSignatureVt(sk, messages[i%len(messages)], t)
+		sigs = append(sigs, sig)
+		pk := genPublicKeyVt(sk, t)
+		pks = append(pks, pk)
+	}
+	return pks, sigs
+}
+
+func TestAggregatedFunctionalityG1(t *testing.T) {
+	message := make([]byte, 20)
+	messages := make([][]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+
+	bls := NewSigPopVt()
+	asig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); !res {
+		t.Errorf("Should verify aggregated signatures with same message")
+	}
+	if res, _ := asig.verify(apk, message, blsSignaturePopVtDst); !res {
+		t.Errorf("MultiSignature.verify failed.")
+	}
+	if res, _ := apk.verify(message, asig, blsSignaturePopVtDst); !res {
+		t.Errorf("MultiPublicKey.verify failed.")
+	}
+}
+
+func TestBadAggregatedFunctionalityG1(t *testing.T) {
+	message := make([]byte, 20)
+	messages := make([][]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+
+	bls := NewSigPopVt()
+
+	apk, err := bls.AggregatePublicKeys(pks[2:]...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	asig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); res {
+		t.Errorf("Should not verify aggregated signatures with same message when some public keys are missing")
+	}
+
+	apk, err = bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	asig, err = bls.AggregateSignatures(sigs[2:]...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); res {
+		t.Errorf("Should not verify aggregated signatures with same message when some signatures are missing")
+	}
+
+	asig, err = bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+
+	badmsg := []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
+	if res, _ := bls.VerifyMultiSignature(apk, badmsg, asig); res {
+		t.Errorf("Should not verify aggregated signature with bad message")
+	}
+}
+
+func TestAggregateVerifyG1Pass(t *testing.T) {
+	messages := make([][]byte, numAggregateG1)
+	for i := 0; i < numAggregateG1; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); !res {
+		t.Errorf("Expected aggregateVerify to pass but failed")
+	}
+}
+
+func TestAggregateVerifyG1MsgSigCntMismatch(t *testing.T) {
+	messages := make([][]byte, 8)
+	for i := 0; i < 8; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); res {
+		t.Errorf("Expected AggregateVerifyG1 to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG1FailDupMsg(t *testing.T) {
+	messages := make([][]byte, 10)
+	for i := 0; i < 9; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	// Duplicate message
+	messages[9] = messages[0]
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); res {
+		t.Errorf("Expected aggregateVerify to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG1FailIncorrectMsg(t *testing.T) {
+	messages := make([][]byte, 10)
+	for i := 0; i < 9; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	// Duplicate message
+	messages[9] = messages[0]
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	if res, _ := bls.AggregateVerify(pks[2:], messages[2:], sigs); res {
+		t.Errorf("Expected aggregateVerify to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG1OneMsg(t *testing.T) {
+	messages := make([][]byte, 1)
+	messages[0] = make([]byte, 20)
+	sk := genSecretKey(t)
+	sig := genSignatureVt(sk, messages[0], t)
+	pk := genPublicKeyVt(sk, t)
+	bls := NewSigPopVt()
+	// Should be the same as verifySignatureVt
+	if res, _ := bls.AggregateVerify([]*PublicKeyVt{pk}, messages, []*SignatureVt{sig}); !res {
+		t.Errorf("Expected AggregateVerifyG1OneMsg to pass but failed")
+	}
+}
+
+func TestVerifyG1Mutability(t *testing.T) {
+	//verify should not change any inputs
+	ikm := make([]byte, 32)
+	ikm_copy := make([]byte, 32)
+	readRand(ikm, t)
+	copy(ikm_copy, ikm)
+	bls := NewSigPopVt()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPopVt.KeygenWithSeed modifies ikm")
+	}
+	if err != nil {
+		t.Errorf("Expected KeygenWithSeed to succeed but failed.")
+	}
+	sig, err := bls.Sign(sk, ikm)
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPopVt.Sign modifies message")
+	}
+	if err != nil {
+		t.Errorf("SigPopVt.KeygenWithSeed to succeed but failed.")
+	}
+	sigCopy := marshalStruct(sig, t)
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Expected verify to succeed but failed.")
+	}
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPopVt.verify modifies message")
+	}
+	if !bytes.Equal(sigCopy, marshalStruct(sig, t)) {
+		t.Errorf("SigPopVt.verify modifies signature")
+	}
+}
+
+func TestPublicKeyG2FromBadBytes(t *testing.T) {
+	pk := make([]byte, 32)
+	err := new(PublicKeyVt).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG2FromBytes to fail but passed")
+	}
+	// All zeros
+	pk = make([]byte, PublicKeyVtSize)
+	// See https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+	// 1 << 7 == compressed
+	// 1 << 6 == infinity or zero
+	pk[0] = 0xc0
+	err = new(PublicKeyVt).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG2FromBytes to fail but passed")
+	}
+	sk := genSecretKey(t)
+	pk1, err := sk.GetPublicKeyVt()
+	if err != nil {
+		t.Errorf("Expected GetPublicKeyVt to pass but failed.")
+	}
+	out := marshalStruct(pk1, t)
+	out[3] ^= out[4]
+	err = new(PublicKeyVt).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG2FromBytes to fail but passed")
+	}
+}
+
+func TestSignatureG1FromBadBytes(t *testing.T) {
+	sig := make([]byte, 32)
+	err := new(SignatureVt).UnmarshalBinary(sig)
+	if err == nil {
+		t.Errorf("Expected SignatureG1FromBytes to fail but passed")
+	}
+	// All zeros
+	sig = make([]byte, SignatureVtSize)
+	// See https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+	// 1 << 7 == compressed
+	// 1 << 6 == infinity or zero
+	sig[0] = 0xc0
+	err = new(SignatureVt).UnmarshalBinary(sig)
+	if err == nil {
+		t.Errorf("Expected SignatureG1FromBytes to fail but passed")
+	}
+}
+
+func TestBadSecretKeyG1(t *testing.T) {
+	x := new(big.Int)
+	sk := &SecretKey{value: *x}
+	pk, err := sk.GetPublicKeyVt()
+	if err == nil {
+		t.Errorf("Expected GetPublicKeyVt to fail with 0 byte secret key but passed: %v", pk)
+	}
+	bls := bls12381.NewG2()
+	_ = sk.UnmarshalBinary(bls.Q().Bytes())
+	pk, err = sk.GetPublicKeyVt()
+	if err == nil {
+		t.Errorf("Expected GetPublicKeyVt to fail with secret key with Q but passed: %v", pk)
+	}
+
+	err = sk.UnmarshalBinary([]byte{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16})
+	if err == nil {
+		t.Errorf("Expected SecretKeyFromBytes to fail with not enough bytes but passed: %v", pk)
+	}
+
+	err = sk.UnmarshalBinary(make([]byte, 32))
+	if err == nil {
+		t.Errorf("Expected SecretKeyFromBytes to fail but passed: %v", pk)
+	}
+}
+
+func TestProofOfPossessionG1Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigPopVt()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Key gen failed but should've succeeded")
+	}
+	pop, err := bls.PopProve(sk)
+	if err != nil {
+		t.Errorf("PopProve failed but should've succeeded")
+	}
+	if res, _ := bls.PopVerify(pk, pop); !res {
+		t.Errorf("PopVerify failed but should've succeeded")
+	}
+}
+
+func TestProofOfPossessionG1FromBadKey(t *testing.T) {
+	ikm := make([]byte, 32)
+	value := new(big.Int)
+	value.SetBytes(ikm)
+	sk := SecretKey{value: *value}
+	_, err := sk.createProofOfPossessionVt(blsSignaturePopVtDst)
+	if err == nil {
+		t.Errorf("createProofOfPossessionVt should've failed but succeeded.")
+	}
+}
+
+func TestProofOfPossessionG1BytesWorks(t *testing.T) {
+	sk := genSecretKey(t)
+	pop, err := sk.createProofOfPossessionVt(blsSignaturePopVtDst)
+	if err != nil {
+		t.Errorf("CreateProofOfPossesionG1 failed but shouldn've succeeded.")
+	}
+	out := marshalStruct(pop, t)
+	if len(out) != ProofOfPossessionVtSize {
+		t.Errorf("ProofOfPossessionBytes incorrect size: expected %v, got %v", ProofOfPossessionVtSize, len(out))
+	}
+	pop2 := new(ProofOfPossessionVt)
+	err = pop2.UnmarshalBinary(out)
+	if err != nil {
+		t.Errorf("ProofOfPossessionVt.UnmarshalBinary failed: %v", err)
+	}
+	out2 := marshalStruct(pop2, t)
+	if !bytes.Equal(out, out2) {
+		t.Errorf("ProofOfPossessionVt.UnmarshalBinary failed, not equal when deserialized")
+	}
+}
+
+func TestProofOfPossessionG1BadBytes(t *testing.T) {
+	zeros := make([]byte, ProofOfPossessionVtSize)
+	temp := new(ProofOfPossessionVt)
+	err := temp.UnmarshalBinary(zeros)
+	if err == nil {
+		t.Errorf("ProofOfPossessionVt.UnmarshalBinary shouldn've failed but succeeded.")
+	}
+}
+
+func TestProofOfPossessionG1Fails(t *testing.T) {
+	sk := genSecretKey(t)
+	pop, err := sk.createProofOfPossessionVt(blsSignaturePopVtDst)
+	if err != nil {
+		t.Errorf("Expected createProofOfPossessionVt to succeed but failed.")
+	}
+
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	sk = genRandSecretKey(ikm, t)
+	bad, err := sk.GetPublicKeyVt()
+	if err != nil {
+		t.Errorf("Expected PublicKeyG2FromBytes to succeed but failed: %v", err)
+	}
+	if res, _ := pop.verify(bad, blsSignaturePopVtDst); res {
+		t.Errorf("Expected ProofOfPossession verify to fail but succeeded.")
+	}
+}
+
+func TestMultiSigG1Bytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	_, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	msig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	msigBytes := marshalStruct(msig, t)
+	if len(msigBytes) != SignatureVtSize {
+		t.Errorf("Invalid multi-sig length. Expected %d bytes, found %d", SignatureVtSize, len(msigBytes))
+	}
+	msig2 := new(MultiSignatureVt)
+	err = msig2.UnmarshalBinary(msigBytes)
+	if err != nil {
+		t.Errorf("MultiSignatureG1FromBytes failed with %v", err)
+	}
+	msigBytes2 := marshalStruct(msig2, t)
+
+	if !bytes.Equal(msigBytes, msigBytes2) {
+		t.Errorf("Bytes methods not equal.")
+	}
+}
+
+func TestMultiSigG1BadBytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	_, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	msig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	msigBytes := marshalStruct(msig, t)
+	if len(msigBytes) != SignatureVtSize {
+		t.Errorf("Invalid multi-sig length. Expected %d bytes, found %d", SignatureSize, len(msigBytes))
+	}
+	msigBytes[0] = 0
+	temp := new(MultiSignatureVt)
+	err = temp.UnmarshalBinary(msigBytes)
+	if err == nil {
+		t.Errorf("MultiSignatureG1FromBytes should've failed but succeeded")
+	}
+	msigBytes = make([]byte, SignatureVtSize)
+	err = temp.UnmarshalBinary(msigBytes)
+	if err == nil {
+		t.Errorf("MultiSignatureG1FromBytes should've failed but succeeded")
+	}
+}
+
+func TestMultiPubkeyG2Bytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	pks, _ := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apkBytes := marshalStruct(apk, t)
+	if len(apkBytes) != PublicKeyVtSize {
+		t.Errorf("MultiPublicKeyVt has an incorrect size")
+	}
+	apk2 := new(MultiPublicKeyVt)
+	err = apk2.UnmarshalBinary(apkBytes)
+	if err != nil {
+		t.Errorf("MultiPublicKeyVt.UnmarshalBinary failed with %v", err)
+	}
+	apk2Bytes := marshalStruct(apk2, t)
+	if !bytes.Equal(apkBytes, apk2Bytes) {
+		t.Errorf("Bytes methods not equal.")
+	}
+}
+
+func TestMultiPubkeyG2BadBytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	pks, _ := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apkBytes := marshalStruct(apk, t)
+	if len(apkBytes) != PublicKeyVtSize {
+		t.Errorf("MultiPublicKeyVt has an incorrect size")
+	}
+	apkBytes[0] = 0
+	temp := new(MultiPublicKeyVt)
+	err = temp.UnmarshalBinary(apkBytes)
+	if err == nil {
+		t.Errorf("MultiPublicKeyVt.UnmarshalBinary should've failed but succeeded")
+	}
+	apkBytes = make([]byte, PublicKeyVtSize)
+	err = temp.UnmarshalBinary(apkBytes)
+	if err == nil {
+		t.Errorf("MultiPublicKeyVt.UnmarshalBinary should've failed but succeeded")
+	}
+}
+
+func TestFastAggregateVerifyConstituentG1Works(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, message, sigs); !res {
+		t.Errorf("FastAggregateVerify failed.")
+	}
+}
+
+func TestFastAggregateVerifyG1Works(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	asig, _ := aggregateSignaturesVt(sigs...)
+	bls := NewSigPopVt()
+
+	if res, _ := bls.FastAggregateVerify(pks, message, asig); !res {
+		t.Errorf("FastAggregateVerify failed.")
+	}
+}
+
+func TestFastAggregateVerifyG1Fails(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG1(messages, t)
+	bls := NewSigPopVt()
+	message[0] = 1
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, message, sigs); res {
+		t.Errorf("FastAggregateVerify verified when it should've failed.")
+	}
+}
+
+func TestCustomPopDstG1Works(t *testing.T) {
+	bls, _ := NewSigPopVtWithDst("BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_POP_TEST",
+		"BLS_POP_BLS12381G1_XMD:SHA-256_SSWU_RO_POP_TEST")
+	msg := make([]byte, 20)
+	ikm := make([]byte, 32)
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Couldn't create custom dst keys: %v", err)
+	}
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Couldn't sign with custom dst: %v", err)
+	}
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("verify fails with custom dst")
+	}
+
+	pks := make([]*PublicKeyVt, 10)
+	sigs := make([]*SignatureVt, 10)
+	pks[0] = pk
+	sigs[0] = sig
+	for i := 1; i < 10; i++ {
+		readRand(ikm, t)
+		pkt, skt, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Couldn't create custom dst keys: %v", err)
+		}
+		sigt, err := bls.Sign(skt, msg)
+		if err != nil {
+			t.Errorf("Couldn't sign with custom dst: %v", err)
+		}
+		pks[i] = pkt
+		sigs[i] = sigt
+	}
+
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, msg, sigs); !res {
+		t.Errorf("FastAggregateVerify failed with custom dst")
+	}
+
+	pop, err := bls.PopProve(sk)
+	if err != nil {
+		t.Errorf("PopProve failed with custom dst")
+	}
+
+	if res, _ := bls.PopVerify(pk, pop); !res {
+		t.Errorf("PopVerify failed with custom dst")
+	}
+}
+
+func TestBlsPopG1KeyGenWithSeed(t *testing.T) {
+	ikm := []byte("Not enough bytes")
+	bls := NewSigPopVt()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Expected KeygenWithSeed to fail but succeeded")
+	}
+}
+
+func TestBlsPopG1KeyGen(t *testing.T) {
+	bls := NewSigPopVt()
+	_, _, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+}
+
+func TestPopVtThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigPopVt()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(1, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestPopVtThresholdKeygen(t *testing.T) {
+	bls := NewSigPopVt()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+
+func TestPopPartialSignVt(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigPopVt()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures succeeded when it should've failed")
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestPopVtPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigPopVt()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignatureVt, total)
+	sigs2 := make([]*PartialSignatureVt, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/usual_bls.go b/pkg/signatures/bls/bls_sig/usual_bls.go
new file mode 100644
index 00000000..1c43b669
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/usual_bls.go
@@ -0,0 +1,440 @@
+package bls_sig
+
+import (
+	"fmt"
+)
+
+const (
+	// Domain separation tag for basic signatures
+	// according to section 4.2.1 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignatureBasicDst = "BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_"
+	// Domain separation tag for basic signatures
+	// according to section 4.2.2 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignatureAugDst = "BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_AUG_"
+	// Domain separation tag for proof of possession signatures
+	// according to section 4.2.3 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsSignaturePopDst = "BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_"
+	// Domain separation tag for proof of possession proofs
+	// according to section 4.2.3 in
+	// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+	blsPopProofDst = "BLS_POP_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_"
+)
+
+type BlsScheme interface {
+	Keygen() (*PublicKey, *SecretKey, error)
+	KeygenWithSeed(ikm []byte) (*PublicKey, *SecretKey, error)
+	Sign(sk *SecretKey, msg []byte) (*Signature, error)
+	Verify(pk *PublicKey, msg []byte, sig *Signature) bool
+	AggregateVerify(pks []*PublicKey, msgs [][]byte, sigs []*Signature) bool
+}
+
+// generateKeys creates 32 bytes of random data to be fed to
+// generateKeysWithSeed
+func generateKeys() (*PublicKey, *SecretKey, error) {
+	ikm, err := generateRandBytes(32)
+	if err != nil {
+		return nil, nil, err
+	}
+	return generateKeysWithSeed(ikm)
+}
+
+// generateKeysWithSeed generates a BLS key pair given input key material (ikm)
+func generateKeysWithSeed(ikm []byte) (*PublicKey, *SecretKey, error) {
+	sk, err := new(SecretKey).Generate(ikm)
+	if err != nil {
+		return nil, nil, err
+	}
+	pk, err := sk.GetPublicKey()
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, sk, nil
+}
+
+// thresholdGenerateKeys will generate random secret key shares and the corresponding public key
+func thresholdGenerateKeys(threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	pk, sk, err := generateKeys()
+	if err != nil {
+		return nil, nil, err
+	}
+	shares, err := thresholdizeSecretKey(sk, threshold, total)
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, shares, nil
+}
+
+// thresholdGenerateKeysWithSeed will generate random secret key shares and the corresponding public key
+// using the corresponding seed `ikm`
+func thresholdGenerateKeysWithSeed(ikm []byte, threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	pk, sk, err := generateKeysWithSeed(ikm)
+	if err != nil {
+		return nil, nil, err
+	}
+	shares, err := thresholdizeSecretKey(sk, threshold, total)
+	if err != nil {
+		return nil, nil, err
+	}
+	return pk, shares, nil
+}
+
+// SigBasic is minimal-pubkey-size scheme that doesn't support FastAggregateVerificiation.
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.1
+type SigBasic struct {
+	dst string
+}
+
+// Creates a new BLS basic signature scheme with the standard domain separation tag used for signatures.
+func NewSigBasic() *SigBasic {
+	return &SigBasic{dst: blsSignatureBasicDst}
+}
+
+// Creates a new BLS basic signature scheme with a custom domain separation tag used for signatures.
+func NewSigBasicWithDst(signDst string) *SigBasic {
+	return &SigBasic{dst: signDst}
+}
+
+// Creates a new BLS key pair
+func (b SigBasic) Keygen() (*PublicKey, *SecretKey, error) {
+	return generateKeys()
+}
+
+// Creates a new BLS key pair
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigBasic) KeygenWithSeed(ikm []byte) (*PublicKey, *SecretKey, error) {
+	return generateKeysWithSeed(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigBasic) ThresholdKeygen(threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeys(threshold, total)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigBasic) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeed(ikm, threshold, total)
+}
+
+// Computes a signature in G2 from sk, a secret key, and a message
+func (b SigBasic) Sign(sk *SecretKey, msg []byte) (*Signature, error) {
+	return sk.createSignature(msg, b.dst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigBasic) PartialSign(sks *SecretKeyShare, msg []byte) (*PartialSignature, error) {
+	return sks.partialSign(msg, b.dst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigBasic) CombineSignatures(sigs ...*PartialSignature) (*Signature, error) {
+	return combineSigs(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+func (b SigBasic) Verify(pk *PublicKey, msg []byte, sig *Signature) (bool, error) {
+	return pk.verifySignature(msg, sig, b.dst)
+}
+
+// The AggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// Each message must be different or this will return false.
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigBasic) AggregateVerify(pks []*PublicKey, msgs [][]byte, sigs []*Signature) (bool, error) {
+	if !allRowsUnique(msgs) {
+		return false, fmt.Errorf("all messages must be distinct")
+	}
+	asig, err := aggregateSignatures(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, msgs, b.dst)
+}
+
+// SigAug is minimal-pubkey-size scheme that doesn't support FastAggregateVerificiation.
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.2
+type SigAug struct {
+	dst string
+}
+
+// Creates a new BLS message augmentation signature scheme with the standard domain separation tag used for signatures.
+func NewSigAug() *SigAug {
+	return &SigAug{dst: blsSignatureAugDst}
+}
+
+// Creates a new BLS message augmentation signature scheme with a custom domain separation tag used for signatures.
+func NewSigAugWithDst(signDst string) *SigAug {
+	return &SigAug{dst: signDst}
+}
+
+// Creates a new BLS key pair
+func (b SigAug) Keygen() (*PublicKey, *SecretKey, error) {
+	return generateKeys()
+}
+
+// Creates a new BLS secret key
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigAug) KeygenWithSeed(ikm []byte) (*PublicKey, *SecretKey, error) {
+	return generateKeysWithSeed(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigAug) ThresholdKeygen(threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeys(threshold, total)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigAug) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeed(ikm, threshold, total)
+}
+
+// Computes a signature in G1 from sk, a secret key, and a message
+// See section 3.2.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigAug) Sign(sk *SecretKey, msg []byte) (*Signature, error) {
+	if len(msg) == 0 {
+		return nil, fmt.Errorf("message cannot be empty or nil")
+	}
+
+	pk, err := sk.GetPublicKey()
+	if err != nil {
+		return nil, err
+	}
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, fmt.Errorf("MarshalBinary failed")
+	}
+	bytes = append(bytes, msg...)
+	return sk.createSignature(bytes, b.dst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigAug) PartialSign(sks *SecretKeyShare, pk *PublicKey, msg []byte) (*PartialSignature, error) {
+	if len(msg) == 0 {
+		return nil, fmt.Errorf("message cannot be empty or nil")
+	}
+
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, fmt.Errorf("MarshalBinary failed")
+	}
+	bytes = append(bytes, msg...)
+	return sks.partialSign(bytes, b.dst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigAug) CombineSignatures(sigs ...*PartialSignature) (*Signature, error) {
+	return combineSigs(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+// See section 3.2.2 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigAug) Verify(pk *PublicKey, msg []byte, sig *Signature) (bool, error) {
+	bytes, err := pk.MarshalBinary()
+	if err != nil {
+		return false, err
+	}
+	bytes = append(bytes, msg...)
+	return pk.verifySignature(bytes, sig, b.dst)
+}
+
+// The AggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// See section 3.2.3 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigAug) AggregateVerify(pks []*PublicKey, msgs [][]byte, sigs []*Signature) (bool, error) {
+	if len(pks) != len(msgs) {
+		return false, fmt.Errorf("the number of public keys does not match the number of messages: %v != %v", len(pks), len(msgs))
+	}
+	data := make([][]byte, len(msgs))
+	for i, msg := range msgs {
+		bytes, err := pks[i].MarshalBinary()
+		if err != nil {
+			return false, err
+		}
+		data[i] = append(bytes, msg...)
+	}
+	asig, err := aggregateSignatures(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, data, b.dst)
+}
+
+// SigEth2 supports signatures on Eth2.
+// Internally is an alias for SigPop
+type SigEth2 = SigPop
+
+// NewSigEth2 Creates a new BLS ETH2 signature scheme with the standard domain separation tag used for signatures.
+func NewSigEth2() *SigEth2 {
+	return NewSigPop()
+}
+
+// SigPop is minimal-pubkey-size scheme that supports FastAggregateVerification
+// and requires using proofs of possession to mitigate rogue-key attacks
+// see: https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03#section-4.2.3
+type SigPop struct {
+	sigDst string
+	popDst string
+}
+
+// Creates a new BLS proof of possession signature scheme with the standard domain separation tag used for signatures.
+func NewSigPop() *SigPop {
+	return &SigPop{sigDst: blsSignaturePopDst, popDst: blsPopProofDst}
+}
+
+// Creates a new BLS message proof of possession signature scheme with a custom domain separation tag used for signatures.
+func NewSigPopWithDst(signDst, popDst string) (*SigPop, error) {
+	if signDst == popDst {
+		return nil, fmt.Errorf("domain separation tags cannot be equal")
+	}
+	return &SigPop{sigDst: signDst, popDst: popDst}, nil
+}
+
+// Creates a new BLS key pair
+func (b SigPop) Keygen() (*PublicKey, *SecretKey, error) {
+	return generateKeys()
+}
+
+// Creates a new BLS secret key
+// Input key material (ikm) MUST be at least 32 bytes long,
+// but it MAY be longer.
+func (b SigPop) KeygenWithSeed(ikm []byte) (*PublicKey, *SecretKey, error) {
+	return generateKeysWithSeed(ikm)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigPop) ThresholdKeygen(threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeys(threshold, total)
+}
+
+// ThresholdKeyGen generates a public key and `total` secret key shares such that
+// `threshold` of them can be combined in signatures
+func (b SigPop) ThresholdKeygenWithSeed(ikm []byte, threshold, total uint) (*PublicKey, []*SecretKeyShare, error) {
+	return thresholdGenerateKeysWithSeed(ikm, threshold, total)
+}
+
+// Computes a signature in G2 from sk, a secret key, and a message
+// See section 2.6 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) Sign(sk *SecretKey, msg []byte) (*Signature, error) {
+	return sk.createSignature(msg, b.sigDst)
+}
+
+// Compute a partial signature in G2 that can be combined with other partial signature
+func (b SigPop) PartialSign(sks *SecretKeyShare, msg []byte) (*PartialSignature, error) {
+	return sks.partialSign(msg, b.sigDst)
+}
+
+// CombineSignatures takes partial signatures to yield a completed signature
+func (b SigPop) CombineSignatures(sigs ...*PartialSignature) (*Signature, error) {
+	return combineSigs(sigs)
+}
+
+// Checks that a signature is valid for the message under the public key pk
+// See section 2.7 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) Verify(pk *PublicKey, msg []byte, sig *Signature) (bool, error) {
+	return pk.verifySignature(msg, sig, b.sigDst)
+}
+
+// The aggregateVerify algorithm checks an aggregated signature over
+// several (PK, message, signature) pairs.
+// Each message must be different or this will return false.
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) AggregateVerify(pks []*PublicKey, msgs [][]byte, sigs []*Signature) (bool, error) {
+	if !allRowsUnique(msgs) {
+		return false, fmt.Errorf("all messages must be distinct")
+	}
+	asig, err := aggregateSignatures(sigs...)
+	if err != nil {
+		return false, err
+	}
+	return asig.aggregateVerify(pks, msgs, b.sigDst)
+}
+
+// Combine many signatures together to form a Multisignature.
+// Multisignatures can be created when multiple signers jointly
+// generate signatures over the same message.
+func (b SigPop) AggregateSignatures(sigs ...*Signature) (*MultiSignature, error) {
+	g1, err := aggregateSignatures(sigs...)
+	if err != nil {
+		return nil, err
+	}
+	return &MultiSignature{value: g1.value}, nil
+}
+
+// Combine many public keys together to form a Multipublickey.
+// Multipublickeys are used to verify multisignatures.
+func (b SigPop) AggregatePublicKeys(pks ...*PublicKey) (*MultiPublicKey, error) {
+	g2, err := aggregatePublicKeys(pks...)
+	if err != nil {
+		return nil, err
+	}
+	return &MultiPublicKey{value: g2.value}, nil
+}
+
+// Checks that a multisignature is valid for the message under the multi public key
+// Similar to FastAggregateVerify except the keys and signatures have already been
+// combined. See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) VerifyMultiSignature(pk *MultiPublicKey, msg []byte, sig *MultiSignature) (bool, error) {
+	s := &Signature{value: sig.value}
+	p := &PublicKey{value: pk.value}
+	return p.verifySignature(msg, s, b.sigDst)
+}
+
+// FastAggregateVerify verifies an aggregated signature against the specified message and set of public keys.
+// See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) FastAggregateVerify(pks []*PublicKey, msg []byte, asig *Signature) (bool, error) {
+	apk, err := aggregatePublicKeys(pks...)
+	if err != nil {
+		return false, nil
+	}
+	return apk.verifySignature(msg, asig, b.sigDst)
+}
+
+// FastAggregateVerifyConstituent aggregates all constituent signatures and the verifies
+// them against the specified message and public keys
+// See section 3.3.4 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) FastAggregateVerifyConstituent(pks []*PublicKey, msg []byte, sigs []*Signature) (bool, error) {
+	// Aggregate the constituent signatures
+	asig, err := aggregateSignatures(sigs...)
+	if err != nil {
+		return false, err
+	}
+	// And verify
+	return b.FastAggregateVerify(pks, msg, asig)
+}
+
+// Create a proof of possession for the corresponding public key.
+// A proof of possession must be created for each public key to be used
+// in FastAggregateVerify or a Multipublickey to avoid rogue key attacks.
+// See section 3.3.2 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) PopProve(sk *SecretKey) (*ProofOfPossession, error) {
+	return sk.createProofOfPossession(b.popDst)
+}
+
+// verify a proof of possession for the corresponding public key is valid.
+// A proof of possession must be created for each public key to be used
+// in FastAggregateVerify or a Multipublickey to avoid rogue key attacks.
+// See section 3.3.3 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (b SigPop) PopVerify(pk *PublicKey, pop2 *ProofOfPossession) (bool, error) {
+	return pop2.verify(pk, b.popDst)
+}
diff --git a/pkg/signatures/bls/bls_sig/usual_bls_sig.go b/pkg/signatures/bls/bls_sig/usual_bls_sig.go
new file mode 100644
index 00000000..5356beda
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/usual_bls_sig.go
@@ -0,0 +1,483 @@
+package bls_sig
+
+import (
+	"crypto/sha256"
+	"fmt"
+	"math/big"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+	"github.com/coinbase/kryptology/pkg/signatures/bls/finitefield"
+)
+
+// Implement BLS signatures on the BLS12-381 curve
+// according to https://crypto.standford.edu/~dabo/pubs/papers/BLSmultisig.html
+// and https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+// this file implements signatures in G2 and public keys in G1.
+// Public Keys and Signatures can be aggregated but the consumer
+// must use proofs of possession to defend against rogue-key attacks.
+
+const (
+	// Public key size in G1
+	PublicKeySize = 48
+	// Signature size in G2
+	SignatureSize = 96
+	// Proof of Possession in G2
+	ProofOfPossessionSize = 96
+)
+
+// Represents a public key in G1
+type PublicKey struct {
+	value bls12381.PointG1
+}
+
+// Serialize a public key to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pk PublicKey) MarshalBinary() ([]byte, error) {
+	return blsEngine.G1.ToCompressed(&pk.value), nil
+}
+
+// Deserialize a public key from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the public key
+// otherwise it will return an error
+func (pk *PublicKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeySize {
+		return fmt.Errorf("public key must be %d bytes", PublicKeySize)
+	}
+	p1, err := blsEngine.G1.FromCompressed(data)
+	if err != nil {
+		return err
+	}
+	if blsEngine.G1.IsZero(p1) {
+		return fmt.Errorf("public keys cannot be zero")
+	}
+	pk.value = *p1
+	return nil
+}
+
+// Represents a BLS signature in G2
+type Signature struct {
+	value bls12381.PointG2
+}
+
+// Serialize a signature to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (sig Signature) MarshalBinary() ([]byte, error) {
+	return blsEngine.G2.ToCompressed(&sig.value), nil
+}
+
+func (sig Signature) verify(pk *PublicKey, message []byte, signDst string) (bool, error) {
+	return pk.verifySignature(message, &sig, signDst)
+}
+
+// The AggregateVerify algorithm checks an aggregated signature over
+// several (PK, message) pairs.
+// The Signature is the output of aggregateSignatures
+// Each message must be different or this will return false
+// See section 3.1.1 from
+// https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (sig Signature) aggregateVerify(pks []*PublicKey, msgs [][]byte, signDst string) (bool, error) {
+	return sig.coreAggregateVerify(pks, msgs, signDst)
+}
+
+func (sig Signature) coreAggregateVerify(pks []*PublicKey, msgs [][]byte, signDst string) (bool, error) {
+	if len(pks) < 1 {
+		return false, fmt.Errorf("at least one key is required")
+	}
+	if len(msgs) < 1 {
+		return false, fmt.Errorf("at least one message is required")
+	}
+	if len(pks) != len(msgs) {
+		return false, fmt.Errorf("the number of public keys does not match the number of messages: %v != %v", len(pks), len(msgs))
+	}
+	if !blsEngine.G2.InCorrectSubgroup(&sig.value) {
+		return false, fmt.Errorf("signature is not in the correct subgroup")
+	}
+
+	dst := []byte(signDst)
+	engine := bls12381.NewEngine()
+	// e(pk_1, H(m_1))*...*e(pk_N, H(m_N)) == e(g1, s)
+	// However, we use only one miller loop
+	// by doing the equivalent of
+	// e(pk_1, H(m_1))*...*e(pk_N, H(m_N)) * e(g1^-1, s) == 1
+	for i, pk := range pks {
+		if pk == nil {
+			return false, fmt.Errorf("public key at %d is nil", i)
+		}
+		if engine.G1.IsZero(&pk.value) || !engine.G1.InCorrectSubgroup(&pk.value) {
+			return false, fmt.Errorf("public key at %d is not in the correct subgroup", i)
+		}
+		p2, err := engine.G2.HashToCurve(sha256.New, msgs[i], dst)
+		if err != nil {
+			return false, err
+		}
+		engine.AddPair(&pk.value, p2)
+	}
+	engine.AddPairInv(engine.G1.One(), &sig.value)
+	return engine.Check()
+}
+
+// Deserialize a signature from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (sig *Signature) UnmarshalBinary(data []byte) error {
+	if len(data) != SignatureSize {
+		return fmt.Errorf("signature must be %d bytes", SignatureSize)
+	}
+	p2, err := blsEngine.G2.FromCompressed(data)
+	if err != nil {
+		return err
+	}
+	if blsEngine.G2.IsZero(p2) {
+		return fmt.Errorf("signatures cannot be zero")
+	}
+	sig.value = *p2
+	return nil
+}
+
+// Get the corresponding public key from a secret key
+// Verifies the public key is in the correct subgroup
+func (sk SecretKey) GetPublicKey() (*PublicKey, error) {
+	result := blsEngine.G1.New()
+	blsEngine.G1.MulScalar(result, blsEngine.G1.One(), &sk.value)
+	if !blsEngine.G1.InCorrectSubgroup(result) || blsEngine.G1.IsZero(result) {
+		return nil, fmt.Errorf("point is not in correct subgroup")
+	}
+	return &PublicKey{value: *result}, nil
+}
+
+// Compute a signature from a secret key and message
+// This signature is deterministic which protects against
+// attacks arising from signing with bad randomness like
+// the nonce reuse attack on ECDSA. `message` is
+// hashed to a point in G2 as described in to
+// https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/?include_text=1
+// See Section 2.6 in https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+// nil message is not permitted but empty slice is allowed
+func (sk SecretKey) createSignature(message []byte, dst string) (*Signature, error) {
+	if message == nil {
+		return nil, fmt.Errorf("message cannot be nil")
+	}
+	if sk.value.Cmp(big.NewInt(0)) == 0 {
+		return nil, fmt.Errorf("invalid secret key")
+	}
+	p2, err := blsEngine.G2.HashToCurve(sha256.New, message, []byte(dst))
+	if err != nil {
+		return nil, err
+	}
+	result := blsEngine.G2.New()
+	blsEngine.G2.MulScalar(result, p2, &sk.value)
+	if !blsEngine.G2.InCorrectSubgroup(result) {
+		return nil, fmt.Errorf("point is not on correct subgroup")
+	}
+	return &Signature{value: *result}, nil
+}
+
+// Verify a signature is valid for the message under this public key.
+// See Section 2.7 in https://tools.ietf.org/html/draft-irtf-cfrg-bls-signature-03
+func (pk PublicKey) verifySignature(message []byte, signature *Signature, dst string) (bool, error) {
+	if signature == nil || message == nil || blsEngine.G1.IsZero(&pk.value) {
+		return false, fmt.Errorf("signature and message and public key cannot be nil or zero")
+	}
+	if blsEngine.G2.IsZero(&signature.value) || !blsEngine.G2.InCorrectSubgroup(&signature.value) {
+		return false, fmt.Errorf("signature is not in the correct subgroup")
+	}
+	engine := bls12381.NewEngine()
+
+	p2, err := engine.G2.HashToCurve(sha256.New, message, []byte(dst))
+	if err != nil {
+		return false, err
+	}
+	// e(pk, H(m)) == e(g1, s)
+	// However, we can reduce the number of miller loops
+	// by doing the equivalent of
+	// e(pk^-1, H(m)) * e(g1, s) == 1
+	engine.AddPair(&pk.value, p2)
+	engine.AddPairInv(engine.G1.One(), &signature.value)
+	return engine.Check()
+}
+
+// Combine public keys into one aggregated key
+func aggregatePublicKeys(pks ...*PublicKey) (*PublicKey, error) {
+	if len(pks) < 1 {
+		return nil, fmt.Errorf("at least one public key is required")
+	}
+	result := blsEngine.G1.New()
+	for i, k := range pks {
+		if k == nil {
+			return nil, fmt.Errorf("key at %d is nil, keys cannot be nil", i)
+		}
+		if !blsEngine.G1.InCorrectSubgroup(&k.value) {
+			return nil, fmt.Errorf("key at %d is not in the correct subgroup", i)
+		}
+		blsEngine.G1.Add(result, result, &k.value)
+	}
+	return &PublicKey{value: *result}, nil
+}
+
+// Combine signatures into one aggregated signature
+func aggregateSignatures(sigs ...*Signature) (*Signature, error) {
+	if len(sigs) < 1 {
+		return nil, fmt.Errorf("at least one signature is required")
+	}
+	result := blsEngine.G2.New()
+	for i, s := range sigs {
+		if s == nil {
+			return nil, fmt.Errorf("signature at %d is nil, signature cannot be nil", i)
+		}
+		if !blsEngine.G2.InCorrectSubgroup(&s.value) {
+			return nil, fmt.Errorf("signature at %d is not in the correct subgroup", i)
+		}
+		blsEngine.G2.Add(result, result, &s.value)
+	}
+	return &Signature{value: *result}, nil
+}
+
+// A proof of possession scheme uses a separate public key validation
+// step, called a proof of possession, to defend against rogue key
+// attacks. This enables an optimization to aggregate signature
+// verification for the case that all signatures are on the same
+// message.
+type ProofOfPossession struct {
+	value bls12381.PointG2
+}
+
+// Generates a proof-of-possession (PoP) for this secret key. The PoP signature should be verified before
+// before accepting any aggregate signatures related to the corresponding pubkey.
+func (sk SecretKey) createProofOfPossession(popDst string) (*ProofOfPossession, error) {
+	pk, err := sk.GetPublicKey()
+	if err != nil {
+		return nil, err
+	}
+	msg, err := pk.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	sig, err := sk.createSignature(msg, popDst)
+	if err != nil {
+		return nil, err
+	}
+	return &ProofOfPossession{value: sig.value}, nil
+}
+
+// Serialize a proof of possession to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pop ProofOfPossession) MarshalBinary() ([]byte, error) {
+	return blsEngine.G2.ToCompressed(&pop.value), nil
+}
+
+// Deserialize a proof of possession from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (pop *ProofOfPossession) UnmarshalBinary(data []byte) error {
+	p2 := new(Signature)
+	err := p2.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	pop.value = p2.value
+	return nil
+}
+
+// Verifies that PoP is valid for this pubkey. In order to prevent rogue key attacks, a PoP must be validated
+// for each pubkey in an aggregated signature.
+func (pop ProofOfPossession) verify(pk *PublicKey, popDst string) (bool, error) {
+	if pk == nil {
+		return false, fmt.Errorf("public key cannot be nil")
+	}
+	msg, err := pk.MarshalBinary()
+	if err != nil {
+		return false, err
+	}
+	return pk.verifySignature(msg, &Signature{value: pop.value}, popDst)
+}
+
+// Represents an MultiSignature in G2. A multisignature is used when multiple signatures
+// are calculated over the same message vs an aggregate signature where each message signed
+// is a unique.
+type MultiSignature struct {
+	value bls12381.PointG2
+}
+
+// Serialize a multi-signature to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (sig MultiSignature) MarshalBinary() ([]byte, error) {
+	return blsEngine.G2.ToCompressed(&sig.value), nil
+}
+
+// Check a multisignature is valid for a multipublickey and a message
+func (sig MultiSignature) verify(pk *MultiPublicKey, message []byte, signDst string) (bool, error) {
+	if pk == nil {
+		return false, fmt.Errorf("public key cannot be nil")
+	}
+	p := PublicKey{value: pk.value}
+	return p.verifySignature(message, &Signature{value: sig.value}, signDst)
+}
+
+// Deserialize a signature from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the Signature
+// otherwise it will return an error
+func (sig *MultiSignature) UnmarshalBinary(data []byte) error {
+	if len(data) != SignatureSize {
+		return fmt.Errorf("multi signature must be %v bytes", SignatureSize)
+	}
+	s2 := new(Signature)
+	err := s2.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	sig.value = s2.value
+	return nil
+}
+
+// Represents accumulated multiple Public Keys in G1 for verifying a multisignature
+type MultiPublicKey struct {
+	value bls12381.PointG1
+}
+
+// Serialize a public key to a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+func (pk MultiPublicKey) MarshalBinary() ([]byte, error) {
+	return blsEngine.G1.ToCompressed(&pk.value), nil
+}
+
+// Deserialize a public key from a byte array in compressed form.
+// See
+// https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+// https://docs.rs/bls12_381/0.1.1/bls12_381/notes/serialization/index.html
+// If successful, it will assign the public key
+// otherwise it will return an error
+func (pk *MultiPublicKey) UnmarshalBinary(data []byte) error {
+	if len(data) != PublicKeySize {
+		return fmt.Errorf("multi public key must be %v bytes", PublicKeySize)
+	}
+	p1 := new(PublicKey)
+	err := p1.UnmarshalBinary(data)
+	if err != nil {
+		return err
+	}
+	pk.value = p1.value
+	return nil
+}
+
+// Check a multisignature is valid for a multipublickey and a message
+func (pk MultiPublicKey) verify(message []byte, sig *MultiSignature, signDst string) (bool, error) {
+	return sig.verify(&pk, message, signDst)
+}
+
+// PartialSignature represents threshold Gap Diffie-Hellman BLS signature
+// that can be combined with other partials to yield a completed BLS signature
+// See section 3.2 in <https://www.cc.gatech.edu/~aboldyre/papers/bold.pdf>
+type PartialSignature struct {
+	identifier byte
+	signature  bls12381.PointG2
+}
+
+// partialSign creates a partial signature that can be combined with other partial signatures
+// to yield a complete signature
+func (sks SecretKeyShare) partialSign(message []byte, signDst string) (*PartialSignature, error) {
+	if len(message) == 0 {
+		return nil, fmt.Errorf("message cannot be empty or nil")
+	}
+	p2, err := blsEngine.G2.HashToCurve(sha256.New, message, []byte(signDst))
+	if err != nil {
+		return nil, err
+	}
+	result := blsEngine.G2.New()
+	blsEngine.G2.MulScalar(result, p2, sks.value.Secret.BigInt())
+	if !blsEngine.G2.InCorrectSubgroup(result) {
+		return nil, fmt.Errorf("point is not on correct subgroup")
+	}
+	return &PartialSignature{identifier: sks.value.Identifier, signature: *result}, nil
+}
+
+// combineSigs gathers partial signatures and yields a complete signature
+func combineSigs(partials []*PartialSignature) (*Signature, error) {
+	if len(partials) < 2 {
+		return nil, fmt.Errorf("must have at least 2 partial signatures")
+	}
+	if len(partials) > 255 {
+		return nil, fmt.Errorf("unsupported to combine more than 255 signatures")
+	}
+
+	field := finitefield.New(blsEngine.G2.Q())
+	xVars, yVars, err := splitXY(field, partials)
+
+	if err != nil {
+		return nil, err
+	}
+
+	sTmp := blsEngine.G2.New()
+	sig := blsEngine.G2.New()
+
+	// Lagrange interpolation
+	x := field.Zero()
+	for i, xi := range xVars {
+		basis := field.One()
+
+		for j, xj := range xVars {
+			if i == j {
+				continue
+			}
+
+			num := x.Sub(xj)  // x - x_m
+			den := xi.Sub(xj) // x_j - x_m
+			if den.IsEqual(field.Zero()) {
+				return nil, fmt.Errorf("signatures cannot be recombined")
+			}
+			basis = basis.Mul(num.Div(den))
+		}
+		blsEngine.G2.MulScalar(sTmp, yVars[i], basis.BigInt())
+		blsEngine.G2.Add(sig, sig, sTmp)
+	}
+	if !blsEngine.G2.InCorrectSubgroup(sig) {
+		return nil, fmt.Errorf("signature is not in the correct subgroup")
+	}
+
+	return &Signature{value: *sig}, nil
+}
+
+// Ensure no duplicates x values and convert x values to field elements
+func splitXY(field *finitefield.Field, partials []*PartialSignature) ([]*finitefield.Element, []*bls12381.PointG2, error) {
+	x := make([]*finitefield.Element, len(partials))
+	y := make([]*bls12381.PointG2, len(partials))
+
+	dup := make(map[byte]bool)
+
+	for i, sp := range partials {
+		if sp == nil {
+			return nil, nil, fmt.Errorf("partial signature cannot be nil")
+		}
+		if _, exists := dup[sp.identifier]; exists {
+			return nil, nil, fmt.Errorf("duplicate signature included")
+		}
+		if !blsEngine.G2.InCorrectSubgroup(&sp.signature) {
+			return nil, nil, fmt.Errorf("signature is not in the correct subgroup")
+		}
+		dup[sp.identifier] = true
+		x[i] = field.ElementFromBytes([]byte{sp.identifier})
+		y[i] = &sp.signature
+	}
+	return x, y, nil
+}
diff --git a/pkg/signatures/bls/bls_sig/usual_bls_sig_aug_test.go b/pkg/signatures/bls/bls_sig/usual_bls_sig_aug_test.go
new file mode 100644
index 00000000..5f39760d
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/usual_bls_sig_aug_test.go
@@ -0,0 +1,406 @@
+package bls_sig
+
+import (
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+func generateAugSignatureG2(sk *SecretKey, msg []byte, t *testing.T) *Signature {
+	bls := NewSigAug()
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Aug Sign failed")
+	}
+	return sig
+}
+
+func generateAugAggregateDataG2(t *testing.T) ([]*PublicKey, []*Signature, [][]byte) {
+	msgs := make([][]byte, numAggregateG2)
+	pks := make([]*PublicKey, numAggregateG2)
+	sigs := make([]*Signature, numAggregateG2)
+	ikm := make([]byte, 32)
+	bls := NewSigAug()
+
+	for i := 0; i < numAggregateG2; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Aug KeyGen failed")
+		}
+		msg := make([]byte, 20)
+		readRand(msg, t)
+		sig := generateAugSignatureG2(sk, msg, t)
+		msgs[i] = msg
+		sigs[i] = sig
+		pks[i] = pk
+	}
+	return pks, sigs, msgs
+}
+
+func TestAugKeyGenG2Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAug()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+}
+
+func TestAugKeyGenG2Fail(t *testing.T) {
+	ikm := make([]byte, 10)
+	readRand(ikm, t)
+	bls := NewSigAug()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Aug KeyGen succeeded when it should've failed")
+	}
+}
+
+func TestAugCustomDstG2(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAugWithDst("BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_AUG_TEST")
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug Custom Dst KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig, err := bls.Sign(sk, ikm)
+
+	if err != nil {
+		t.Errorf("Aug Custom Dst Sign failed")
+	}
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Aug Custon Dst Verify failed")
+	}
+
+	ikm[0] = 0
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Aug Custom Dst Verify succeeded when it should've failed.")
+	}
+}
+
+func TestAugSigningG2(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigAug()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig := generateAugSignatureG2(sk, ikm, t)
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Aug Verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Aug Verify succeeded when it should've failed.")
+	}
+}
+
+func TestAugSignEmptyMessage(t *testing.T) {
+	bls := NewSigAug()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+
+	// Sign a nil message
+	_, err = bls.Sign(sk, nil)
+	if err == nil {
+		t.Errorf("Expected sign of nil message to fail")
+	}
+}
+
+func TestAugSignNilMessage(t *testing.T) {
+	bls := NewSigAug()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Aug KeyGen failed")
+	}
+
+	// Sign an empty message
+	_, err = bls.Sign(sk, []byte{})
+	if err == nil {
+		t.Errorf("Expected sign of empty message to fail")
+	}
+}
+
+func TestAugAggregateVerifyG2Works(t *testing.T) {
+	pks, sigs, msgs := generateAugAggregateDataG2(t)
+	bls := NewSigAug()
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug AggregateVerify failed")
+	}
+}
+
+func TestAugAggregateVerifyG2BadPks(t *testing.T) {
+	bls := NewSigAug()
+	pks, sigs, msgs := generateAugAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug AggregateVerify failed")
+	}
+
+	pks[0] = pks[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug AggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g1 := bls12381.NewG1()
+	pkValue := g1.New()
+	pks[0] = &PublicKey{value: *pkValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug AggregateVerify succeeded with zero byte public key it should've failed")
+	}
+
+	// Try with base generator
+	pkValue = g1.One()
+	pks[0] = &PublicKey{value: *pkValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with the base generator public key it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG2BadSigs(t *testing.T) {
+	bls := NewSigAug()
+	pks, sigs, msgs := generateAugAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed")
+	}
+
+	sigs[0] = sigs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g1 := bls12381.NewG2()
+	sigValue := g1.New()
+	sigs[0] = &Signature{value: *sigValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with zero byte signature it should've failed")
+	}
+
+	// Try with base generator
+	sigValue = g1.One()
+	sigs[0] = &Signature{value: *sigValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded with the base generator signature it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG2BadMsgs(t *testing.T) {
+	bls := NewSigAug()
+	pks, sigs, msgs := generateAugAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed")
+	}
+
+	// Test len(pks) != len(msgs)
+	if res, _ := bls.AggregateVerify(pks, msgs[0:8], sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+
+	msgs[0] = msgs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Aug aggregateVerify succeeded when it should've failed")
+	}
+}
+
+func TestAugAggregateVerifyG2DupMsg(t *testing.T) {
+	bls := NewSigAug()
+
+	// Only two messages but repeated
+	messages := make([][]byte, numAggregateG2)
+	messages[0] = []byte("Yes")
+	messages[1] = []byte("No")
+	for i := 2; i < numAggregateG2; i++ {
+		messages[i] = messages[i%2]
+	}
+
+	pks := make([]*PublicKey, numAggregateG2)
+	sigs := make([]*Signature, numAggregateG2)
+
+	ikm := make([]byte, 32)
+	for i := 0; i < numAggregateG2; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Aug KeyGen failed")
+		}
+
+		sig := generateAugSignatureG2(sk, messages[i], t)
+		pks[i] = pk
+		sigs[i] = sig
+	}
+
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); !res {
+		t.Errorf("Aug aggregateVerify failed for duplicate messages")
+	}
+}
+
+func TestBlsAugG2KeyGen(t *testing.T) {
+	bls := NewSigAug()
+	_, _, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+}
+
+func TestAugThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigAug()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(1, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestAugThresholdKeygen(t *testing.T) {
+	bls := NewSigAug()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+
+func TestAugPartialSign(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigAug()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], pk, msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], pk, msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures succeeded when it should've failed")
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestAugPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigAug()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignature, total)
+	sigs2 := make([]*PartialSignature, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], pk1, msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], pk2, msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
+
+func TestAugPartialSignEmptyMessage(t *testing.T) {
+	bls := NewSigAug()
+	pk, sks, err := bls.ThresholdKeygen(2, 2)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+
+	// Test signing an empty message
+	_, err = bls.PartialSign(sks[0], pk, []byte{})
+	if err == nil {
+		t.Errorf("Expected partial sign of empty message to fail")
+	}
+}
+
+func TestAugPartialSignNilMessage(t *testing.T) {
+	bls := NewSigAug()
+	pk, sks, err := bls.ThresholdKeygen(7, 7)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+
+	// Test signing a nil message
+	_, err = bls.PartialSign(sks[0], pk, nil)
+	if err == nil {
+		t.Errorf("Expected partial sign of nil message to fail")
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/usual_bls_sig_basic_test.go b/pkg/signatures/bls/bls_sig/usual_bls_sig_basic_test.go
new file mode 100644
index 00000000..3eac7bb9
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/usual_bls_sig_basic_test.go
@@ -0,0 +1,406 @@
+package bls_sig
+
+import (
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+func generateBasicSignatureG2(sk *SecretKey, msg []byte, t *testing.T) *Signature {
+	bls := NewSigBasic()
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Basic Sign failed")
+	}
+	return sig
+}
+
+func generateBasicAggregateDataG2(t *testing.T) ([]*PublicKey, []*Signature, [][]byte) {
+	msgs := make([][]byte, numAggregateG2)
+	pks := make([]*PublicKey, numAggregateG2)
+	sigs := make([]*Signature, numAggregateG2)
+	ikm := make([]byte, 32)
+	bls := NewSigBasic()
+
+	for i := 0; i < numAggregateG2; i++ {
+		readRand(ikm, t)
+		pk, sk, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Basic KeyGen failed")
+		}
+		msg := make([]byte, 20)
+		readRand(msg, t)
+		sig := generateBasicSignatureG2(sk, msg, t)
+		msgs[i] = msg
+		sigs[i] = sig
+		pks[i] = pk
+	}
+	return pks, sigs, msgs
+}
+
+func TestBasicKeyGenG2Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasic()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+}
+
+func TestBasicKeyGenG2Fail(t *testing.T) {
+	ikm := make([]byte, 10)
+	readRand(ikm, t)
+	bls := NewSigBasic()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Basic KeyGen succeeded when it should've failed")
+	}
+}
+
+func TestBasicCustomDstG2(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasicWithDst("BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_TEST")
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic Custom Dst KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig, err := bls.Sign(sk, ikm)
+
+	if err != nil {
+		t.Errorf("Basic Custom Dst Sign failed")
+	}
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Basic Custon Dst verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Basic Custom Dst verify succeeded when it should've failed.")
+	}
+}
+
+func TestBasicSigningG2(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigBasic()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	readRand(ikm, t)
+	sig := generateBasicSignatureG2(sk, ikm, t)
+
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Basic verify failed")
+	}
+
+	ikm[0] ^= ikm[1]
+	if res, _ := bls.Verify(pk, ikm, sig); res {
+		t.Errorf("Basic verify succeeded when it should've failed.")
+	}
+}
+
+func TestBasicSigningG2EmptyMessage(t *testing.T) {
+	// So basic
+	bls := NewSigBasic()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	// Sign an empty message
+	_, err = bls.Sign(sk, []byte{})
+	if err != nil {
+		t.Errorf("Expected signing empty message to succeed: %v", err)
+	}
+}
+
+func TestBasicSigningG2NilMessage(t *testing.T) {
+	// So basic
+	bls := NewSigBasic()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Basic KeyGen failed")
+	}
+
+	// Sign an empty message
+	_, err = bls.Sign(sk, nil)
+	if err == nil {
+		t.Errorf("Expected signing nil message to fail")
+	}
+}
+
+func TestBasicAggregateVerifyG2Works(t *testing.T) {
+	pks, sigs, msgs := generateBasicAggregateDataG2(t)
+	bls := NewSigBasic()
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic AggregateVerify failed")
+	}
+}
+
+func TestBasicAggregateVerifyG2BadPks(t *testing.T) {
+	bls := NewSigBasic()
+	pks, sigs, msgs := generateBasicAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic AggregateVerify failed")
+	}
+
+	pks[0] = pks[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic AggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g1 := bls12381.NewG1()
+	pkValue := g1.New()
+	pks[0] = &PublicKey{value: *pkValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic AggregateVerify succeeded with zero byte public key it should've failed")
+	}
+
+	// Try with base generator
+	pkValue = g1.One()
+	pks[0] = &PublicKey{value: *pkValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with the base generator public key it should've failed")
+	}
+}
+
+func TestBasicAggregateVerifyG2BadSigs(t *testing.T) {
+	bls := NewSigBasic()
+	pks, sigs, msgs := generateBasicAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic aggregateVerify failed")
+	}
+
+	sigs[0] = sigs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded when it should've failed")
+	}
+
+	// Try a zero key to make sure it doesn't crash
+	g2 := bls12381.NewG2()
+	sigValue := g2.New()
+	sigs[0] = &Signature{value: *sigValue}
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with zero byte signature it should've failed")
+	}
+
+	// Try with base generator
+	sigValue = g2.One()
+	sigs[0] = &Signature{value: *sigValue}
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded with the base generator signature it should've failed")
+	}
+}
+
+func TestBasicAggregateVerifyG2BadMsgs(t *testing.T) {
+	bls := NewSigBasic()
+	pks, sigs, msgs := generateBasicAggregateDataG2(t)
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); !res {
+		t.Errorf("Basic aggregateVerify failed")
+	}
+
+	msgs[0] = msgs[1]
+
+	if res, _ := bls.AggregateVerify(pks, msgs, sigs); res {
+		t.Errorf("Basic aggregateVerify succeeded when it should've failed")
+	}
+}
+
+func TestBasicThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigBasic()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(1, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestBasicThresholdKeygen(t *testing.T) {
+	bls := NewSigBasic()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+
+func TestBasicPartialSign(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigBasic()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures succeeded when it should've failed")
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that duplicate partial signatures cannot be used to create a complete one
+func TestBasicPartialDuplicateShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigBasic()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignature, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining duplicates from group 1
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[0], sigs1[1], sigs1[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded")
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with duplicate partial signatures")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestBasicPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigBasic()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignature, total)
+	sigs2 := make([]*PartialSignature, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
+
+func TestIdentityPublicKey(t *testing.T) {
+	bls := NewSigBasic()
+	_, sk, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+	msg := []byte{0, 0, 0, 0}
+	sig, _ := bls.Sign(sk, msg)
+	pk := PublicKey{value: *bls12381.NewG1().Zero()}
+	if res, _ := bls.Verify(&pk, msg, sig); res {
+		t.Errorf("Verify succeeded when the public key is the identity.")
+	}
+}
+
+func TestThresholdSignTooHighAndLow(t *testing.T) {
+	bls := NewSigBasic()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	msg := make([]byte, 10)
+
+	ps, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("PartialSign failed: %v", err)
+	}
+
+	_, err = bls.CombineSignatures(ps)
+	if err == nil {
+		t.Errorf("CombinSignatures succeeded when it should've failed")
+	}
+
+	pss := make([]*PartialSignature, 256)
+
+	_, err = bls.CombineSignatures(pss...)
+	if err == nil {
+		t.Errorf("CombinSignatures succeeded when it should've failed")
+	}
+}
diff --git a/pkg/signatures/bls/bls_sig/usual_bls_sig_pop_test.go b/pkg/signatures/bls/bls_sig/usual_bls_sig_pop_test.go
new file mode 100644
index 00000000..0eed2335
--- /dev/null
+++ b/pkg/signatures/bls/bls_sig/usual_bls_sig_pop_test.go
@@ -0,0 +1,862 @@
+package bls_sig
+
+import (
+	"bytes"
+	"math/big"
+	"math/rand"
+	"testing"
+
+	bls12381 "github.com/coinbase/kryptology/pkg/core/curves/native/bls12-381"
+)
+
+const numAggregateG2 = 10
+
+func TestGetPublicKeyG1(t *testing.T) {
+	sk := genSecretKey(t)
+	pk := genPublicKey(sk, t)
+	actual := marshalStruct(pk, t)
+	expected := []byte{166, 149, 173, 50, 93, 252, 126, 17, 145, 251, 201, 241, 134, 245, 142, 255, 66, 166, 52, 2, 151, 49, 177, 131, 128, 255, 137, 191, 66, 196, 100, 164, 44, 184, 202, 85, 178, 0, 240, 81, 245, 127, 30, 24, 147, 198, 135, 89}
+	if !bytes.Equal(actual, expected) {
+		t.Errorf("Expected GetPublicKey to pass but failed.")
+	}
+}
+
+func testSignG2(message []byte, t *testing.T) {
+	sk := genSecretKey(t)
+	sig := genSignature(sk, message, t)
+	pk := genPublicKey(sk, t)
+
+	bls := NewSigPop()
+
+	if res, err := bls.Verify(pk, message, sig); !res {
+		t.Errorf("createSignature failed when it should've passed: %v", err)
+	}
+}
+
+func TestSignG2EmptyMessage(t *testing.T) {
+	bls := NewSigPop()
+	sk := genSecretKey(t)
+	sig, _ := bls.Sign(sk, nil)
+	pk := genPublicKey(sk, t)
+
+	if res, _ := bls.Verify(pk, nil, sig); res {
+		t.Errorf("createSignature succeeded when it should've failed")
+	}
+
+	message := []byte{}
+	sig = genSignature(sk, message, t)
+
+	if res, err := bls.Verify(pk, message, sig); !res {
+		t.Errorf("create and verify failed on empty message: %v", err)
+	}
+}
+
+func TestSignG2OneByteMessage(t *testing.T) {
+	message := []byte{1}
+	testSignG2(message, t)
+}
+
+func TestSignG2LargeMessage(t *testing.T) {
+	message := make([]byte, 1048576)
+	testSignG2(message, t)
+}
+
+func TestSignG2RandomMessage(t *testing.T) {
+	message := make([]byte, 65537)
+	readRand(message, t)
+	testSignG2(message, t)
+}
+
+func TestSignG2BadMessage(t *testing.T) {
+	message := make([]byte, 1024)
+	sk := genSecretKey(t)
+	sig := genSignature(sk, message, t)
+	pk := genPublicKey(sk, t)
+	message = []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
+
+	bls := NewSigPop()
+
+	if res, _ := bls.Verify(pk, message, sig); res {
+		t.Errorf("Expected signature to not verify")
+	}
+}
+
+func TestBadConversionsG2(t *testing.T) {
+	sk := genSecretKey(t)
+	message := []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 0}
+	sig := genSignature(sk, message, t)
+	pk := genPublicKey(sk, t)
+
+	bls := NewSigPop()
+
+	if res, _ := bls.Verify(pk, message, sig); !res {
+		t.Errorf("Signature should be valid")
+	}
+	if res, _ := sig.verify(pk, message, blsSignaturePopDst); !res {
+		t.Errorf("Signature should be valid")
+	}
+
+	// Convert public key to signature in G2
+	sig2 := new(SignatureVt)
+	err := sig2.UnmarshalBinary(marshalStruct(pk, t))
+	if err != nil {
+		t.Errorf("Should be able to convert to signature in G2")
+	}
+	pk2 := new(PublicKeyVt)
+	err = pk2.UnmarshalBinary(marshalStruct(sig, t))
+	if err != nil {
+		t.Errorf("Should be able to convert to public key in G1")
+	}
+
+	if res, _ := pk2.verifySignatureVt(message, sig2, blsSignaturePopDst); res {
+		t.Errorf("The signature shouldn't verify")
+	}
+}
+
+func TestAggregatePublicKeysG1(t *testing.T) {
+	pks := []*PublicKey{}
+	ikm := make([]byte, 32)
+	for i := 0; i < 20; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		pk := genPublicKey(sk, t)
+		pks = append(pks, pk)
+	}
+	apk1, err := aggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	rand.Seed(1234567890)
+	rand.Shuffle(len(pks), func(i, j int) { pks[i], pks[j] = pks[j], pks[i] })
+	apk2, err := aggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(apk1, t), marshalStruct(apk2, t)) {
+		t.Errorf("Aggregated public keys should be equal")
+	}
+	rand.Shuffle(len(pks), func(i, j int) { pks[i], pks[j] = pks[j], pks[i] })
+	apk1, err = aggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(apk1, t), marshalStruct(apk2, t)) {
+		t.Errorf("Aggregated public keys should be equal")
+	}
+}
+
+func TestAggregateSignaturesG2(t *testing.T) {
+	var sigs []*Signature
+	ikm := make([]byte, 32)
+	for i := 0; i < 20; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		sig := genSignature(sk, ikm, t)
+		sigs = append(sigs, sig)
+	}
+	asig1, err := aggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	rand.Seed(1234567890)
+	rand.Shuffle(len(sigs), func(i, j int) { sigs[i], sigs[j] = sigs[j], sigs[i] })
+	asig2, err := aggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(asig1, t), marshalStruct(asig2, t)) {
+		t.Errorf("Aggregated signatures should be equal")
+	}
+	rand.Shuffle(len(sigs), func(i, j int) { sigs[i], sigs[j] = sigs[j], sigs[i] })
+	asig1, err = aggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if !bytes.Equal(marshalStruct(asig1, t), marshalStruct(asig2, t)) {
+		t.Errorf("Aggregated signatures should be equal")
+	}
+}
+
+func initAggregatedTestValuesG2(messages [][]byte, t *testing.T) ([]*PublicKey, []*Signature) {
+	pks := []*PublicKey{}
+	sigs := []*Signature{}
+	ikm := make([]byte, 32)
+	for i := 0; i < numAggregateG2; i++ {
+		readRand(ikm, t)
+		sk := genRandSecretKey(ikm, t)
+		sig := genSignature(sk, messages[i%len(messages)], t)
+		sigs = append(sigs, sig)
+		pk := genPublicKey(sk, t)
+		pks = append(pks, pk)
+	}
+	return pks, sigs
+}
+
+func TestAggregatedFunctionalityG2(t *testing.T) {
+	message := make([]byte, 20)
+	messages := make([][]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+
+	bls := NewSigPop()
+	asig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); !res {
+		t.Errorf("Should verify aggregated signatures with same message")
+	}
+	if res, _ := asig.verify(apk, message, blsSignaturePopDst); !res {
+		t.Errorf("MultiSignature.verify failed.")
+	}
+	if res, _ := apk.verify(message, asig, blsSignaturePopDst); !res {
+		t.Errorf("MultiPublicKey.verify failed.")
+	}
+}
+
+func TestBadAggregatedFunctionalityG2(t *testing.T) {
+	message := make([]byte, 20)
+	messages := make([][]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+
+	bls := NewSigPop()
+
+	apk, err := bls.AggregatePublicKeys(pks[2:]...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	asig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); res {
+		t.Errorf("Should not verify aggregated signatures with same message when some public keys are missing")
+	}
+
+	apk, err = bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	asig, err = bls.AggregateSignatures(sigs[2:]...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	if res, _ := bls.VerifyMultiSignature(apk, message, asig); res {
+		t.Errorf("Should not verify aggregated signatures with same message when some signatures are missing")
+	}
+
+	asig, err = bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+
+	badmsg := []byte{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
+	if res, _ := bls.VerifyMultiSignature(apk, badmsg, asig); res {
+		t.Errorf("Should not verify aggregated signature with bad message")
+	}
+}
+
+func TestAggregateVerifyG2Pass(t *testing.T) {
+	messages := make([][]byte, numAggregateG2)
+	for i := 0; i < numAggregateG2; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); !res {
+		t.Errorf("Expected aggregateVerify to pass but failed")
+	}
+}
+
+func TestAggregateVerifyG2MsgSigCntMismatch(t *testing.T) {
+	messages := make([][]byte, 8)
+	for i := 0; i < 8; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); res {
+		t.Errorf("Expected AggregateVerifyG2 to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG2FailDupMsg(t *testing.T) {
+	messages := make([][]byte, 10)
+	for i := 0; i < 9; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	// Duplicate message
+	messages[9] = messages[0]
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	if res, _ := bls.AggregateVerify(pks, messages, sigs); res {
+		t.Errorf("Expected aggregateVerify to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG2FailIncorrectMsg(t *testing.T) {
+	messages := make([][]byte, 10)
+	for i := 0; i < 9; i++ {
+		message := make([]byte, 20)
+		readRand(message, t)
+		messages[i] = message
+	}
+	// Duplicate message
+	messages[9] = messages[0]
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	if res, _ := bls.AggregateVerify(pks[2:], messages[2:], sigs); res {
+		t.Errorf("Expected aggregateVerify to fail with duplicate message but passed")
+	}
+}
+
+func TestAggregateVerifyG2OneMsg(t *testing.T) {
+	messages := make([][]byte, 1)
+	messages[0] = make([]byte, 20)
+	sk := genSecretKey(t)
+	sig := genSignature(sk, messages[0], t)
+	pk := genPublicKey(sk, t)
+	bls := NewSigPop()
+	// Should be the same as verifySignature
+	if res, _ := bls.AggregateVerify([]*PublicKey{pk}, messages, []*Signature{sig}); !res {
+		t.Errorf("Expected AggregateVerifyG2OneMsg to pass but failed")
+	}
+}
+
+func TestVerifyG2Mutability(t *testing.T) {
+	//verify should not change any inputs
+	ikm := make([]byte, 32)
+	ikm_copy := make([]byte, 32)
+	readRand(ikm, t)
+	copy(ikm_copy, ikm)
+	bls := NewSigPop()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPop.KeygenWithSeed modifies ikm")
+	}
+	if err != nil {
+		t.Errorf("Expected KeygenWithSeed to succeed but failed.")
+	}
+	sig, err := bls.Sign(sk, ikm)
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPop.Sign modifies message")
+	}
+	if err != nil {
+		t.Errorf("SigPop.KeygenWithSeed to succeed but failed.")
+	}
+	sigCopy := marshalStruct(sig, t)
+	if res, _ := bls.Verify(pk, ikm, sig); !res {
+		t.Errorf("Expected verify to succeed but failed.")
+	}
+	if !bytes.Equal(ikm, ikm_copy) {
+		t.Errorf("SigPop.verify modifies message")
+	}
+	if !bytes.Equal(sigCopy, marshalStruct(sig, t)) {
+		t.Errorf("SigPop.verify modifies signature")
+	}
+}
+
+func TestPublicKeyG1FromBadBytes(t *testing.T) {
+	pk := make([]byte, 32)
+	err := new(PublicKey).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG1FromBytes to fail but passed")
+	}
+	// All zeros
+	pk = make([]byte, PublicKeySize)
+	// See https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+	// 1 << 7 == compressed
+	// 1 << 6 == infinity or zero
+	pk[0] = 0xc0
+	err = new(PublicKey).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG1FromBytes to fail but passed")
+	}
+	sk := genSecretKey(t)
+	pk1, err := sk.GetPublicKey()
+	if err != nil {
+		t.Errorf("Expected GetPublicKey to pass but failed.")
+	}
+	out := marshalStruct(pk1, t)
+	out[3] ^= out[4]
+	err = new(PublicKey).UnmarshalBinary(pk)
+	if err == nil {
+		t.Errorf("Expected PublicKeyG1FromBytes to fail but passed")
+	}
+}
+
+func TestSignatureG2FromBadBytes(t *testing.T) {
+	sig := make([]byte, 32)
+	err := new(Signature).UnmarshalBinary(sig)
+	if err == nil {
+		t.Errorf("Expected SignatureG2FromBytes to fail but passed")
+	}
+	// All zeros
+	sig = make([]byte, SignatureSize)
+	// See https://github.com/zcash/librustzcash/blob/master/pairing/src/bls12_381/README.md#serialization
+	// 1 << 7 == compressed
+	// 1 << 6 == infinity or zero
+	sig[0] = 0xc0
+	err = new(Signature).UnmarshalBinary(sig)
+	if err == nil {
+		t.Errorf("Expected SignatureG2FromBytes to fail but passed")
+	}
+}
+
+func TestBadSecretKeyG2(t *testing.T) {
+	x := new(big.Int)
+	sk := &SecretKey{value: *x}
+	pk, err := sk.GetPublicKey()
+	if err == nil {
+		t.Errorf("Expected GetPublicKey to fail with 0 byte secret key but passed: %v", pk)
+	}
+	bls := bls12381.NewG1()
+	_ = sk.UnmarshalBinary(bls.Q().Bytes())
+	pk, err = sk.GetPublicKey()
+	if err == nil {
+		t.Errorf("Expected GetPublicKey to fail with secret key with Q but passed: %v", pk)
+	}
+
+	err = sk.UnmarshalBinary([]byte{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16})
+	if err == nil {
+		t.Errorf("Expected SecretKeyFromBytes to fail with not enough bytes but passed: %v", pk)
+	}
+
+	err = sk.UnmarshalBinary(make([]byte, 32))
+	if err == nil {
+		t.Errorf("Expected SecretKeyFromBytes to fail with all zeros but passed: %v", pk)
+	}
+}
+
+func TestProofOfPossessionG2Works(t *testing.T) {
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	bls := NewSigPop()
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Key gen failed but should've succeeded")
+	}
+	pop, err := bls.PopProve(sk)
+	if err != nil {
+		t.Errorf("PopProve failed but should've succeeded")
+	}
+	if res, _ := bls.PopVerify(pk, pop); !res {
+		t.Errorf("PopVerify failed but should've succeeded")
+	}
+}
+
+func TestProofOfPossessionG2FromBadKey(t *testing.T) {
+	ikm := make([]byte, 32)
+	value := new(big.Int)
+	value.SetBytes(ikm)
+	sk := SecretKey{value: *value}
+	_, err := sk.createProofOfPossession(blsSignaturePopDst)
+	if err == nil {
+		t.Errorf("createProofOfPossession should've failed but succeeded.")
+	}
+}
+
+func TestProofOfPossessionG2BytesWorks(t *testing.T) {
+	sk := genSecretKey(t)
+	pop, err := sk.createProofOfPossession(blsSignaturePopDst)
+	if err != nil {
+		t.Errorf("CreateProofOfPossesionG2 failed but shouldn've succeeded.")
+	}
+	out := marshalStruct(pop, t)
+	if len(out) != ProofOfPossessionSize {
+		t.Errorf("ProofOfPossessionBytes incorrect size: expected %v, got %v", ProofOfPossessionSize, len(out))
+	}
+	pop2 := new(ProofOfPossession)
+	err = pop2.UnmarshalBinary(out)
+	if err != nil {
+		t.Errorf("ProofOfPossession.UnmarshalBinary failed: %v", err)
+	}
+	out2 := marshalStruct(pop2, t)
+	if !bytes.Equal(out, out2) {
+		t.Errorf("ProofOfPossession.UnmarshalBinary failed, not equal when deserialized")
+	}
+}
+
+func TestProofOfPossessionG2BadBytes(t *testing.T) {
+	zeros := make([]byte, ProofOfPossessionSize)
+	temp := new(ProofOfPossession)
+	err := temp.UnmarshalBinary(zeros)
+	if err == nil {
+		t.Errorf("ProofOfPossession.UnmarshalBinary shouldn've failed but succeeded.")
+	}
+}
+
+func TestProofOfPossessionG2Fails(t *testing.T) {
+	sk := genSecretKey(t)
+	pop, err := sk.createProofOfPossession(blsSignaturePopDst)
+	if err != nil {
+		t.Errorf("Expected createProofOfPossession to succeed but failed.")
+	}
+
+	ikm := make([]byte, 32)
+	readRand(ikm, t)
+	sk = genRandSecretKey(ikm, t)
+	bad, err := sk.GetPublicKey()
+	if err != nil {
+		t.Errorf("Expected PublicKeyG1FromBytes to succeed but failed: %v", err)
+	}
+	if res, _ := pop.verify(bad, blsSignaturePopDst); res {
+		t.Errorf("Expected ProofOfPossession verify to fail but succeeded.")
+	}
+}
+
+func TestMultiSigG2Bytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	_, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	msig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	msigBytes := marshalStruct(msig, t)
+	if len(msigBytes) != SignatureSize {
+		t.Errorf("Invalid multi-sig length. Expected %d bytes, found %d", SignatureSize, len(msigBytes))
+	}
+	msig2 := new(MultiSignature)
+	err = msig2.UnmarshalBinary(msigBytes)
+	if err != nil {
+		t.Errorf("MultiSignatureG2FromBytes failed with %v", err)
+	}
+	msigBytes2 := marshalStruct(msig2, t)
+
+	if !bytes.Equal(msigBytes, msigBytes2) {
+		t.Errorf("Bytes methods not equal.")
+	}
+}
+
+func TestMultiSigG2BadBytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	_, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	msig, err := bls.AggregateSignatures(sigs...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	msigBytes := marshalStruct(msig, t)
+	if len(msigBytes) != SignatureSize {
+		t.Errorf("Invalid multi-sig length. Expected %d bytes, found %d", SignatureSize, len(msigBytes))
+	}
+	msigBytes[0] = 0
+	temp := new(MultiSignature)
+	err = temp.UnmarshalBinary(msigBytes)
+	if err == nil {
+		t.Errorf("MultiSignatureG2FromBytes should've failed but succeeded")
+	}
+	msigBytes = make([]byte, SignatureSize)
+	err = temp.UnmarshalBinary(msigBytes)
+	if err == nil {
+		t.Errorf("MultiSignatureG2FromBytes should've failed but succeeded")
+	}
+}
+
+func TestMultiPubkeyG1Bytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	pks, _ := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apkBytes := marshalStruct(apk, t)
+	if len(apkBytes) != PublicKeySize {
+		t.Errorf("MultiPublicKey has an incorrect size")
+	}
+	apk2 := new(MultiPublicKey)
+	err = apk2.UnmarshalBinary(apkBytes)
+	if err != nil {
+		t.Errorf("MultiPublicKey.UnmarshalBinary failed with %v", err)
+	}
+	apk2Bytes := marshalStruct(apk2, t)
+	if !bytes.Equal(apkBytes, apk2Bytes) {
+		t.Errorf("Bytes methods not equal.")
+	}
+}
+
+func TestMultiPubkeyG1BadBytes(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 20)
+	messages[0] = message
+	pks, _ := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	apk, err := bls.AggregatePublicKeys(pks...)
+	if err != nil {
+		t.Errorf("%v", err)
+	}
+	apkBytes := marshalStruct(apk, t)
+	if len(apkBytes) != PublicKeySize {
+		t.Errorf("MultiPublicKey has an incorrect size")
+	}
+	apkBytes[0] = 0
+	temp := new(MultiPublicKey)
+	err = temp.UnmarshalBinary(apkBytes)
+	if err == nil {
+		t.Errorf("MultiPublicKey.UnmarshalBinary should've failed but succeeded")
+	}
+	apkBytes = make([]byte, PublicKeySize)
+	err = temp.UnmarshalBinary(apkBytes)
+	if err == nil {
+		t.Errorf("MultiPublicKey.UnmarshalBinary should've failed but succeeded")
+	}
+}
+
+func TestFastAggregateVerifyG2Works(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	asigs, _ := aggregateSignatures(sigs...)
+	bls := NewSigPop()
+	if res, _ := bls.FastAggregateVerify(pks, message, asigs); !res {
+		t.Errorf("FastAggregateVerify failed.")
+	}
+}
+
+func TestFastAggregateVerifyConstituentG2Works(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, message, sigs); !res {
+		t.Errorf("FastAggregateVerify failed.")
+	}
+}
+
+func TestFastAggregateVerifyG2Fails(t *testing.T) {
+	messages := make([][]byte, 1)
+	message := make([]byte, 1)
+	messages[0] = message
+	pks, sigs := initAggregatedTestValuesG2(messages, t)
+	bls := NewSigPop()
+	message[0] = 1
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, message, sigs); res {
+		t.Errorf("FastAggregateVerify verified when it should've failed.")
+	}
+}
+
+func TestCustomPopDstG2Works(t *testing.T) {
+	bls, _ := NewSigPopWithDst("BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_TEST",
+		"BLS_POP_BLS12381G2_XMD:SHA-256_SSWU_RO_POP_TEST")
+	msg := make([]byte, 20)
+	ikm := make([]byte, 32)
+	pk, sk, err := bls.KeygenWithSeed(ikm)
+	if err != nil {
+		t.Errorf("Couldn't create custom dst keys: %v", err)
+	}
+	sig, err := bls.Sign(sk, msg)
+	if err != nil {
+		t.Errorf("Couldn't sign with custom dst: %v", err)
+	}
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("verify fails with custom dst")
+	}
+
+	pks := make([]*PublicKey, 10)
+	sigs := make([]*Signature, 10)
+	pks[0] = pk
+	sigs[0] = sig
+	for i := 1; i < 10; i++ {
+		readRand(ikm, t)
+		pkt, skt, err := bls.KeygenWithSeed(ikm)
+		if err != nil {
+			t.Errorf("Couldn't create custom dst keys: %v", err)
+		}
+		sigt, err := bls.Sign(skt, msg)
+		if err != nil {
+			t.Errorf("Couldn't sign with custom dst: %v", err)
+		}
+		pks[i] = pkt
+		sigs[i] = sigt
+	}
+
+	if res, _ := bls.FastAggregateVerifyConstituent(pks, msg, sigs); !res {
+		t.Errorf("FastAggregateVerify failed with custom dst")
+	}
+
+	pop, err := bls.PopProve(sk)
+	if err != nil {
+		t.Errorf("PopProve failed with custom dst")
+	}
+
+	if res, _ := bls.PopVerify(pk, pop); !res {
+		t.Errorf("PopVerify failed with custom dst")
+	}
+}
+
+func TestBlsPopG2KeyGenWithSeed(t *testing.T) {
+	ikm := []byte("Not enough bytes")
+	bls := NewSigPop()
+	_, _, err := bls.KeygenWithSeed(ikm)
+	if err == nil {
+		t.Errorf("Expected KeygenWithSeed to fail but succeeded")
+	}
+}
+
+func TestBlsPopG2KeyGen(t *testing.T) {
+	bls := NewSigPop()
+	_, _, err := bls.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+}
+
+func TestPopThresholdKeygenBadInputs(t *testing.T) {
+	bls := NewSigPop()
+	_, _, err := bls.ThresholdKeygen(0, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(1, 0)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+	_, _, err = bls.ThresholdKeygen(3, 2)
+	if err == nil {
+		t.Errorf("ThresholdKeygen should've failed but succeeded")
+	}
+}
+
+func TestPopThresholdKeygen(t *testing.T) {
+	bls := NewSigPop()
+	_, sks, err := bls.ThresholdKeygen(3, 5)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	if len(sks) != 5 {
+		t.Errorf("ThresholdKeygen did not produce enough shares")
+	}
+}
+func TestPopPartialSign(t *testing.T) {
+	ikm := make([]byte, 32)
+	bls := NewSigPop()
+	pk, sks, err := bls.ThresholdKeygenWithSeed(ikm, 2, 4)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed")
+	}
+	msg := make([]byte, 10)
+	sig1, err := bls.PartialSign(sks[0], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig2, err := bls.PartialSign(sks[1], msg)
+	if err != nil {
+		t.Errorf("partialSign failed: %v", err)
+	}
+	sig, err := bls.CombineSignatures(sig1, sig2)
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+
+	if res, _ := bls.Verify(pk, msg, sig); !res {
+		t.Errorf("Combined signature does not verify")
+	}
+
+	sig, err = bls.CombineSignatures(sig1)
+	if err == nil {
+		t.Errorf("CombineSignatures succeeded when it should've failed")
+	}
+	if res, _ := bls.Verify(pk, msg, sig); res {
+		t.Errorf("Combined signature verify succeeded when it should've failed")
+	}
+}
+
+// Ensure that mixed partial signatures from distinct origins create invalid composite signatures
+func TestPopPartialMixupShares(t *testing.T) {
+	total := uint(5)
+	ikm := make([]byte, 32)
+	bls := NewSigPop()
+	pk1, sks1, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+	for i := range ikm {
+		ikm[i] = 1
+	}
+	pk2, sks2, err := bls.ThresholdKeygenWithSeed(ikm, 3, total)
+	if err != nil {
+		t.Errorf("ThresholdKeygen failed: %v", err)
+	}
+
+	// Generate partial signatures for both sets of keys
+	msg := make([]byte, 10)
+	sigs1 := make([]*PartialSignature, total)
+	sigs2 := make([]*PartialSignature, total)
+	for i := range sks1 {
+		sigs1[i], err = bls.PartialSign(sks1[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+		sigs2[i], err = bls.PartialSign(sks2[i], msg)
+		if err != nil {
+			t.Errorf("PartialSign failed: %v", err)
+		}
+	}
+
+	// Try combining 2 from group 1 and 2 from group 2
+	sig, err := bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[2], sigs2[3])
+	if err != nil {
+		t.Errorf("CombineSignatures failed: %v", err)
+	}
+	// Signature shouldn't validate
+	if res, _ := bls.Verify(pk1, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	if res, _ := bls.Verify(pk2, msg, sig); res {
+		t.Errorf("CombineSignatures worked with different shares of two secret keys for the same message")
+	}
+	// Should error out due to duplicate identifiers
+	_, err = bls.CombineSignatures(sigs1[0], sigs1[1], sigs2[0], sigs2[1])
+	if err == nil {
+		t.Errorf("CombineSignatures expected to fail but succeeded.")
+	}
+}
+
+func TestNewSigEth2KeyGen(t *testing.T) {
+	eth2 := NewSigEth2()
+	_, _, err := eth2.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+}
+
+func TestSigEth2SignRoundTrip(t *testing.T) {
+	eth2 := NewSigEth2()
+	pop := NewSigPop()
+	eth2Pk, eth2Sk, err := eth2.Keygen()
+	if err != nil {
+		t.Errorf("Keygen failed: %v", err)
+	}
+
+	sig, err := pop.Sign(eth2Sk, []byte{0, 0})
+	if err != nil {
+		t.Errorf("Sign failed: %v", err)
+	}
+	if ok, err := eth2.Verify(eth2Pk, []byte{0, 0}, sig); err != nil || !ok {
+		t.Errorf("Verify failed: %v", err)
+	}
+}
diff --git a/pkg/signatures/bls/docs/audit-kudeski-coinbase-bls.pdf b/pkg/signatures/bls/docs/audit-kudeski-coinbase-bls.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..43a446ad60fea478fa8b011e2c7bda7cbbba8146
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literal 0
HcmV?d00001

diff --git a/pkg/signatures/bls/docs/pull_request_template.md b/pkg/signatures/bls/docs/pull_request_template.md
new file mode 100644
index 00000000..bcdd9ea9
--- /dev/null
+++ b/pkg/signatures/bls/docs/pull_request_template.md
@@ -0,0 +1,4 @@
+
+type=routine
+risk=low
+impact=sev5
\ No newline at end of file
diff --git a/pkg/signatures/bls/finitefield/finitefield.go b/pkg/signatures/bls/finitefield/finitefield.go
new file mode 100644
index 00000000..c783b2d9
--- /dev/null
+++ b/pkg/signatures/bls/finitefield/finitefield.go
@@ -0,0 +1,188 @@
+/*
+Package finitefield provides a finite field type (Field) that wraps big.Int operations and verifies that all
+mutations to the value are done within the field.
+
+This implementation IS NOT constant time as it leverages math/big for big number operations.
+*/
+package finitefield
+
+import (
+	"crypto/rand"
+	"fmt"
+	"io"
+	"math/big"
+)
+
+// Field is a finite field.
+type Field struct {
+	Modulus *big.Int
+}
+
+// Element is a group element within a finite field.
+type Element struct {
+	*Field
+	value *big.Int
+}
+
+// The probability of returning true for a randomly chosen
+// non-prime is at most ¼ⁿ. 64 is a widely used standard
+// that is more than sufficient.
+const millerRabinRounds = 64
+
+// New is a constructor for a Field.
+func New(modulus *big.Int) *Field {
+	// For our purposes we never expect to be dealing with a non-prime field. This provides some protection against
+	// accidentally doing that.
+	if !modulus.ProbablyPrime(millerRabinRounds) {
+		panic(fmt.Sprintf("modulus: %x is not a prime", modulus))
+	}
+
+	return &Field{modulus}
+}
+
+func newElement(field *Field, value *big.Int) *Element {
+	if !field.IsValid(value) {
+		panic(fmt.Sprintf("value: %x is not within field: %x", value, field.Modulus))
+	}
+
+	return &Element{field, value}
+}
+
+// IsValid returns whether or not the value is within [0, modulus)
+func (f Field) IsValid(value *big.Int) bool {
+	// value < modulus && value >= 0
+	return value.Cmp(f.Modulus) < 0 && value.Sign() >= 0
+}
+
+func (f Field) NewElement(value *big.Int) *Element {
+	return newElement(&f, value)
+}
+
+func (f Field) Zero() *Element {
+	return newElement(&f, big.NewInt(0))
+}
+
+func (f Field) One() *Element {
+	return newElement(&f, big.NewInt(1))
+}
+
+func (f Field) RandomElement(r io.Reader) (*Element, error) {
+	if r == nil {
+		r = rand.Reader
+	}
+	// Read a random integer within the field. This is defined as [0, max) so we don't need to
+	// explicitly check it is within the field. If it is not, NewElement will panic anyways.
+	randInt, err := rand.Int(r, f.Modulus)
+	if err != nil {
+		return nil, err
+	}
+
+	return newElement(&f, randInt), nil
+}
+
+// ElementFromBytes initializes a new field element from big-endian bytes
+func (f Field) ElementFromBytes(bytes []byte) *Element {
+	return newElement(&f, new(big.Int).SetBytes(bytes))
+}
+
+// ReducedElementFromBytes initializes a new field element from big-endian bytes and reduces it by
+// the modulus of the field.
+//
+// WARNING: If this is used with cryptographic constructions which rely on a uniform distribution of
+// values, this may introduce a bias to the value of the returned field element. This happens when
+// the integer range of the provided bytes is not an integer multiple of the field order.
+//
+// Assume we are working in field which a modulus of 3 and the range of the uniform random bytes we
+// provide as input is 5. Thus, the set of field elements is {0, 1, 2} and the set of integer values
+// for the input bytes is: {0, 1, 2, 3, 4}. What is the distribution of the output values produced
+// by this function?
+//
+//   ReducedElementFromBytes(0) => 0
+//   ReducedElementFromBytes(1) => 1
+//   ReducedElementFromBytes(2) => 2
+//   ReducedElementFromBytes(3) => 0
+//   ReducedElementFromBytes(4) => 1
+//
+// For a value space V and random value v, a uniform distribution is defined as P[V = v] = 1/|V|
+// where |V| is to the order of the field. Using the results from above, we see that P[v = 0] = 2/5,
+// P[v = 1] = 2/5, and P[v = 2] = 1/5. For a uniform distribution we would expect these to each be
+// equal to 1/3. As they do not, this does not return uniform output for that example.
+//
+// To see why this is okay if the range is a multiple of the field order, change the input range to
+// 6 and notice that now each output has a probability of 2/6 = 1/3, and the output is uniform.
+func (f Field) ReducedElementFromBytes(bytes []byte) *Element {
+	value := new(big.Int).SetBytes(bytes)
+	value.Mod(value, f.Modulus)
+	return newElement(&f, value)
+}
+
+// Add returns the sum x+y
+func (x Element) Add(y *Element) *Element {
+	x.validateFields(y)
+
+	sum := new(big.Int).Add(x.value, y.value)
+	sum.Mod(sum, x.Modulus)
+	return newElement(x.Field, sum)
+}
+
+// Sub returns the difference x-y
+func (x Element) Sub(y *Element) *Element {
+	x.validateFields(y)
+
+	difference := new(big.Int).Sub(x.value, y.value)
+	difference.Mod(difference, x.Modulus)
+	return newElement(x.Field, difference)
+}
+
+// Mul returns the product x*y
+func (x Element) Mul(y *Element) *Element {
+	x.validateFields(y)
+
+	product := new(big.Int).Mul(x.value, y.value)
+	product.Mod(product, x.Modulus)
+	return newElement(x.Field, product)
+}
+
+// Div returns the quotient x/y
+func (x Element) Div(y *Element) *Element {
+	x.validateFields(y)
+
+	yInv := new(big.Int).ModInverse(y.value, x.Modulus)
+	quotient := new(big.Int).Mul(x.value, yInv)
+	quotient.Mod(quotient, x.Modulus)
+	return newElement(x.Field, quotient)
+}
+
+// BigInt returns value as a big.Int
+func (x Element) BigInt() *big.Int {
+	return x.value
+}
+
+// Bytes returns the value as bytes
+func (x Element) Bytes() []byte {
+	return x.BigInt().Bytes()
+}
+
+// IsEqual returns x == y
+func (x Element) IsEqual(y *Element) bool {
+	if !x.isEqualFields(y) {
+		return false
+	}
+
+	return x.value.Cmp(y.value) == 0
+}
+
+// Clone returns a new copy of the element
+func (x Element) Clone() *Element {
+	return x.Field.ElementFromBytes(x.Bytes())
+}
+
+func (x Element) isEqualFields(y *Element) bool {
+	return x.Field.Modulus.Cmp(y.Field.Modulus) == 0
+}
+
+func (x Element) validateFields(y *Element) {
+	if !x.isEqualFields(y) {
+		panic("fields must match for valid binary operation")
+	}
+}
diff --git a/pkg/signatures/bls/finitefield/finitefield_test.go b/pkg/signatures/bls/finitefield/finitefield_test.go
new file mode 100644
index 00000000..e32156a8
--- /dev/null
+++ b/pkg/signatures/bls/finitefield/finitefield_test.go
@@ -0,0 +1,254 @@
+package finitefield
+
+import (
+	"errors"
+	"fmt"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	one                = big.NewInt(1)
+	modulus, modulusOk = new(big.Int).SetString(
+		"1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
+		16,
+	)
+	oneBelowModulus = zero().Sub(modulus, one)
+	oneAboveModulus = zero().Add(modulus, one)
+	field           = New(modulus)
+)
+
+type buggedReader struct{}
+
+func (r buggedReader) Read(p []byte) (n int, err error) {
+	return 0, errors.New("EOF")
+}
+
+func zero() *big.Int {
+	return new(big.Int)
+}
+
+func assertElementZero(t *testing.T, e *Element) {
+	assert.Equal(t, zero().Bytes(), e.Bytes())
+}
+
+type binaryOperation func(*Element) *Element
+
+func assertUnequalFieldsPanic(t *testing.T, b binaryOperation) {
+	altField := New(big.NewInt(23))
+	altElement := altField.NewElement(one)
+
+	assert.PanicsWithValue(
+		t,
+		"fields must match for valid binary operation",
+		func() { b(altElement) },
+	)
+}
+
+func TestModulus(t *testing.T) {
+	assert.True(t, modulusOk)
+}
+
+func TestNew(t *testing.T) {
+	assert.PanicsWithValue(
+		t,
+		fmt.Sprintf("modulus: %x is not a prime", oneBelowModulus),
+		func() { New(oneBelowModulus) },
+	)
+	assert.NotPanics(
+		t,
+		func() { New(modulus) },
+	)
+}
+
+func TestNewElement(t *testing.T) {
+	assert.PanicsWithValue(
+		t,
+		fmt.Sprintf("value: %x is not within field: %x", modulus, field.Modulus),
+		func() { newElement(field, modulus) },
+	)
+	assert.NotPanics(
+		t,
+		func() { newElement(field, oneBelowModulus) },
+	)
+}
+
+func TestIsValid(t *testing.T) {
+	assert.False(t, field.IsValid(zero().Neg(one)))
+	assert.False(t, field.IsValid(modulus))
+	assert.False(t, field.IsValid(oneAboveModulus))
+	assert.True(t, field.IsValid(oneBelowModulus))
+}
+
+func TestFieldNewElement(t *testing.T) {
+	element := field.NewElement(oneBelowModulus)
+
+	assert.Equal(t, oneBelowModulus, element.value)
+	assert.Equal(t, field, element.Field)
+}
+
+func TestZero(t *testing.T) {
+	assert.Equal(t, zero(), field.Zero().value)
+	assert.Equal(t, field, field.Zero().Field)
+}
+
+func TestOne(t *testing.T) {
+	assert.Equal(t, field.One().value, one)
+	assert.Equal(t, field.One().Field, field)
+}
+
+func TestRandomElement(t *testing.T) {
+	randomElement1, err := field.RandomElement(nil)
+	require.NoError(t, err)
+	randomElement2, err := field.RandomElement(nil)
+	require.NoError(t, err)
+	randomElement3, err := field.RandomElement(new(buggedReader))
+	require.Error(t, err)
+
+	assert.Equal(t, field, randomElement1.Field)
+	assert.Equal(t, field, randomElement2.Field)
+	assert.NotEqual(t, randomElement1.value, randomElement2.value)
+	assert.Nil(t, randomElement3)
+}
+
+func TestElementFromBytes(t *testing.T) {
+	element := field.ElementFromBytes(oneBelowModulus.Bytes())
+
+	assert.Equal(t, field, element.Field)
+	assert.Equal(t, oneBelowModulus, element.value)
+}
+
+func TestReducedElementFromBytes(t *testing.T) {
+	element := field.ReducedElementFromBytes(oneBelowModulus.Bytes())
+
+	assert.Equal(t, field, element.Field)
+	assert.Equal(t, oneBelowModulus, element.value)
+
+	element = field.ReducedElementFromBytes(oneAboveModulus.Bytes())
+
+	assert.Equal(t, field, element.Field)
+	assert.Equal(t, one, element.value)
+}
+
+func TestAdd(t *testing.T) {
+	element1 := field.NewElement(one)
+	element2 := field.NewElement(big.NewInt(2))
+	element3 := field.NewElement(oneBelowModulus)
+	element4 := &Element{field, modulus}
+
+	assert.Equal(t, element2, element1.Add(element1))
+	assert.Equal(t, big.NewInt(3), element1.Add(element2).value)
+	assert.Equal(t, big.NewInt(3), element2.Add(element1).value)
+	assert.Equal(t, one, element1.Add(element4).value)
+	assert.Equal(t, one, element3.Add(element2).value)
+	assertElementZero(t, element1.Add(element3))
+	assertUnequalFieldsPanic(t, element1.Add)
+}
+
+func TestSub(t *testing.T) {
+	element1 := field.NewElement(one)
+	element2 := field.NewElement(big.NewInt(2))
+	element3 := field.NewElement(oneBelowModulus)
+	element4 := &Element{field, modulus}
+
+	assertElementZero(t, element1.Sub(element1))
+	assert.Equal(t, element3, element1.Sub(element2))
+	assert.Equal(t, element1, element2.Sub(element1))
+	assert.Equal(t, element1, element1.Sub(element4))
+	assert.Equal(t, element3, element4.Sub(element1))
+	assert.Equal(t, element1, element4.Sub(element3))
+	assert.Equal(t, element3, element3.Sub(element4))
+	assertUnequalFieldsPanic(t, element1.Sub)
+}
+
+func TestMul(t *testing.T) {
+	element1 := field.NewElement(one)
+	element2 := field.NewElement(big.NewInt(2))
+	element3 := field.NewElement(oneBelowModulus)
+	element4 := field.NewElement(zero())
+	expectedProduct, ok := new(big.Int).SetString(
+		"1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3eb",
+		16,
+	)
+	require.True(t, ok)
+
+	assertElementZero(t, element1.Mul(element4))
+	assertElementZero(t, element4.Mul(element1))
+	assert.Equal(t, element3, element1.Mul(element3))
+	assert.Equal(t, element3, element3.Mul(element1))
+	assert.Equal(t, expectedProduct, element3.Mul(element2).value)
+	assert.Equal(t, expectedProduct, element2.Mul(element3).value)
+	assertUnequalFieldsPanic(t, element1.Mul)
+}
+
+func TestDiv(t *testing.T) {
+	element1 := field.NewElement(one)
+	element2 := field.NewElement(big.NewInt(2))
+	element3 := field.NewElement(oneBelowModulus)
+	element4 := field.NewElement(zero())
+	expectedQuotient1, ok := new(big.Int).SetString(
+		"80000000000000000000000000000000a6f7cef517bce6b2c09318d2e7ae9f6",
+		16,
+	)
+	require.True(t, ok)
+	expectedQuotient2, ok := new(big.Int).SetString(
+		"1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3eb",
+		16,
+	)
+	require.True(t, ok)
+
+	assertElementZero(t, element4.Div(element3))
+	assert.Equal(t, element3, element3.Div(element1))
+	assert.Equal(t, expectedQuotient1, element3.Div(element2).value)
+	assert.Equal(t, expectedQuotient2, element2.Div(element3).value)
+	assert.Panics(t, func() { element3.Div(element4) })
+	assertUnequalFieldsPanic(t, element1.Div)
+}
+
+func TestIsEqual(t *testing.T) {
+	element1 := field.NewElement(oneBelowModulus)
+	element2 := field.NewElement(big.NewInt(23))
+	element3 := field.NewElement(oneBelowModulus)
+	altField := New(big.NewInt(23))
+	altElement1 := altField.NewElement(one)
+
+	assert.False(t, element1.IsEqual(element2))
+	assert.True(t, element1.IsEqual(element3))
+	assert.True(t, element1.IsEqual(element1))
+	assert.False(t, element1.IsEqual(altElement1))
+}
+
+func TestBigInt(t *testing.T) {
+	element := field.NewElement(oneBelowModulus)
+
+	assert.Equal(t, oneBelowModulus, element.BigInt())
+}
+
+func TestBytes(t *testing.T) {
+	element := field.NewElement(oneBelowModulus)
+
+	assert.Equal(
+		t,
+		[]byte{
+			0x10, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
+			0x0, 0x0, 0x0, 0x0, 0x0, 0x14, 0xde, 0xf9, 0xde, 0xa2,
+			0xf7, 0x9c, 0xd6, 0x58, 0x12, 0x63, 0x1a, 0x5c, 0xf5,
+			0xd3, 0xec,
+		},
+		element.Bytes(),
+	)
+}
+
+func TestClone(t *testing.T) {
+	element := field.NewElement(oneBelowModulus)
+	clone := element.Clone()
+
+	assert.Equal(t, clone, element)
+
+	clone.value.Add(one, one)
+
+	assert.NotEqual(t, clone, element)
+}
diff --git a/pkg/signatures/bls/rust/Cargo.toml b/pkg/signatures/bls/rust/Cargo.toml
new file mode 100644
index 00000000..1cfc5149
--- /dev/null
+++ b/pkg/signatures/bls/rust/Cargo.toml
@@ -0,0 +1,17 @@
+[package]
+name = "miracl"
+version = "0.1.0"
+authors = ["Mike Lodder <mike.lodder@coinbase.com>"]
+edition = "2018"
+
+[dependencies]
+bls_sigs_ref = "0.3"
+hex = "0.4"
+miracl_core = { version = "2.3", features = ["bls12381"], default-features = false }
+pairing-plus = "0.19"
+rand = "0.8"
+serious = { version = "0.1", git = "https://github.com/mikelodder7/malutils" }
+serde = { version = "1.0", features = ["derive"] }
+serde_json = "1.0"
+sha2 = "0.8"
+structopt = "0.3"
\ No newline at end of file
diff --git a/pkg/signatures/bls/rust/src/main.rs b/pkg/signatures/bls/rust/src/main.rs
new file mode 100644
index 00000000..1a3d8722
--- /dev/null
+++ b/pkg/signatures/bls/rust/src/main.rs
@@ -0,0 +1,392 @@
+use bls_sigs_ref::BLSSignaturePop;
+use miracl_core::{
+    bls12381::{
+        big::BIG, ecp::ECP, ecp2::ECP2, rom::MODULUS,
+    }
+};
+use pairing_plus::{
+    CurveProjective,
+    bls12_381::{
+        Fr, G1, G2,
+    },
+    hash_to_field::BaseFromRO,
+    serdes::SerDes,
+};
+use rand::prelude::*;
+use serious::Encoding;
+use serde::Deserialize;
+use sha2::digest::generic_array::GenericArray;
+use structopt::StructOpt;
+use std::{
+    fs::File,
+    io::{self, Read, Cursor},
+    path::PathBuf,
+};
+
+fn main() {
+    let args = CliArgs::from_args();
+
+    match args {
+        CliArgs::Generate { number } => generate(number),
+        CliArgs::PublicKey { keys } => pubkey(keys),
+        CliArgs::Sign { number , data} => sign(number, data),
+        CliArgs::Verify { keys } => verify(keys),
+    }
+}
+
+fn generate(number: usize) {
+    let mut rng = thread_rng();
+    print!("[");
+    let mut sep = "";
+    for _ in 0..number {
+
+        let mut buf = [0u8; 48];
+        rng.fill_bytes(&mut buf);
+        // let mut sk = buf;
+        let fr = Fr::from_okm(GenericArray::from_slice(&buf));
+        let mut pk = G1::one();
+        pk.mul_assign(fr);
+
+        pk.serialize(&mut buf.as_mut(), true).unwrap();
+        print!("{}\"{}\"", sep, hex::encode(buf));
+        sep = ",";
+
+        // Miracl expects 48 bytes for secret key even though the top 16 bytes are zeros
+        // sk = [0u8; 48];
+        // fr.serialize(&mut sk[16..].as_mut(), true).unwrap();
+        // let s = BIG::frombytes(&sk[..]);
+        // let x = _compress_g1(g1mul(&ECP::generator(), &s));
+        //
+        // println!("Miracl = {}", hex::encode(x));
+    }
+    print!("]");
+}
+
+/// Compress to BLS12-381 standard vs ANSI X9.62
+fn _compress_g1(pk: ECP) -> [u8; 48] {
+    let mut x = [0u8; 48];
+    pk.getx().tobytes(&mut x);
+    if pk.is_infinity() {
+        // Set the second-most significant bit to indicate this point
+        // is at infinity.
+        x[0] |= 1 << 6;
+    } else {
+        let m = BIG { w: MODULUS };
+        let mut negy = BIG::new();
+        negy.add(&BIG::modneg(&pk.gety(), &m));
+        negy.rmod(&m);
+        negy.norm();
+        // Set the third most significant bit if the correct y-coordinate
+        // is lexicographically largest.
+        if BIG::comp(&pk.gety(), &negy) == 1 {
+            x[0] |= 1 << 5;
+        }
+    }
+    // Set highest bit to distinguish this as a compressed element.
+    x[0] |= 1 << 7;
+    x
+}
+
+fn _compress_g2(sig: ECP2) -> [u8; 96] {
+    let mut x = [0u8; 96];
+    sig.getx().geta().tobytes(&mut x[..48]);
+    sig.getx().getb().tobytes(&mut x[48..]);
+    if sig.is_infinity() {
+        // Set the second-most significant bit to indicate this point
+        // is at infinity.
+        x[0] |= 1 << 6;
+    } else {
+        let mut negy = sig.clone();
+        negy.neg();
+
+        // Set the third most significant bit if the correct y-coordinate
+        // is lexicographically largest.
+        negy.sub(&sig);
+
+        if negy.gety().sign() > 0 {
+            x[0] |= 1 << 5;
+        }
+    }
+    // Set highest bit to distinguish this as a compressed element.
+    x[0] |= 1 << 7;
+    x
+}
+
+fn pubkey(keys: String) {
+    let res = read_input(&keys).unwrap();
+
+    for pubkey in serde_json::from_slice::<Vec<String>>(&res).unwrap() {
+        let res = hex::decode(&pubkey);
+        if res.is_err() {
+            println!("Invalid hex format {}", res.unwrap_err());
+            continue;
+        }
+        let mut key = res.unwrap();
+        let mut cur = Cursor::new(key.as_slice());
+        print!("ZCash  {} - ", pubkey);
+        let res = G1::deserialize(&mut cur, true);
+
+        if let Err(e) = res {
+            println!("fail - {}", e);
+        } else {
+            println!("pass");
+        }
+
+        let res = _uncompress_g1(key.as_mut_slice());
+
+        print!("Miracl {} - ", pubkey);
+        if let Err(e) = res {
+            println!("fail - {}", e);
+        } else {
+            println!("pass");
+        }
+    }
+}
+
+fn _uncompress_g1(d: &[u8]) -> Result<ECP, String> {
+    if d.len() != 48 {
+        return Err("Invalid length".to_string());
+    }
+
+    if d[0] & 0x80 != 0x80 {
+        return Err("Expected compressed point".to_string());
+    }
+
+    // Expect point at infinity
+    if d[0] & 0x40 == 0x40 {
+        return if !d.iter().skip(1).all(|b| *b == 0) {
+            Err("Expected point at infinity but found another point".to_string())
+        } else {
+            Ok(ECP::new())
+        }
+    }
+
+    let s = d[0] & 0x20;
+    // Unset top bits
+    let mut dd = [0u8; 48];
+    dd.copy_from_slice(d);
+    dd[0] &= 0x1F;
+    let x = BIG::frombytes(&dd);
+    Ok(ECP::new_bigint(&x, s as isize))
+}
+
+fn _uncompress_g2(d: &[u8]) -> Result<ECP2, String> {
+    if d.len() != 96 {
+        return Err("Invalid length".to_string());
+    }
+
+    if d[0] & 0x80 != 0x80 {
+        return Err("Expected compressed point".to_string());
+    }
+
+    // Expect point at infinity
+    if d[0] & 0x40 == 0x40 {
+        return if !d.iter().skip(1).all(|b| *b == 0) {
+            Err("Expected point at infinity but found another point".to_string())
+        } else {
+            Ok(ECP2::new())
+        }
+    }
+
+    let s = d[0] & 0x20;
+    let mut dd = [0u8; 97];
+    dd[1..].copy_from_slice(d);
+    dd[1] &= 0x1F;
+    // Unset top bits
+    dd[0] = if s > 0 { 0x3 } else { 0x2 };
+    Ok(ECP2::frombytes(&dd))
+}
+
+fn sign(number: usize, data: String) {
+    let mut rng = thread_rng();
+    let bytes = data.as_bytes();
+    let mut sep = "";
+    print!("[");
+    for _ in 0..number {
+        let mut buf = [0u8; 48];
+        rng.fill_bytes(&mut buf);
+        let fr = Fr::from_okm(GenericArray::from_slice(&buf));
+        let mut pk = G1::one();
+        pk.mul_assign(fr);
+
+        let mut pubkey = [0u8; 48];
+        pk.serialize(&mut pubkey.as_mut(), true).unwrap();
+
+        let signature = G2::sign(fr, bytes);
+        let mut sig = [0u8; 96];
+        signature.serialize(&mut sig.as_mut(), true).unwrap();
+
+        print!("{}{{", sep);
+        print!(r#""data":"{}","#, data);
+        print!(r#""public_key":"{}","#, Encoding::encode(pubkey, Encoding::LowHex).into_string());
+        print!(r#""signature":"{}""#, Encoding::encode(sig, Encoding::LowHex).into_string());
+        print!("}}");
+        sep = ",";
+    }
+    print!("]");
+}
+
+fn verify(keys: String) {
+    let res = read_input(&keys).unwrap();
+
+    for req in serde_json::from_slice::<Vec<VerifyRequest>>(&res).unwrap() {
+        let pubkey = Encoding::decode(&req.public_key, Encoding::LowHex).unwrap();
+        let sig = Encoding::decode(&req.signature, Encoding::LowHex).unwrap();
+        let mut cur = Cursor::new(pubkey.as_slice());
+        let verkey = G1::deserialize(&mut cur, true).unwrap();
+        cur = Cursor::new(sig.as_slice());
+        let signature = G2::deserialize(&mut cur, true).unwrap();
+
+        print!("ZCash  {} - ", req.public_key);
+        if G2::verify(verkey, signature, req.data.as_bytes()) {
+            println!("pass");
+        } else {
+            println!("fail");
+        }
+    }
+}
+
+#[derive(Debug, StructOpt)]
+enum CliArgs {
+    Generate {
+        #[structopt(short, long)]
+        number: usize,
+    },
+    PublicKey {
+        #[structopt(name = "KEYS")]
+        keys: String,
+    },
+    Sign {
+        #[structopt(short, long)]
+        number: usize,
+        #[structopt(short, long)]
+        data: String,
+    },
+    Verify {
+        #[structopt(name = "KEYS")]
+        keys: String,
+    }
+}
+
+#[derive(Deserialize)]
+struct VerifyRequest {
+    data: String,
+    public_key: String,
+    signature: String
+}
+
+fn read_input(value: &str) -> Result<Vec<u8>, String> {
+    if !value.is_empty() {
+        match get_file(value) {
+            Some(file) => {
+                match File::open(file.as_path()) {
+                    Ok(mut f) => {
+                        Ok(read_stream(&mut f))
+                    },
+                    Err(_) => {
+                        Err(format!("Unable to read file {}", file.to_str().unwrap()))
+                    }
+                }
+            }
+            None => {
+                Ok(value.as_bytes().to_vec())
+            }
+        }
+    } else {
+        let mut f = io::stdin();
+        Ok(read_stream(&mut f))
+    }
+}
+
+fn read_stream<R: Read>(f: &mut R) -> Vec<u8> {
+    let mut bytes = Vec::new();
+    let mut buffer = [0u8; 4096];
+
+    let mut read = f.read(&mut buffer);
+    while read.is_ok() {
+        let n = read.unwrap();
+
+        if n == 0 {
+            break;
+        }
+
+        bytes.extend_from_slice(&buffer[..n]);
+
+        read = f.read(&mut buffer);
+    }
+
+    bytes
+}
+
+fn get_file(name: &str) -> Option<PathBuf> {
+    if name.len() > 256 {
+        // too long to be a file
+        return None;
+    }
+    let mut file = PathBuf::new();
+    file.push(name);
+    if file.as_path().is_file() {
+        let metadata = file
+            .as_path()
+            .symlink_metadata()
+            .expect("symlink_metadata call failed");
+        if metadata.file_type().is_symlink() {
+            if let Ok(f) = file.as_path().read_link() {
+                file = f
+            } else {
+                return None;
+            }
+        }
+        Some(file)
+    } else {
+        None
+    }
+}
+
+
+// fn from_encoding(src: &str) -> Result<Encoding, std::io::Error> {
+//    Encoding::parse(src).map_err(|e| std::io::Error::new(std::io::ErrorKind::InvalidInput, e))
+// }
+
+// fn hash_to_g2(d: &[u8]) -> ECP2 {
+//     const DST: &'static str = "BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_";
+//     let y = <G2 as HashToCurve<ExpandMsgXmd<sha2::Sha256>>>::hash_to_curve(d.as_ref(), DST);
+//     let mut d = [0u8; 193];
+//     d[0] = 0x4;
+//     y.serialize(&mut d[1..].as_mut(), false);
+//     ECP2::frombytes(&d)
+// }
+
+// fn ceil(a: usize, b: usize) -> usize {
+//     (a-1)/b+1
+// }
+//
+// fn hash_to_field(hash: usize, hlen: usize, u: &mut [FP2], dst: &[u8], m: &[u8], ctr: usize) {
+//     let q = BIG { w: MODULUS };
+//     let el = ceil(q.nbits()+AESKEY*16, 8);
+//
+//     let mut okm = [0u8; 512];
+//     let mut fd = [0u8; 256];
+//     xmd_expand(hash, hlen, &mut okm, el*ctr, &dst, &m);
+//     u[0] = FP2::new_fps(
+//         &FP::new_big(&DBIG::frombytes(&okm[0..el]).dmod(&q)),
+//         &FP::new_big(&DBIG::frombytes(&okm[el..(2*el)]).dmod(&q))
+//     );
+//     u[1] = FP2::new_fps(
+//         &FP::new_big(&DBIG::frombytes(&okm[(2*el)..(3*el)]).dmod(&q)),
+//         &FP::new_big(&DBIG::frombytes(&okm[(3*el)..]).dmod(&q))
+//     );
+// }
+//
+// fn hash_to_ecp2(m: &[u8]) -> ECP2 {
+//     let dst = b"BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_";
+//     let mut u = [FP2::new(); 2];
+//     hash_to_field(hmac::MC_SHA2, ecp::HASH_TYPE, &mut u, &dst[..], m, 2);
+//
+//     let mut p = ECP2::map2point(&u[0]);
+//     let q = ECP2::map2point(&u[1]);
+//     p.add(&q);
+//     p.cfp();
+//     p.affine();
+//     p
+// }
\ No newline at end of file
diff --git a/pkg/signatures/bls/shamir/shamir.go b/pkg/signatures/bls/shamir/shamir.go
new file mode 100644
index 00000000..30191726
--- /dev/null
+++ b/pkg/signatures/bls/shamir/shamir.go
@@ -0,0 +1,269 @@
+/*
+Package shamir is a port of the hashicorp/vault implementation of Shamir's Secret Sharing
+which has been modified to work with a finite field rather than arbitrary length content.
+
+Their implementation splits every byte independently into shares and transposes the output
+together to form a single secret. For our purposes, we expect to be able to combine secrets using
+addition and then reconstruct a shared polynomial which doesn't work with the byte wise sharing.
+
+This implementation IS NOT constant time as it leverages math/big for big number operations through the finitefield
+package.
+*/
+package shamir
+
+import (
+	"fmt"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/signatures/bls/finitefield"
+	"github.com/pkg/errors"
+)
+
+// Polynomial represents a polynomial of arbitrary degree
+type Polynomial struct {
+	Coefficients []*finitefield.Element
+}
+
+// Dealer knows the secret and constructs the polynomial
+type Dealer struct {
+	field *finitefield.Field
+}
+
+// Combiner reconstructs the secret
+type Combiner struct {
+	field *finitefield.Field
+}
+
+// Share is a part of the split secret
+type Share struct {
+	Identifier byte                 // x-coordinate
+	Secret     *finitefield.Element // y-coordinate
+}
+
+// ShareSet represents a set of shares generated from the embedded polynomial. The polynomial is included so that
+// consumers of the shamir package can generate a VSS from the output.
+type ShareSet struct {
+	Shares []*Share
+	Polynomial
+}
+
+// NewShare is a Share constructor
+func NewShare(x byte, y []byte, f *finitefield.Field) *Share {
+	return &Share{x, f.ElementFromBytes(y)}
+}
+
+// Order is the order of the Share's finite field.
+func (s Share) Order() *big.Int {
+	return s.field().Modulus
+}
+
+// Field is the Share's finite Field.
+func (s Share) field() *finitefield.Field {
+	return s.Secret.Field
+}
+
+// Add returns the sum of two Shares.
+func (s Share) Add(other *Share) *Share {
+	if s.Identifier != other.Identifier {
+		panic("identifiers must match for valid addition")
+	}
+
+	newSecret := s.Secret.Add(other.Secret)
+
+	return NewShare(s.Identifier, newSecret.Bytes(), s.field())
+}
+
+// Bytes returns the byte representation of the share: `identifier(1-byte) || secret`
+func (s Share) Bytes() []byte {
+	out := make([]byte, len(s.Secret.Bytes())+1)
+	copy(out, s.Secret.Bytes())
+	out[len(out)-1] = s.Identifier
+
+	return out
+}
+
+func (s Share) BytesLe() []byte {
+	bytes := make([]byte, len(s.Secret.Bytes()))
+	copy(bytes, s.Secret.Bytes())
+
+	// reverse slice
+	for i, j := 0, len(bytes)-1; i < j; i, j = i+1, j-1 {
+		bytes[i], bytes[j] = bytes[j], bytes[i]
+	}
+
+	return bytes
+}
+
+func ShareFromBytes(b []byte, f *finitefield.Field) *Share {
+	identifier := b[len(b)-1]
+	secret := b[:len(b)-1]
+
+	return NewShare(identifier, secret, f)
+}
+
+func NewDealer(f *finitefield.Field) *Dealer {
+	return &Dealer{f}
+}
+
+// Split takes secret and generates a `parts` number of shares, `threshold` of which are required to reconstruct the
+// secret. The parts and threshold must be at least 2, and less than 256. The returned shares are each one byte longer
+// than the secret as they attach a tag used to reconstruct the secret.
+func (d Dealer) Split(secret []byte, threshold, parts int) (*ShareSet, error) {
+	field := d.field
+	// Sanity check the input
+	if parts < threshold {
+		return nil, fmt.Errorf("parts cannot be less than threshold")
+	}
+	if parts > 255 {
+		return nil, fmt.Errorf("parts cannot exceed 255")
+	}
+	if threshold < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+	if threshold > 255 {
+		return nil, fmt.Errorf("threshold cannot exceed 255")
+	}
+	if len(secret) == 0 {
+		return nil, fmt.Errorf("cannot split an empty secret")
+	}
+	intSecret := new(big.Int).SetBytes(secret)
+	if !field.IsValid(intSecret) {
+		return nil, fmt.Errorf("secret is too large")
+	}
+
+	// Create the random polynomial of degree threshold-1 to split the secret with
+	secretElem := field.NewElement(intSecret)
+	polynomial, err := d.makePolynomial(secretElem, uint8(threshold-1))
+	if err != nil {
+		return nil, errors.Wrap(err, "failed to generate polynomial")
+	}
+
+	// Generate a `parts` number of (x,y) pairs and place into shares variable to be returned.
+	// x coordinates increment from 1 to parts+1. 0 is reserved for the secret.
+	shares := make([]*Share, parts)
+	for i := 0; i < parts; i++ {
+		xByte := uint8(i) + 1
+		x := field.ElementFromBytes([]byte{xByte})
+		y := polynomial.evaluate(x)
+
+		shares[i] = NewShare(xByte, y.Bytes(), d.field)
+	}
+
+	return &ShareSet{shares, polynomial}, nil
+}
+
+func NewCombiner(f *finitefield.Field) *Combiner {
+	return &Combiner{f}
+}
+
+// Combine is used to reverse a Split and reconstruct a secret
+// once at least `threshold` number of parts are available.
+func (c Combiner) Combine(shares []*Share) ([]byte, error) {
+	field := c.field
+	// Verify enough shares provided
+	if len(shares) < 2 {
+		return nil, fmt.Errorf("less than two shares cannot be used to reconstruct the secret")
+	}
+
+	// Verify the secrets are non-empty and identifiers are valid
+	for _, s := range shares {
+		if len(s.Secret.Bytes()) == 0 {
+			return nil, fmt.Errorf("share must have a non-zero length secret")
+		}
+
+		if s.Identifier == 0 {
+			return nil, fmt.Errorf("share must have non-zero identifier")
+		}
+	}
+
+	// Ensure there are no duplicate identifiers as that doesn't make sense for reconstruction
+	checkMap := map[byte]bool{}
+	for _, s := range shares {
+		samp := s.Identifier
+		if exists := checkMap[samp]; exists {
+			return nil, fmt.Errorf("duplicate share detected")
+		}
+		checkMap[samp] = true
+	}
+
+	// Set the (x, y) value for each sample
+	xSamples := make([]*finitefield.Element, len(shares))
+	ySamples := make([]*finitefield.Element, len(shares))
+	for i, s := range shares {
+		xSamples[i] = field.NewElement(big.NewInt(int64(s.Identifier)))
+		ySamples[i] = s.Secret
+	}
+
+	// Interpolate the polynomial and compute the value at 0
+	secret := c.interpolatePolynomial(xSamples, ySamples, field.Zero())
+
+	return secret.Bytes(), nil
+}
+
+// makePolynomial constructs a random polynomial of the given degree but with the provided intercept
+// value.
+func (d Dealer) makePolynomial(intercept *finitefield.Element, degree uint8) (Polynomial, error) {
+	// Create a wrapper
+	p := Polynomial{
+		Coefficients: make([]*finitefield.Element, degree+1),
+	}
+
+	// Ensure the intercept is set
+	p.Coefficients[0] = intercept
+
+	// Assign random co-efficients to the polynomial
+	// Start at 1 since 0 is the intercept and it is not chosen randomly
+	for i := 1; i < len(p.Coefficients); i++ {
+		coefficient, err := d.field.RandomElement(nil)
+		if err != nil {
+			return p, err
+		}
+		p.Coefficients[i] = coefficient
+	}
+
+	return p, nil
+}
+
+// evaluate returns the value of the polynomial for the given x
+func (p Polynomial) evaluate(x *finitefield.Element) *finitefield.Element {
+	// Special case the origin
+	if x.BigInt().Cmp(big.NewInt(0)) == 0 {
+		return p.Coefficients[0]
+	}
+
+	// Compute the polynomial value using Horner's method.
+	degree := len(p.Coefficients) - 1
+	out := p.Coefficients[degree].Clone()
+	for i := degree - 1; i >= 0; i-- {
+		out = out.Mul(x).Add(p.Coefficients[i])
+	}
+
+	return out
+}
+
+// interpolatePolynomial takes N sample points and returns
+// the value at a given x using a lagrange interpolation.
+func (c Combiner) interpolatePolynomial(
+	xSamples, ySamples []*finitefield.Element,
+	x *finitefield.Element,
+) *finitefield.Element {
+	field := c.field
+	limit := len(xSamples)
+	result := field.Zero()
+
+	for i := 0; i < limit; i++ {
+		basis := field.One()
+		for j := 0; j < limit; j++ {
+			if i == j {
+				continue
+			}
+			num := x.Sub(xSamples[j])             // x - x_m
+			denom := xSamples[i].Sub(xSamples[j]) // x_j - x_m
+			basis = basis.Mul(num.Div(denom))
+		}
+		group := ySamples[i].Mul(basis)
+		result = result.Add(group)
+	}
+
+	return result
+}
diff --git a/pkg/signatures/bls/shamir/shamir_test.go b/pkg/signatures/bls/shamir/shamir_test.go
new file mode 100644
index 00000000..00ecb61b
--- /dev/null
+++ b/pkg/signatures/bls/shamir/shamir_test.go
@@ -0,0 +1,237 @@
+package shamir
+
+import (
+	"bytes"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+
+	"github.com/coinbase/kryptology/pkg/signatures/bls/finitefield"
+)
+
+// Ed25519 subgroup order
+var modulus, _ = new(big.Int).SetString("1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED", 16)
+var globalField = finitefield.New(modulus)
+var dealer = NewDealer(globalField)
+var combiner = NewCombiner(globalField)
+
+func TestSplit_invalid_args(t *testing.T) {
+	secret := []byte("test")
+
+	if _, err := dealer.Split(secret, 0, 0); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	if _, err := dealer.Split(secret, 3, 2); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	if _, err := dealer.Split(secret, 3, 1000); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	if _, err := dealer.Split(secret, 1, 10); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	if _, err := dealer.Split(nil, 2, 3); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	if _, err := dealer.Split(secret, 256, 300); err == nil {
+		t.Fatalf("expect error")
+	}
+
+	tooBigSecret := []byte("thisistoobig-thisistoobig-thisist")
+	if _, err := dealer.Split(tooBigSecret, 2, 3); err == nil {
+		t.Fatalf("expect error")
+	}
+}
+
+func TestCombine_invalid(t *testing.T) {
+	// No shares
+	shares := []*Share{
+		NewShare(1, []byte("b"), globalField),
+	}
+	_, err := combiner.Combine(shares)
+	assert.Equal(t, "less than two shares cannot be used to reconstruct the secret", err.Error())
+
+	// No secret
+	shares = []*Share{
+		NewShare(1, []byte(""), globalField),
+		NewShare(2, []byte(""), globalField),
+	}
+	_, err = combiner.Combine(shares)
+	assert.Equal(t, "share must have a non-zero length secret", err.Error())
+
+	// Zero identifier
+	shares = []*Share{
+		NewShare(0, []byte("abc"), globalField),
+		NewShare(2, []byte("abc"), globalField),
+	}
+	_, err = combiner.Combine(shares)
+	assert.Equal(t, "share must have non-zero identifier", err.Error())
+
+	// Duplicate shares
+	shares = []*Share{
+		NewShare(1, []byte("abc"), globalField),
+		NewShare(1, []byte("abc"), globalField),
+	}
+	_, err = combiner.Combine(shares)
+	assert.Equal(t, "duplicate share detected", err.Error())
+}
+
+func TestCombine_single(t *testing.T) {
+	secret := []byte("hello")
+
+	shareSet, err := dealer.Split(secret, 2, 3)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	shares := shareSet.Shares
+	parts := []*Share{shares[0], shares[1]}
+	recomb, err := combiner.Combine(parts)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	if !bytes.Equal(recomb, secret) {
+		t.Errorf("parts: %v", parts)
+		t.Fatalf("bad: %v %v", recomb, secret)
+	}
+}
+
+func TestCombine_all_permutations(t *testing.T) {
+	secret := []byte("hello")
+
+	shareSet, err := dealer.Split(secret, 3, 5)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	shares := shareSet.Shares
+	// There is 5*4*3 possible choices,
+	// we will just brute force try them all
+	for i := 0; i < 5; i++ {
+		for j := 0; j < 5; j++ {
+			if j == i {
+				continue
+			}
+			for k := 0; k < 5; k++ {
+				if k == i || k == j {
+					continue
+				}
+				parts := []*Share{shares[i], shares[j], shares[k]}
+				recomb, err := combiner.Combine(parts)
+				if err != nil {
+					t.Fatalf("err: %v", err)
+				}
+
+				if !bytes.Equal(recomb, secret) {
+					t.Errorf("parts: (i:%d, j:%d, k:%d) %v", i, j, k, parts)
+					t.Fatalf("bad: %v %v", recomb, secret)
+				}
+			}
+		}
+	}
+}
+
+func TestShare_Add(t *testing.T) {
+	field := finitefield.New(big.NewInt(7))
+	one := NewShare(0, []byte{0x01}, field)
+	two := NewShare(0, []byte{0x02}, field)
+
+	// basic addition
+	sum := one.Add(two)
+	assert.Equal(t, byte(0), sum.Identifier)
+	assert.Equal(t, []byte{0x03}, sum.Secret.Bytes())
+
+	// addition is performed within the globalField
+	sum = two.Add(NewShare(0, []byte{0x06}, field))
+	assert.Equal(t, byte(0), sum.Identifier)
+	assert.Equal(t, []byte{0x01}, sum.Secret.Bytes())
+}
+
+func TestShare_Add_errors(t *testing.T) {
+	field := finitefield.New(big.NewInt(7))
+	one := NewShare(0, []byte{0x01}, field)
+	two := NewShare(1, []byte{0x02}, field)
+
+	assert.PanicsWithValue(t, "identifiers must match for valid addition", func() { one.Add(two) })
+}
+
+func TestCombine_added_shares(t *testing.T) {
+	one := []byte{0x01}
+	two := []byte{0x02}
+
+	shareSet1, err := dealer.Split(one, 2, 3)
+	assert.Nil(t, err)
+	shareSet2, err := dealer.Split(two, 2, 3)
+	assert.Nil(t, err)
+
+	sharesForOne := shareSet1.Shares
+	sharesForTwo := shareSet2.Shares
+
+	share1 := sharesForOne[0].Add(sharesForTwo[0])
+	share2 := sharesForOne[1].Add(sharesForTwo[1])
+	shares := []*Share{share1, share2}
+
+	recomb, err := combiner.Combine(shares)
+	assert.Nil(t, err)
+	assert.Equal(t, []byte{0x03}, recomb)
+}
+
+func TestPolynomial_SetsIntercept(t *testing.T) {
+	intercept := globalField.NewElement(big.NewInt(42))
+	p, err := NewDealer(globalField).makePolynomial(intercept, 2)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	if !p.Coefficients[0].IsEqual(intercept) {
+		t.Fatalf("bad: %v", p.Coefficients)
+	}
+}
+
+func TestPolynomial_Eval(t *testing.T) {
+	intercept := globalField.NewElement(big.NewInt(42))
+	p, err := NewDealer(globalField).makePolynomial(intercept, 1)
+	if err != nil {
+		t.Fatalf("err: %v", err)
+	}
+
+	if out := p.evaluate(globalField.Zero()); !out.IsEqual(intercept) {
+		t.Fatalf("bad: %v", out)
+	}
+
+	out := p.evaluate(globalField.One())
+	exp := intercept.Add(p.Coefficients[1])
+	if !out.IsEqual(exp) {
+		t.Fatalf("bad: %v %v %v", out, exp, p.Coefficients)
+	}
+}
+
+func TestInterpolate_Rand(t *testing.T) {
+	var (
+		f1 = globalField.NewElement(big.NewInt(1))
+		f2 = globalField.NewElement(big.NewInt(2))
+		f3 = globalField.NewElement(big.NewInt(3))
+	)
+
+	for i := 0; i < 256; i++ {
+		intercept := globalField.NewElement(big.NewInt(int64(i)))
+		p, err := dealer.makePolynomial(intercept, 2)
+		if err != nil {
+			t.Fatalf("err: %v", err)
+		}
+
+		xVals := []*finitefield.Element{f1, f2, f3}
+		yVals := []*finitefield.Element{p.evaluate(f1), p.evaluate(f2), p.evaluate(f3)}
+		out := combiner.interpolatePolynomial(xVals, yVals, globalField.Zero())
+		if !out.IsEqual(intercept) {
+			t.Fatalf("Bad: %v %d", out, i)
+		}
+	}
+}
diff --git a/pkg/signatures/bls/tests/bls/main.go b/pkg/signatures/bls/tests/bls/main.go
new file mode 100644
index 00000000..d3d02067
--- /dev/null
+++ b/pkg/signatures/bls/tests/bls/main.go
@@ -0,0 +1,230 @@
+package main
+
+import (
+	"bufio"
+	"encoding/hex"
+	"encoding/json"
+	"flag"
+	"fmt"
+	bls "github.com/coinbase/kryptology/pkg/signatures/bls/bls_sig"
+	"io/ioutil"
+	"os"
+)
+
+type signOp struct {
+	Data      string `json:"data"`
+	PublicKey string `json:"public_key"`
+	Signature string `json:"signature"`
+}
+
+type cmdFlags struct {
+	Generate   bool
+	PublicKeys bool
+	Sign       bool
+	Verify     bool
+	Number     int
+}
+
+func parseCliArgs() cmdFlags {
+	var generate, publickeys, sign, verify bool
+	var number int
+	flag.BoolVar(&generate, "g", false, "Generate public keys")
+	flag.BoolVar(&publickeys, "p", false, "Verify public keys")
+	flag.BoolVar(&sign, "s", false, "Generate signatures")
+	flag.BoolVar(&verify, "v", false, "Verify signatures")
+	flag.IntVar(&number, "n", 25, "The number of items to generate")
+	flag.Parse()
+	return cmdFlags{
+		generate, publickeys, sign, verify, number,
+	}
+}
+
+func main() {
+	flags := parseCliArgs()
+
+	if flags.Generate {
+		generate(flags.Number)
+	} else if flags.PublicKeys {
+		publicKeys()
+	} else if flags.Sign {
+		sign(flags.Number)
+	} else if flags.Verify {
+		verify()
+	}
+}
+
+func generate(number int) {
+	scheme := bls.NewSigPop()
+	publicKeys := make([]string, number)
+	for i := 0; i < number; i++ {
+		publicKey, _, err := scheme.Keygen()
+		if err != nil {
+			fmt.Printf("Keygen error occurred: %v\n", err)
+			os.Exit(1)
+		}
+		b, _ := publicKey.MarshalBinary()
+		publicKeys[i] = hex.EncodeToString(b)
+	}
+	out, _ := json.Marshal(publicKeys)
+	fmt.Println(string(out))
+}
+
+func publicKeys() {
+	input, err := getInput()
+	if err != nil {
+		fmt.Printf("Unable to read input: %v", err)
+		os.Exit(1)
+	}
+	var pubkeys []string
+	err = json.Unmarshal(input, &pubkeys)
+	if err != nil {
+		fmt.Printf("Unable to parse json input: %v", err)
+		os.Exit(1)
+	}
+	fmt.Printf("Checking public keys")
+	for _, pk := range pubkeys {
+		data, err := hex.DecodeString(pk)
+		if err != nil {
+			fmt.Printf("Unable to parse hex input: %v", err)
+			os.Exit(1)
+		}
+		pubkey := new(bls.PublicKey)
+		fmt.Printf("Checking %s - ", pk)
+		err = pubkey.UnmarshalBinary(data)
+		if err != nil {
+			fmt.Printf("fail\n")
+			os.Exit(1)
+		}
+		fmt.Printf("pass\n")
+	}
+}
+
+func sign(number int) {
+	tests := []string{
+		"", "aaa", "aaaaaa", "aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa",
+	}
+
+	var err error
+	scheme := bls.NewSigPop()
+	secretKeys := make([]*bls.SecretKey, number)
+	publicKeys := make([]*bls.PublicKey, number)
+	for i := 0; i < number; i++ {
+		publicKeys[i], secretKeys[i], err = scheme.Keygen()
+		if err != nil {
+			fmt.Printf("Keygen error occurred: %v\n", err)
+			os.Exit(1)
+		}
+	}
+
+	sigs := make([]*signOp, number*len(tests))
+
+	k := 0
+	for _, t := range tests {
+		for j := 0; j < len(secretKeys); j++ {
+			signature, err := scheme.Sign(secretKeys[j], []byte(t))
+			if err != nil {
+				fmt.Printf("Signing failed: %v\n", err)
+				os.Exit(1)
+			}
+			pk, _ := publicKeys[j].MarshalBinary()
+			sig, _ := signature.MarshalBinary()
+			sigs[k] = &signOp{
+				Data:      t,
+				PublicKey: hex.EncodeToString(pk),
+				Signature: hex.EncodeToString(sig),
+			}
+			k++
+		}
+	}
+
+	data, err := json.Marshal(sigs)
+	if err != nil {
+		fmt.Printf("Unable to convert signatures to json")
+		os.Exit(1)
+	}
+	fmt.Print(string(data))
+}
+
+func verify() {
+	input, err := getInput()
+	if err != nil {
+		fmt.Printf("Unable to read input: %v", err)
+		os.Exit(1)
+	}
+	var operations []signOp
+	err = json.Unmarshal(input, &operations)
+	if err != nil {
+		fmt.Printf("Unable to parse json input: %v", err)
+		os.Exit(1)
+	}
+	scheme := bls.NewSigPop()
+	for _, op := range operations {
+		fmt.Printf("Checking %s - ", op.PublicKey)
+		data, err := hex.DecodeString(op.PublicKey)
+		if err != nil {
+			fmt.Printf("fail. Unable to parse hex input: %v", err)
+			os.Exit(1)
+		}
+		pubkey := new(bls.PublicKey)
+		err = pubkey.UnmarshalBinary(data)
+		if err != nil {
+			fmt.Printf("fail. Invalid public key: %v", err)
+			os.Exit(1)
+		}
+		data, err = hex.DecodeString(op.Signature)
+		if err != nil {
+			fmt.Printf("fail. Unable to parse hex input: %v", err)
+			os.Exit(1)
+		}
+		sig := new(bls.Signature)
+		err = sig.UnmarshalBinary(data)
+		if err != nil {
+			fmt.Printf("fail. Invalid signature format: %v", err)
+			os.Exit(1)
+		}
+		ok, err := scheme.Verify(pubkey, []byte(op.Data), sig)
+		if !ok || err != nil {
+			fmt.Printf("fail. Invalid signature")
+			os.Exit(1)
+		}
+		fmt.Printf("pass.")
+	}
+}
+
+func getInput() ([]byte, error) {
+	fi, _ := os.Stdin.Stat()
+
+	var data []byte
+
+	if (fi.Mode() & os.ModeCharDevice) == 0 {
+		// Read from pipe
+		scanner := bufio.NewScanner(os.Stdin)
+		for scanner.Scan() {
+			data = append(data, scanner.Bytes()...)
+		}
+
+		if err := scanner.Err(); err != nil {
+			return nil, err
+		}
+	} else {
+		// Read from file
+		arguments := flag.Args()
+		if len(arguments) < 1 {
+			return nil, fmt.Errorf("expected data argument")
+		}
+
+		_, err := os.Stat(arguments[0])
+
+		if os.IsNotExist(err) {
+			data = []byte(arguments[0])
+		} else {
+			contents, err := ioutil.ReadFile(arguments[0])
+			if err != nil {
+				return nil, err
+			}
+			data = contents
+		}
+	}
+
+	return data, nil
+}
diff --git a/pkg/signatures/bls/tmp.json b/pkg/signatures/bls/tmp.json
new file mode 100644
index 00000000..6f025c6a
--- /dev/null
+++ b/pkg/signatures/bls/tmp.json
@@ -0,0 +1 @@
+["8f69b452faa4f2a451237988c70d844ea1311c991c55311ccad0b37863c668774c5ecf4b6d5dbca8578f24048a34b717"]
diff --git a/pkg/signatures/common/README.md b/pkg/signatures/common/README.md
new file mode 100755
index 00000000..83fa1043
--- /dev/null
+++ b/pkg/signatures/common/README.md
@@ -0,0 +1,259 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# common
+
+```go
+import "github.com/coinbase/kryptology/pkg/signatures/common"
+```
+
+## Index
+
+- [type Challenge](<#type-challenge>)
+- [type Commitment](<#type-commitment>)
+- [type HmacDrbg](<#type-hmacdrbg>)
+  - [func NewHmacDrbg(entropy, nonce, pers []byte, hasher func() hash.Hash) *HmacDrbg](<#func-newhmacdrbg>)
+  - [func (drbg *HmacDrbg) Read(dst []byte) (n int, err error)](<#func-hmacdrbg-read>)
+  - [func (drbg *HmacDrbg) Reseed(entropy []byte)](<#func-hmacdrbg-reseed>)
+- [type Nonce](<#type-nonce>)
+- [type ProofCommittedBuilder](<#type-proofcommittedbuilder>)
+  - [func NewProofCommittedBuilder(curve *curves.Curve) *ProofCommittedBuilder](<#func-newproofcommittedbuilder>)
+  - [func (pcb *ProofCommittedBuilder) Commit(point curves.Point, scalar curves.Scalar) error](<#func-proofcommittedbuilder-commit>)
+  - [func (pcb *ProofCommittedBuilder) CommitRandom(point curves.Point, reader io.Reader) error](<#func-proofcommittedbuilder-commitrandom>)
+  - [func (pcb ProofCommittedBuilder) GenerateProof(challenge curves.Scalar, secrets []curves.Scalar) ([]curves.Scalar, error)](<#func-proofcommittedbuilder-generateproof>)
+  - [func (pcb *ProofCommittedBuilder) Get(index int) (curves.Point, curves.Scalar)](<#func-proofcommittedbuilder-get>)
+  - [func (pcb ProofCommittedBuilder) GetChallengeContribution() []byte](<#func-proofcommittedbuilder-getchallengecontribution>)
+- [type ProofMessage](<#type-proofmessage>)
+- [type ProofSpecificMessage](<#type-proofspecificmessage>)
+  - [func (ps ProofSpecificMessage) GetBlinding(reader io.Reader) curves.Scalar](<#func-proofspecificmessage-getblinding>)
+  - [func (ps ProofSpecificMessage) GetMessage() curves.Scalar](<#func-proofspecificmessage-getmessage>)
+  - [func (ps ProofSpecificMessage) IsHidden() bool](<#func-proofspecificmessage-ishidden>)
+- [type RevealedMessage](<#type-revealedmessage>)
+  - [func (r RevealedMessage) GetBlinding(reader io.Reader) curves.Scalar](<#func-revealedmessage-getblinding>)
+  - [func (r RevealedMessage) GetMessage() curves.Scalar](<#func-revealedmessage-getmessage>)
+  - [func (r RevealedMessage) IsHidden() bool](<#func-revealedmessage-ishidden>)
+- [type SharedBlindingMessage](<#type-sharedblindingmessage>)
+  - [func (ps SharedBlindingMessage) GetBlinding(reader io.Reader) curves.Scalar](<#func-sharedblindingmessage-getblinding>)
+  - [func (ps SharedBlindingMessage) GetMessage() curves.Scalar](<#func-sharedblindingmessage-getmessage>)
+  - [func (ps SharedBlindingMessage) IsHidden() bool](<#func-sharedblindingmessage-ishidden>)
+- [type SignatureBlinding](<#type-signatureblinding>)
+
+
+## type [Challenge](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/challenge.go#L14>)
+
+Challenge generated by fiat\-shamir heuristic
+
+```go
+type Challenge = curves.Scalar
+```
+
+## type [Commitment](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/commitment.go#L15>)
+
+Commitment represents a point Pedersen commitment of one or more points multiplied by scalars
+
+```go
+type Commitment = curves.Point
+```
+
+## type [HmacDrbg](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/hmacdrbg.go#L17-L21>)
+
+HmacDrbg is an HMAC deterministic random bit generator that can use any hash function\. Handles reseeding automatically
+
+```go
+type HmacDrbg struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewHmacDrbg](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/hmacdrbg.go#L23>)
+
+```go
+func NewHmacDrbg(entropy, nonce, pers []byte, hasher func() hash.Hash) *HmacDrbg
+```
+
+### func \(\*HmacDrbg\) [Read](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/hmacdrbg.go#L40>)
+
+```go
+func (drbg *HmacDrbg) Read(dst []byte) (n int, err error)
+```
+
+### func \(\*HmacDrbg\) [Reseed](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/hmacdrbg.go#L61>)
+
+```go
+func (drbg *HmacDrbg) Reseed(entropy []byte)
+```
+
+## type [Nonce](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/nonce.go#L15>)
+
+Nonce is used for zero\-knowledge proofs to prevent replay attacks and prove freshness
+
+```go
+type Nonce = curves.Scalar
+```
+
+## type [ProofCommittedBuilder](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L21-L25>)
+
+ProofCommittedBuilder is used to create proofs from multiple commitments where each secret is committed with a random blinding factor and turned into a Schnorr proof
+
+```go
+type ProofCommittedBuilder struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewProofCommittedBuilder](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L28>)
+
+```go
+func NewProofCommittedBuilder(curve *curves.Curve) *ProofCommittedBuilder
+```
+
+NewProofCommittedBuilder creates a new builder using the specified curve
+
+### func \(\*ProofCommittedBuilder\) [Commit](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L47>)
+
+```go
+func (pcb *ProofCommittedBuilder) Commit(point curves.Point, scalar curves.Scalar) error
+```
+
+Commit uses the specified point and scalar to create a commitment
+
+### func \(\*ProofCommittedBuilder\) [CommitRandom](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L37>)
+
+```go
+func (pcb *ProofCommittedBuilder) CommitRandom(point curves.Point, reader io.Reader) error
+```
+
+CommitRandom uses the specified point and commits a random value to it
+
+### func \(ProofCommittedBuilder\) [GenerateProof](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L75>)
+
+```go
+func (pcb ProofCommittedBuilder) GenerateProof(challenge curves.Scalar, secrets []curves.Scalar) ([]curves.Scalar, error)
+```
+
+GenerateProof converts the blinding factors and secrets into Schnorr proofs
+
+### func \(\*ProofCommittedBuilder\) [Get](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L57>)
+
+```go
+func (pcb *ProofCommittedBuilder) Get(index int) (curves.Point, curves.Scalar)
+```
+
+Get returns the point and scalar at the specified index
+
+### func \(ProofCommittedBuilder\) [GetChallengeContribution](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_committed_builder.go#L66>)
+
+```go
+func (pcb ProofCommittedBuilder) GetChallengeContribution() []byte
+```
+
+GetChallengeContribution returns the bytes that should be added to a sigma protocol transcript for generating the challenge
+
+## type [ProofMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L18-L30>)
+
+ProofMessage classifies how a message is presented in a proof Either Revealed or Hidden\. Hidden has two sub categories: proof specific i\.e\. the message is only used for this proof or shared i\.e\. the message should be proved to be common across proofs
+
+```go
+type ProofMessage interface {
+    // IsHidden indicates the message should be hidden
+    IsHidden() bool
+    // GetBlinding is used for hidden messages
+    // blindings can either be proof specific to a signature
+    // or involved with other proofs like boundchecks,
+    // set memberships, or inequalities so the blinding
+    // factor is shared among proofs to produce a common
+    // schnorr linking proof
+    GetBlinding(reader io.Reader) curves.Scalar
+    // GetMessage returns the underlying message
+    GetMessage() curves.Scalar
+}
+```
+
+## type [ProofSpecificMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L48-L50>)
+
+```go
+type ProofSpecificMessage struct {
+    Message curves.Scalar
+}
+```
+
+### func \(ProofSpecificMessage\) [GetBlinding](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L56>)
+
+```go
+func (ps ProofSpecificMessage) GetBlinding(reader io.Reader) curves.Scalar
+```
+
+### func \(ProofSpecificMessage\) [GetMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L60>)
+
+```go
+func (ps ProofSpecificMessage) GetMessage() curves.Scalar
+```
+
+### func \(ProofSpecificMessage\) [IsHidden](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L52>)
+
+```go
+func (ps ProofSpecificMessage) IsHidden() bool
+```
+
+## type [RevealedMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L32-L34>)
+
+```go
+type RevealedMessage struct {
+    Message curves.Scalar
+}
+```
+
+### func \(RevealedMessage\) [GetBlinding](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L40>)
+
+```go
+func (r RevealedMessage) GetBlinding(reader io.Reader) curves.Scalar
+```
+
+### func \(RevealedMessage\) [GetMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L44>)
+
+```go
+func (r RevealedMessage) GetMessage() curves.Scalar
+```
+
+### func \(RevealedMessage\) [IsHidden](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L36>)
+
+```go
+func (r RevealedMessage) IsHidden() bool
+```
+
+## type [SharedBlindingMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L64-L66>)
+
+```go
+type SharedBlindingMessage struct {
+    Message, Blinding curves.Scalar
+}
+```
+
+### func \(SharedBlindingMessage\) [GetBlinding](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L72>)
+
+```go
+func (ps SharedBlindingMessage) GetBlinding(reader io.Reader) curves.Scalar
+```
+
+### func \(SharedBlindingMessage\) [GetMessage](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L76>)
+
+```go
+func (ps SharedBlindingMessage) GetMessage() curves.Scalar
+```
+
+### func \(SharedBlindingMessage\) [IsHidden](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/proof_message.go#L68>)
+
+```go
+func (ps SharedBlindingMessage) IsHidden() bool
+```
+
+## type [SignatureBlinding](<https://github.com/coinbase/kryptology/blob/master/pkg/signatures/common/signature_blinding.go#L14>)
+
+SignatureBlinding is a value used for computing blind signatures
+
+```go
+type SignatureBlinding = curves.PairingScalar
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/signatures/common/challenge.go b/pkg/signatures/common/challenge.go
new file mode 100644
index 00000000..55c309f0
--- /dev/null
+++ b/pkg/signatures/common/challenge.go
@@ -0,0 +1,14 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Challenge generated by fiat-shamir heuristic
+type Challenge = curves.Scalar
diff --git a/pkg/signatures/common/commitment.go b/pkg/signatures/common/commitment.go
new file mode 100644
index 00000000..f57094fc
--- /dev/null
+++ b/pkg/signatures/common/commitment.go
@@ -0,0 +1,15 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Commitment represents a point Pedersen commitment of one or more
+// points multiplied by scalars
+type Commitment = curves.Point
diff --git a/pkg/signatures/common/hmacdrbg.go b/pkg/signatures/common/hmacdrbg.go
new file mode 100644
index 00000000..025e3dfe
--- /dev/null
+++ b/pkg/signatures/common/hmacdrbg.go
@@ -0,0 +1,99 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"crypto/hmac"
+	"hash"
+)
+
+// HmacDrbg is an HMAC deterministic random bit generator
+// that can use any hash function. Handles reseeding
+// automatically
+type HmacDrbg struct {
+	k, v   []byte
+	count  int
+	hasher func() hash.Hash
+}
+
+func NewHmacDrbg(entropy, nonce, pers []byte, hasher func() hash.Hash) *HmacDrbg {
+	drbg := new(HmacDrbg)
+	h := hasher()
+	drbg.k = make([]byte, h.Size())
+	drbg.v = make([]byte, h.Size())
+	drbg.count = 0
+	drbg.hasher = hasher
+
+	for i := range drbg.v {
+		drbg.v[i] = 1
+	}
+
+	drbg.update([][]byte{entropy, nonce, pers})
+	drbg.count += 1
+	return drbg
+}
+
+func (drbg *HmacDrbg) Read(dst []byte) (n int, err error) {
+	toRead := len(dst)
+	if toRead == 0 {
+		return 0, nil
+	}
+	i := 0
+	for i < toRead {
+		vmac := drbg.getHmac()
+		_, _ = vmac.Write(drbg.v)
+		drbg.v = vmac.Sum(nil)
+
+		for j, b := range drbg.v {
+			dst[i+j] = b
+		}
+		i += len(drbg.v)
+	}
+	drbg.update(nil)
+	drbg.count++
+	return i, nil
+}
+
+func (drbg *HmacDrbg) Reseed(entropy []byte) {
+	drbg.update([][]byte{entropy})
+}
+
+func (drbg *HmacDrbg) getHmac() hash.Hash {
+	return hmac.New(drbg.hasher, drbg.k)
+}
+
+func (drbg *HmacDrbg) update(seeds [][]byte) {
+	kmac := drbg.getHmac()
+	_, _ = kmac.Write(drbg.v)
+	_, _ = kmac.Write([]byte{0})
+	if len(seeds) > 0 {
+		for _, seed := range seeds {
+			_, _ = kmac.Write(seed)
+		}
+	}
+	drbg.k = kmac.Sum(nil)
+
+	vmac := drbg.getHmac()
+	_, _ = vmac.Write(drbg.v)
+	drbg.v = vmac.Sum(nil)
+
+	if len(seeds) == 0 {
+		return
+	}
+
+	kmac = drbg.getHmac()
+	_, _ = kmac.Write(drbg.v)
+	_, _ = kmac.Write([]byte{1})
+	for _, seed := range seeds {
+		_, _ = kmac.Write(seed)
+	}
+	drbg.k = kmac.Sum(nil)
+
+	vmac = drbg.getHmac()
+	_, _ = vmac.Write(drbg.v)
+	drbg.v = vmac.Sum(nil)
+}
diff --git a/pkg/signatures/common/nonce.go b/pkg/signatures/common/nonce.go
new file mode 100644
index 00000000..cab98ffd
--- /dev/null
+++ b/pkg/signatures/common/nonce.go
@@ -0,0 +1,15 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Nonce is used for zero-knowledge proofs to prevent replay attacks
+// and prove freshness
+type Nonce = curves.Scalar
diff --git a/pkg/signatures/common/proof_committed_builder.go b/pkg/signatures/common/proof_committed_builder.go
new file mode 100644
index 00000000..ac1454a3
--- /dev/null
+++ b/pkg/signatures/common/proof_committed_builder.go
@@ -0,0 +1,85 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+const limit = 65535
+
+// ProofCommittedBuilder is used to create
+// proofs from multiple commitments where
+// each secret is committed with a random blinding factor
+// and turned into a Schnorr proof
+type ProofCommittedBuilder struct {
+	points  []curves.Point
+	scalars []curves.Scalar
+	curve   *curves.Curve
+}
+
+// NewProofCommittedBuilder creates a new builder using the specified curve
+func NewProofCommittedBuilder(curve *curves.Curve) *ProofCommittedBuilder {
+	return &ProofCommittedBuilder{
+		points:  []curves.Point{},
+		scalars: []curves.Scalar{},
+		curve:   curve,
+	}
+}
+
+// CommitRandom uses the specified point and commits a random value to it
+func (pcb *ProofCommittedBuilder) CommitRandom(point curves.Point, reader io.Reader) error {
+	if len(pcb.points) > limit {
+		return fmt.Errorf("limit for commitments reached")
+	}
+	pcb.points = append(pcb.points, point)
+	pcb.scalars = append(pcb.scalars, pcb.curve.Scalar.Random(reader))
+	return nil
+}
+
+// Commit uses the specified point and scalar to create a commitment
+func (pcb *ProofCommittedBuilder) Commit(point curves.Point, scalar curves.Scalar) error {
+	if len(pcb.points) > limit {
+		return fmt.Errorf("limit for commitments reached")
+	}
+	pcb.points = append(pcb.points, point)
+	pcb.scalars = append(pcb.scalars, scalar)
+	return nil
+}
+
+// Get returns the point and scalar at the specified index
+func (pcb *ProofCommittedBuilder) Get(index int) (curves.Point, curves.Scalar) {
+	if index >= len(pcb.points) || index < 0 {
+		return nil, nil
+	}
+	return pcb.points[index], pcb.scalars[index]
+}
+
+// GetChallengeContribution returns the bytes that should be added to
+// a sigma protocol transcript for generating the challenge
+func (pcb ProofCommittedBuilder) GetChallengeContribution() []byte {
+	commitment := pcb.curve.Point.SumOfProducts(pcb.points, pcb.scalars)
+	if commitment == nil {
+		return nil
+	}
+	return commitment.ToAffineCompressed()
+}
+
+// GenerateProof converts the blinding factors and secrets into Schnorr proofs
+func (pcb ProofCommittedBuilder) GenerateProof(challenge curves.Scalar, secrets []curves.Scalar) ([]curves.Scalar, error) {
+	if len(secrets) != len(pcb.scalars) {
+		return nil, fmt.Errorf("secrets is not equal to blinding factors")
+	}
+
+	proofs := make([]curves.Scalar, len(pcb.scalars))
+	for i, sc := range pcb.scalars {
+		proofs[i] = secrets[i].MulAdd(challenge, sc)
+	}
+	return proofs, nil
+}
diff --git a/pkg/signatures/common/proof_message.go b/pkg/signatures/common/proof_message.go
new file mode 100644
index 00000000..841afc7b
--- /dev/null
+++ b/pkg/signatures/common/proof_message.go
@@ -0,0 +1,78 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+)
+
+// ProofMessage classifies how a message is presented in a proof
+// Either Revealed or Hidden. Hidden has two sub categories:
+// proof specific i.e. the message is only used for this proof or
+// shared i.e. the message should be proved to be common across proofs
+type ProofMessage interface {
+	// IsHidden indicates the message should be hidden
+	IsHidden() bool
+	// GetBlinding is used for hidden messages
+	// blindings can either be proof specific to a signature
+	// or involved with other proofs like boundchecks,
+	// set memberships, or inequalities so the blinding
+	// factor is shared among proofs to produce a common
+	// schnorr linking proof
+	GetBlinding(reader io.Reader) curves.Scalar
+	// GetMessage returns the underlying message
+	GetMessage() curves.Scalar
+}
+
+type RevealedMessage struct {
+	Message curves.Scalar
+}
+
+func (r RevealedMessage) IsHidden() bool {
+	return false
+}
+
+func (r RevealedMessage) GetBlinding(reader io.Reader) curves.Scalar {
+	return nil
+}
+
+func (r RevealedMessage) GetMessage() curves.Scalar {
+	return r.Message
+}
+
+type ProofSpecificMessage struct {
+	Message curves.Scalar
+}
+
+func (ps ProofSpecificMessage) IsHidden() bool {
+	return true
+}
+
+func (ps ProofSpecificMessage) GetBlinding(reader io.Reader) curves.Scalar {
+	return ps.Message.Random(reader)
+}
+
+func (ps ProofSpecificMessage) GetMessage() curves.Scalar {
+	return ps.Message
+}
+
+type SharedBlindingMessage struct {
+	Message, Blinding curves.Scalar
+}
+
+func (ps SharedBlindingMessage) IsHidden() bool {
+	return true
+}
+
+func (ps SharedBlindingMessage) GetBlinding(reader io.Reader) curves.Scalar {
+	return ps.Blinding
+}
+
+func (ps SharedBlindingMessage) GetMessage() curves.Scalar {
+	return ps.Message
+}
diff --git a/pkg/signatures/common/signature_blinding.go b/pkg/signatures/common/signature_blinding.go
new file mode 100644
index 00000000..33a3b9e9
--- /dev/null
+++ b/pkg/signatures/common/signature_blinding.go
@@ -0,0 +1,14 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package common
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// SignatureBlinding is a value used for computing blind signatures
+type SignatureBlinding = curves.PairingScalar
diff --git a/pkg/tecdsa/dkls/README.md b/pkg/tecdsa/dkls/README.md
new file mode 100755
index 00000000..fb96f5d0
--- /dev/null
+++ b/pkg/tecdsa/dkls/README.md
@@ -0,0 +1,448 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# dkls
+
+```go
+import "github.com/coinbase/kryptology/pkg/tecdsa/dkls"
+```
+
+Package dkls implements the 2\-of\-2 threshold ECDSA signing algorithm of \[Doerner\, Kondi\, Lee\, and shelat\]\(https://eprint.iacr.org/2018/499\)\. For an example of use\, look at sign\.go\.
+
+It is currently a work in progress; do not use it in real\-life scenarios yet\. TODO: Docs to be completed\.
+
+## Index
+
+- [func EncodeAlice(a *Alice) ([]byte, error)](<#func-encodealice>)
+- [func EncodeBob(b *Bob) ([]byte, error)](<#func-encodebob>)
+- [func NewPipeWrappers() (*pipeWrapper, *pipeWrapper)](<#func-newpipewrappers>)
+- [type Alice](<#type-alice>)
+  - [func DecodeAlice(params *Params, b []byte) (*Alice, error)](<#func-decodealice>)
+  - [func NewAlice(params *Params) *Alice](<#func-newalice>)
+  - [func (alice *Alice) DKG(rw io.ReadWriter) error](<#func-alice-dkg>)
+  - [func (alice *Alice) Sign(m []byte, rw io.ReadWriter) error](<#func-alice-sign>)
+- [type AliceDkg](<#type-alicedkg>)
+  - [func NewAliceDkg(params *Params) *AliceDkg](<#func-newalicedkg>)
+  - [func (a *AliceDkg) Result() (interface{}, error)](<#func-alicedkg-result>)
+  - [func (a *AliceDkg) SetDebug(log io.Writer)](<#func-alicedkg-setdebug>)
+- [type AliceSign](<#type-alicesign>)
+  - [func NewAliceSign(params *Params, msg []byte, dkgResult []byte) (*AliceSign, error)](<#func-newalicesign>)
+  - [func (a *AliceSign) Result() (interface{}, error)](<#func-alicesign-result>)
+  - [func (a *AliceSign) SetDebug(log io.Writer)](<#func-alicesign-setdebug>)
+- [type Bob](<#type-bob>)
+  - [func DecodeBob(params *Params, b []byte) (*Bob, error)](<#func-decodebob>)
+  - [func NewBob(params *Params) *Bob](<#func-newbob>)
+  - [func (bob *Bob) DKG(rw io.ReadWriter) error](<#func-bob-dkg>)
+  - [func (bob *Bob) Sign(m []byte, rw io.ReadWriter) error](<#func-bob-sign>)
+- [type BobDkg](<#type-bobdkg>)
+  - [func NewBobDkg(params *Params) *BobDkg](<#func-newbobdkg>)
+  - [func (b *BobDkg) Result() (interface{}, error)](<#func-bobdkg-result>)
+  - [func (b *BobDkg) SetDebug(log io.Writer)](<#func-bobdkg-setdebug>)
+- [type BobSign](<#type-bobsign>)
+  - [func NewBobSign(params *Params, msg []byte, dkgResult []byte) (*BobSign, error)](<#func-newbobsign>)
+  - [func (d *BobSign) Result() (interface{}, error)](<#func-bobsign-result>)
+  - [func (b *BobSign) SetDebug(log io.Writer)](<#func-bobsign-setdebug>)
+- [type DkgResult](<#type-dkgresult>)
+- [type MultiplyReceiver](<#type-multiplyreceiver>)
+  - [func NewMultiplyReceiver(multiplicity int, sender *seedOTSender) *MultiplyReceiver](<#func-newmultiplyreceiver>)
+  - [func (receiver *MultiplyReceiver) MultiplyInit(idExt [32]byte, beta []*big.Int, w io.Writer) error](<#func-multiplyreceiver-multiplyinit>)
+  - [func (receiver *MultiplyReceiver) MultiplyTransfer(r io.Reader) error](<#func-multiplyreceiver-multiplytransfer>)
+- [type MultiplySender](<#type-multiplysender>)
+  - [func NewMultiplySender(multiplicity int, receiver *seedOTReceiver) *MultiplySender](<#func-newmultiplysender>)
+  - [func (sender *MultiplySender) Multiply(idExt [32]byte, alpha []*big.Int, rw io.ReadWriter) error](<#func-multiplysender-multiply>)
+- [type Params](<#type-params>)
+  - [func NewParams(curve elliptic.Curve, scalar curves.EcScalar) (*Params, error)](<#func-newparams>)
+- [type ProtocolIterator](<#type-protocoliterator>)
+- [type Schnorr](<#type-schnorr>)
+  - [func (proof *Schnorr) DecommitVerify(com []byte) error](<#func-schnorr-decommitverify>)
+  - [func (proof *Schnorr) Prove(x *big.Int) error](<#func-schnorr-prove>)
+  - [func (proof *Schnorr) ProveCommit(x *big.Int) ([]byte, error)](<#func-schnorr-provecommit>)
+  - [func (proof *Schnorr) Verify() error](<#func-schnorr-verify>)
+
+
+## func [EncodeAlice](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L280>)
+
+```go
+func EncodeAlice(a *Alice) ([]byte, error)
+```
+
+Encodes an alice object as a byte sequence after DKG has been completed\.
+
+## func [EncodeBob](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L294>)
+
+```go
+func EncodeBob(b *Bob) ([]byte, error)
+```
+
+Encodes a bob object as a byte sequence after DKG has been completed\.
+
+## func [NewPipeWrappers](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/conn.go#L29>)
+
+```go
+func NewPipeWrappers() (*pipeWrapper, *pipeWrapper)
+```
+
+## type [Alice](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L23-L31>)
+
+Alice struct encoding Alice's state during one execution of the overall signing algorithm\. At the end of the joint computation\, Alice will NOT obtain the signature\.
+
+```go
+type Alice struct {
+    PkA      *Schnorr // this is a "schnorr statement" for pkA.
+    Receiver *seedOTReceiver
+    SkA      *big.Int // the witness
+    Pk       *curves.EcPoint
+    // contains filtered or unexported fields
+}
+```
+
+### func [DecodeAlice](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L287>)
+
+```go
+func DecodeAlice(params *Params, b []byte) (*Alice, error)
+```
+
+Decodes an alice object that was encoded after DKG\.
+
+### func [NewAlice](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L55>)
+
+```go
+func NewAlice(params *Params) *Alice
+```
+
+NewAlice creates a party that can participate in 2\-of\-2 DKG and threshold signature\.
+
+### func \(\*Alice\) [DKG](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/dkg.go#L80>)
+
+```go
+func (alice *Alice) DKG(rw io.ReadWriter) error
+```
+
+### func \(\*Alice\) [Sign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L275>)
+
+```go
+func (alice *Alice) Sign(m []byte, rw io.ReadWriter) error
+```
+
+Sign this is an illustrative helper method which shows the overall flow for Alice\. in practice this will be replaced by a method which actually sends messages back and forth\.
+
+## type [AliceDkg](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L51-L54>)
+
+AliceDkg DKLS DKG implementation that satisfies the protocol iterator interface\.
+
+```go
+type AliceDkg struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewAliceDkg](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L108>)
+
+```go
+func NewAliceDkg(params *Params) *AliceDkg
+```
+
+NewAliceDkg creates a new protocol that can compute a DKG as Alice
+
+### func \(\*AliceDkg\) [Result](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L147>)
+
+```go
+func (a *AliceDkg) Result() (interface{}, error)
+```
+
+Result Returns an encoded version of Alice as sequence of bytes that can be used to initialize an AliceSign protocol\.
+
+### func \(\*AliceDkg\) [SetDebug](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L142>)
+
+```go
+func (a *AliceDkg) SetDebug(log io.Writer)
+```
+
+## type [AliceSign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L63-L66>)
+
+AliceSign DKLS sign implementation that satisfies the protocol iterator interface\.
+
+```go
+type AliceSign struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewAliceSign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L217>)
+
+```go
+func NewAliceSign(params *Params, msg []byte, dkgResult []byte) (*AliceSign, error)
+```
+
+Creates a new protocol that can compute a signature as Alice\. Requires dkg state that was produced at the end of DKG\.Result\(\)\.
+
+### func \(\*AliceSign\) [Result](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L256>)
+
+```go
+func (a *AliceSign) Result() (interface{}, error)
+```
+
+Result always returns errNoSig\. Alice does not compute a signature in the DKLS protocol; only Bob computes the signature\.
+
+### func \(\*AliceSign\) [SetDebug](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L250>)
+
+```go
+func (a *AliceSign) SetDebug(log io.Writer)
+```
+
+## type [Bob](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L35-L52>)
+
+Bob struct encoding Bob's state during one execution of the overall signing algorithm\. At the end of the joint computation\, Bob will obtain the signature\.
+
+```go
+type Bob struct {
+    // Exported fields
+    PkB    *Schnorr // this is a "schnorr statement" for pkB.
+    Sender *seedOTSender
+    SkB    *big.Int
+    Pk     *curves.EcPoint
+    Sig    *curves.EcdsaSignature // The resulting digital signature
+    // contains filtered or unexported fields
+}
+```
+
+### func [DecodeBob](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L301>)
+
+```go
+func DecodeBob(params *Params, b []byte) (*Bob, error)
+```
+
+Decodes an bob object that was encoded after DKG\.
+
+### func [NewBob](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L65>)
+
+```go
+func NewBob(params *Params) *Bob
+```
+
+NewBob creates a party that can participate in 2\-of\-2 DKG and threshold signature\. This party is the receiver of the signature at the end\.
+
+### func \(\*Bob\) [DKG](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/dkg.go#L90>)
+
+```go
+func (bob *Bob) DKG(rw io.ReadWriter) error
+```
+
+### func \(\*Bob\) [Sign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/sign.go#L280>)
+
+```go
+func (bob *Bob) Sign(m []byte, rw io.ReadWriter) error
+```
+
+Sign this is an illustrative helper method which shows the overall flow for Bob\.
+
+## type [BobDkg](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L57-L60>)
+
+BobDkg DKLS DKG implementation that satisfies the protocol iterator interface\.
+
+```go
+type BobDkg struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewBobDkg](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L126>)
+
+```go
+func NewBobDkg(params *Params) *BobDkg
+```
+
+NewBobDkg Creates a new protocol that can compute a DKG as Bob
+
+### func \(\*BobDkg\) [Result](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L185>)
+
+```go
+func (b *BobDkg) Result() (interface{}, error)
+```
+
+Result returns an encoded version of Alice as sequence of bytes that can be used to initialize an AliceSign protocol\.
+
+### func \(\*BobDkg\) [SetDebug](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L179>)
+
+```go
+func (b *BobDkg) SetDebug(log io.Writer)
+```
+
+## type [BobSign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L69-L72>)
+
+BobSign DKLS sign implementation that satisfies the protocol iterator interface\.
+
+```go
+type BobSign struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewBobSign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L234>)
+
+```go
+func NewBobSign(params *Params, msg []byte, dkgResult []byte) (*BobSign, error)
+```
+
+NewBobSign creates a new protocol that can compute a signature as Bob\. Requires dkg state that was produced at the end of DKG\.Result\(\)\.
+
+### func \(\*BobSign\) [Result](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L266>)
+
+```go
+func (d *BobSign) Result() (interface{}, error)
+```
+
+If the signing protocol completed successfully\, returns the signature that Bob computed as a \*core\.EcdsaSignature\.
+
+### func \(\*BobSign\) [SetDebug](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L260>)
+
+```go
+func (b *BobSign) SetDebug(log io.Writer)
+```
+
+## type [DkgResult](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L46-L49>)
+
+DKG protocols produce the following result on successful completion
+
+```go
+type DkgResult struct {
+    DkgState []byte
+    Pubkey   *curves.EcPoint
+}
+```
+
+## type [MultiplyReceiver](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L28-L34>)
+
+```go
+type MultiplyReceiver struct {
+    TB []*big.Int
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewMultiplyReceiver](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L45>)
+
+```go
+func NewMultiplyReceiver(multiplicity int, sender *seedOTSender) *MultiplyReceiver
+```
+
+### func \(\*MultiplyReceiver\) [MultiplyInit](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L92>)
+
+```go
+func (receiver *MultiplyReceiver) MultiplyInit(idExt [32]byte, beta []*big.Int, w io.Writer) error
+```
+
+MultiplyInit Protocol 5\.\, Multiplication\, 3\)\. Bob \(receiver\) encodes beta and initiates the cOT extension\!
+
+### func \(\*MultiplyReceiver\) [MultiplyTransfer](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L142>)
+
+```go
+func (receiver *MultiplyReceiver) MultiplyTransfer(r io.Reader) error
+```
+
+MultiplyTransfer Protocol 5\.\, Multiplication\, 3\) and 6\)\. Bob finalizes the cOT extension\. using that and Alice's multiplication message\, Bob completes the multiplication protocol\, including checks\. at the end\, Bob's values tB\_j are populated\.
+
+## type [MultiplySender](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L21-L26>)
+
+```go
+type MultiplySender struct {
+    TA []*big.Int
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewMultiplySender](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L36>)
+
+```go
+func NewMultiplySender(multiplicity int, receiver *seedOTReceiver) *MultiplySender
+```
+
+### func \(\*MultiplySender\) [Multiply](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/multiply.go#L104>)
+
+```go
+func (sender *MultiplySender) Multiply(idExt [32]byte, alpha []*big.Int, rw io.ReadWriter) error
+```
+
+Multiply Protocol 5\.\, steps 3\) 5\)\, 7\)\. Alice \_responds\_ to Bob's initial cOT message\, using a vector of alphas as input\. doesn't actually send that message yet\, only stashes it\, and moves onto the next steps of the multiplication protocol specifically\, Alice can then do step 5\) \(compute the outputs of the multiplication protocol\)\, also stashes this\. finishes up by taking care of 7\)\, after that\, Alice is totally done with multiplication and has stashed the outputs\.
+
+## type [Params](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/params.go#L23-L28>)
+
+```go
+type Params struct {
+    Curve     elliptic.Curve
+    Scalar    curves.EcScalar
+    Generator *curves.EcPoint
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/params.go#L32>)
+
+```go
+func NewParams(curve elliptic.Curve, scalar curves.EcScalar) (*Params, error)
+```
+
+NewParams receives an implementation of the curve and scalar interfaces and sets the parameters needed for DKG and Threshold ECDSA of DKLS\.
+
+## type [ProtocolIterator](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/proto.go#L21-L36>)
+
+ProtocolIterator a generalized interface for multi\-party protocols that follows the iterator pattern\.
+
+```go
+type ProtocolIterator interface {
+    // Next runs the next round of the protocol.
+    // Inputs are read from rw.Read(); outputs are written to rw.Write().
+    // Returns io.EOF when protocol has completed.
+    Next(rw io.ReadWriter) error
+
+    // Result returns the final result, if any, of the completed protocol.
+    // Reports an error if the protocol has not yet terminated
+    // or if an error was encountered during protocol execution.
+    Result() (interface{}, error)
+
+    // SetDebug enables or disables (passing a nil value as input) debugging.
+    // At the moment, we only print the final dkls dkg result as json value to this log, but if needed more debugging
+    // can be added for various steps of the other protocols.
+    SetDebug(log io.Writer)
+}
+```
+
+## type [Schnorr](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/schnorr.go#L17-L22>)
+
+```go
+type Schnorr struct {
+    Pub *curves.EcPoint // this is the public point.
+    C   *big.Int
+    S   *big.Int
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*Schnorr\) [DecommitVerify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/schnorr.go#L100>)
+
+```go
+func (proof *Schnorr) DecommitVerify(com []byte) error
+```
+
+### func \(\*Schnorr\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/schnorr.go#L24>)
+
+```go
+func (proof *Schnorr) Prove(x *big.Int) error
+```
+
+### func \(\*Schnorr\) [ProveCommit](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/schnorr.go#L80>)
+
+```go
+func (proof *Schnorr) ProveCommit(x *big.Int) ([]byte, error)
+```
+
+this "commits to" a schnorr proof which is later revealed; see Functionality 7\. it mutates \`st\` by adding a proof to it\, and then also returns the commitment to the proof\.
+
+### func \(\*Schnorr\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/dkls/schnorr.go#L52>)
+
+```go
+func (proof *Schnorr) Verify() error
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/tecdsa/dkls/conn.go b/pkg/tecdsa/dkls/conn.go
new file mode 100644
index 00000000..df6ccfa3
--- /dev/null
+++ b/pkg/tecdsa/dkls/conn.go
@@ -0,0 +1,33 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import "io"
+
+type pipeWrapper struct {
+	r         *io.PipeReader
+	w         *io.PipeWriter
+	exchanged int // basically we only use this during testing, to track bytes exchanged
+}
+
+func (wrapper *pipeWrapper) Write(p []byte) (n int, err error) {
+	n, err = wrapper.w.Write(p)
+	wrapper.exchanged += n
+	return
+}
+
+func (wrapper *pipeWrapper) Read(p []byte) (n int, err error) {
+	n, err = wrapper.r.Read(p)
+	wrapper.exchanged += n
+	return
+}
+
+func NewPipeWrappers() (*pipeWrapper, *pipeWrapper) {
+	leftOut, leftIn := io.Pipe()
+	rightOut, rightIn := io.Pipe()
+	return &pipeWrapper{r: leftOut, w: rightIn}, &pipeWrapper{r: rightOut, w: leftIn}
+}
diff --git a/pkg/tecdsa/dkls/dkg.go b/pkg/tecdsa/dkls/dkg.go
new file mode 100644
index 00000000..cc41cff5
--- /dev/null
+++ b/pkg/tecdsa/dkls/dkg.go
@@ -0,0 +1,98 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"encoding/gob"
+	"io"
+)
+
+func (alice *Alice) dkgCommit(w io.Writer) error {
+	var err error
+	enc := gob.NewEncoder(w)
+	if alice.SkA, err = alice.params.Scalar.Random(); err != nil {
+		return err
+	}
+	alice.PkA = &Schnorr{params: alice.params}      // kind of awkward where this should be defined.
+	result, err := alice.PkA.ProveCommit(alice.SkA) // will mutate `pkA`
+	if err != nil {
+		return err
+	}
+	return enc.Encode(&result)
+}
+
+// dkgCommit receives Bob's commitment and returns schnorr statment + proof.
+func (bob *Bob) dkgCommit(rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	var err error
+	if err = dec.Decode(&bob.com); err != nil {
+		return err
+	}
+	if bob.SkB, err = bob.params.Scalar.Random(); err != nil {
+		return err
+	}
+	bob.PkB = &Schnorr{params: bob.params}
+	if err = bob.PkB.Prove(bob.SkB); err != nil {
+		return err
+	}
+	return enc.Encode(bob.PkB)
+}
+
+// dkgVerify input: Bob's statement + schnorr proof.
+func (alice *Alice) dkgVerify(rw io.ReadWriter) error {
+	dec := gob.NewDecoder(rw)
+	enc := gob.NewEncoder(rw)
+	var err error
+	input := &Schnorr{params: alice.params}
+	if err = dec.Decode(input); err != nil {
+		return err
+	}
+	if err = input.Verify(); err != nil {
+		return err
+	}
+	if alice.Pk, err = input.Pub.ScalarMult(alice.SkA); err != nil {
+		return err
+	}
+	return enc.Encode(alice.PkA)
+}
+
+func (bob *Bob) dkgVerify(r io.Reader) error {
+	dec := gob.NewDecoder(r)
+	var err error
+	input := &Schnorr{params: bob.params}
+	if err = dec.Decode(input); err != nil {
+		return err
+	}
+	if err = input.DecommitVerify(bob.com); err != nil {
+		return err
+	}
+	if bob.Pk, err = input.Pub.ScalarMult(bob.SkB); err != nil {
+		return err
+	}
+	return nil
+}
+
+func (alice *Alice) DKG(rw io.ReadWriter) error {
+	if err := alice.dkgCommit(rw); err != nil {
+		return err
+	}
+	if err := alice.dkgVerify(rw); err != nil {
+		return err
+	}
+	return alice.Receiver.kosSetup(rw)
+}
+
+func (bob *Bob) DKG(rw io.ReadWriter) error {
+	if err := bob.dkgCommit(rw); err != nil {
+		return err
+	}
+	if err := bob.dkgVerify(rw); err != nil {
+		return err
+	}
+	return bob.Sender.kosSetup(rw)
+}
diff --git a/pkg/tecdsa/dkls/dkg_test.go b/pkg/tecdsa/dkls/dkg_test.go
new file mode 100644
index 00000000..1cff6f79
--- /dev/null
+++ b/pkg/tecdsa/dkls/dkg_test.go
@@ -0,0 +1,73 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/core/curves"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+func testDKG(alice *Alice, bob *Bob, alicePipe *pipeWrapper, bobPipe *pipeWrapper) error {
+	errors := make(chan error, 2)
+
+	go func() {
+		errors <- alice.DKG(alicePipe)
+	}()
+	go func() {
+		errors <- bob.DKG(bobPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		if err := <-errors; err != nil {
+			return err // leakage? what if the second goroutine is "suspended"?
+		}
+	}
+	return verifyOt(alice, bob)
+}
+
+func TestDKG(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.Nil(t, err)
+	alice := NewAlice(params)
+	bob := NewBob(params)
+
+	alicePipe, bobPipe := NewPipeWrappers()
+	require.Nil(t, testDKG(alice, bob, alicePipe, bobPipe))
+}
+
+func BenchmarkDKG(b *testing.B) {
+	if testing.Short() {
+		b.SkipNow()
+	}
+
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.Nil(b, err)
+	alice := NewAlice(params)
+	bob := NewBob(params)
+	b.ResetTimer()
+	bytes := 0
+	for n := 0; n < b.N; n++ {
+		alicePipe, bobPipe := NewPipeWrappers()
+		require.Nil(b, testDKG(alice, bob, alicePipe, bobPipe))
+		bytes += alicePipe.exchanged
+	}
+	b.ReportMetric(float64(bytes)/float64(b.N), "bytes/op")
+}
+
+// Verify correctness of the OT subprotocol after DKG has completed
+func verifyOt(alice *Alice, bob *Bob) error {
+	for i := 0; i < kappa; i++ {
+		if alice.Receiver.Rho[i] != bob.Sender.Rho[i][alice.Receiver.choice[i]] {
+			return fmt.Errorf("oblivious transfer is incorrect at index i=%v", i)
+		}
+	}
+	return nil
+}
diff --git a/pkg/tecdsa/dkls/doc.go b/pkg/tecdsa/dkls/doc.go
new file mode 100644
index 00000000..a1a2e138
--- /dev/null
+++ b/pkg/tecdsa/dkls/doc.go
@@ -0,0 +1,13 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Package dkls implements the 2-of-2 threshold ECDSA signing algorithm of
+// [Doerner, Kondi, Lee, and shelat](https://eprint.iacr.org/2018/499).
+// For an example of use, look at sign.go.
+//
+// It is currently a work in progress; do not use it in real-life scenarios yet.
+// TODO: Docs to be completed.
+package dkls
diff --git a/pkg/tecdsa/dkls/multiply.go b/pkg/tecdsa/dkls/multiply.go
new file mode 100644
index 00000000..63ae8891
--- /dev/null
+++ b/pkg/tecdsa/dkls/multiply.go
@@ -0,0 +1,172 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/rand"
+	"crypto/subtle"
+	"io"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+)
+
+// this implements the _coalesced_ multiplication, in which Alice and Bob perform 2 "parallel" multiplication protocols
+// they wind up with additive sharings of the respective two products.
+
+type MultiplySender struct {
+	sender *cOTSender
+	TA     []*big.Int
+
+	multiplicity int
+}
+
+type MultiplyReceiver struct {
+	receiver *cOTReceiver
+	TB       []*big.Int
+
+	omega        []byte // stashing this here, though ironically the cOT doesn't need to stash it.
+	multiplicity int
+}
+
+func NewMultiplySender(multiplicity int, receiver *seedOTReceiver) *MultiplySender {
+	sender := newCOTSender(multiplicity, receiver)
+	return &MultiplySender{
+		sender:       sender,
+		TA:           make([]*big.Int, multiplicity),
+		multiplicity: multiplicity,
+	}
+}
+
+func NewMultiplyReceiver(multiplicity int, sender *seedOTSender) *MultiplyReceiver {
+	receiver := newCOTReceiver(multiplicity, sender)
+	return &MultiplyReceiver{
+		receiver:     receiver,
+		TB:           make([]*big.Int, multiplicity),
+		multiplicity: multiplicity,
+	}
+}
+
+// Algorithm 5. in DKLs. this "encodes" Bob's secret input scalars `beta` in the right way, using the opts.
+// the idea is that if Bob were to just put beta's as the choice vector, then Alice could learn a few of Bob's bits.
+// using selective failure attacks. so you subtract random components of a public random vector. see paper for details.
+// note that we're using the optimization now where both multiplications get "coalesced".
+func (receiver *MultiplyReceiver) encode(beta []*big.Int) ([]byte, error) {
+	// passing beta by value, so that we can mutate it locally. check that this does what i want.
+	bytes := make([][]byte, receiver.multiplicity)
+	params := receiver.receiver.sender.params
+	result := make([]byte, receiver.receiver.l>>3)
+	for i := 0; i < receiver.multiplicity; i++ {
+		bytes[i] = params.Scalar.Bytes(beta[i])
+		if _, err := rand.Read(result[(1+i*2)*kappa>>3 : (2+i*2)*kappa>>3]); err != nil {
+			return nil, err
+		}
+	}
+	if _, err := rand.Read(result[2*receiver.multiplicity*kappa>>3 : (2*receiver.multiplicity*kappa+s)>>3]); err != nil {
+		return nil, err
+	}
+	for i := 0; i < receiver.multiplicity; i++ {
+		for j := 0; j < kappa; j++ {
+			bit := int(result[((1+2*i)*kappa+j)>>3]) >> (j & 0x07) & 0x01
+			mask := params.Scalar.Bytes(params.Scalar.Sub(new(big.Int).SetBytes(bytes[i][:]), params.gadget[kappa+j]))
+			subtle.ConstantTimeCopy(bit, bytes[i][:], mask)
+		}
+		// some converting from bytes and back. a bit cumbersome, but in practice this will be negligible
+		// it'd be simpler to just keep running big ints, which we are subtracting from.
+		// but we can only `ConstantTimeCopy` byte slices (as opposed to big ints). so keep them as bytes.
+		for j := 0; j < 2*s; j++ {
+			bit := int(result[(2*receiver.multiplicity*kappa+j)>>3]) >> (j & 0x07) & 0x01
+			mask := params.Scalar.Bytes(params.Scalar.Sub(new(big.Int).SetBytes(bytes[i][:]), params.gadget[2*kappa+j]))
+			subtle.ConstantTimeCopy(bit, bytes[i][:], mask)
+		}
+		copy(result[2*i*kappa>>3:(2*i+1)*kappa>>3], internal.ReverseScalarBytes(bytes[i][:]))
+	}
+	return result, nil
+}
+
+// MultiplyInit Protocol 5., Multiplication, 3). Bob (receiver) encodes beta and initiates the cOT extension!
+func (receiver *MultiplyReceiver) MultiplyInit(idExt [32]byte, beta []*big.Int, w io.Writer) error {
+	var err error
+	if receiver.omega, err = receiver.encode(beta); err != nil {
+		return err
+	}
+	return receiver.receiver.init(idExt, receiver.omega, w)
+}
+
+// Multiply Protocol 5., steps 3) 5), 7). Alice _responds_ to Bob's initial cOT message, using a vector of alphas as input.
+// doesn't actually send that message yet, only stashes it, and moves onto the next steps of the multiplication protocol
+// specifically, Alice can then do step 5) (compute the outputs of the multiplication protocol), also stashes this.
+// finishes up by taking care of 7), after that, Alice is totally done with multiplication and has stashed the outputs.
+func (sender *MultiplySender) Multiply(idExt [32]byte, alpha []*big.Int, rw io.ReadWriter) error {
+	inputMain := make([]*big.Int, 2*sender.multiplicity*kappa)
+	inputOT := [2 * s][]*big.Int{} // inputOT := [2 * s][2 * sender.multiplicity]*big.Int{}
+	for i := range inputOT {
+		inputOT[i] = make([]*big.Int, sender.multiplicity)
+	}
+	var err error
+	params := sender.sender.receiver.params
+	for i := 0; i < sender.multiplicity; i++ {
+		for j := 0; j < 2*kappa; j++ {
+			inputMain[kappa*2*i+j] = params.Scalar.Mul(params.gadget[j], alpha[i])
+		}
+		for j := 0; j < 2*s; j++ {
+			inputOT[j][i] = params.Scalar.Mul(params.gadget[j+2*kappa], alpha[i])
+		}
+	}
+	if err = sender.sender.transfer(idExt, inputMain, inputOT, rw); err != nil {
+		return err
+	}
+
+	scalar := sender.sender.receiver.params.Scalar // stash this just to shorten the expressions
+	for i := 0; i < sender.multiplicity; i++ {
+		sender.TA[i] = new(big.Int)
+		for j := 0; j < 2*kappa; j++ {
+			sender.TA[i] = scalar.Add(sender.TA[i], sender.sender.tA[2*kappa*i+j])
+		}
+	}
+	for i := 0; i < 2*s; i++ {
+		for j := 0; j < sender.multiplicity; j++ {
+			sender.TA[j] = scalar.Add(sender.TA[j], sender.sender.tAOT[i][j])
+		}
+	}
+	return nil
+}
+
+// MultiplyTransfer Protocol 5., Multiplication, 3) and 6). Bob finalizes the cOT extension.
+// using that and Alice's multiplication message, Bob completes the multiplication protocol, including checks.
+// at the end, Bob's values tB_j are populated.
+func (receiver *MultiplyReceiver) MultiplyTransfer(r io.Reader) error {
+	if err := receiver.receiver.transfer(r); err != nil {
+		return err
+	}
+	scalar := receiver.receiver.sender.params.Scalar
+	for i := 0; i < receiver.multiplicity; i++ {
+		receiver.TB[i] = new(big.Int)
+		for j := 0; j < 2*kappa; j++ {
+			receiver.TB[i] = scalar.Add(receiver.TB[i], receiver.receiver.tB[2*kappa*i+j])
+		}
+	}
+	for i := 0; i < 2*s; i++ {
+		for j := 0; j < receiver.multiplicity; j++ {
+			receiver.TB[j] = scalar.Add(receiver.TB[j], receiver.receiver.tBOT[i][j])
+		}
+	}
+	return nil
+}
+
+// illustrative helper method which goes through the whole flow for Bob, assuming a channel to pass messages through.
+func (receiver *MultiplyReceiver) multiply(idExt [32]byte, beta []*big.Int, rw io.ReadWriter) error {
+	if err := receiver.MultiplyInit(idExt, beta, rw); err != nil {
+		return err
+	}
+	return receiver.MultiplyTransfer(rw)
+}
+
+// illustrative helper method which goes through the whole flow for Alice, assuming a channel.
+func (sender *MultiplySender) multiply(idExt [32]byte, alpha []*big.Int, rw io.ReadWriter) error {
+	return sender.Multiply(idExt, alpha, rw)
+}
diff --git a/pkg/tecdsa/dkls/multiply_test.go b/pkg/tecdsa/dkls/multiply_test.go
new file mode 100644
index 00000000..dcd68ffe
--- /dev/null
+++ b/pkg/tecdsa/dkls/multiply_test.go
@@ -0,0 +1,66 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+func TestMultiply(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.Nil(t, err)
+	const multiplicity = 2
+	sender := NewMultiplySender(multiplicity, &seedOTReceiver{params: params})
+	receiver := NewMultiplyReceiver(multiplicity, &seedOTSender{params: params})
+
+	senderPipe, receiverPipe := NewPipeWrappers()
+	errors := make(chan error, 2) // warning: if one party errors, the other will sit there forever. add timeouts.
+	go func() {
+		errors <- sender.sender.receiver.kosSetup(senderPipe)
+	}()
+	go func() {
+		errors <- receiver.receiver.sender.kosSetup(receiverPipe)
+	}()
+	// warning: will these goroutines above "leak" if one errors and the other is waiting?
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errors)
+	}
+	for i := 0; i < kappa; i++ {
+		require.Equal(t, sender.sender.receiver.Rho[i], receiver.receiver.sender.Rho[i][sender.sender.receiver.choice[i]])
+	}
+	alpha := [multiplicity]*big.Int{}
+	beta := [multiplicity]*big.Int{}
+	for i := 0; i < multiplicity; i++ {
+		alpha[i], err = params.Scalar.Random()
+		require.Nil(t, err)
+		beta[i], err = params.Scalar.Random()
+		require.Nil(t, err)
+	}
+	idExt := [32]byte{}
+	_, err = rand.Read(idExt[:])
+	require.Nil(t, err)
+	go func() {
+		errors <- sender.multiply(idExt, alpha[:], senderPipe)
+	}()
+	go func() {
+		errors <- receiver.multiply(idExt, beta[:], receiverPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errors)
+	}
+	for i := 0; i < multiplicity; i++ {
+		product := params.Scalar.Mul(alpha[i], beta[i])
+		sum := params.Scalar.Add(sender.TA[i], receiver.TB[i])
+		require.Zero(t, product.Cmp(sum))
+	}
+}
diff --git a/pkg/tecdsa/dkls/ot.go b/pkg/tecdsa/dkls/ot.go
new file mode 100644
index 00000000..3077ca22
--- /dev/null
+++ b/pkg/tecdsa/dkls/ot.go
@@ -0,0 +1,534 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"crypto/subtle"
+	"encoding/gob"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+type (
+	seedOtVerification = [kappa][32]byte
+	seedOtFinal        = [kappa][2][32]byte
+	seedOtTransfer     = [kappa]*curves.EcPoint
+)
+
+// seedOTSender stores state for the "sender" role in seed OT. see Protocol 7 in Appendix A of DKLs
+type seedOTSender struct {
+	// Exported fields are marshaled
+	Rho seedOtFinal // this will store the (vectorized) outputs of kappa executions of (random) seed OT.
+
+	// Intermediate values that should not be marshaled
+	params *Params
+	b      *big.Int        // discrete log of B, which will be (re)used in _all_ executions of the seed OT.
+	pub    *curves.EcPoint // the public key of b.
+}
+
+// seedOTReceiver stores state for the "receiver" role in seed OT. Protocol 7, Appendix A, of DKLs.
+type seedOTReceiver struct {
+	// Exported fields are marshaled
+	Packed [kappa >> 3]byte   // a packed version of the above vector; used later during cOT for performance reasons
+	Rho    seedOtVerification // output of seed OT. for the receiver, there is just 1 output per execution
+
+	// Unexported fields don't get marshaled
+	params *Params
+	choice []int              // choice vector represented as compact binary array. Initialed from Packed
+	pub    *curves.EcPoint    // i guess this is "B".
+	xi     seedOtVerification // basically this just has to be kept between rounds for checking purposes, but won't be used outside
+}
+
+func (sender *seedOTSender) pubKey(w io.Writer) error {
+	// returns pub, as well as the schnorr proof. serialized / packed.
+	// since the return type here is exactly the same as DKG datatype, i am going to cheat and reuse that one.
+	enc := gob.NewEncoder(w)
+	var err error // https://github.com/golang/go/issues/6842
+	if sender.b, err = sender.params.Scalar.Random(); err != nil {
+		return err
+	}
+	if sender.pub, err = curves.NewScalarBaseMult(sender.params.Curve, sender.b); err != nil {
+		return err
+	}
+	proof := &Schnorr{params: sender.params, Pub: sender.pub}
+	if err = proof.Prove(sender.b); err != nil {
+		return err
+	}
+	if err = enc.Encode(proof); err != nil {
+		return err
+	}
+	if sender.pub.Y, err = core.Neg(sender.pub.Y, sender.params.Curve.Params().P); err != nil { // using Weierstrass
+		return err
+	}
+	// ^^^ this is basically a trick, we will only "use" B (i.e., pub) from this point forward by subtracting it from A
+	// so just do the negation once and then we can just "add" B from this point forward.
+	return err
+}
+
+func (receiver *seedOTReceiver) pubKey(r io.Reader) error {
+	dec := gob.NewDecoder(r)
+	var err error
+	input := &Schnorr{params: receiver.params}
+	if err = dec.Decode(input); err != nil {
+		return err
+	}
+	receiver.pub = input.Pub
+	if err = input.Verify(); err != nil {
+		return err
+	}
+	return nil
+}
+
+// Initializes the choice array from the Packed array
+func (receiver *seedOTReceiver) initChoice() {
+	// unpack the random values in Packed into bits in Choice
+	receiver.choice = make([]int, kappa)
+	for i := 0; i < len(receiver.choice); i++ {
+		receiver.choice[i] = int(receiver.Packed[i>>3] >> (i & 0x07) & 0x01)
+	}
+}
+
+// padTransfer this is the receiver's "Pad Transfer" phase in seed OT; see p. 16 of https://eprint.iacr.org/2018/499.pdf.
+// note that we "vectorize" this kappa times; all kappa executions are blocked in this function.
+// any error returned by this function will come from "below", as opposed to from this function.
+func (receiver *seedOTReceiver) padTransfer(w io.Writer) error {
+	enc := gob.NewEncoder(w)
+	// fill the seed OT choice vector with random bytes.
+	if _, err := rand.Read(receiver.Packed[:]); err != nil {
+		return err
+	}
+	// And unpack into Choice bits
+	receiver.initChoice()
+
+	result := &[kappa]*curves.EcPoint{}
+	for i := 0; i < kappa; i++ {
+		a, err := receiver.params.Scalar.Random()
+		if err != nil {
+			return err
+		}
+		if result[i], err = curves.NewScalarBaseMult(receiver.params.Curve, a); err != nil {
+			return err
+		}
+		temp := result[i].Bytes()
+		if result[i], err = result[i].Add(receiver.pub); err != nil {
+			return err
+		}
+		mask := result[i].Bytes()
+		subtle.ConstantTimeCopy(receiver.choice[i], temp, mask)
+		if result[i], err = curves.PointFromBytesUncompressed(receiver.params.Curve, temp); err != nil {
+			return err
+		}
+		rho, err := receiver.pub.ScalarMult(a)
+		if err != nil {
+			return err
+		}
+		receiver.Rho[i] = sha256.Sum256(append(rho.Bytes(), byte(i))) // check whether this cuts it as a "nonce"
+	}
+	return enc.Encode(result)
+}
+
+func (sender *seedOTSender) padTransfer(rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	// returns the challenges xi, concated into a block.
+	input := &seedOtTransfer{}
+	if err := dec.Decode(input); err != nil {
+		return err
+	}
+	result := &seedOtVerification{}
+
+	for i := 0; i < kappa; i++ {
+		d, err := input[i].ScalarMult(sender.b)
+		if err != nil {
+			return err
+		}
+		sender.Rho[i][0] = sha256.Sum256(append(d.Bytes(), byte(i)))
+		if input[i], err = input[i].Add(sender.pub); err != nil {
+			return err
+		} // caution: overwrite
+		d, err = input[i].ScalarMult(sender.b)
+		if err != nil {
+			return err
+		}
+		sender.Rho[i][1] = sha256.Sum256(append(d.Bytes(), byte(i)))
+		temp0 := sha256.Sum256(sender.Rho[i][0][:])
+		temp0 = sha256.Sum256(temp0[:])
+		temp1 := sha256.Sum256(sender.Rho[i][1][:])
+		temp1 = sha256.Sum256(temp1[:])
+		for j := 0; j < 32; j++ {
+			result[i][j] = temp0[j] ^ temp1[j]
+		}
+	}
+	return enc.Encode(result)
+}
+
+// verification corresponds to initial round of the receiver's "Verification" phase, see p. 16. cf. also "final" below.
+// this is just the start of verification—in this round, the receiver outputs "rho'", which the sender will check.
+func (receiver *seedOTReceiver) verification(rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	if err := dec.Decode(&receiver.xi); err != nil {
+		return err
+	}
+	result := &seedOtVerification{}
+	for i := 0; i < kappa; i++ {
+		temp0 := sha256.Sum256(receiver.Rho[i][:])
+		temp0 = sha256.Sum256(temp0[:])
+		temp1 := [32]byte{}
+		for j := 0; j < 32; j++ {
+			temp1[j] = receiver.xi[i][j] ^ temp0[j]
+		}
+		subtle.ConstantTimeCopy(receiver.choice[i], temp0[:], temp1[:])
+		copy(result[i][:], temp0[:])
+	}
+	return enc.Encode(result) // this is "rho'", all in a block.
+}
+
+func (sender *seedOTSender) verification(rw io.ReadWriter) error {
+	// message is rho'. returns H(rho^0) || H(rho^1)
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	input := &seedOtVerification{}
+	if err := dec.Decode(&input); err != nil {
+		return err
+	}
+	result := &seedOtFinal{}
+	for i := 0; i < kappa; i++ {
+		temp0 := sha256.Sum256(sender.Rho[i][0][:])
+		temp1 := sha256.Sum256(temp0[:])
+		if subtle.ConstantTimeCompare(temp1[:], input[i][:]) != 1 {
+			return fmt.Errorf("receiver's challenge response didn't match H(H(rho^0))")
+		}
+		temp2 := sha256.Sum256(sender.Rho[i][1][:])
+		copy(result[i][0][:], temp0[:])
+		copy(result[i][1][:], temp2[:])
+	}
+	return enc.Encode(result)
+}
+
+// final this is the _last_ part of the "Verification" phase of seed OT; see p. 16 of https://eprint.iacr.org/2018/499.pdf.
+// message is (supposedly) the concatenation of all kappa `H(rho^0) || H(rho^1)`s; we will check them ourselves.
+func (receiver *seedOTReceiver) final(r io.Reader) error {
+	dec := gob.NewDecoder(r)
+	input := &seedOtFinal{}
+	if err := dec.Decode(&input); err != nil {
+		return err
+	}
+	for i := 0; i < kappa; i++ {
+		temp0 := sha256.Sum256(receiver.Rho[i][:])
+		temp1 := [32]byte{}
+		subtle.ConstantTimeCopy(1-receiver.choice[i], temp1[:], input[i][0][:])
+		subtle.ConstantTimeCopy(receiver.choice[i], temp1[:], input[i][1][:])
+		if subtle.ConstantTimeCompare(temp0[:], temp1[:]) != 1 {
+			return fmt.Errorf("sender's supposed H(rho^omega) doesn't match our own")
+		}
+		temp0 = sha256.Sum256(input[i][0][:])
+		temp1 = sha256.Sum256(input[i][1][:])
+		for j := 0; j < 32; j++ {
+			temp0[j] ^= temp1[j]
+		}
+		if subtle.ConstantTimeCompare(temp0[:], receiver.xi[i][:]) != 1 {
+			return fmt.Errorf("sender's openings H(rho^0) and H(rho^1) didn't decommit to its prior message xi")
+		}
+	}
+	return nil
+}
+
+func (receiver *seedOTReceiver) kosSetup(rw io.ReadWriter) error {
+	// this is an illustrative high-level helper method which goes through the full flow of the KOS seed OT protocol.
+	// all it does it call all the right stages in the right order, and send and receive the messages to the other party
+	if err := receiver.pubKey(rw); err != nil {
+		return err
+	}
+	if err := receiver.padTransfer(rw); err != nil {
+		return err
+	}
+	if err := receiver.verification(rw); err != nil {
+		return err
+	}
+	return receiver.final(rw)
+}
+
+func (sender *seedOTSender) kosSetup(rw io.ReadWriter) error {
+	// again a high-level helper method showing the overall flow, this time for the sender.
+	if err := sender.pubKey(rw); err != nil {
+		return err
+	}
+	if err := sender.padTransfer(rw); err != nil {
+		return err
+	}
+	return sender.verification(rw)
+}
+
+type cOTReceiver struct {
+	sender       *seedOTSender      // kinda-sorta reversed?!?
+	w            []byte             // storage for choice vector || gamma^{ext}, packed.
+	psi          [][kappa >> 3]byte // transpose of v^0. gets retained between messages
+	tB           []*big.Int         // [2 * Multiplicity]*big.Int
+	tBOT         [2 * s][]*big.Int  // [2 * s][Multiplicity]*big.Int
+	l            int
+	lPrime       int
+	multiplicity int
+}
+
+type cOTSender struct {
+	receiver     *seedOTReceiver   // kinda-sorta reversed?!?
+	tA           []*big.Int        // ultimate output received. basically just the "pads"
+	tAOT         [2 * s][]*big.Int // [2 * s][Multiplicity]*big.Int
+	l            int
+	lPrime       int
+	multiplicity int
+}
+
+func newCOTReceiver(multiplicity int, sender *seedOTSender) *cOTReceiver {
+	l := 2*multiplicity*kappa + 2*s
+	lPrime := l + kappaOT
+	var tBOT [2 * s][]*big.Int
+	for i := 0; i < 2*s; i++ {
+		tBOT[i] = make([]*big.Int, multiplicity)
+	}
+	return &cOTReceiver{
+		sender:       sender,
+		w:            make([]byte, lPrime>>3),
+		psi:          make([][kappa >> 3]byte, lPrime),
+		tB:           make([]*big.Int, 2*kappa*multiplicity),
+		tBOT:         tBOT,
+		l:            l,
+		lPrime:       lPrime,
+		multiplicity: multiplicity,
+	}
+}
+
+func newCOTSender(multiplicity int, receiver *seedOTReceiver) *cOTSender {
+	l := 2*multiplicity*kappa + 2*s
+	lPrime := l + kappaOT
+	var tAOT [2 * s][]*big.Int
+	for i := 0; i < 2*s; i++ {
+		tAOT[i] = make([]*big.Int, multiplicity)
+	}
+	return &cOTSender{
+		receiver:     receiver,
+		tA:           make([]*big.Int, 2*kappa*multiplicity),
+		tAOT:         tAOT,
+		l:            l,
+		lPrime:       lPrime,
+		multiplicity: multiplicity,
+	}
+}
+
+type cOTInitStorage struct {
+	WPrime [32]byte
+	VPrime [32]byte
+	U      [kappa][]byte
+}
+
+type cOTStorage struct {
+	TauMain []*big.Int
+	TauOT   [2 * s][]*big.Int
+}
+
+func (receiver *cOTReceiver) init(idExt [32]byte, choice []byte, w io.Writer) error {
+	// input choice vector is "packed".
+	copy(receiver.w[0:receiver.l>>3], choice[:])                     // write the input choice vector into our local data.
+	if _, err := rand.Read(receiver.w[receiver.l>>3:]); err != nil { // fill the rest with random bytes; this is "gamma^{ext}"
+		return err
+	}
+	hash := sha256.New()    // basically this will contain a hash of the matrix U.
+	v := [2][kappa][]byte{} // kappa * l array of _bits_, in "dense" form. contains _both_ v_0 and v_1.
+	for i := 0; i < 2; i++ {
+		for j := 0; j < kappa; j++ {
+			v[i][j] = make([]byte, receiver.lPrime>>3) // annoying
+		}
+	}
+	result := &cOTInitStorage{}
+	enc := gob.NewEncoder(w)
+	for i := 0; i < kappa; i++ {
+		result.U[i] = make([]byte, receiver.lPrime>>3)
+	}
+	hash.Reset()
+	for i := 0; i < kappa; i++ {
+		for j := 0; j < 2; j++ {
+			row, err := core.ExpandMessageXmd(sha256.New, receiver.sender.Rho[i][j][:], idExt[:], receiver.lPrime>>3)
+			if err != nil {
+				return err
+			}
+			// this is the core pseudorandom expansion of the secret OT input seeds s_i^0 and s_i^1
+			// see Extension, 2), in Protocol 9, page 17 of DKLs https://eprint.iacr.org/2018/499.pdf
+			// use the idExt as the "domain separator", and the _secret_ seed rho as the input!
+			copy(v[j][i][:], row) // could easily use a shake3 and "Read" it directly in.
+		}
+		for j := 0; j < receiver.lPrime>>3; j++ {
+			result.U[i][j] = v[0][i][j] ^ v[1][i][j] ^ receiver.w[j]
+			// U := v_i^0 ^ v_i^1 ^ w. note: in step 4) of Prot. 9, i think `w` should be bolded?
+			for k := 0; k < 8; k++ {
+				receiver.psi[j<<3+k][i>>3] |= v[0][i][j] >> k & 0x01 << (i & 0x07)
+				// this is fairly tricky. basically, this is assigning psi to be the transpose of the boolean matrix v_0.
+				// but because both matrices are densely packed (represented as bytes), we have to do some bitwise tricks.
+			}
+		}
+		if _, err := hash.Write(result.U[i][:]); err != nil {
+			return err
+		}
+	}
+	digest := hash.Sum(nil) // go ahead and record this, so that we only have to hash the big matrix U once.
+	for j := 0; j < receiver.lPrime; j++ {
+		chiJ := sha256.Sum256(append(digest, byte(j&0x07), byte(j>>3))) // represent j = (j % 8, j // 8) as 2 bytes.
+		wJ := receiver.w[j>>3] >> (j & 0x07) & 0x01                     // extract j^th bit from vector of bytes w.
+		wJ = ^(wJ - 0x01)                                               // convert it into a bitmask (all 1s if true, all 0s if false).
+		for k := 0; k < kappa>>3; k++ {
+			result.WPrime[k] ^= wJ & chiJ[k]
+			result.VPrime[k] ^= receiver.psi[j][k] & chiJ[k]
+		}
+	}
+	// result is the concatenation of WPrime, VPrime, then the entire matrix U (row-flattened).
+	return enc.Encode(result)
+}
+
+func (sender *cOTSender) transfer(idExt [32]byte, inputMain []*big.Int, inputOT [2 * s][]*big.Int, rw io.ReadWriter) error {
+	// input message: Bob's values WPrime, VPrime, and U. output: tau.
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	input := &cOTInitStorage{}
+	if err := dec.Decode(input); err != nil {
+		return err
+	}
+	z := [kappa][]byte{}
+	for i := 0; i < kappa; i++ {
+		z[i] = make([]byte, sender.lPrime>>3)
+	}
+	zeta := make([][kappa >> 3]byte, sender.lPrime)
+	hash := sha256.New() // basically this will contain a hash of the matrix U.
+
+	// Unpack the random bytes in Packed into the choice array in the receiver
+	sender.receiver.initChoice()
+
+	for i := 0; i < kappa; i++ {
+		row, err := core.ExpandMessageXmd(sha256.New, sender.receiver.Rho[i][:], idExt[:], sender.lPrime>>3)
+		if err != nil {
+			return err
+		}
+		// use the idExt as the domain separator, and the _secret_ seed rho as the input!
+		v := make([]byte, sender.lPrime>>3) // we only need to retain one row of v at a time.
+		copy(v[:], row)
+		mask := byte(^(sender.receiver.choice[i] - 1))
+		for j := 0; j < sender.lPrime>>3; j++ {
+			z[i][j] = v[j] ^ mask&input.U[i][j]
+			// U := v_i^0 ^ v_i^1 ^ w. note: in step 4) of Prot. 9, i think `w` should be bolded?
+			for k := 0; k < 8; k++ {
+				zeta[j<<3+k][i>>3] |= z[i][j] >> k & 0x01 << (i & 0x07)
+				// assigning to zeta the matrix transposition of z. see notes above.
+			}
+		}
+		if _, err = hash.Write(input.U[i][:]); err != nil {
+			return err
+		}
+	}
+	digest := hash.Sum(nil) // go ahead and record this, so that we only have to hash the big matrix U once.
+	zPrime := [32]byte{}
+	for j := 0; j < sender.lPrime; j++ {
+		chiJ := sha256.Sum256(append(digest, byte(j&0x07), byte(j>>3))) // represent j = (j % 8, j // 8) as 2 bytes.
+		for k := 0; k < kappa>>3; k++ {
+			zPrime[k] ^= zeta[j][k] & chiJ[k]
+		}
+	}
+	rhs := [32]byte{}
+	for i := 0; i < 32; i++ {
+		rhs[i] = input.VPrime[i] ^ sender.receiver.Packed[i]&input.WPrime[i]
+	}
+	if subtle.ConstantTimeCompare(zPrime[:], rhs[:]) != 1 {
+		return fmt.Errorf("receiver's initial cOT message failed to verify")
+	}
+	result := &cOTStorage{}
+	result.TauMain = make([]*big.Int, 2*kappa*sender.multiplicity)
+	for j := 0; j < 2*kappa*sender.multiplicity; j++ {
+		column := sha256.Sum256(append(zeta[j][:], byte(j&0x07), byte(j>>3)))
+		sender.tA[j] = new(big.Int).SetBytes(column[:]) // not bothering to mod this. shouldn't be necessary.
+		for i := 0; i < 32; i++ {
+			zeta[j][i] ^= sender.receiver.Packed[i] // warning: overwrites zeta_j!!!!!! just using it as a place to store
+		}
+		column = sha256.Sum256(append(zeta[j][:], byte(j&0x07), byte(j>>3)))
+		result.TauMain[j] = new(big.Int).SetBytes(column[:])
+		result.TauMain[j] = sender.receiver.params.Scalar.Sub(result.TauMain[j], sender.tA[j])
+		result.TauMain[j] = sender.receiver.params.Scalar.Add(result.TauMain[j], inputMain[j])
+	}
+	length := 32 * sender.multiplicity
+	for j := 0; j < 2*s; j++ {
+		result.TauOT[j] = make([]*big.Int, sender.multiplicity)
+		column, err := core.ExpandMessageXmd(sha256.New, append(zeta[2*kappa*sender.multiplicity+j][:], byte(j&0x07), byte(j>>3)), []byte("Coinbase_tECDSA"), length)
+		if err != nil {
+			return err
+		}
+		for k := 0; k < sender.multiplicity; k++ {
+			sender.tAOT[j][k] = new(big.Int).SetBytes(column[k*32 : (k+1)*32]) // not bothering to mod this. shouldn't be necessary.
+		}
+		for i := 0; i < 32; i++ {
+			zeta[2*kappa*sender.multiplicity+j][i] ^= sender.receiver.Packed[i] // warning: overwrites zeta_j!!!!!! just using it as a place to store
+		}
+		column, err = core.ExpandMessageXmd(sha256.New, append(zeta[2*kappa*sender.multiplicity+j][:], byte(j&0x07), byte(j>>3)), []byte("Coinbase_tECDSA"), length)
+		if err != nil {
+			return err
+		}
+		for k := 0; k < sender.multiplicity; k++ {
+			result.TauOT[j][k] = new(big.Int).SetBytes(column[k*32 : (k+1)*32])
+			result.TauOT[j][k] = sender.receiver.params.Scalar.Sub(result.TauOT[j][k], sender.tAOT[j][k])
+			result.TauOT[j][k] = sender.receiver.params.Scalar.Add(result.TauOT[j][k], inputOT[j][k])
+		}
+	}
+	return enc.Encode(result)
+}
+
+func (receiver *cOTReceiver) transfer(r io.Reader) error {
+	dec := gob.NewDecoder(r)
+	input := &cOTStorage{}
+	if err := dec.Decode(input); err != nil {
+		return err
+	}
+	for j := 0; j < 2*kappa*receiver.multiplicity; j++ {
+		column := sha256.Sum256(append(receiver.psi[j][:], byte(j&0x07), byte(j>>3)))
+		bit := int(receiver.w[j>>3]) >> (j & 0x07) & 0x01
+		receiver.tB[j] = new(big.Int).SetBytes(column[:])
+		receiver.tB[j] = receiver.sender.params.Scalar.Neg(receiver.tB[j])
+		wj0 := receiver.sender.params.Scalar.Bytes(receiver.tB[j])
+		wj1 := receiver.sender.params.Scalar.Bytes(receiver.sender.params.Scalar.Add(receiver.tB[j], input.TauMain[j]))
+		subtle.ConstantTimeCopy(bit, wj0, wj1)
+		receiver.tB[j].SetBytes(wj0)
+	}
+	length := 32 * receiver.multiplicity
+	for j := 0; j < 2*s; j++ {
+		column, err := core.ExpandMessageXmd(sha256.New, append(receiver.psi[2*kappa*receiver.multiplicity+j][:], byte(j&0x07), byte(j>>3)), []byte("Coinbase_tECDSA"), length)
+		if err != nil {
+			return err
+		}
+		bit := int(receiver.w[(2*kappa*receiver.multiplicity+j)>>3]) >> (j & 0x07) & 0x01
+		for k := 0; k < receiver.multiplicity; k++ {
+			receiver.tBOT[j][k] = new(big.Int).SetBytes(column[k*32 : (k+1)*32])
+			receiver.tBOT[j][k] = receiver.sender.params.Scalar.Neg(receiver.tBOT[j][k])
+			wj0 := receiver.sender.params.Scalar.Bytes(receiver.tBOT[j][k])
+			wj1 := receiver.sender.params.Scalar.Bytes(receiver.sender.params.Scalar.Add(receiver.tBOT[j][k], input.TauOT[j][k]))
+			subtle.ConstantTimeCopy(bit, wj0, wj1)
+			receiver.tBOT[j][k].SetBytes(wj0)
+		}
+	}
+	return nil
+}
+
+func (receiver *cOTReceiver) cOT(idExt [32]byte, choice []byte, rw io.ReadWriter) error {
+	if err := receiver.init(idExt, choice, rw); err != nil {
+		return err
+	}
+	return receiver.transfer(rw)
+}
+
+func (sender *cOTSender) cOT(idExt [32]byte, input []*big.Int, inputOT [2 * s][]*big.Int, rw io.ReadWriter) error {
+	return sender.transfer(idExt, input, inputOT, rw)
+}
diff --git a/pkg/tecdsa/dkls/ot_test.go b/pkg/tecdsa/dkls/ot_test.go
new file mode 100644
index 00000000..bfb1a3a5
--- /dev/null
+++ b/pkg/tecdsa/dkls/ot_test.go
@@ -0,0 +1,112 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/rand"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+func TestSeedOT(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.Nil(t, err)
+	sender := &seedOTSender{params: params}
+	receiver := &seedOTReceiver{params: params}
+
+	senderPipe, receiverPipe := NewPipeWrappers()
+	errors := make(chan error, 2) // warning: if one party errors, the other will sit there forever. add timeouts.
+	go func() {
+		errors <- sender.kosSetup(senderPipe)
+	}()
+	go func() {
+		errors <- receiver.kosSetup(receiverPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errors)
+	}
+	for i := 0; i < kappa; i++ {
+		require.Equal(t, receiver.Rho[i], sender.Rho[i][receiver.choice[i]])
+	}
+}
+
+func TestCOTExtension(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.Nil(t, err)
+	const multiplicity = 2
+	sender := newCOTSender(multiplicity, &seedOTReceiver{params: params})
+	receiver := newCOTReceiver(multiplicity, &seedOTSender{params: params})
+
+	senderPipe, receiverPipe := NewPipeWrappers()
+	errors := make(chan error, 2) // warning: if one party errors, the other will sit there forever. add timeouts.
+	go func() {
+		errors <- receiver.sender.kosSetup(receiverPipe)
+	}()
+	go func() {
+		errors <- sender.receiver.kosSetup(senderPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errors)
+	}
+	for i := 0; i < kappa; i++ {
+		require.Equal(t, sender.receiver.Rho[i], receiver.sender.Rho[i][sender.receiver.choice[i]])
+	}
+	idExt := [32]byte{}
+	_, err = rand.Read(idExt[:])
+	require.Nil(t, err)
+	choice := make([]byte, receiver.l>>3) // Bob's
+	_, err = rand.Read(choice[:])
+	require.Nil(t, err)
+	input := [2 * kappa * multiplicity]*big.Int{} // Alice's
+	inputOT := [2 * s][]*big.Int{}                // Alice's
+	for i := 0; i < 2*s; i++ {
+		inputOT[i] = make([]*big.Int, multiplicity)
+	}
+	for j := 0; j < 2*kappa*multiplicity; j++ {
+		input[j], err = params.Scalar.Random()
+		require.Nil(t, err)
+	}
+	for j := 0; j < 2*s; j++ {
+		for k := 0; k < multiplicity; k++ {
+			inputOT[j][k], err = params.Scalar.Random()
+			require.Nil(t, err)
+		}
+	}
+	go func() {
+		errors <- receiver.cOT(idExt, choice, receiverPipe)
+	}()
+	go func() {
+		errors <- sender.cOT(idExt, input[:], inputOT, senderPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		require.Nil(t, <-errors)
+	}
+	for j := 0; j < 2*kappa*multiplicity; j++ {
+		bit := choice[j>>3]>>(j&0x07)&0x01 == 1
+		temp := params.Scalar.Add(sender.tA[j], receiver.tB[j])
+		if bit {
+			require.Zero(t, temp.Cmp(input[j]))
+		} else {
+			require.Zero(t, temp.Cmp(new(big.Int)))
+		}
+	}
+	for j := 0; j < 2*s; j++ {
+		bit := choice[(2*kappa*multiplicity+j)>>3]>>(j&0x07)&0x01 == 1
+		for k := 0; k < multiplicity; k++ {
+			temp := params.Scalar.Add(sender.tAOT[j][k], receiver.tBOT[j][k])
+			if bit {
+				require.Zero(t, temp.Cmp(inputOT[j][k]))
+			} else {
+				require.Zero(t, temp.Cmp(new(big.Int)))
+			}
+		}
+	}
+}
diff --git a/pkg/tecdsa/dkls/params.go b/pkg/tecdsa/dkls/params.go
new file mode 100644
index 00000000..e307b313
--- /dev/null
+++ b/pkg/tecdsa/dkls/params.go
@@ -0,0 +1,48 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/elliptic"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"golang.org/x/crypto/sha3"
+)
+
+const (
+	kappa   = 256 // Computational security parameter.
+	s       = 80  // statistical security parameter. does this have to be so high?! i've seen 40. // TODO: investigate why 80
+	kappaOT = kappa + s
+)
+
+type Params struct {
+	Curve     elliptic.Curve
+	Scalar    curves.EcScalar
+	Generator *curves.EcPoint
+	gadget    [2*kappa + 2*s]*big.Int
+}
+
+// NewParams receives an implementation of the curve and scalar interfaces and
+// sets the parameters needed for DKG and Threshold ECDSA of DKLS.
+func NewParams(curve elliptic.Curve, scalar curves.EcScalar) (*Params, error) {
+	params := &Params{Curve: curve, Scalar: scalar}
+	params.Generator = &curves.EcPoint{Curve: curve, X: curve.Params().Gx, Y: curve.Params().Gy}
+	for i := 0; i < kappa; i++ {
+		params.gadget[i] = new(big.Int).Lsh(big.NewInt(1), uint(i))
+	}
+	shake := sha3.NewCShake256(nil, []byte("Play as a championship team."))
+	for i := kappa; i < 2*kappa+2*s; i++ {
+		var err error
+		bytes := [32]byte{}
+		if _, err = shake.Read(bytes[:]); err != nil {
+			return nil, err
+		}
+		params.gadget[i] = new(big.Int).SetBytes(bytes[:])
+	}
+	return params, nil
+}
diff --git a/pkg/tecdsa/dkls/proto.go b/pkg/tecdsa/dkls/proto.go
new file mode 100644
index 00000000..d9956663
--- /dev/null
+++ b/pkg/tecdsa/dkls/proto.go
@@ -0,0 +1,305 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"bytes"
+	"encoding/gob"
+	"encoding/json"
+	"fmt"
+	"io"
+
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+type (
+	// ProtocolIterator a generalized interface for multi-party protocols that follows the iterator pattern.
+	ProtocolIterator interface {
+		// Next runs the next round of the protocol.
+		// Inputs are read from rw.Read(); outputs are written to rw.Write().
+		// Returns io.EOF when protocol has completed.
+		Next(rw io.ReadWriter) error
+
+		// Result returns the final result, if any, of the completed protocol.
+		// Reports an error if the protocol has not yet terminated
+		// or if an error was encountered during protocol execution.
+		Result() (interface{}, error)
+
+		// SetDebug enables or disables (passing a nil value as input) debugging.
+		// At the moment, we only print the final dkls dkg result as json value to this log, but if needed more debugging
+		// can be added for various steps of the other protocols.
+		SetDebug(log io.Writer)
+	}
+
+	// Basic protocol interface implementation that calls the next step func in a pre-defined list
+	protoStepper struct {
+		steps []func(rw io.ReadWriter) error
+		step  uint
+		log   io.Writer //nolint:structcheck // This is only used in some of the protocols.
+	}
+
+	// DKG protocols produce the following result on successful completion
+	DkgResult struct {
+		DkgState []byte
+		Pubkey   *curves.EcPoint
+	}
+	// AliceDkg DKLS DKG implementation that satisfies the protocol iterator interface.
+	AliceDkg struct {
+		protoStepper
+		alice *Alice
+	}
+
+	// BobDkg DKLS DKG implementation that satisfies the protocol iterator interface.
+	BobDkg struct {
+		protoStepper
+		bob *Bob
+	}
+
+	// AliceSign DKLS sign implementation that satisfies the protocol iterator interface.
+	AliceSign struct {
+		protoStepper
+		alice *Alice
+	}
+
+	// BobSign DKLS sign implementation that satisfies the protocol iterator interface.
+	BobSign struct {
+		protoStepper
+		bob *Bob
+	}
+)
+
+var (
+	// Static type assertions
+	_ ProtocolIterator = &AliceDkg{}
+	_ ProtocolIterator = &BobDkg{}
+	_ ProtocolIterator = &AliceSign{}
+	_ ProtocolIterator = &BobSign{}
+
+	errProtocolNotComplete = fmt.Errorf("protocol has not completed")
+	errNotInitialized      = fmt.Errorf("object has not been initialized")
+	errNoSig               = fmt.Errorf("dkls.Alice does not produce a signature")
+)
+
+// Reports true if the step index exceeds the number of steps
+func (p *protoStepper) complete() bool { return int(p.step) >= len(p.steps) }
+
+// Next runs the next step in the protocol and reports errors or increments the step index
+func (p *protoStepper) Next(rw io.ReadWriter) error {
+	// Signal EOF if the protocol has completed.
+	if p.complete() {
+		return io.EOF
+	}
+
+	// Run the current protocol step and report any errors
+	if err := p.steps[p.step](rw); err != nil {
+		return err
+	}
+
+	// Increment the step index and report success
+	p.step++
+	return nil
+}
+
+// NewAliceDkg creates a new protocol that can compute a DKG as Alice
+func NewAliceDkg(params *Params) *AliceDkg {
+	a := &AliceDkg{alice: NewAlice(params)}
+	a.steps = []func(rw io.ReadWriter) error{
+		func(rw io.ReadWriter) error { return a.alice.dkgCommit(rw) },
+		a.alice.dkgVerify,
+		func(rw io.ReadWriter) error {
+			if err := a.alice.Receiver.pubKey(rw); err != nil {
+				return err
+			}
+			return a.alice.Receiver.padTransfer(rw)
+		},
+		a.alice.Receiver.verification,
+		func(rw io.ReadWriter) error { return a.alice.Receiver.final(rw) },
+	}
+	return a
+}
+
+// NewBobDkg Creates a new protocol that can compute a DKG as Bob
+func NewBobDkg(params *Params) *BobDkg {
+	b := &BobDkg{bob: NewBob(params)}
+	b.steps = []func(rw io.ReadWriter) error{
+		b.bob.dkgCommit,
+		func(rw io.ReadWriter) error {
+			if err := b.bob.dkgVerify(rw); err != nil {
+				return err
+			}
+			return b.bob.Sender.pubKey(rw)
+		},
+		b.bob.Sender.padTransfer,
+		b.bob.Sender.verification,
+	}
+	return b
+}
+
+func (a *AliceDkg) SetDebug(log io.Writer) {
+	a.log = log
+}
+
+// Result Returns an encoded version of Alice as sequence of bytes that can be used to initialize an AliceSign protocol.
+func (a *AliceDkg) Result() (interface{}, error) {
+	// Sanity check
+	if !a.complete() {
+		return nil, errProtocolNotComplete
+	}
+	if a.alice == nil {
+		return nil, errNotInitialized
+	}
+
+	// Encode DKG state of alice for future signing
+	state, err := EncodeAlice(a.alice)
+	if err != nil {
+		return nil, err
+	}
+
+	result := &DkgResult{
+		DkgState: state,
+		Pubkey:   a.alice.Pk,
+	}
+
+	if a.log != nil {
+		resultBytes, err := json.Marshal(result)
+		if err != nil {
+			_, _ = a.log.Write([]byte(fmt.Sprintf("Error while json marshaling the results: %v", err)))
+		} else {
+			_, _ = a.log.Write([]byte("Alice Dkg result:\n"))
+			_, _ = a.log.Write(resultBytes)
+		}
+	}
+	return result, nil
+}
+
+func (b *BobDkg) SetDebug(log io.Writer) {
+	b.log = log
+}
+
+// Result returns an encoded version of Alice as sequence of bytes that can be used to
+// initialize an AliceSign protocol.
+func (b *BobDkg) Result() (interface{}, error) {
+	// Sanity check
+	if !b.complete() {
+		return nil, errProtocolNotComplete
+	}
+	if b.bob == nil {
+		return nil, errNotInitialized
+	}
+	// Encode DKG state of bob for future signing
+	state, err := EncodeBob(b.bob)
+	if err != nil {
+		return nil, err
+	}
+
+	result := &DkgResult{
+		DkgState: state,
+		Pubkey:   b.bob.Pk,
+	}
+	if b.log != nil {
+		resultBytes, err := json.Marshal(result)
+		if err != nil {
+			_, _ = b.log.Write([]byte(fmt.Sprintf("Error while json marshaling the results: %v", err)))
+		} else {
+			_, _ = b.log.Write([]byte("Alice Dkg result:\n"))
+			_, _ = b.log.Write(resultBytes)
+		}
+	}
+	return result, nil
+}
+
+// Creates a new protocol that can compute a signature as Alice.
+// Requires dkg state that was produced at the end of DKG.Result().
+func NewAliceSign(params *Params, msg []byte, dkgResult []byte) (*AliceSign, error) {
+	// Reconstitute Alice
+	alice, err := DecodeAlice(params, dkgResult)
+	if err != nil {
+		return nil, err
+	}
+
+	// Configure Alice with her 1 signing step
+	a := &AliceSign{alice: alice}
+	a.steps = []func(rw io.ReadWriter) error{
+		func(rw io.ReadWriter) error { return alice.signInit(msg, rw) },
+	}
+	return a, nil
+}
+
+// NewBobSign creates a new protocol that can compute a signature as Bob.
+// Requires dkg state that was produced at the end of DKG.Result().
+func NewBobSign(params *Params, msg []byte, dkgResult []byte) (*BobSign, error) {
+	// Reconstitute Bob
+	bob, err := DecodeBob(params, dkgResult)
+	if err != nil {
+		return nil, err
+	}
+
+	// Configure Bob with 2 signing steps
+	b := &BobSign{bob: bob}
+	b.steps = []func(rw io.ReadWriter) error{
+		func(rw io.ReadWriter) error { return bob.signInit(rw) },
+		func(rw io.ReadWriter) error { return bob.signFinal(msg, rw) },
+	}
+	return b, nil
+}
+
+func (a *AliceSign) SetDebug(log io.Writer) {
+	a.log = log
+}
+
+// Result always returns errNoSig.
+// Alice does not compute a signature in the DKLS protocol; only Bob computes the signature.
+func (a *AliceSign) Result() (interface{}, error) {
+	return nil, errNoSig
+}
+
+func (b *BobSign) SetDebug(log io.Writer) {
+	b.log = log
+}
+
+// If the signing protocol completed successfully, returns the signature that
+// Bob computed as a *core.EcdsaSignature.
+func (d *BobSign) Result() (interface{}, error) {
+	// We can't produce a signature until the protocol completes
+	if !d.complete() {
+		return nil, errProtocolNotComplete
+	}
+	if d.bob == nil {
+		// Object wasn't created with NewXSign()
+		return nil, errNotInitialized
+
+	}
+	return d.bob.Sig, nil
+}
+
+// Encodes an alice object as a byte sequence after DKG has been completed.
+func EncodeAlice(a *Alice) ([]byte, error) {
+	var buf bytes.Buffer
+	err := gob.NewEncoder(&buf).Encode(a)
+	return buf.Bytes(), err
+}
+
+// Decodes an alice object that was encoded after DKG.
+func DecodeAlice(params *Params, b []byte) (*Alice, error) {
+	alice := NewAlice(params)
+	err := gob.NewDecoder(bytes.NewBuffer(b)).Decode(alice)
+	return alice, err
+}
+
+// Encodes a bob object as a byte sequence after DKG has been completed.
+func EncodeBob(b *Bob) ([]byte, error) {
+	var buf bytes.Buffer
+	err := gob.NewEncoder(&buf).Encode(b)
+	return buf.Bytes(), err
+}
+
+// Decodes an bob object that was encoded after DKG.
+func DecodeBob(params *Params, b []byte) (*Bob, error) {
+	bob := NewBob(params)
+	err := gob.NewDecoder(bytes.NewBuffer(b)).Decode(bob)
+	return bob, err
+}
diff --git a/pkg/tecdsa/dkls/proto_test.go b/pkg/tecdsa/dkls/proto_test.go
new file mode 100644
index 00000000..542b617d
--- /dev/null
+++ b/pkg/tecdsa/dkls/proto_test.go
@@ -0,0 +1,269 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"bytes"
+	"crypto/sha256"
+	"io"
+	"io/ioutil"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+// Runs a DKG on initialized Alice/Bob objects. Reports any errors encountered.
+func iteratedDkg(alice *AliceDkg, bob *BobDkg) (error, error) {
+	var (
+		buf  bytes.Buffer
+		aErr error
+		bErr error
+	)
+
+	for aErr != io.EOF || bErr != io.EOF {
+		// Crank each protocol forward one iteration
+		aErr = alice.Next(&buf)
+		if aErr != nil && aErr != io.EOF {
+			return aErr, nil
+		}
+
+		bErr = bob.Next(&buf)
+		if bErr != nil && bErr != io.EOF {
+			return nil, bErr
+		}
+	}
+	return aErr, bErr
+}
+
+// Runs Sign protocol on initialized alice/bob objects.
+func iteratedSign(alice *AliceSign, bob *BobSign) (error, error) {
+	var (
+		aErr, bErr error
+		buf        bytes.Buffer
+	)
+
+	// Run until both parties complete the protocol
+	for !(aErr == io.EOF && bErr == io.EOF) {
+		aErr = alice.Next(&buf)
+		if !(aErr == nil || aErr == io.EOF) {
+			break
+		}
+
+		bErr = bob.Next(&buf)
+		if !(bErr == nil || bErr == io.EOF) {
+			break
+		}
+	}
+	return aErr, bErr
+}
+
+// Running steps in sequence ensures that no hidden read/write dependency exist in the read/write interfaces.
+func TestDkgProto(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.K256Scalar{})
+	require.NoError(t, err)
+
+	alice := NewAliceDkg(params)
+	bob := NewBobDkg(params)
+	aErr, bErr := iteratedDkg(alice, bob)
+
+	t.Run("both alice/bob complete simultaneously", func(t *testing.T) {
+		require.ErrorIs(t, aErr, io.EOF)
+		require.ErrorIs(t, bErr, io.EOF)
+	})
+
+	t.Run("OT results are correct", func(t *testing.T) {
+		assert.NoError(t, verifyOt(alice.alice, bob.bob))
+	})
+
+	t.Run("Both parties produces identical composite pubkey", func(t *testing.T) {
+		assert.Equal(t,
+			alice.alice.Pk,
+			bob.bob.Pk,
+		)
+	})
+
+	var aliceResult *DkgResult
+	var bobResult *DkgResult
+	t.Run("alices produces valid result", func(t *testing.T) {
+		// Get the result
+		r, err := alice.Result()
+
+		// Test
+		require.NoError(t, err)
+		require.NotNil(t, r)
+		require.IsType(t, &DkgResult{}, r)
+		aliceResult = r.(*DkgResult)
+
+		// Decode and verify
+		_, err = NewAliceSign(params, nil, aliceResult.DkgState)
+		assert.NoError(t, err)
+	})
+	t.Run("alices produces valid result", func(t *testing.T) {
+		// Get the result
+		r, err := bob.Result()
+
+		// Test
+		require.NoError(t, err)
+		require.NotNil(t, r)
+		require.IsType(t, &DkgResult{}, r)
+		bobResult = r.(*DkgResult)
+
+		// Decode and verify
+		_, err = NewBobSign(params, nil, bobResult.DkgState)
+		assert.NoError(t, err)
+	})
+
+	t.Run("alice/bob agree on pubkey", func(t *testing.T) {
+		assert.Equal(t, aliceResult.Pubkey, bobResult.Pubkey)
+	})
+}
+
+// DKG > Result > NewDklsSign > Sign > Result
+func TestDkgSignProto(t *testing.T) {
+	// Setup
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.NoError(t, err)
+
+	aliceDkg := NewAliceDkg(params)
+	bobDkg := NewBobDkg(params)
+
+	// DKG
+	aErr, bErr := iteratedDkg(aliceDkg, bobDkg)
+	require.ErrorIs(t, aErr, io.EOF)
+	require.ErrorIs(t, bErr, io.EOF)
+
+	// Result
+	aliceDkgResult, err := aliceDkg.Result()
+	require.NoError(t, err)
+
+	bobDkgResult, err := bobDkg.Result()
+	require.NoError(t, err)
+
+	// New DklsSign
+	msg := []byte("As soon as you trust yourself, you will know how to live.")
+	digest := sha256.Sum256(msg)
+	aliceSign, err := NewAliceSign(params, digest[:], aliceDkgResult.(*DkgResult).DkgState)
+	require.NoError(t, err)
+	bobSign, err := NewBobSign(params, digest[:], bobDkgResult.(*DkgResult).DkgState)
+	require.NoError(t, err)
+
+	// Sign
+	t.Run("sign", func(t *testing.T) {
+		aErr, bErr = iteratedSign(aliceSign, bobSign)
+		assert.ErrorIs(t, aErr, io.EOF)
+		assert.ErrorIs(t, bErr, io.EOF)
+	})
+	// Don't continue to verifying results if sign didn't run to completion.
+	require.ErrorIs(t, aErr, io.EOF)
+	require.ErrorIs(t, bErr, io.EOF)
+
+	// Result
+	var result interface{}
+	t.Run("bob produces result of correct type", func(t *testing.T) {
+		result, err = bobSign.Result()
+		assert.NoError(t, err)
+	})
+	require.NotNil(t, result)
+	require.IsType(t, &curves.EcdsaSignature{}, result)
+
+	t.Run("valid signature", func(t *testing.T) {
+		assert.True(t,
+			curves.VerifyEcdsa(aliceDkg.alice.Pk,
+				digest[:],
+				result.(*curves.EcdsaSignature),
+			),
+			"signature failed verification",
+		)
+	})
+}
+
+// Decode > NewDklsSign > Sign > Result
+// NOTE: this cold-start test ensures backwards compatibility with durable,
+// encoding DKG state that may exist within production systems like test
+// Breaking changes must consider downstream production impacts.
+func TestSignColdStart(t *testing.T) {
+	msg := []byte("We see in the world that which we carry in our heart")
+	digest := sha256.Sum256(msg)
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.NoError(t, err)
+
+	// Decode alice/bob state from file
+	aliceDkg, err := ioutil.ReadFile("testdata/alice-dkls-dkg.bin")
+	require.NoError(t, err)
+	bobDkg, err := ioutil.ReadFile("testdata/bob-dkls-dkg.bin")
+	require.NoError(t, err)
+
+	// Decode proto objects
+	alice, err := NewAliceSign(params, digest[:], aliceDkg)
+	require.NoError(t, err)
+
+	bob, err := NewBobSign(params, digest[:], bobDkg)
+	require.NoError(t, err)
+
+	// Sign
+	aErr, bErr := iteratedSign(alice, bob)
+	require.ErrorIs(t, aErr, io.EOF, "got err=%v", aErr)
+	require.ErrorIs(t, bErr, io.EOF, "got err=%v", bErr)
+
+	// Extract the result and verify the type
+	result, err := bob.Result()
+	require.NoError(t, err)
+	require.IsType(t, &curves.EcdsaSignature{}, result)
+
+	// Test the result
+	assert.True(t,
+		curves.VerifyEcdsa(alice.alice.Pk,
+			digest[:],
+			result.(*curves.EcdsaSignature),
+		),
+		"signature failed verification",
+	)
+}
+
+func TestEncodeDecode(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.K256Scalar{})
+	require.NoError(t, err)
+
+	alice := NewAliceDkg(params)
+	bob := NewBobDkg(params)
+	_, _ = iteratedDkg(alice, bob)
+
+	var aliceBytes []byte
+	var bobBytes []byte
+	t.Run("Encode Alice/Bob", func(t *testing.T) {
+		aliceBytes, err = EncodeAlice(alice.alice)
+		require.NoError(t, err)
+
+		bobBytes, err = EncodeBob(bob.bob)
+		require.NoError(t, err)
+	})
+	require.NotEmpty(t, aliceBytes)
+	require.NotEmpty(t, bobBytes)
+
+	t.Run("Decode Alice", func(t *testing.T) {
+		decodedAlice, err := DecodeAlice(params, aliceBytes)
+		require.NoError(t, err)
+		require.NotNil(t, decodedAlice)
+
+		assert.Equal(t, alice.alice.Pk, decodedAlice.Pk)
+		assert.Equal(t, alice.alice.PkA, decodedAlice.PkA)
+		assert.Equal(t, alice.alice.SkA, decodedAlice.SkA)
+	})
+
+	t.Run("Decode Bob", func(t *testing.T) {
+		decodedBob, err := DecodeBob(params, bobBytes)
+		require.NoError(t, err)
+		require.NotNil(t, decodedBob)
+
+		assert.Equal(t, bob.bob.Pk, decodedBob.Pk)
+		assert.Equal(t, bob.bob.PkB, decodedBob.PkB)
+		assert.Equal(t, bob.bob.SkB, decodedBob.SkB)
+	})
+}
diff --git a/pkg/tecdsa/dkls/schnorr.go b/pkg/tecdsa/dkls/schnorr.go
new file mode 100644
index 00000000..335dedaf
--- /dev/null
+++ b/pkg/tecdsa/dkls/schnorr.go
@@ -0,0 +1,112 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/sha256"
+	"crypto/subtle"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+)
+
+type Schnorr struct {
+	params *Params
+	Pub    *curves.EcPoint // this is the public point.
+	C      *big.Int
+	S      *big.Int
+}
+
+func (proof *Schnorr) Prove(x *big.Int) error {
+	// assumes that params, Base, and pub are already populated. populates the fields c and s...
+	var err error
+	proof.Pub, err = curves.NewScalarBaseMult(proof.params.Curve, x) // populate the statement
+	if err != nil {
+		return err
+	}
+	k, err := proof.params.Scalar.Random()
+	if err != nil {
+		return err
+	}
+	random, err := curves.NewScalarBaseMult(proof.params.Curve, k)
+	if err != nil {
+		return err
+	}
+	hash := sha256.New()
+	if _, err = hash.Write(proof.Pub.Bytes()); err != nil {
+		return err
+	}
+	if _, err = hash.Write(random.Bytes()); err != nil {
+		return err
+	}
+	// do we need to hash anything further here...? maybe some kind of session token or something?
+	proof.C = new(big.Int).SetBytes(hash.Sum(nil))
+	proof.S = proof.params.Scalar.Add(proof.params.Scalar.Mul(proof.C, x), k)
+	return nil
+}
+
+func (proof *Schnorr) Verify() error {
+	gs, err := curves.NewScalarBaseMult(proof.params.Curve, proof.S)
+	if err != nil {
+		return err
+	}
+	xc, err := proof.Pub.ScalarMult(proof.params.Scalar.Neg(proof.C))
+	if err != nil {
+		return err
+	}
+	random, err := gs.Add(xc)
+	if err != nil {
+		return err
+	}
+	hash := sha256.New()
+	if _, err = hash.Write(proof.Pub.Bytes()); err != nil {
+		return err
+	}
+	if _, err = hash.Write(random.Bytes()); err != nil {
+		return err
+	}
+	if subtle.ConstantTimeCompare(proof.params.Scalar.Bytes(proof.C), hash.Sum(nil)) != 1 {
+		return fmt.Errorf("Schnorr verification failed")
+	}
+	return nil
+}
+
+// this "commits to" a schnorr proof which is later revealed; see Functionality 7.
+// it mutates `st` by adding a proof to it, and then also returns the commitment to the proof.
+func (proof *Schnorr) ProveCommit(x *big.Int) ([]byte, error) {
+	// it remains to be seen why this is actually necessary in the paper. it's unsual.
+	// i suspect it is some "abstract nonsense" necessary for the security proof to go through.
+	// in the implementation (see https://gitlab.com/neucrypt/mpecdsa/-/blob/release/src/zkpok.rs),
+	// they implement this just by hashing the schnorr proof; we do the same (using c, s as the proof instead of K, s).
+	// it's a bit weird that no randomness is used, but "hiding" shouldn't really be an issue, as the proof is random.
+	// confirm that this actually matches how they implement it, and/or is secure. i don't think it should be an issue.
+	if err := proof.Prove(x); err != nil {
+		return nil, err
+	}
+	hash := sha256.New()
+	if _, err := hash.Write(proof.params.Scalar.Bytes(proof.C)); err != nil {
+		return nil, err
+	}
+	if _, err := hash.Write(proof.params.Scalar.Bytes(proof.S)); err != nil {
+		return nil, err
+	}
+	return hash.Sum(nil), nil
+}
+
+func (proof *Schnorr) DecommitVerify(com []byte) error {
+	hash := sha256.New()
+	if _, err := hash.Write(proof.params.Scalar.Bytes(proof.C)); err != nil {
+		return err
+	}
+	if _, err := hash.Write(proof.params.Scalar.Bytes(proof.S)); err != nil {
+		return err
+	}
+	if subtle.ConstantTimeCompare(hash.Sum(nil), com) != 1 {
+		return fmt.Errorf("initial hash decommitment failed")
+	}
+	return proof.Verify()
+}
diff --git a/pkg/tecdsa/dkls/sign.go b/pkg/tecdsa/dkls/sign.go
new file mode 100644
index 00000000..6018d124
--- /dev/null
+++ b/pkg/tecdsa/dkls/sign.go
@@ -0,0 +1,285 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/ecdsa"
+	"crypto/rand"
+	"crypto/sha256"
+	"encoding/gob"
+	"fmt"
+	"io"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Alice struct encoding Alice's state during one execution of the overall signing algorithm.
+// At the end of the joint computation, Alice will NOT obtain the signature.
+type Alice struct {
+	PkA      *Schnorr // this is a "schnorr statement" for pkA.
+	Receiver *seedOTReceiver
+	SkA      *big.Int // the witness
+	Pk       *curves.EcPoint
+
+	// Note: unexported fields are marshaled during Encode
+	params *Params
+}
+
+// Bob struct encoding Bob's state during one execution of the overall signing algorithm.
+// At the end of the joint computation, Bob will obtain the signature.
+type Bob struct {
+	// Exported fields
+	PkB    *Schnorr // this is a "schnorr statement" for pkB.
+	Sender *seedOTSender
+	SkB    *big.Int
+	Pk     *curves.EcPoint
+	Sig    *curves.EcdsaSignature // The resulting digital signature
+
+	// Intermediate values and those used only during sign or DKG are not exported
+
+	// Commitment to Alice's schnorr proof.
+	params *Params
+	// Only used during DKG so it's not persisted during encoding
+	com []byte
+	tB  *MultiplyReceiver // the receiver for additive shares of the multiplication.
+	kB  *big.Int
+	dB  *curves.EcPoint
+}
+
+// NewAlice creates a party that can participate in 2-of-2 DKG and threshold signature.
+func NewAlice(params *Params) *Alice {
+	return &Alice{
+		params:   params,
+		Receiver: &seedOTReceiver{params: params},
+		PkA:      &Schnorr{params: params},
+	}
+}
+
+// NewBob creates a party that can participate in 2-of-2 DKG and threshold signature. This party
+// is the receiver of the signature at the end.
+func NewBob(params *Params) *Bob {
+	return &Bob{
+		params: params,
+		Sender: &seedOTSender{params: params},
+		PkB:    &Schnorr{params: params},
+	}
+}
+
+type signInitStorage struct {
+	Seed [32]byte // hash seed for idExt?
+	DB   *curves.EcPoint
+}
+
+type signStorage struct {
+	RPrime *curves.EcPoint
+	EtaPhi *big.Int
+	EtaSig *big.Int
+}
+
+// signInit Bob's initial message, which kicks off the signature process. Protocol 1, Bob's steps 1) - 3).
+// Bob's work here entails beginning the Diffie–Hellman-like construction of the instance key / nonce,
+// as well as preparing the inputs which he will feed into the multiplication protocol,
+// and moreover actually initiating the (first message of) the multiplication protocol using these inputs.
+// this latter step in turn amounts to sending the initial message in a new cOT extension.
+// all the resulting data gets packaged and sent to Alice.
+func (bob *Bob) signInit(w io.Writer) error {
+	bob.tB = NewMultiplyReceiver(2, bob.Sender)
+	// assumes that the seed OT has already been taken care of.
+	// result is an instance seed _plus_ partial instance dB key plus _two_ concurrent first messages in the multiplication protocol!
+	result := &signInitStorage{}
+	enc := gob.NewEncoder(w)
+	var err error
+	if _, err = rand.Read(result.Seed[:]); err != nil {
+		return err
+	}
+	idExt := sha256.Sum256(result.Seed[:])
+
+	if bob.kB, err = bob.params.Scalar.Random(); err != nil {
+		return err
+	}
+	if bob.dB, err = curves.NewScalarBaseMult(bob.params.Curve, bob.kB); err != nil {
+		return err
+	}
+	result.DB = bob.dB // ?
+	kBInv := bob.params.Scalar.Div(big.NewInt(1), bob.kB)
+	if err = enc.Encode(result); err != nil {
+		return err
+	}
+	return bob.tB.MultiplyInit(idExt, []*big.Int{kBInv, bob.params.Scalar.Mul(bob.SkB, kBInv)}, w)
+}
+
+// signInit Alice's first message. Alice is the _responder_; she is responding to Bob's initial message.
+// this is Protocol 1 (p. 6), and contains Alice's steps 3) -- 8). these can all be combined into one message.
+// Alice's job here is to finish computing the shared instance key / nonce, as well as multiplication input values;
+// then to invoke the coalesced multiplication on these two input values (appending the result to her running message),
+// then to use the _output_ of the multiplication (which she already possesses as of the end of her computation),
+// and use that to compute some final values which will help Bob compute the final signature.
+//
+// Note: the protocol has been modified to receive the message digest instead of the message to make the protocol
+// compatible with various blockchains as they each use a different hashing algorithm. For example,
+// 2xSHA2 for Bitcoin and keccak-256 for Ethereum. We have investigated the security of receiving hash as input and
+// the result is available at TODO: add the link to the document containing the analysis.
+func (alice *Alice) signInit(digest []byte, rw io.ReadWriter) error {
+	enc := gob.NewEncoder(rw)
+	dec := gob.NewDecoder(rw)
+	input := &signInitStorage{}
+	if err := dec.Decode(input); err != nil {
+		return err
+	}
+	tA := NewMultiplySender(2, alice.Receiver)
+	// digest is the hashed message to be signed. i use the name `message` throughout for crypto messages.
+	// note: things could go badly if Bob doesn't pick a _new_ / random "seed". verify how to handle this.
+	idExt := sha256.Sum256(input.Seed[:])
+
+	result := &signStorage{} // make([]byte, tA.MultiplyOutputSize+192) // again pretty convoluted here.
+	kPrimeA, err := alice.params.Scalar.Random()
+	if err != nil {
+		return err
+	}
+	if result.RPrime, err = input.DB.ScalarMult(kPrimeA); err != nil {
+		return err
+	}
+	temp := sha256.Sum256(result.RPrime.Bytes())
+	kA := alice.params.Scalar.Add(new(big.Int).SetBytes(temp[:]), kPrimeA)
+	r, err := input.DB.ScalarMult(kA)
+	if err != nil {
+		return err
+	}
+	phi, err := alice.params.Scalar.Random()
+	if err != nil {
+		return err
+	}
+	kAInv := alice.params.Scalar.Div(big.NewInt(1), kA)
+
+	// Alice's response here is _two_ (i.e., collated) responses to the multiplication protocol.
+	// followed by Alice's R', followed by a schnorr proof for R (!). folllowed by \eta^{\phi} and \eta^{sig}.
+	if err = tA.Multiply(idExt, []*big.Int{alice.params.Scalar.Add(phi, kAInv), alice.params.Scalar.Mul(alice.SkA, kAInv)}, rw); err != nil {
+		return err
+	}
+
+	gamma1, err := curves.NewScalarBaseMult(alice.params.Curve, kA)
+	if err != nil {
+		return err
+	}
+	gamma1, err = gamma1.ScalarMult(phi)
+	if err != nil {
+		return err
+	}
+	other, err := r.ScalarMult(alice.params.Scalar.Neg(tA.TA[0]))
+	if err != nil {
+		return err
+	}
+	gamma1, err = gamma1.Add(other)
+	if err != nil {
+		return err
+	}
+	gamma1, err = gamma1.Add(alice.params.Generator)
+	if err != nil {
+		return err
+	}
+	temp = sha256.Sum256(gamma1.Bytes())
+	result.EtaPhi = alice.params.Scalar.Add(new(big.Int).SetBytes(temp[:]), phi)
+	sigA := alice.params.Scalar.Add(
+		alice.params.Scalar.Mul(
+			new(big.Int).SetBytes(digest),
+			tA.TA[0],
+		),
+		alice.params.Scalar.Mul(
+			r.X, tA.TA[1],
+		),
+	)
+	gamma2, err := alice.Pk.ScalarMult(tA.TA[0])
+	if err != nil {
+		return err
+	}
+	other, err = curves.NewScalarBaseMult(alice.params.Curve, alice.params.Scalar.Neg(tA.TA[1]))
+	if err != nil {
+		return err
+	}
+	gamma2, err = gamma2.Add(other)
+	if err != nil {
+		return err
+	}
+	temp = sha256.Sum256(gamma2.Bytes())
+	result.EtaSig = alice.params.Scalar.Add(new(big.Int).SetBytes(temp[:]), sigA)
+	return enc.Encode(result)
+}
+
+// signFinal this is Bob's last portion of the signature computation, and ultimately results in the complete signature
+// corresponds to Protocol 1, Bob's steps 3) -- 10).
+// Bob begins by _finishing_ the OT-based multiplication, using Alice's one and only message to him re: the mult.
+// Bob then move's onto the remainder of Alice's message, which contains extraneous data used to finish the signature.
+// using this data, Bob completes the signature, which gets stored in `Bob.Sig`. Bob also verifies it.
+//
+// Note: the protocol has been modified to receive the message digest instead of the message to make the protocol
+// compatible with various blockchains as they each use a different hashing algorithm. For example,
+// 2xSHA2 for Bitcoin and keccak-256 for Ethereum. We have investigated the security of receiving hash as input and
+// the result is available at TODO: add the link to the document containing the analysis.
+func (bob *Bob) signFinal(digest []byte, r io.Reader) error {
+	bob.Sig = &curves.EcdsaSignature{}
+	if err := bob.tB.MultiplyTransfer(r); err != nil {
+		return err
+	}
+	dec := gob.NewDecoder(r)
+	input := &signStorage{}
+	if err := dec.Decode(input); err != nil {
+		return err
+	}
+	temp := sha256.Sum256(input.RPrime.Bytes())
+	R, err := bob.dB.ScalarMult(new(big.Int).SetBytes(temp[:]))
+	if err != nil {
+		return err
+	}
+	R, err = R.Add(input.RPrime)
+	if err != nil {
+		return err
+	}
+	bob.Sig.R = R.X // NOT modding by q...?
+	bob.Sig.V = int(R.Y.Bit(0))
+	gamma1, err := R.ScalarMult(bob.tB.TB[0])
+	if err != nil {
+		return err
+	}
+	temp = sha256.Sum256(gamma1.Bytes())
+	phi := bob.params.Scalar.Sub(input.EtaPhi, new(big.Int).SetBytes(temp[:]))
+	theta := bob.params.Scalar.Sub(bob.tB.TB[0], bob.params.Scalar.Div(phi, bob.kB))
+	sigB := bob.params.Scalar.Add(bob.params.Scalar.Mul(new(big.Int).SetBytes(digest), theta), bob.params.Scalar.Mul(bob.Sig.R, bob.tB.TB[1]))
+	gamma2, err := curves.NewScalarBaseMult(bob.params.Curve, bob.tB.TB[1])
+	if err != nil {
+		return err
+	}
+	other, err := bob.Pk.ScalarMult(bob.params.Scalar.Neg(theta))
+	if err != nil {
+		return err
+	}
+	gamma2, err = gamma2.Add(other)
+	if err != nil {
+		return err
+	}
+	temp = sha256.Sum256(gamma2.Bytes())
+	bob.Sig.S = bob.params.Scalar.Add(sigB, bob.params.Scalar.Sub(input.EtaSig, new(big.Int).SetBytes(temp[:])))
+	// now verify the signature
+	if !ecdsa.Verify(&ecdsa.PublicKey{Curve: bob.params.Curve, X: bob.Pk.X, Y: bob.Pk.Y}, digest, bob.Sig.R, bob.Sig.S) {
+		return fmt.Errorf("final signature failed to verify")
+	}
+	return nil
+}
+
+// Sign this is an illustrative helper method which shows the overall flow for Alice.
+// in practice this will be replaced by a method which actually sends messages back and forth.
+func (alice *Alice) Sign(m []byte, rw io.ReadWriter) error {
+	return alice.signInit(m, rw)
+}
+
+// Sign this is an illustrative helper method which shows the overall flow for Bob.
+func (bob *Bob) Sign(m []byte, rw io.ReadWriter) error {
+	if err := bob.signInit(rw); err != nil {
+		return err
+	}
+	return bob.signFinal(m, rw)
+}
diff --git a/pkg/tecdsa/dkls/sign_test.go b/pkg/tecdsa/dkls/sign_test.go
new file mode 100644
index 00000000..4130c006
--- /dev/null
+++ b/pkg/tecdsa/dkls/sign_test.go
@@ -0,0 +1,65 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dkls
+
+import (
+	"crypto/sha256"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+func TestSign(t *testing.T) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.NoError(t, err)
+	alice := NewAlice(params)
+	bob := NewBob(params)
+
+	alicePipe, bobPipe := NewPipeWrappers()
+	require.NoError(t, testDKG(alice, bob, alicePipe, bobPipe))
+	require.NoError(t, testSign(alice, bob, alicePipe, bobPipe))
+}
+
+func BenchmarkSign(b *testing.B) {
+	params, err := NewParams(btcec.S256(), curves.NewK256Scalar())
+	require.NoError(b, err)
+	alice := NewAlice(params)
+	bob := NewBob(params)
+	alicePipe, bobPipe := NewPipeWrappers()
+	require.NoError(b, testDKG(alice, bob, alicePipe, bobPipe))
+	b.ResetTimer()
+	bytes := 0
+	for n := 0; n < b.N; n++ {
+		alicePipe, bobPipe = NewPipeWrappers()
+		require.NoError(b, testSign(alice, bob, alicePipe, bobPipe))
+		bytes += alicePipe.exchanged
+	}
+	b.ReportMetric(float64(bytes)/float64(b.N), "bytes/op")
+}
+
+// Helper function that runs signing
+func testSign(alice *Alice, bob *Bob, alicePipe *pipeWrapper, bobPipe *pipeWrapper) error {
+	// ^^^ a bit clunky that we have to pass these in, but i don't see an easier way as far as benchmarking the bytes
+	errors := make(chan error, 2) // warning: if one party errors, the other will sit there forever. add timeouts.
+
+	m := []byte("Our mission is to increase economic freedom in the world.")
+	digest := sha256.Sum256(m)
+	go func() {
+		errors <- alice.Sign(digest[:], alicePipe)
+	}()
+	go func() {
+		errors <- bob.Sign(digest[:], bobPipe)
+	}()
+	for i := 0; i < 2; i++ {
+		if err := <-errors; err != nil {
+			return err
+		}
+	}
+	return nil
+}
diff --git a/pkg/tecdsa/dkls/testdata/alice-dkls-dkg.bin b/pkg/tecdsa/dkls/testdata/alice-dkls-dkg.bin
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diff --git a/pkg/tecdsa/dkls/testdata/bob-dkls-dkg.bin b/pkg/tecdsa/dkls/testdata/bob-dkls-dkg.bin
new file mode 100644
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diff --git a/pkg/tecdsa/gg20/README.md b/pkg/tecdsa/gg20/README.md
new file mode 100644
index 00000000..123b3387
--- /dev/null
+++ b/pkg/tecdsa/gg20/README.md
@@ -0,0 +1,694 @@
+# Threshold ECDSA
+
+```go
+import "github.com/coinbase/kryptology/pkg/tecdsa/gg20"
+```
+
+Package tecdsa contains the implementation of threshold ECDSA (tECDSA) pseudocode for Coinbase [[specV5]](docs/Coinbase_Pseudocode_v5.pdf). 
+It supports tECDSA with two different key generation approaches: (1). key generation with a trusted dealer and (2). distributed key generation.
+We introduce them separately in the following context.
+## KeyGenType
+KeyGenType is designed to determine which key generation mode a tECDSA participant should use. The corresponding interfaces and functions are defined in `tecdsa/dealer/keygentype.go`.
+
+```go
+type KeyGenType interface {
+	IsTrustedDealer() bool
+	GetProofParams(id uint32) *ProofParams
+}
+```
+KeyGenType encapsulates the different methods that tecdsa can generate keys. Currently TrustedDealer or Distributed Key Generation
+
+```go
+type TrustedDealerKeyGenType struct {
+	ProofParams *ProofParams
+}
+```
+`TrustedDealerKeyGenType` is used when we generate keys using a trusted dealer. It 
+means the same proof parameters will be used by all participants and be distributed by the trusted dealer.
+
+```go
+type DistributedKeyGenType struct {
+	ProofParams map[uint32]*ProofParams
+}
+```
+`DistributedKeyGenType` is used when we use distributed key generation. It 
+means each participant has their own proof params that were distributed to each other
+participant.
+
+### Usage
+```go
+func (td TrustedDealerKeyGenType) IsTrustedDealer() bool 
+```
+`IsTrustedDealer` returns true if in trusted dealer mode.
+
+```go
+func (td TrustedDealerKeyGenType) GetProofParams(_ uint32) *ProofParams
+```
+`GetProofParams` returns the proof params specified by the participant id in trusted dealer mode.
+
+```go
+func (dkg DistributedKeyGenType) IsTrustedDealer() bool
+```
+`IsTrustedDealer` returns false if in distributed key generation mode
+
+```go
+func (dkg DistributedKeyGenType) GetProofParams(id uint32) *ProofParams
+```
+`GetProofParams` returns the proof params specified by the participant id in distributed key generation mode.
+
+## Participant
+tECDSA is run by multiple participants and these participants create a signature together. We define different types of participants and 
+corresponding functions in `tecdsa/participant/participant.go`. 
+
+### type DkgParticipant
+```go
+type DkgParticipant struct {
+	Curve elliptic.Curve
+	state *dkgstate
+	id    uint32
+	Round uint
+}
+```
+`DkgParticipant` is a DKG player that contains information needed to perform DKG rounds and finally get info for signing rounds.
+
+### type dkgstate
+```go
+type dkgstate struct {
+	// Round 1 variables
+	D  *crypto.Witness
+	Sk *paillier.SecretKey
+	Pk *paillier.PublicKey
+	N  *big.Int
+	H1 *big.Int
+	H2 *big.Int
+	// This participants verifiers from FeldmanShare
+	V []*sharing.ShareVerifier
+	// This participants shares from FeldmanShare
+	X         []*sharing.ShamirShare
+	Y         *crypto.EcPoint
+	Threshold uint32
+	Limit     uint32
+	// Commitments and paillier public keys received from other participants
+	otherParticipantData map[uint32]*dkgParticipantData
+	// xi returned from Round 3
+	Xi *big.Int
+	// X1,...,Xn returned from Round 3
+	PublicShares []*crypto.EcPoint
+}
+```
+`dkgstate` encapsulates all the values used in the dkg rounds state machine
+
+### type dkgParticipantData
+```go
+type dkgParticipantData struct {
+	PublicKey   *paillier.PublicKey
+	ProofParams *dealer.ProofParams
+	Commitment  crypto.Commitment
+}
+```
+`dkgParticipantData` encapsulates all the values that need to be stored in `dkgstate`
+
+### type Participant
+```go
+type Participant struct {
+	dealer.Share
+	sk *paillier.SecretKey
+}
+```
+`Participant` is a tECDSA player. Note that `Participant` is not already a 
+co-signer of tECDSA. If it is in trusted dealer mode, it receives information from the 
+trusted dealer. If it is in distributed key generation mode, the participant generates 
+or receives those information via the distributed key generation protocol. 
+
+### type Signer
+```go
+type Signer struct {
+	sk              *paillier.SecretKey            // paillier secret key assigned to this signer
+	share           *sharing.ShamirShare           // secret signing share for this signer
+	publicSharesMap map[uint32]*dealer.PublicShare // public shares of our cosigners
+	id              uint32                         // The ID assigned to this signer's shamir share
+	// This is minimum number of signers required to produce a valid signature,
+	// not the security threshold (as specified in [spec][GG20])
+	threshold uint
+	PublicKey *crypto.EcPoint
+	Curve     elliptic.Curve
+	Round     uint   // current signing round in our linear state machine
+	state     *state // Accumulated intermediate values associated with signing
+}
+```
+`Signer` is a tECDSA player that holds the additive shares needed for performing the signing operation. 
+`Signer` is the actual participant joining tECDSA signing operations. 
+
+### type EcdsaSignature
+```go
+type EcdsaSignature struct {
+	R, S *big.Int
+}
+```
+`EcdsaSignature` represents a (composite) digital signature
+
+### type EcdsaVerify
+```go
+type EcdsaVerify func(pubKey *crypto.EcPoint, hash []byte, signature *EcdsaSignature) bool
+```
+`EcdsaVerify` runs a curve- or algorithm-specific ECDSA verification function on input
+an ECDSA public (verification) key, a message digest, and an ECDSA signature.
+It must return true if all the parameters are sane and the ECDSA signature is valid, 
+and false otherwise
+
+### func (*Signer) verifyStateMap
+```go
+func (signer *Signer) verifyStateMap(round uint, in interface{}) error
+```
+`verifyStateMap` verifies the round is the expected round number and
+that the set of signers from `in.keys()` exactly matches the set
+in `state.cosigners`.
+
+### func (*Signer) setCosigners
+```go
+func (signer *Signer) setCosigners(in []uint32) error
+```
+`setCosigners` establishes the list of cosigner IDs. This may or may not include self ID.
+
+### func (*Signer) resetSignRound
+```go
+func (signer *Signer) resetSignRound()
+```
+`resetSignRound` sets the signer to a pre-round1 state.
+
+### func (Participant) convertToAdditive
+```go
+func (p Participant) convertToAdditive(curve elliptic.Curve, publicSharesMap map[uint32]*dealer.PublicShare) (*Signer, error)
+```
+`convertToAdditive` takes all the publicShares and changes them to their additive form
+for this participant. Only t shares are needed for this step. See fig.6 in [[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+
+### func (Participant) PrepareToSign
+```go
+func (p Participant) PrepareToSign(pubKey *crypto.EcPoint,
+	verify EcdsaVerify,
+	curve elliptic.Curve,
+	keyGenType dealer.KeyGenType,
+	publicSharesMap map[uint32]*dealer.PublicShare,
+	pubKeys map[uint32]*paillier.PublicKey) (*Signer, error)
+```
+`PrepareToSign` creates a `Signer` out of a `Participant`. The expected co-signers for the signing rounds are
+expected to be exactly those included in the `publicSharesMap`
+
+### func makeXMap
+```go
+func makeXMap(curve elliptic.Curve, publicSharesMap map[uint32]*dealer.PublicShare) (map[uint32]*sharing.Element, error)
+```
+`makeXMap` creates a map of polynomial x-coordinates that are field elements.
+
+### func (*DkgParticipant) verifyDkgRound
+```go
+func (dp *DkgParticipant) verifyDkgRound(dkground uint) error
+```
+`verifyDkgRound` checks DKG round number is valid. 
+
+## Trusted Dealer Mode
+Recall that our tECDSA can work with two key generation modes. One is the trusted dealer mode
+and another one is the distributed key generation mode. In trusted dealer mode, the dealer is responsible to prepare input values for 
+all participants to run tECDSA. The output of the key generation (using trusted dealer)
+should contain the following
+- A public ECDSA signing key, 
+- Private key shares for each signer corresponding to the public signing key.
+- Paillier key pairs for each player
+- Trusted parameters for instantiating the zero-knowledge proofs that
+will be employed during the signing protocol. 
+
+The types and functions defined for the trusted dealer are defined in `tecdsa/dealer/dealer.go`
+
+### type ParticipantData
+```go
+type ParticipantData struct {
+	Id             uint32
+	DecryptKey     *paillier.SecretKey
+	SecretKeyShare *Share
+	// Public values set to all signing participants
+	EcdsaPublicKey *crypto.EcPoint
+	KeyGenType     KeyGenType
+	PublicShares   map[uint32]*PublicShare
+	EncryptKeys    map[uint32]*paillier.PublicKey
+}
+```
+`ParticipantData` represents all data to be sent to a participant after the dealer is finished
+
+### type ParticipantDataJson
+```go
+type ParticipantDataJson struct {
+	Id             uint32
+	DecryptKey     *paillier.SecretKey
+	SecretKeyShare *Share
+	// Public values set to all signing participants
+	EcdsaPublicKey    *crypto.EcPoint
+	DealerParams      *ProofParams
+	ParticipantParams map[uint32]*ProofParams
+	PublicShares      map[uint32]*PublicShare
+	EncryptKeys       map[uint32]*paillier.PublicKey
+}
+```
+`ParticipantDataJson` encapsulates the data that is serialized to JSON used internally and not for external use. Public so other pieces can use for serialization
+
+### func (ParticipantData) MarshalJSON
+```go
+func (pd ParticipantData) MarshalJSON() ([]byte, error)
+```
+`MarshalJSON` converts `ParticipantData` into json format
+
+### func (*ParticipantData) UnmarshalJSON
+```go
+func (pd *ParticipantData) UnmarshalJSON(bytes []byte) error
+```
+`UnmarshalJSON` converts json format data into this `ParticipantData`
+
+### type ProofParams
+```go
+type ProofParams struct {
+	// n is the modulus for the signing rounds, product of two safe primes
+	N *big.Int
+	// h1 random value quadratic residue in n
+	H1 *big.Int
+	// h2 is a random modular power of h1
+	H2 *big.Int
+}
+```
+`ProofParams` is the modulus and generators used when constructing keys and completing the signing rounds
+
+### type PublicShare
+```go
+type PublicShare struct {
+	Point *crypto.EcPoint
+}
+```
+`PublicShare` can be sent to a Participant as a part of `ParticipantData` so it can be used to convert Share to its additive form.
+
+### type Share
+```go
+type Share struct {
+	*sharing.ShamirShare
+	Point *crypto.EcPoint
+}
+```
+`Share` represents a piece of the tECDSA private key and a commitment to the share.
+
+### type ShareJson
+```go
+type ShareJson struct {
+	Identifier uint32   // x-coordinate
+	Value      *big.Int // y-coordinate
+	Point      *crypto.EcPoint
+}
+```
+`ShareJson` encapsulates the data that is serialized to JSON
+used internally and not for external use. Public so other pieces
+can use for serialization
+
+### func (Share) MarshalJSON
+```go
+func (s Share) MarshalJSON() ([]byte, error)
+```
+`MarshalJSON` converts `Share` into json format
+
+### func (*Share) UnmarshalJSON
+```go
+func (s *Share) UnmarshalJSON(bytes []byte) error
+```
+`UnmarshalJSON` converts json format data into this `Share`
+
+### func NewProofParams
+```go
+func NewProofParams() (*ProofParams, error)
+```
+`NewProofParams` creates new ProofParams with "bits" sized values
+
+### func NewProofParamsWithPrimes
+```go
+func NewProofParamsWithPrimes(p, q *big.Int) (*ProofParams, error)
+```
+`NewProofParamsWithPrimes` creates new ProofParams using the parameters as safe primes
+
+### func PreparePublicShares
+```go
+func PreparePublicShares(sharesMap map[uint32]*Share) (map[uint32]*PublicShare, error)
+```
+`PreparePublicShares` makes public shares that can be sent to the participant to compute their additive shares and participate in signing rounds
+
+### func NewSecret
+```go
+func NewSecret(curve elliptic.Curve) (*big.Int, error)
+```
+`NewSecret` generates a new (randomly sampled) secret key.
+
+### func DerivePublicKey
+```go
+func DerivePublicKey(curve elliptic.Curve, secretKey *big.Int) (*crypto.EcPoint, error)
+```
+`DerivePublicKey` generates a public key by taking input a secret key. 
+
+### func NewDealerShares
+```go
+func NewDealerShares(curve elliptic.Curve, threshold, total uint32, ikm *big.Int) (*crypto.EcPoint, map[uint32]*Share, error)
+```
+`NewDealerShares` generates the Secp256k1 private key shares and public key. if the parameter `ikm=nil`, a new
+private key will be generated, otherwise using `ikm` as the private key. 
+
+### func genProofParams
+```go
+func genProofParams(genSafePrime func(uint) (*big.Int, error), genRandInMod func(*big.Int) (*big.Int, error), bits uint) (*ProofParams, error)
+```
+`genProofParams` creates all the values needed for ProofParams using the specified genSafePrime function, genRandInMod function, and number of bits.
+
+## Distributed Key Generation (DKG) Mode
+Another approach to generate tECDSA input values is using the DKG mode.
+Unlike the trusted dealer mode in which the trusted dealer generates input values
+for all tECDSA participants, all participants in the DKG mode run a 4-round distributed 
+key generation protocol to generate their own input values without a trusted
+dealer. The output of the DKG mode should contain the following
+
+- A public ECDSA signing key,
+- Private key shares for each signer corresponding to the public signing key.
+- Paillier key pairs for each player
+- Per-player parameters for instantiating the zero-knowledge proofs that will be employed during the
+  signing protocol.
+  
+### DKG Round 1
+#### type DkgRound1Bcast
+```go
+type DkgRound1Bcast struct {
+    Identifier       uint32
+    Ci               crypto.Commitment
+    Pki              *paillier.PublicKey
+    H1i, H2i, Ni     *big.Int
+    Proof1i, Proof2i *proof.CdlProof
+}
+```
+`DkgRound1Bcast` contains values to be broadcast to all players after the completion of DKG round 1.
+
+#### func (*DkgParticipant) DkgRound1
+```go
+func (dp *DkgParticipant) DkgRound1(threshold, total uint32) (*DkgRound1Bcast, error)
+```
+`DkgRound1` performs round 1 distributed key generation operation. See fig.5 - DistKeyGenRound1 in [[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+
+### DKG Round 2
+#### type DkgRound2Bcast
+```go
+type DkgRound2Bcast struct {
+	Di *crypto.Witness
+}
+```
+`DkgRound2Bcast` contains value that will be echo broadcast to all other players after DKG round 2.
+
+#### type DkgRound2P2PSend
+```go
+type DkgRound2P2PSend struct {
+	xij *sharing.ShamirShare
+}
+```
+`DkgRound2P2PSend` contains value that will be P2PSend to all other player Pj after Dkg round 2.
+
+#### func (*DkgParticipant) DkgRound2
+```go
+func (dp *DkgParticipant) DkgRound2(params map[uint32]*DkgRound1Bcast) (*DkgRound2Bcast, map[uint32]*DkgRound2P2PSend, error)
+```
+`DkgRound2` implements distributed key generation round 2. See fig.5 - DistKeyGenRound2 in [[specV5]](docs/Coinbase_Pseudocode_v5.pdf)
+
+### DKG Round 3
+
+#### func (*DkgParticipant) DkgRound3
+```go
+func (dp *DkgParticipant) DkgRound3(d map[uint32]*crypto.Witness, x map[uint32]*sharing.ShamirShare) (proof.PsfProof, error)
+```
+DkgRound3 computes dkg round 3 as shown in [[specV5]](docs/Coinbase_Pseudocode_v5.pdf) fig. 5 - DistKeyGenRound3.
+
+#### func unmarshalFeldmanVerifiers
+```go
+func unmarshalFeldmanVerifiers(curve elliptic.Curve, msg []byte, verifierSize, threshold int) ([]*sharing.ShareVerifier, error)
+```
+### DKG Round 4
+#### type DkgResult
+```go
+type DkgResult struct {
+	PublicShares    []*crypto.EcPoint
+	VerificationKey *crypto.EcPoint
+	SigningKeyShare *big.Int
+	EncryptionKey   *paillier.SecretKey
+	ParticipantData map[uint32]*DkgParticipantData
+}
+```
+`DkgResult` contains all the data generated from the DKG.
+
+#### type DkgParticipantData
+```go
+type DkgParticipantData struct {
+	PublicKey   *paillier.PublicKey
+	ProofParams *dealer.ProofParams
+}
+```
+`DkgParticipantData` contains values that should be output as a part of `DkgResult`.
+
+#### func (*DkgParticipant) DkgRound4
+```go
+func (dp *DkgParticipant) DkgRound4(psfProof map[uint32]proof.PsfProof) (*DkgResult, error)
+```
+`DkgRound4` implements DKG round 4. See fig.5 - DistKeyGenRound4 in [[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+
+## tECDSA Signing Rounds
+After the key generation phase either via the trusted dealer mode or the DKG mode. tECDSA co-signers
+have obtained their input values and they are ready to run the 6-round signing protocol to create a valid signature.
+
+### Sign Round 1
+#### type Round1Bcast
+```go
+type Round1Bcast struct {
+	Identifier uint32
+	C          crypto.Commitment
+	Ctxt       *big.Int
+	Proof      *proof.Range1Proof
+}
+```
+`Round1Bcast` contains values to be broadcast to all players after the completion of singing round 1.
+
+#### type Round1P2PSend
+```go
+type Round1P2PSend = proof.Range1Proof
+```
+`Round1P2PSend` contains the value to be P2P send to all other players Pj after the completion of signing round 1.
+
+#### func (*Signer) SignRound1
+```go
+func (signer *Signer) SignRound1() (*Round1Bcast, map[uint32]*Round1P2PSend, error)
+```
+`SignRound1` performs round 1 signing operation.
+See [[specV5]](docs/Coinbase_Pseudocode_v5.pdf) for details:
+- If in the trusted dealer mode, see fig.7 - SignRound1
+- If in the DKG mode, see fig.8 - SignRound1
+
+NOTE: Pseudocode shows N~, h1, h2, the curve's g, q, and signer's public key as inputs.
+Since `signer` already knows the paillier secret and public keys, this input is not necessary here
+`participant.PrepareToSign` receives the other inputs and stores them as state variables.
+
+### Sign Round 2
+#### type P2PSend
+```go
+type P2PSend struct {
+	Proof2, Proof3 proof.ResponseFinalizer
+}
+```
+`P2PSend` is all the values that need to be sent to each player after completion of signing round 2.
+
+#### func (*P2PSend) UnmarshalJSON
+```go
+func (p2ps *P2PSend) UnmarshalJSON(bytes []byte) error
+```
+`UnmarshalJSON` explicitly unmarshals into ResponseProofs instead of ResponsFinalizer interface.
+
+#### func (*Signer) SignRound2
+```go
+func (signer *Signer) SignRound2(params map[uint32]*Round1Bcast, p2p map[uint32]*Round1P2PSend) (map[uint32]*P2PSend, error)
+```
+SignRound2 performs round 2 signing operations for a single signer.
+See [[specV5]](docs/Coinbase_Pseudocode_v5.pdf) for details:
+- If in the trusted dealer mode, see fig.7 - SignRound2
+- If in the DKG mode, see fig.8 - SignRound2
+
+### Sign Round 3
+#### type Round3Bcast and Round3BcastJSON
+```go
+type (
+	Round3Bcast struct {
+		// Note that deltaElement is some element of the entire δ vector.
+		// In this round, it's δ_i. For the recepients of this message in the next round
+		// this will be δ_j
+		deltaElement *big.Int
+		// The reason we can't do something straightforward like `type BetterRound3Bcast *big.int`
+		// is that although `big.int` has some methods implementing marshaler,
+		// they won't be accessible to `BetterRound3Bcast`. So the json.Marhsal uses the default methods
+		// and since the two fields of `big.int` are not exported, the data of `BetterRound3Bcast`
+		// won't actually be serialized and its deserialization results in nil.
+	}
+
+	Round3BcastJSON struct {
+		DeltaElement *big.Int
+	}
+)
+```
+`Round3Bcast` represents the value to be broadcast to all players at the conclusion of round 3.
+`Round3BcastJSON` represents the json format of `Round3Bcast`.
+
+#### func (Round3Bcast) MarshalJSON
+```go
+func (r3b Round3Bcast) MarshalJSON() ([]byte, error)
+```
+`MarshalJSON` converts `Round3Bcast` to its json format. 
+
+#### func (*Round3Bcast) UnmarshalJSON
+```go
+func (r3b *Round3Bcast) UnmarshalJSON(data []byte) error
+```
+`UnmarshalJSON` converts the input json format data into this `Round3Bcast`.
+
+#### func (*Signer) SignRound3
+```go
+func (s *Signer) SignRound3(in map[uint32]*P2PSend) (*Round3Bcast, error)
+```
+SignRound3 performs the round 3 signing operation according to [[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+- If in the trusted dealer mode, see fig.7 - SignRound3.
+- If in the DKG mode, see fig.8 - SignRound3.
+
+### Sign Round 4
+#### type Round4Bcast
+```go
+type Round4Bcast struct {
+	Witness *crypto.Witness
+}
+```
+`Round4Bcast` are the values to be broadcast to the other players at the conclusion of signing round 4.
+
+#### func (*Signer) SignRound4
+```go
+func (s *Signer) SignRound4(deltas map[uint32]*Round3Bcast) (*Round4Bcast, error)
+```
+`SignRound4` performs the round 4 signing operation. It takes input the delta_j values broadcast from signers at the conclusion of round 3.
+See [[specV5]](docs/Coinbase_Pseudocode_v5.pdf) for details:
+- If in the trusted dealer mode, see fig.7 - SignRound4.
+- If in the DKG mode, see fig.8 - SignRound4.
+
+### Sign Round 5
+#### type Round5Bcast
+```go
+type Round5Bcast struct {
+	Rbar  *crypto.EcPoint
+	Proof *proof.PdlProof
+}
+```
+`Round5Bcast` are the values to be broadcast to the other players at the conclusion of signing round 5.
+
+#### type Round5P2PSend
+```go
+type Round5P2PSend = proof.PdlProof
+```
+`Round5P2PSend` are the values sent to each participant at the conclusion of signing round 5.
+
+#### func (*Signer) SignRound5
+```go
+func (signer *Signer) SignRound5(witnesses map[uint32]*Round4Bcast) (*Round5Bcast, map[uint32]*Round5P2PSend, error)
+```
+`SignRound5` performs the round 5 signing operation. It takes input
+the Witness values broadcast from signers at the conclusion of
+round 4.
+- If in the trusted dealer mode, see fig.7 - SignRound5.
+- If in the DKG mode, see fig.8 - SignRound5.
+
+### Sign Round 6
+#### type Round6FullBcast and Round6FullBcastJSON
+```go
+type (
+	Round6FullBcast struct {
+		// Note that sElement is some element of the entire s vector.
+		// In this round, it's s_i. For the recipients of this message in the final
+		// sign output round, this will be s_j
+		sElement *big.Int
+		// The reason we can't do something straightforward like `type BetterRound6FullBcast *big.int`
+		// is that although `big.int` has some methods implementing marshaler,
+		// they won't be accessible to `BetterRound6FullBcast`. So the json.Marhsal uses the default methods
+		// and since the two fields of `big.int` are not exported, the data of `BetterRound6FullBcast`
+		// won't actually be serialized and its deserialization results in nil.
+	}
+
+	Round6FullBcastJSON struct {
+		SElement *big.Int
+	}
+)
+```
+`Round6FullBcast` are the values to be broadcast to the other players. 
+This is the s_i value from [[specV5]](docs/Coinbase_Pseudocode_v5.pdf) - fig 7.SignRound6.step 9.
+
+#### func (Round6FullBcast) MarshalJSON
+```go
+func (r6b Round6FullBcast) MarshalJSON() ([]byte, error)
+```
+`MarshalJSON` converts `Round6FullBcast` to its json format.
+
+#### func (*Round6FullBcast) UnmarshalJSON
+```go
+func (r6b *Round6FullBcast) UnmarshalJSON(data []byte) error
+```
+`UnmarshalJSOn` converts the input json format data to this `Round6FullBcast`.
+
+#### func (*Signer) SignRound6Full
+```go
+func (signer *Signer) SignRound6Full(hash []byte, in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) (*Round6FullBcast, error)
+```
+`SignRound6Full` performs the round 6 signing operation according to
+[[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+- If in the trusted dealer mode, see fig.7 - SignRound6.
+- If in the DKG mode, see fig.8 - SignRound6.
+
+#### func (*Signer) signRound6Offline
+```go
+func (signer *Signer) signRound6Offline(in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) error
+```
+`signRound6Offline` performs the round 6 signing operation according to
+[[specV5]](docs/Coinbase_Pseudocode_v5.pdf) - fig.9 - SignRound6Offline. 
+
+#### func (*Signer) signRound6Online
+```go
+func (signer *Signer) signRound6Online(hash []byte) (*Round6FullBcast, error)
+```
+`SignRound6Online` performs the round 6 signing operation according to
+[[specV5]](docs/Coinbase_Pseudocode_v5.pdf) - fig.9 - SignRound6Online.
+
+#### func (*Signer) SignOutput
+```go
+func (signer *Signer) SignOutput(in map[uint32]*Round6FullBcast) (*EcdsaSignature, error)
+```
+`SignOutput` performs the signature aggregation step according to [[specV5]](docs/Coinbase_Pseudocode_v5.pdf).
+- If in the trusted dealer mode, see fig.7 - SignOutput.
+- If in the DKG mode, see fig.8 - SignOutput.
+
+#### func (Signer) normalize
+```go
+func (signer Signer) normalizeS(s *big.Int) *big.Int
+```
+Normalize the signature to a "low S" form. In ECDSA, signatures are
+of the form (r, s) where r and s are numbers lying in some finite
+field. The verification equation will pass for (r, s) iff it passes
+for (r, -s), so it is possible to ``modify'' signatures in transit
+by flipping the sign of s. This does not constitute a forgery since
+the signed message still cannot be changed, but for some applications,
+changing even the signature itself can be a problem. Such applications
+require a "strong signature". It is believed that ECDSA is a strong
+signature except for this ambiguity in the sign of s, so to accommodate
+these applications we will only produce signatures for which
+s is in the lower half of the field range. This eliminates the
+ambiguity.
+
+However, for some systems, signatures with high s-values are considered
+valid. (For example, parsing the historic Bitcoin blockchain requires
+this.) We normalize to the low S form which ensures that the s value
+lies in the lower half of its range.
+See <https://en.bitcoin.it/wiki/BIP_0062#Low_S_values_in_signatures>.
+  
diff --git a/pkg/tecdsa/gg20/dealer/README.md b/pkg/tecdsa/gg20/dealer/README.md
new file mode 100755
index 00000000..487cb732
--- /dev/null
+++ b/pkg/tecdsa/gg20/dealer/README.md
@@ -0,0 +1,252 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# dealer
+
+```go
+import "github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+```
+
+## Index
+
+- [func DerivePublicKey(curve elliptic.Curve, secretKey *big.Int) (*curves.EcPoint, error)](<#func-derivepublickey>)
+- [func NewDealerShares(curve elliptic.Curve, threshold, total uint32, ikm *big.Int) (*curves.EcPoint, map[uint32]*Share, error)](<#func-newdealershares>)
+- [func NewSecret(curve elliptic.Curve) (*big.Int, error)](<#func-newsecret>)
+- [func PreparePublicShares(sharesMap map[uint32]*Share) (map[uint32]*PublicShare, error)](<#func-preparepublicshares>)
+- [type DistributedKeyGenType](<#type-distributedkeygentype>)
+  - [func (dkg DistributedKeyGenType) GetProofParams(id uint32) *ProofParams](<#func-distributedkeygentype-getproofparams>)
+  - [func (dkg DistributedKeyGenType) IsTrustedDealer() bool](<#func-distributedkeygentype-istrusteddealer>)
+- [type KeyGenType](<#type-keygentype>)
+- [type ParticipantData](<#type-participantdata>)
+  - [func (pd ParticipantData) MarshalJSON() ([]byte, error)](<#func-participantdata-marshaljson>)
+  - [func (pd *ParticipantData) UnmarshalJSON(bytes []byte) error](<#func-participantdata-unmarshaljson>)
+- [type ParticipantDataJson](<#type-participantdatajson>)
+- [type ProofParams](<#type-proofparams>)
+  - [func NewProofParams() (*ProofParams, error)](<#func-newproofparams>)
+  - [func NewProofParamsWithPrimes(p, q *big.Int) (*ProofParams, error)](<#func-newproofparamswithprimes>)
+- [type PublicShare](<#type-publicshare>)
+- [type Share](<#type-share>)
+  - [func (s Share) MarshalJSON() ([]byte, error)](<#func-share-marshaljson>)
+  - [func (s *Share) UnmarshalJSON(bytes []byte) error](<#func-share-unmarshaljson>)
+- [type ShareJson](<#type-sharejson>)
+- [type TrustedDealerKeyGenType](<#type-trusteddealerkeygentype>)
+  - [func (td TrustedDealerKeyGenType) GetProofParams(_ uint32) *ProofParams](<#func-trusteddealerkeygentype-getproofparams>)
+  - [func (td TrustedDealerKeyGenType) IsTrustedDealer() bool](<#func-trusteddealerkeygentype-istrusteddealer>)
+
+
+## func [DerivePublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L178>)
+
+```go
+func DerivePublicKey(curve elliptic.Curve, secretKey *big.Int) (*curves.EcPoint, error)
+```
+
+## func [NewDealerShares](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L184>)
+
+```go
+func NewDealerShares(curve elliptic.Curve, threshold, total uint32, ikm *big.Int) (*curves.EcPoint, map[uint32]*Share, error)
+```
+
+NewDealerShares generates the Secp256k1 private key shares and public key if ikm == nil\, a new private key will be generated
+
+## func [NewSecret](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L174>)
+
+```go
+func NewSecret(curve elliptic.Curve) (*big.Int, error)
+```
+
+New Secret generates a new private key
+
+## func [PreparePublicShares](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L159>)
+
+```go
+func PreparePublicShares(sharesMap map[uint32]*Share) (map[uint32]*PublicShare, error)
+```
+
+PreparePublicShares makes public shares that can be sent to the participant to compute their additive shares and participate in signing rounds
+
+## type [DistributedKeyGenType](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L26-L28>)
+
+DistributedKeyGenType means each participant has their own proof params that were distributed to each other participant
+
+```go
+type DistributedKeyGenType struct {
+    ProofParams map[uint32]*ProofParams
+}
+```
+
+### func \(DistributedKeyGenType\) [GetProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L46>)
+
+```go
+func (dkg DistributedKeyGenType) GetProofParams(id uint32) *ProofParams
+```
+
+GetProofParams returns the proof params specified by the participant id
+
+### func \(DistributedKeyGenType\) [IsTrustedDealer](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L41>)
+
+```go
+func (dkg DistributedKeyGenType) IsTrustedDealer() bool
+```
+
+IsTrustedDealer return true if TrustedDealerKeyGenType
+
+## type [KeyGenType](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L12-L15>)
+
+KeyGenType encapsulates the different methods that tecdsa can generate keys\. Currently TrustedDealer or Distributed Key Generation
+
+```go
+type KeyGenType interface {
+    IsTrustedDealer() bool
+    GetProofParams(id uint32) *ProofParams
+}
+```
+
+## type [ParticipantData](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L23-L32>)
+
+ParticipantData represents all data to be sent to a participant after the dealer is finished
+
+```go
+type ParticipantData struct {
+    Id             uint32
+    DecryptKey     *paillier.SecretKey
+    SecretKeyShare *Share
+    // Public values set to all signing participants
+    EcdsaPublicKey *curves.EcPoint
+    KeyGenType     KeyGenType
+    PublicShares   map[uint32]*PublicShare
+    EncryptKeys    map[uint32]*paillier.PublicKey
+}
+```
+
+### func \(ParticipantData\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L46>)
+
+```go
+func (pd ParticipantData) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*ParticipantData\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L63>)
+
+```go
+func (pd *ParticipantData) UnmarshalJSON(bytes []byte) error
+```
+
+## type [ParticipantDataJson](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L34-L44>)
+
+```go
+type ParticipantDataJson struct {
+    Id             uint32
+    DecryptKey     *paillier.SecretKey
+    SecretKeyShare *Share
+    // Public values set to all signing participants
+    EcdsaPublicKey    *curves.EcPoint
+    DealerParams      *ProofParams
+    ParticipantParams map[uint32]*ProofParams
+    PublicShares      map[uint32]*PublicShare
+    EncryptKeys       map[uint32]*paillier.PublicKey
+}
+```
+
+## type [ProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L88-L95>)
+
+ProofParams is the modulus and generators used when constructing keys and completing the signing rounds
+
+```go
+type ProofParams struct {
+    // n is the modulus for the signing rounds, product of two safe primes
+    N   *big.Int
+    // h1 random value quadratic residue in n
+    H1  *big.Int
+    // h2 is a random modular power of h1
+    H2  *big.Int
+}
+```
+
+### func [NewProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L140>)
+
+```go
+func NewProofParams() (*ProofParams, error)
+```
+
+NewProofParams creates new ProofParams with \`bits\` sized values
+
+### func [NewProofParamsWithPrimes](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L146>)
+
+```go
+func NewProofParamsWithPrimes(p, q *big.Int) (*ProofParams, error)
+```
+
+NewProofParamsWithPrimes creates new ProofParams using the parameters as the primes
+
+## type [PublicShare](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L98-L100>)
+
+PublicShare can be sent to a Participant so it can be used to convert Share to its additive form
+
+```go
+type PublicShare struct {
+    Point *curves.EcPoint
+}
+```
+
+## type [Share](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L103-L106>)
+
+Share represents a piece of the ECDSA private key and a commitment to the share
+
+```go
+type Share struct {
+    *v1.ShamirShare
+    Point *curves.EcPoint
+}
+```
+
+### func \(Share\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L117>)
+
+```go
+func (s Share) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*Share\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L125>)
+
+```go
+func (s *Share) UnmarshalJSON(bytes []byte) error
+```
+
+## type [ShareJson](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/dealer.go#L111-L115>)
+
+ShareJson encapsulates the data that is serialized to JSON used internally and not for external use\. Public so other pieces can use for serialization
+
+```go
+type ShareJson struct {
+    Identifier uint32   // x-coordinate
+    Value      *big.Int // y-coordinate
+    Point      *curves.EcPoint
+}
+```
+
+## type [TrustedDealerKeyGenType](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L19-L21>)
+
+TrustedDealerKeyGenType means the same proof parameters will be used by all participants
+
+```go
+type TrustedDealerKeyGenType struct {
+    ProofParams *ProofParams
+}
+```
+
+### func \(TrustedDealerKeyGenType\) [GetProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L36>)
+
+```go
+func (td TrustedDealerKeyGenType) GetProofParams(_ uint32) *ProofParams
+```
+
+GetProofParams returns the proof params specified by the participant id
+
+### func \(TrustedDealerKeyGenType\) [IsTrustedDealer](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/dealer/keygentype.go#L31>)
+
+```go
+func (td TrustedDealerKeyGenType) IsTrustedDealer() bool
+```
+
+IsTrustedDealer return true if TrustedDealerKeyGenType
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/tecdsa/gg20/dealer/dealer.go b/pkg/tecdsa/gg20/dealer/dealer.go
new file mode 100644
index 00000000..ab1df45f
--- /dev/null
+++ b/pkg/tecdsa/gg20/dealer/dealer.go
@@ -0,0 +1,297 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dealer
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// ParticipantData represents all data to be sent to a participant
+// after the dealer is finished
+type ParticipantData struct {
+	Id             uint32
+	DecryptKey     *paillier.SecretKey
+	SecretKeyShare *Share
+	// Public values set to all signing participants
+	EcdsaPublicKey *curves.EcPoint
+	KeyGenType     KeyGenType
+	PublicShares   map[uint32]*PublicShare
+	EncryptKeys    map[uint32]*paillier.PublicKey
+}
+
+type ParticipantDataJson struct {
+	Id             uint32
+	DecryptKey     *paillier.SecretKey
+	SecretKeyShare *Share
+	// Public values set to all signing participants
+	EcdsaPublicKey    *curves.EcPoint
+	DealerParams      *ProofParams
+	ParticipantParams map[uint32]*ProofParams
+	PublicShares      map[uint32]*PublicShare
+	EncryptKeys       map[uint32]*paillier.PublicKey
+}
+
+func (pd ParticipantData) MarshalJSON() ([]byte, error) {
+	data := ParticipantDataJson{
+		Id:             pd.Id,
+		DecryptKey:     pd.DecryptKey,
+		SecretKeyShare: pd.SecretKeyShare,
+		EcdsaPublicKey: pd.EcdsaPublicKey,
+		PublicShares:   pd.PublicShares,
+		EncryptKeys:    pd.EncryptKeys,
+	}
+	if pd.KeyGenType.IsTrustedDealer() {
+		data.DealerParams = pd.KeyGenType.GetProofParams(0)
+	} else {
+		data.ParticipantParams = pd.KeyGenType.(DistributedKeyGenType).ProofParams
+	}
+	return json.Marshal(data)
+}
+
+func (pd *ParticipantData) UnmarshalJSON(bytes []byte) error {
+	data := new(ParticipantDataJson)
+	if err := json.Unmarshal(bytes, data); err != nil {
+		return err
+	}
+	if data.DealerParams != nil {
+		pd.KeyGenType = TrustedDealerKeyGenType{
+			ProofParams: data.DealerParams,
+		}
+	} else {
+		pd.KeyGenType = DistributedKeyGenType{
+			ProofParams: data.ParticipantParams,
+		}
+	}
+	pd.Id = data.Id
+	pd.EncryptKeys = data.EncryptKeys
+	pd.DecryptKey = data.DecryptKey
+	pd.SecretKeyShare = data.SecretKeyShare
+	pd.PublicShares = data.PublicShares
+	pd.EcdsaPublicKey = data.EcdsaPublicKey
+	return nil
+}
+
+// ProofParams is the modulus and generators
+// used when constructing keys and completing the signing rounds
+type ProofParams struct {
+	// n is the modulus for the signing rounds, product of two safe primes
+	N *big.Int
+	// h1 random value quadratic residue in n
+	H1 *big.Int
+	// h2 is a random modular power of h1
+	H2 *big.Int
+}
+
+// PublicShare can be sent to a Participant so it can be used to convert Share to its additive form
+type PublicShare struct {
+	Point *curves.EcPoint
+}
+
+// Share represents a piece of the ECDSA private key and a commitment to the share
+type Share struct {
+	*v1.ShamirShare
+	Point *curves.EcPoint
+}
+
+// ShareJson encapsulates the data that is serialized to JSON
+// used internally and not for external use. Public so other pieces
+// can use for serialization
+type ShareJson struct {
+	Identifier uint32   // x-coordinate
+	Value      *big.Int // y-coordinate
+	Point      *curves.EcPoint
+}
+
+func (s Share) MarshalJSON() ([]byte, error) {
+	return json.Marshal(ShareJson{
+		Identifier: s.Identifier,
+		Value:      s.Value.BigInt(),
+		Point:      s.Point,
+	})
+}
+
+func (s *Share) UnmarshalJSON(bytes []byte) error {
+	sh := ShareJson{}
+	err := json.Unmarshal(bytes, &sh)
+	if err != nil {
+		return err
+	}
+	s.ShamirShare = new(v1.ShamirShare)
+	s.ShamirShare.Identifier = sh.Identifier
+	f := curves.NewField(sh.Point.Curve.Params().N)
+	s.ShamirShare.Value = f.NewElement(sh.Value)
+	s.Point = sh.Point
+	return nil
+}
+
+// NewProofParams creates new ProofParams with `bits` sized values
+func NewProofParams() (*ProofParams, error) {
+	return genProofParams(core.GenerateSafePrime, core.Rand, paillier.PaillierPrimeBits)
+}
+
+// NewProofParamsWithPrimes creates new ProofParams using the
+// parameters as the primes
+func NewProofParamsWithPrimes(p, q *big.Int) (*ProofParams, error) {
+	pIdx := 0
+	safePrimes := []*big.Int{p, q}
+	f := func(bits uint) (*big.Int, error) {
+		r := safePrimes[pIdx]
+		pIdx = (pIdx + 1) % 2
+		return r, nil
+	}
+	return genProofParams(f, core.Rand, paillier.PaillierPrimeBits)
+}
+
+// PreparePublicShares makes public shares that can be sent
+// to the participant to compute their additive shares and participate in signing rounds
+func PreparePublicShares(sharesMap map[uint32]*Share) (map[uint32]*PublicShare, error) {
+	if len(sharesMap) == 0 {
+		return nil, fmt.Errorf("sharesMap cannot be nil or empty")
+	}
+	publicSharesMap := make(map[uint32]*PublicShare, len(sharesMap))
+	for i, p := range sharesMap {
+		if p == nil {
+			return nil, fmt.Errorf("share cannot be nil")
+		}
+		publicSharesMap[i] = &PublicShare{p.Point}
+	}
+	return publicSharesMap, nil
+}
+
+// New Secret generates a new private key
+func NewSecret(curve elliptic.Curve) (*big.Int, error) {
+	return core.Rand(curve.Params().N)
+}
+
+func DerivePublicKey(curve elliptic.Curve, secretKey *big.Int) (*curves.EcPoint, error) {
+	return curves.NewScalarBaseMult(curve, secretKey)
+}
+
+// NewDealerShares generates the Secp256k1 private key shares and public key
+// if ikm == nil, a new private key will be generated
+func NewDealerShares(curve elliptic.Curve, threshold, total uint32, ikm *big.Int) (*curves.EcPoint, map[uint32]*Share, error) {
+	if total < threshold {
+		return nil, nil, fmt.Errorf("parts cannot be less than threshold")
+	}
+	if total > 255 {
+		return nil, nil, fmt.Errorf("parts cannot exceed 255")
+	}
+	if threshold < 2 {
+		return nil, nil, fmt.Errorf("threshold must be at least 2")
+	}
+	if threshold > 255 {
+		return nil, nil, fmt.Errorf("threshold cannot exceed 255")
+	}
+	if curve.Params().BitSize != 256 {
+		return nil, nil, fmt.Errorf("invalid curve size")
+	}
+	var err error
+	if ikm == nil {
+		ikm, err = NewSecret(curve)
+		if err != nil {
+			return nil, nil, err
+		}
+	}
+
+	pk, err := DerivePublicKey(curve, ikm)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	q := curves.NewField(curve.Params().N)
+	shamir, err := v1.NewShamir(int(threshold), int(total), q)
+	if err != nil {
+		return nil, nil, err
+	}
+	// Create the shares to be distributed to participants
+	shares, err := shamir.Split(ikm.Bytes())
+	if err != nil {
+		return nil, nil, err
+	}
+
+	dSharesMap := make(map[uint32]*Share, total)
+	for i, s := range shares {
+		// Create a commitment to the private share value
+		publicShare, err := curves.NewScalarBaseMult(curve, s.Value.BigInt())
+		if err != nil {
+			return nil, nil, err
+		}
+		dSharesMap[uint32(i+1)] = &Share{
+			s,
+			publicShare,
+		}
+	}
+	return pk, dSharesMap, nil
+}
+
+// genProofParams creates all the values needed for ProofParams using the specified
+// genSafePrime function, genRandInMod function, and number of bits
+func genProofParams(genSafePrime func(uint) (*big.Int, error), genRandInMod func(*big.Int) (*big.Int, error), bits uint) (*ProofParams, error) {
+
+	values := make(chan *big.Int, 2)
+	errors := make(chan error, 2)
+
+	var p, q *big.Int
+
+	for p == q {
+		for range []int{1, 2} {
+			go func() {
+				value, err := genSafePrime(bits)
+				values <- value
+				errors <- err
+			}()
+		}
+
+		for _, err := range []error{<-errors, <-errors} {
+			if err != nil {
+				return nil, err
+			}
+		}
+
+		p, q = <-values, <-values
+	}
+
+	// Compute modulus
+	n := new(big.Int).Mul(p, q)
+
+	var f, alpha *big.Int
+
+	for f == alpha {
+		for range []int{1, 2} {
+			go func() {
+				value, err := genRandInMod(n)
+				values <- value
+				errors <- err
+			}()
+		}
+
+		for _, err := range []error{<-errors, <-errors} {
+			if err != nil {
+				return nil, err
+			}
+		}
+
+		f, alpha = <-values, <-values
+	}
+
+	// Compute Quadratic Residue generator h1
+	h1, err := core.Mul(f, f, n)
+	if err != nil {
+		return nil, err
+	}
+	// Compute a modular exponent of h1 as h2
+	h2 := new(big.Int).Exp(h1, alpha, n)
+	return &ProofParams{n, h1, h2}, nil
+}
diff --git a/pkg/tecdsa/gg20/dealer/dealer_test.go b/pkg/tecdsa/gg20/dealer/dealer_test.go
new file mode 100644
index 00000000..970c31bc
--- /dev/null
+++ b/pkg/tecdsa/gg20/dealer/dealer_test.go
@@ -0,0 +1,298 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dealer
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+	"testing"
+
+	tt "github.com/coinbase/kryptology/internal"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+type proofParamsTest struct {
+	bits                      uint
+	p, q, f, alpha, n, h1, h2 *big.Int
+}
+
+func TestProofParamsDistinct(t *testing.T) {
+	if testing.Short() {
+		t.Skip("Skipping TestNewProofParams")
+	}
+	proofParams1, err := NewProofParams()
+	tt.AssertNoError(t, err)
+	proofParams2, err := NewProofParams()
+	tt.AssertNoError(t, err)
+	// Ensure two fresh params are distinct
+	tt.AssertBigIntNe(t, proofParams1.N, proofParams2.N)
+	tt.AssertBigIntNe(t, proofParams1.H1, proofParams2.H1)
+	tt.AssertBigIntNe(t, proofParams1.H2, proofParams2.H2)
+	tt.AssertBigIntNe(t, proofParams1.H1, proofParams2.H2)
+	tt.AssertBigIntNe(t, proofParams2.H1, proofParams1.H2)
+}
+
+func TestNewProofParamsKnownInputs(t *testing.T) {
+	testValues := []*proofParamsTest{
+		// Small values
+		{
+			bits:  32,
+			p:     tt.B10("3532369103"),
+			q:     tt.B10("3649146287"),
+			n:     tt.B10("12890131596525970561"),
+			f:     tt.B10("8088109122034248022"),
+			alpha: tt.B10("1662308981529268576"),
+			h1:    tt.B10("7740598546761717939"),
+			h2:    tt.B10("682354612026984561"),
+		},
+		{
+			bits:  32,
+			p:     tt.B10("3944080607"),
+			q:     tt.B10("3428458883"),
+			n:     tt.B10("13522118192337181981"),
+			f:     tt.B10("5840701024459274822"),
+			alpha: tt.B10("2412272517404271893"),
+			h1:    tt.B10("4853557737722970495"),
+			h2:    tt.B10("5994934451042525431"),
+		},
+		// Moderate values
+		{
+			bits:  128,
+			p:     tt.B10("322329737381194646436245717594125402007"),
+			q:     tt.B10("282826037495283584562306655618616030003"),
+			n:     tt.B10("91163242390418667918364564787170632477479160976682613402974201249506748416021"),
+			f:     tt.B10("17638430582866531982508662722842743174558403736326834628201276897756690386088"),
+			alpha: tt.B10("34615543197795812347714957897096525833286000039984371937454209042089659280135"),
+			h1:    tt.B10("40851724117810430297136359930266015275847955981156240132756117915444116044667"),
+			h2:    tt.B10("2951900472097897505645026011582677410773252477374130422613343770046117166202"),
+		},
+		{
+			bits:  128,
+			p:     tt.B10("292157587181890702665335334652613040839"),
+			q:     tt.B10("325151157188330058469323448521916671923"),
+			n:     tt.B10("94995377553542186895398706765950144779729213880991236718991546482239763663397"),
+			f:     tt.B10("26654717808934280883230015589496263972208518550642662982505593055882359111187"),
+			alpha: tt.B10("7966520803638388496765803768628435924825241054572312029050259003983212755370"),
+			h1:    tt.B10("5179570387906113412737648546624738048023020835338868529502169468678133964537"),
+			h2:    tt.B10("10547660360737303449442765975692388640388451365836709448045978219828751728319"),
+		},
+		{
+			bits:  256,
+			p:     tt.B10("107033239041727130475722739799997676073864393791537660670383998236210681119623"),
+			q:     tt.B10("101044016059784163555459318277136957252800092661593566159166914417570906646479"),
+			n:     tt.B10("10815068324662993508164204692909269429257853772524581783499643160896147777579932560873002543907262462663453338979819981987639157192530671167315407970757417"),
+			f:     tt.B10("1953061770018232252742159833594632380255058093321781494393026400131699755086780416725368511941904170619021125367199106612073013879151950545295494471917586"),
+			alpha: tt.B10("3834737493713501721754032502075239025227523335638258845915381809661597402119775003441676291390662996252213319663808209050925460873587874764050296101685895"),
+			h1:    tt.B10("4320863187178906616455838434320546185913714725291410243809642735069293363508952325120395870462907728649344143321941759468514069154751317138801024570168772"),
+			h2:    tt.B10("120718613217412490133304046154402631667794560287874694847992615611850656731360431202354938411320852540513514674759337083384626860820954644419583411766351"),
+		},
+		{
+			bits:  384,
+			p:     tt.B10("32084004412756729129951801667785515880675761456063995183947188458613139063207470311815946953832968900352953230728387"),
+			q:     tt.B10("29916944379760549540437351937971471314912245460177593896040174973102477981114163011201660299005185209119438597828359"),
+			n:     tt.B10("959855375496435098250249215425472550633883273892366636418539818992965634591339629957717390484127329139909742919598777040561784144823812817912999056501521038131720434324215292734547756922118558391569327009178732840170816605974926933"),
+			f:     tt.B10("385587253104646973526979645949729332346264096947680952768033869130436857081349140581602832593968949445974766461768488933252048270498136280086338674644694131509548710522098707848381318033383109609217157024017362912090271855148305753"),
+			alpha: tt.B10("802185911525259396858796733147029250385269666421140433965082754581471367564078646151444020878683709745451191116608505247291434446513232310868194940814603767895499634946931851453036837571701496215847350658468841482052820517809333229"),
+			h1:    tt.B10("178008912521451997980828179602129531520630311485835136079559640359862691552613136589163589576614000919533806943298596513924271315778839665428154562258548640808571695748963797268761082739205874075388473490030003603923689503067183040"),
+			h2:    tt.B10("745214268481251149009481704337976102510789515926575612825292375296159794448793242061611805039939202276919677151010882286558923931416568852289471804803844816398728119129991210671518959645714106367269729755312158228329249816980475270"),
+		},
+		// Large values
+		{
+			bits:  512,
+			p:     tt.B10("13402506741879909705247508951754644667693815954510447147853401275166715648653624953727875501571997058765483588107170836999606735577380807635904979215471223"),
+			q:     tt.B10("11653902873241241454023189143953837349357783829238806459834283425558693905220509553841347340456113574524451192031086644221307515208152789001650663503660563"),
+			n:     tt.B10("156191511827829389348931232517809021193737031236087728136517838199389943369965856590107829262785004698503828473513808786810233768538839579197933368379417834150601329312673673331620361860375096296875273339782921082363787492351296298975304355190651921368035999591115305805841234398665476692295221538383486478549"),
+			f:     tt.B10("105921637008007596242687136291215115379726727456238235988373686146222434936223500056214726834331554510844058841770826956376123791662340879537052405342520755293551902415159117602408529783890097619872151969618325933434785364935566958887498479829791790980528973576902755163741033898337074607062877295575097398027"),
+			alpha: tt.B10("25789967854521552702486904432614912173720577957067512132821791246814877842721436035270615425020444434024971512294898663888264691831827542714695372062387891168110143236989908534429568576918984768687539132492516591672303697698170624423203504297159536671946076838229266401524840183833222277329757013745584001546"),
+			h1:    tt.B10("109148140769505087324733385900286462326732849630583465544259040792765915286334491396382542664592507525818592725480821200175041450931363165947024379763315328559232391113072007292588635875180031961190886952268563630792514713201393588092419634985147285618899976278717726255619641744498785998181329854711823095546"),
+			h2:    tt.B10("94378737602960275292210693440145810570305300627429873229499389511900935499225116793780120613621237391570231775304193964237372206306035564013470561242055886111069484714672545735756099242908140870434477147472839262127337437981240832226964726355298825863677601914170172556735529230548373855322923244573123279503"),
+		},
+		{
+			bits:  768,
+			p:     tt.B10("1172772268222869135746475976449967443220728362530972350209215332326944127327313132623800901521121085140613636265094266218948641934493008389679978199334246856112769202086824359372598961726505267139083231588791834137172543234789315807"),
+			q:     tt.B10("1314405892055491780007828981914086343593182251638676771033374221066923695698195814335147429260730862492680087129273760043532686847298160063261905415386263791411919171601989373598015912958550608858030660357193476090089828897530026363"),
+			n:     tt.B10("1541498779391422781877621899609182891994518423831078971398095064093240181958395952087587523810155282992062102677958880273569778308399535365070591300847802232397362358553902180950726216134823595994312857807899016362827564748344426602306284583250792792955584830704699574352786228055898787779684334887796554135523740299232752418576979598495344283249523357041872944823359212536062188372536232252883102629174357505712906918947289385294555564404297090523111007442619941"),
+			f:     tt.B10("677989603002668106538546698801906687540953878286266137841947147184500778764869778659833934984587317604513819283010285362738864682953146933651161066202621461396232147445569683175461296649543802796602231833030736121285930269157674257535891093504924867936400869024264116704856719772498384123109010763539447471532256330132326434718941018313194910829655497567041642775909179031155007288364436570606906729509686118354750765498089348483611766753776448842378876138519492"),
+			alpha: tt.B10("114288744075004384976717863018507283999460985427750993906297463893507876719107609356624383942527236695629514992610734269119471173538706034473306129332325931042872977327331297527020478557239451077438243523906598820487675455784275310274645270668758013883553399018822156980090134267245285532188867755106999667490195000880243418087891029246273568999920979861679097466175735879692809171018736759443882860496755786381993875691404126612248980033959651714747792276147737"),
+			h1:    tt.B10("620967314571677993621097689227639136272103014757170315573975110856397012072491377414649496358698230838195501545740286798426409144254723458159053919007894986391912508160206658806451241744234372321843332002338225864899335573077301759675298903687495806772704923690781848994603501089797921531725638938738179420863221589774213217232543640290387805947665372254697970073247897667521511659457860642449029569029517623767487058427274486859786874744942405492665199950785432"),
+			h2:    tt.B10("76914751581970807907441569885723431665256967585278657498014680460706690630690511580918136412833880806036782416407924930702533867597105318751032916063690482766856596872705517306464852735714057981896630822244930789132183799641349424925415175723846703728891058389586627867213281285663436964887344556696099523277630280786499528890816178997513077407863541104914946885418721934064536344132808255638281693284725391856052235328538580328974443057077286389922807376719663"),
+		},
+		{
+			bits:  1024,
+			p:     tt.B10("143755035639380470881675053832887329127071994369082228734251178758720295757727746866602803885188916682941316933470494309842642978838563803093231719031787157346353241144419080311914813130902891433725104776371931366053979438257736721584736553640620915684339223777632919031284192033212292380442862701004222839839"),
+			q:     tt.B10("157610148541756483881391781006962391307552138517291043623605820440922385872835081567152281545287738290719615978200227103612218411158996749276828547434997453805807400563395441995925455411524662188622149635847181006072308124274294119590441349155209514553371838079002517661151936444244814496603165994642070193603"),
+			n:     tt.B10("22657252520748253292205422817162431301953923432914829530688424232913850279325496327198502914522231560238552529734156383924448818535517634061008476071362010781638360092704508943571866960229942049437914690556866055765377519627454975682400206932320319743805083072214857842762721537739950074695623974079312071498296625705376593890814889314744719469735809152488403143751157723139035869185892099006348653635981206799193781030834368833947197930944812082594326193527332208252230115672713914945889734620959932802893197325106135662762752470236627025599443912886530954179753873735786171937758916890000958846322096261981191349917"),
+			f:     tt.B10("1837638079389833117482811954367448162039150688934715357008176167854778196053567600507723116000842565891056468100639254152368756271384552650513939509902426167341409789748254644062944719126858575456567236001716746439508326036437929236231071381297886734438184468608864990027398302196877407296053037503604568299961010754385824604920003026632557650533262397423669648421709810685765745708396444919011990421325895569050175267461506858799263552873376629134365398033677037055272530963036099599403027301535753296115083718072540480783858873095117364364266062755097447466435769729951908277760553710182836153846164530411975604918"),
+			alpha: tt.B10("10180338097046484720218938053574123628365802528878792921163521672678754788791478828324990427578268448710957792590062710921525369303666382188088935948462358688112248543323147863535957259946701818603149864941901611000864295172043472766639565354776537620683789487713327494120406803876018608041033830876741801587506282628346530619373455471179490747306225596783791589245228576159393496935812211359325406330371083545331242665519420884314024434338105230632567436938752428628410605413507478781802047209792610815229258139499934699515945155157568537597419579199189161997145564214140538430818340200949175908048368010772725324603"),
+			h1:    tt.B10("1656240578726656472982971149349519787334711917407365099302234533544813508569815627980683589661064462432530865415359056057808102091523404507258432558908205534552293741530636994509001244876063100184310152841421199340736107615594714300348773466097241418448144156166001659986260228183904703220818795694087610910042320395937374686902326940538583574324286121691672644406892835183587590587202614663009833189341162830624857807052409882165022116236155557756122995333309543614144793788263137215939462312172467168512721258271559466365919027756907792017876708485439503402393043941731729574262940831871878730655264809864217559480"),
+			h2:    tt.B10("14402453257845659067057298000258011503319998232626269706984076352133770609685418836115347557347426169382037951633347064435045381846434457869015364415080444373680323708145947051971271955375310253866278892655687643826235776329111596605765760603463133947524568629075859958729387193155836149415340890049121874989262064208424476603584205725570597892845954158554057663626043501240089826176762119712071675190787646116090239837347676973220240416596698697171855421900633747224108875362350155229834913561333497452922143478131464246300744179904539036740021278776277717870280483008305379221666473338482907287695159341884476431429"),
+		},
+	}
+
+	for _, test := range testValues {
+		pIdx := 0
+		safePrimes := []*big.Int{test.p, test.q}
+		randVars := []*big.Int{test.f, test.alpha}
+		f := func(bits uint) (*big.Int, error) {
+			r := safePrimes[pIdx]
+			pIdx = (pIdx + 1) % 2
+			return r, nil
+		}
+		rIdx := 0
+		g := func(nn *big.Int) (*big.Int, error) {
+			r := randVars[rIdx]
+			rIdx = (rIdx + 1) % 2
+			return r, nil
+		}
+
+		params, err := genProofParams(f, g, test.bits)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, params.N, test.n)
+		tt.AssertBigIntEq(t, params.H1, test.h1)
+		tt.AssertBigIntEq(t, params.H2, test.h2)
+	}
+}
+
+func TestSameResult(t *testing.T) {
+	test := proofParamsTest{
+		bits:  32,
+		p:     tt.B10("3532369103"),
+		q:     tt.B10("3649146287"),
+		n:     tt.B10("12890131596525970561"),
+		f:     tt.B10("8088109122034248022"),
+		alpha: tt.B10("1662308981529268576"),
+		h1:    tt.B10("7740598546761717939"),
+		h2:    tt.B10("682354612026984561"),
+	}
+
+	idx := 0
+	safePrimes := []*big.Int{test.p, test.q}
+	f := func(bits uint) (*big.Int, error) {
+		r := safePrimes[idx]
+		idx = (idx + 1) % 2
+		return r, nil
+	}
+	randVars := []*big.Int{test.f, test.alpha}
+	rIdx := 0
+	g := func(nn *big.Int) (*big.Int, error) {
+		r := randVars[rIdx]
+		rIdx = (rIdx + 1) % 2
+		return r, nil
+	}
+	params1, err := genProofParams(f, g, 32)
+	tt.AssertNoError(t, err)
+	params2, err := genProofParams(f, g, 32)
+	tt.AssertNoError(t, err)
+	tt.AssertBigIntEq(t, params1.N, params2.N)
+	tt.AssertBigIntEq(t, params1.H1, params2.H1)
+	tt.AssertBigIntEq(t, params1.H2, params2.H2)
+}
+
+func TestNewDealerShares(t *testing.T) {
+	curve := btcec.S256()
+	for _, secretIsNil := range []bool{true, false} {
+		t.Run(fmt.Sprintf("NewDealerShare should not fail if bool(ikm == nil) is %t", secretIsNil), func(t *testing.T) {
+			var ikm *big.Int
+			var err error
+			if secretIsNil {
+				ikm, err = NewSecret(curve)
+				tt.AssertNoError(t, err)
+			}
+			pk, sharesMap, err := NewDealerShares(curve, 2, 3, ikm)
+			if err != nil {
+				t.Errorf("NewDealerShares failed: %v", err)
+				t.FailNow()
+			}
+
+			if pk == nil {
+				t.Errorf("NewDealerShares public key is nil")
+				t.FailNow()
+			}
+
+			if secretIsNil {
+				derivedPublicKey, err := DerivePublicKey(curve, ikm)
+				tt.AssertNoError(t, err)
+				tt.AssertBigIntEq(t, pk.X, derivedPublicKey.X)
+				tt.AssertBigIntEq(t, pk.Y, derivedPublicKey.Y)
+			}
+
+			if len(sharesMap) != 3 {
+				t.Errorf("NewDealerShares didn't produce enough shares")
+				t.FailNow()
+			}
+
+			for _, s := range sharesMap {
+				if s.ShamirShare == nil {
+					t.Errorf("NewDealerShares didn't produce valid sharesMap")
+					t.FailNow()
+				}
+				if s.Point == nil {
+					t.Errorf("NewDealerShares didn't produce valid public sharesMap")
+					t.FailNow()
+				}
+				x, y := curve.ScalarMult(curve.Gx, curve.Gy, s.ShamirShare.Value.Bytes())
+				tt.AssertBigIntEq(t, x, s.Point.X)
+				tt.AssertBigIntEq(t, y, s.Point.Y)
+			}
+
+			n := curves.NewField(curve.N)
+			combiner, err := v1.NewShamir(2, 3, n)
+			tt.AssertNoError(t, err)
+
+			sShareArray := make([]*v1.ShamirShare, len(sharesMap))
+			for i, s := range sharesMap {
+				// Skip sharesMap[0] which is always nil
+				if i == 0 && s != nil {
+					t.Errorf("expected sharesMap[0] to be nil")
+					t.FailNow()
+				} else {
+					sShareArray[i-1] = s.ShamirShare
+				}
+			}
+			sk, err := combiner.Combine(sShareArray...)
+			if err != nil {
+				t.Errorf("Shares could not be recombined")
+			}
+			pkx, pky := curve.ScalarBaseMult(sk)
+			tt.AssertNotNil(t, pkx, pky)
+			tt.AssertBigIntEq(t, pkx, pk.X) // nolint
+			tt.AssertBigIntEq(t, pky, pk.Y) // nolint
+
+		})
+	}
+}
+
+func TestPreparePublicShares(t *testing.T) {
+	curve := btcec.S256()
+	pk, sharesMap, err := NewDealerShares(curve, 2, 3, nil)
+	if err != nil {
+		t.Errorf("NewDealerShares failed: %v", err)
+	}
+
+	if pk == nil {
+		t.Errorf("NewDealerShares public key is nil")
+	}
+
+	if len(sharesMap) != 3 {
+		t.Errorf("NewDealerShares didn't produce enough sharesMap")
+	}
+
+	publicShares, err := PreparePublicShares(sharesMap)
+	if err != nil {
+		t.Errorf("PreparePublicShares failed: %v", err)
+	}
+
+	if len(publicShares) != len(sharesMap) {
+		t.Errorf("len(publicShares) != len(sharesMap): %d != %d", len(publicShares), len(sharesMap))
+	}
+	for i := range publicShares {
+		tt.AssertBigIntEq(t, publicShares[i].Point.X, sharesMap[i].Point.X)
+		tt.AssertBigIntEq(t, publicShares[i].Point.Y, sharesMap[i].Point.Y)
+	}
+}
diff --git a/pkg/tecdsa/gg20/dealer/keygentype.go b/pkg/tecdsa/gg20/dealer/keygentype.go
new file mode 100644
index 00000000..abe4f27c
--- /dev/null
+++ b/pkg/tecdsa/gg20/dealer/keygentype.go
@@ -0,0 +1,48 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package dealer
+
+// KeyGenType encapsulates the different methods
+// that tecdsa can generate keys. Currently
+// TrustedDealer or Distributed Key Generation
+type KeyGenType interface {
+	IsTrustedDealer() bool
+	GetProofParams(id uint32) *ProofParams
+}
+
+// TrustedDealerKeyGenType means the same proof parameters
+// will be used by all participants
+type TrustedDealerKeyGenType struct {
+	ProofParams *ProofParams
+}
+
+// DistributedKeyGenType means each participant has their
+// own proof params that were distributed to each other
+// participant
+type DistributedKeyGenType struct {
+	ProofParams map[uint32]*ProofParams
+}
+
+// IsTrustedDealer return true if TrustedDealerKeyGenType
+func (td TrustedDealerKeyGenType) IsTrustedDealer() bool {
+	return true
+}
+
+// GetProofParams returns the proof params specified by the participant id
+func (td TrustedDealerKeyGenType) GetProofParams(_ uint32) *ProofParams {
+	return td.ProofParams
+}
+
+// IsTrustedDealer return true if TrustedDealerKeyGenType
+func (dkg DistributedKeyGenType) IsTrustedDealer() bool {
+	return false
+}
+
+// GetProofParams returns the proof params specified by the participant id
+func (dkg DistributedKeyGenType) GetProofParams(id uint32) *ProofParams {
+	return dkg.ProofParams[id]
+}
diff --git a/pkg/tecdsa/gg20/participant/README.md b/pkg/tecdsa/gg20/participant/README.md
new file mode 100755
index 00000000..921e5e89
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/README.md
@@ -0,0 +1,379 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# participant
+
+```go
+import "github.com/coinbase/kryptology/pkg/tecdsa/gg20/participant"
+```
+
+## Index
+
+- [type DkgParticipant](<#type-dkgparticipant>)
+  - [func (dp *DkgParticipant) DkgRound1(threshold, total uint32) (*DkgRound1Bcast, error)](<#func-dkgparticipant-dkground1>)
+  - [func (dp *DkgParticipant) DkgRound2(params map[uint32]*DkgRound1Bcast) (*DkgRound2Bcast, map[uint32]*DkgRound2P2PSend, error)](<#func-dkgparticipant-dkground2>)
+  - [func (dp *DkgParticipant) DkgRound3(d map[uint32]*core.Witness, x map[uint32]*v1.ShamirShare) (paillier.PsfProof, error)](<#func-dkgparticipant-dkground3>)
+  - [func (dp *DkgParticipant) DkgRound4(psfProof map[uint32]paillier.PsfProof) (*DkgResult, error)](<#func-dkgparticipant-dkground4>)
+- [type DkgParticipantData](<#type-dkgparticipantdata>)
+- [type DkgResult](<#type-dkgresult>)
+- [type DkgRound1Bcast](<#type-dkground1bcast>)
+- [type DkgRound2Bcast](<#type-dkground2bcast>)
+- [type DkgRound2P2PSend](<#type-dkground2p2psend>)
+- [type P2PSend](<#type-p2psend>)
+  - [func (p2ps *P2PSend) UnmarshalJSON(bytes []byte) error](<#func-p2psend-unmarshaljson>)
+- [type Participant](<#type-participant>)
+  - [func (p Participant) PrepareToSign(pubKey *curves.EcPoint, verify curves.EcdsaVerify, curve elliptic.Curve, keyGenType dealer.KeyGenType, publicSharesMap map[uint32]*dealer.PublicShare, pubKeys map[uint32]*paillier.PublicKey) (*Signer, error)](<#func-participant-preparetosign>)
+- [type Round1Bcast](<#type-round1bcast>)
+- [type Round1P2PSend](<#type-round1p2psend>)
+- [type Round3Bcast](<#type-round3bcast>)
+  - [func (r3b Round3Bcast) MarshalJSON() ([]byte, error)](<#func-round3bcast-marshaljson>)
+  - [func (r3b *Round3Bcast) UnmarshalJSON(data []byte) error](<#func-round3bcast-unmarshaljson>)
+- [type Round3BcastJSON](<#type-round3bcastjson>)
+- [type Round4Bcast](<#type-round4bcast>)
+- [type Round5Bcast](<#type-round5bcast>)
+- [type Round5P2PSend](<#type-round5p2psend>)
+- [type Round6FullBcast](<#type-round6fullbcast>)
+  - [func (r6b Round6FullBcast) MarshalJSON() ([]byte, error)](<#func-round6fullbcast-marshaljson>)
+  - [func (r6b *Round6FullBcast) UnmarshalJSON(data []byte) error](<#func-round6fullbcast-unmarshaljson>)
+- [type Round6FullBcastJSON](<#type-round6fullbcastjson>)
+- [type Signer](<#type-signer>)
+  - [func NewSigner(info *dealer.ParticipantData, cosigners []uint32) (*Signer, error)](<#func-newsigner>)
+  - [func (signer *Signer) SignOutput(in map[uint32]*Round6FullBcast) (*curves.EcdsaSignature, error)](<#func-signer-signoutput>)
+  - [func (signer *Signer) SignRound1() (*Round1Bcast, map[uint32]*Round1P2PSend, error)](<#func-signer-signround1>)
+  - [func (signer *Signer) SignRound2(params map[uint32]*Round1Bcast, p2p map[uint32]*Round1P2PSend) (map[uint32]*P2PSend, error)](<#func-signer-signround2>)
+  - [func (s *Signer) SignRound3(in map[uint32]*P2PSend) (*Round3Bcast, error)](<#func-signer-signround3>)
+  - [func (s *Signer) SignRound4(deltas map[uint32]*Round3Bcast) (*Round4Bcast, error)](<#func-signer-signround4>)
+  - [func (signer *Signer) SignRound5(witnesses map[uint32]*Round4Bcast) (*Round5Bcast, map[uint32]*Round5P2PSend, error)](<#func-signer-signround5>)
+  - [func (signer *Signer) SignRound6Full(hash []byte, in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) (*Round6FullBcast, error)](<#func-signer-signround6full>)
+
+
+## type [DkgParticipant](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/participant.go#L299-L304>)
+
+DkgParticipant is a DKG player that contains information needed to perform DKG rounds and finally get info for signing rounds\.
+
+```go
+type DkgParticipant struct {
+    Curve elliptic.Curve
+
+    Round uint
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*DkgParticipant\) [DkgRound1](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round1.go#L31>)
+
+```go
+func (dp *DkgParticipant) DkgRound1(threshold, total uint32) (*DkgRound1Bcast, error)
+```
+
+DkgRound1 performs round 1 distributed key generation operation \[spec\] fig 5: DistKeyGenRound1
+
+### func \(\*DkgParticipant\) [DkgRound2](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round2.go#L31>)
+
+```go
+func (dp *DkgParticipant) DkgRound2(params map[uint32]*DkgRound1Bcast) (*DkgRound2Bcast, map[uint32]*DkgRound2P2PSend, error)
+```
+
+DkgRound2 implements distributed key generation round 2 \[spec\] fig 5: DistKeyGenRound2
+
+### func \(\*DkgParticipant\) [DkgRound3](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round3.go#L23>)
+
+```go
+func (dp *DkgParticipant) DkgRound3(d map[uint32]*core.Witness, x map[uint32]*v1.ShamirShare) (paillier.PsfProof, error)
+```
+
+DkgRound3 computes dkg round 3 as shown in \[spec\] fig\. 5: DistKeyGenRoun3
+
+### func \(\*DkgParticipant\) [DkgRound4](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round4.go#L35>)
+
+```go
+func (dp *DkgParticipant) DkgRound4(psfProof map[uint32]paillier.PsfProof) (*DkgResult, error)
+```
+
+DkgRound4 computes dkg round 4 as shown in \[spec\] fig\. 5: DistKeyGenRound4
+
+## type [DkgParticipantData](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round4.go#L28-L31>)
+
+```go
+type DkgParticipantData struct {
+    PublicKey   *paillier.PublicKey
+    ProofParams *dealer.ProofParams
+}
+```
+
+## type [DkgResult](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round4.go#L20-L26>)
+
+DkgResult is all the data generated from the DKG
+
+```go
+type DkgResult struct {
+    PublicShares    []*curves.EcPoint
+    VerificationKey *curves.EcPoint
+    SigningKeyShare *big.Int
+    EncryptionKey   *paillier.SecretKey
+    ParticipantData map[uint32]*DkgParticipantData
+}
+```
+
+## type [DkgRound1Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round1.go#L21-L27>)
+
+DkgRound1Bcast contains values to be broadcast to all players after the completion of DKG round 1
+
+```go
+type DkgRound1Bcast struct {
+    Identifier       uint32
+    Ci               core.Commitment
+    Pki              *paillier.PublicKey
+    H1i, H2i, Ni     *big.Int
+    Proof1i, Proof2i *proof.CdlProof
+}
+```
+
+## type [DkgRound2Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round2.go#L20-L22>)
+
+DkgRound2Bcast contains value that will be echo broadcast to all other players\.
+
+```go
+type DkgRound2Bcast struct {
+    Di *core.Witness
+}
+```
+
+## type [DkgRound2P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/dkg_round2.go#L25-L27>)
+
+DkgRound2P2PSend contains value that will be P2PSend to all other player Pj
+
+```go
+type DkgRound2P2PSend struct {
+    // contains filtered or unexported fields
+}
+```
+
+## type [P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round2.go#L20-L22>)
+
+P2PSend is all the values that need to be sent to each player
+
+```go
+type P2PSend struct {
+    Proof2, Proof3 proof.ResponseFinalizer
+}
+```
+
+### func \(\*P2PSend\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round2.go#L25>)
+
+```go
+func (p2ps *P2PSend) UnmarshalJSON(bytes []byte) error
+```
+
+UnmarshalJSON explicitly unmarshals into ResponseProofs instead of ResponsFinalizer interface
+
+## type [Participant](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/participant.go#L25-L28>)
+
+Participant is a tECDSA player that receives information from a trusted dealer
+
+```go
+type Participant struct {
+    dealer.Share
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Participant\) [PrepareToSign](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/participant.go#L247-L252>)
+
+```go
+func (p Participant) PrepareToSign(pubKey *curves.EcPoint, verify curves.EcdsaVerify, curve elliptic.Curve, keyGenType dealer.KeyGenType, publicSharesMap map[uint32]*dealer.PublicShare, pubKeys map[uint32]*paillier.PublicKey) (*Signer, error)
+```
+
+PrepareToSign creates a Signer out of a Participant\. The expected co\-signers for the signing rounds are expected to be exactly those included in the publicSharesMap
+
+## type [Round1Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round1.go#L21-L26>)
+
+Round1Bcast contains values to be broadcast to all players after the completion of singing round 1
+
+```go
+type Round1Bcast struct {
+    Identifier uint32
+    C          core.Commitment
+    Ctxt       *big.Int
+    Proof      *proof.Range1Proof
+}
+```
+
+## type [Round1P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round1.go#L28>)
+
+```go
+type Round1P2PSend = proof.Range1Proof
+```
+
+## type [Round3Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round3.go#L22-L32>)
+
+Round3Bcast represents the value to be broadcast to all players at the conclusion of round 3
+
+```go
+type Round3Bcast struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Round3Bcast\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round3.go#L39>)
+
+```go
+func (r3b Round3Bcast) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*Round3Bcast\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round3.go#L43>)
+
+```go
+func (r3b *Round3Bcast) UnmarshalJSON(data []byte) error
+```
+
+## type [Round3BcastJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round3.go#L34-L36>)
+
+Round3Bcast represents the value to be broadcast to all players at the conclusion of round 3
+
+```go
+type Round3BcastJSON struct {
+    DeltaElement *big.Int
+}
+```
+
+## type [Round4Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round4.go#L17-L19>)
+
+Round4Bcast are the values to be broadcast to the other players at the conclusion of signing round 4
+
+```go
+type Round4Bcast struct {
+    Witness *core.Witness
+}
+```
+
+## type [Round5Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round5.go#L19-L22>)
+
+Round5Bcast are the values to be broadcast to the other players at the conclusion of signing round 5
+
+```go
+type Round5Bcast struct {
+    Rbar  *curves.EcPoint
+    Proof *proof.PdlProof
+}
+```
+
+## type [Round5P2PSend](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round5.go#L26>)
+
+Round5P2PSend are the values sent to each participant at the conclusion of signing round 5
+
+```go
+type Round5P2PSend = proof.PdlProof
+```
+
+## type [Round6FullBcast](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L23-L33>)
+
+Round6FullBcast are the values to be broadcast to the other players This is the s\_i value from §5\.fig 5\.SignRound6\.step 9
+
+```go
+type Round6FullBcast struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Round6FullBcast\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L40>)
+
+```go
+func (r6b Round6FullBcast) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*Round6FullBcast\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L44>)
+
+```go
+func (r6b *Round6FullBcast) UnmarshalJSON(data []byte) error
+```
+
+## type [Round6FullBcastJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L35-L37>)
+
+Round6FullBcast are the values to be broadcast to the other players This is the s\_i value from §5\.fig 5\.SignRound6\.step 9
+
+```go
+type Round6FullBcastJSON struct {
+    SElement *big.Int
+}
+```
+
+## type [Signer](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/participant.go#L31-L43>)
+
+Signer is a tECDSA player that holds the additive shares needed for performing the signing operation
+
+```go
+type Signer struct {
+    PublicKey *curves.EcPoint
+    Curve     elliptic.Curve
+    Round     uint // current signing round in our linear state machine
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewSigner](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/participant.go#L46>)
+
+```go
+func NewSigner(info *dealer.ParticipantData, cosigners []uint32) (*Signer, error)
+```
+
+NewSigner C=creates a new signer from a dealer\-provided output and a specific set of co\-signers
+
+### func \(\*Signer\) [SignOutput](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L172>)
+
+```go
+func (signer *Signer) SignOutput(in map[uint32]*Round6FullBcast) (*curves.EcdsaSignature, error)
+```
+
+SignOutput performs the signature aggregation step in \[spec\] §5\.fig 5
+
+### func \(\*Signer\) [SignRound1](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round1.go#L36>)
+
+```go
+func (signer *Signer) SignRound1() (*Round1Bcast, map[uint32]*Round1P2PSend, error)
+```
+
+SignRound1 performs round 1 signing operation Trusted Dealer Mode: see \[spec\] fig 7: SignRound1 DKG Mode: see \[spec\] fig 8: SignRound1 NOTE: Pseudocode shows N\~\, h1\, h2\, the curve's g\, q\, and signer's public key as inputs Since \`signer\` already knows the paillier secret and public keys\, this input is not necessary here \`participant\.PrepareToSign\` receives the other inputs and stores them as state variables\.
+
+### func \(\*Signer\) [SignRound2](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round2.go#L45>)
+
+```go
+func (signer *Signer) SignRound2(params map[uint32]*Round1Bcast, p2p map[uint32]*Round1P2PSend) (map[uint32]*P2PSend, error)
+```
+
+SignRound2 performs round 2 signing operations for a single signer Trusted Dealer Mode: see \[spec\] fig 7: SignRound2 DKG Mode: see \[spec\] fig 8: SignRound2
+
+### func \(\*Signer\) [SignRound3](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round3.go#L56>)
+
+```go
+func (s *Signer) SignRound3(in map[uint32]*P2PSend) (*Round3Bcast, error)
+```
+
+SignRound3 performs the round 3 signing operation according to Trusted Dealer Mode: see \[spec\] fig 7: SignRound3 DKG Mode: see \[spec\] fig 8: SignRound3
+
+### func \(\*Signer\) [SignRound4](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round4.go#L26>)
+
+```go
+func (s *Signer) SignRound4(deltas map[uint32]*Round3Bcast) (*Round4Bcast, error)
+```
+
+SignRound4 performs the round 4 signing operation\. It takes input the delta\_j values broadcast from signers at the conclusion of round 3\. Trusted Dealer Mode: see \[spec\] fig 7: SignRound4 DKG Mode: see \[spec\] fig 8: SignRound4
+
+### func \(\*Signer\) [SignRound5](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round5.go#L33>)
+
+```go
+func (signer *Signer) SignRound5(witnesses map[uint32]*Round4Bcast) (*Round5Bcast, map[uint32]*Round5P2PSend, error)
+```
+
+SignRound5 performs the round 5 signing operation\. It takes input the Witness values broadcast from signers at the conclusion of round 4\. Trusted Dealer Mode: see \[spec\] fig 7: SignRound5 DKG Mode: see \[spec\] fig 8: SignRound5
+
+### func \(\*Signer\) [SignRound6Full](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/participant/round6.go#L57>)
+
+```go
+func (signer *Signer) SignRound6Full(hash []byte, in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) (*Round6FullBcast, error)
+```
+
+SignRound6Full performs the round 6 signing operation according to Trusted Dealer Mode: see \[spec\] fig 7: SignRound6 DKG Mode: see \[spec\] fig 8: SignRound6
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/tecdsa/gg20/participant/benches_test.go b/pkg/tecdsa/gg20/participant/benches_test.go
new file mode 100644
index 00000000..bbe7b470
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/benches_test.go
@@ -0,0 +1,595 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func BenchmarkDealingProofParams(b *testing.B) {
+	if testing.Short() {
+		b.SkipNow()
+	}
+
+	for i := 0; i < b.N; i++ {
+		_, err := dealer.NewProofParams()
+		assert.NoError(b, err)
+	}
+}
+
+func BenchmarkDealingShares(b *testing.B) {
+	// Skip these benchmarks in short-mode because they're high-variance and
+	// they trigger the regression testing hook.
+	if testing.Short() {
+		b.SkipNow()
+	}
+
+	curve := btcec.S256()
+	b.Run("Secp256k1 - 2 of 2", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 2, 2)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 2 of 3", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 2, 3)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 3 of 5", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 3, 5)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 4 of 7", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 4, 7)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 5 of 9", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 5, 9)
+			assert.NoError(b, err)
+		}
+	})
+
+	b.Run("Secp256k1 - 10 of 19", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 10, 19)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 25 of 49", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 25, 49)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 50 of 99", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 50, 99)
+			assert.NoError(b, err)
+		}
+	})
+	b.Run("Secp256k1 - 100 of 199", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			err := benchDealShares(curve, 100, 199)
+			assert.NoError(b, err)
+		}
+	})
+}
+
+func benchDealShares(curve elliptic.Curve, threshold, count uint32) error {
+	_, sharesMap, err := dealer.NewDealerShares(curve, threshold, count, nil)
+	if err != nil {
+		return err
+	}
+	for len(sharesMap) > 3 {
+		delete(sharesMap, uint32(len(sharesMap)))
+	}
+	_, err = dealer.PreparePublicShares(sharesMap)
+	return err
+}
+
+func BenchmarkDealingPaillierKeys(b *testing.B) {
+	if testing.Short() {
+		b.SkipNow()
+	}
+
+	for i := 0; i < b.N; i++ {
+		_, _, err := paillier.NewKeys()
+		assert.NoError(b, err)
+	}
+}
+
+func BenchmarkSigning(b *testing.B) {
+	curve := btcec.S256()
+	hash, err := core.Hash([]byte("It is not good to have a rule of many."), curve)
+	require.NoError(b, err)
+	hashBytes := hash.Bytes()
+
+	b.Run("Secp256k1 - 2 of 2", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 2, 2),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 2 of 3", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 2, 3),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 3 of 5", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 3, 5),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 4 of 7", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 4, 7),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 5 of 9", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 5, 9),
+			)
+		}
+	})
+
+	// Skip long-running tests in `-short` mode
+	if testing.Short() {
+		b.SkipNow()
+	}
+
+	b.Run("Secp256k1 - 10 of 19", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 10, 19),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 25 of 49", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 25, 49),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 50 of 99", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 50, 99),
+			)
+		}
+	})
+	b.Run("Secp256k1 - 100 of 199", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			assert.NoError(b,
+				benchSign(b, hashBytes, curve, k256Verifier, 100, 199),
+			)
+		}
+	})
+}
+
+func benchSign(b *testing.B, hash []byte, curve elliptic.Curve, verify curves.EcdsaVerify, threshold, count uint32) error {
+	// Setup signers
+	b.StopTimer()
+
+	pk, sharesMap, _ := dealer.NewDealerShares(curve, threshold, count, nil)
+	for len(sharesMap) > int(threshold) {
+		delete(sharesMap, uint32(len(sharesMap)))
+	}
+	pubSharesMap, _ := dealer.PreparePublicShares(sharesMap)
+	keysMap := make(map[uint32]*paillier.SecretKey, threshold)
+	pubKeys := make(map[uint32]*paillier.PublicKey, threshold)
+	keyPrimesArray := genPrimesArray(int(threshold))
+	for i := range sharesMap {
+		keysMap[i], _ = paillier.NewSecretKey(keyPrimesArray[i-1].p, keyPrimesArray[i-1].q)
+		pubKeys[i] = &keysMap[i].PublicKey
+	}
+	proofParams := &dealer.TrustedDealerKeyGenType{
+		ProofParams: dealerParams,
+	}
+
+	signersMap := make(map[uint32]*Signer, threshold)
+	for i, k := range keysMap {
+		p := Participant{*sharesMap[i], k}
+		signersMap[i], _ = p.PrepareToSign(pk, verify, curve, proofParams, pubSharesMap, pubKeys)
+	}
+
+	// Ignore the setup in the benchmarks
+	b.StartTimer()
+
+	// Run signing rounds
+	// Sign Round 1
+	var err error
+	signerOut := make(map[uint32]*Round1Bcast, threshold)
+	for i, s := range signersMap {
+		signerOut[i], _, err = s.SignRound1()
+		if err != nil {
+			return err
+		}
+	}
+
+	// Sign Round 2
+	p2p := make(map[uint32]map[uint32]*P2PSend)
+	for i, s := range signersMap {
+		in := make(map[uint32]*Round1Bcast, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = signerOut[j]
+		}
+		p2p[i], err = s.SignRound2(in, nil) // TODO: fix me later
+		if err != nil {
+			return nil
+		}
+	}
+
+	// Sign Round 3
+	r3Bcast := make(map[uint32]*Round3Bcast, threshold)
+	for i, s := range signersMap {
+		in := make(map[uint32]*P2PSend, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = p2p[j][i]
+		}
+		r3Bcast[i], err = s.SignRound3(in)
+		if err != nil {
+			return err
+		}
+	}
+
+	// Sign Round 4
+	r4Bcast := make(map[uint32]*Round4Bcast, threshold)
+	for i, s := range signersMap {
+		in := make(map[uint32]*Round3Bcast, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = r3Bcast[j]
+		}
+		r4Bcast[i], err = s.SignRound4(in)
+		if err != nil {
+			return err
+		}
+	}
+
+	// Sign Round 5
+	r5Bcast := make(map[uint32]*Round5Bcast, threshold)
+	r5P2p := make(map[uint32]map[uint32]*Round5P2PSend, threshold)
+	for i, s := range signersMap {
+		in := make(map[uint32]*Round4Bcast, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = r4Bcast[j]
+		}
+		r5Bcast[i], r5P2p[i], err = s.SignRound5(in)
+		if err != nil {
+			return err
+		}
+	}
+
+	// Sign Round 6
+	r6Bcast := make(map[uint32]*Round6FullBcast, threshold)
+	for i, s := range signersMap {
+		in := make(map[uint32]*Round5Bcast, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = r5Bcast[j]
+		}
+		r6Bcast[i], err = s.SignRound6Full(hash, in, r5P2p[i])
+		if err != nil {
+			return err
+		}
+	}
+
+	// Signature output
+	for i, s := range signersMap {
+		in := make(map[uint32]*Round6FullBcast, threshold-1)
+		for j := range signersMap {
+			if i == j {
+				continue
+			}
+			in[j] = r6Bcast[j]
+		}
+		_, err = s.SignOutput(in)
+		if err != nil {
+			return err
+		}
+	}
+
+	return nil
+}
+
+// Benchmark 2-party signing
+func BenchmarkSign2p(b *testing.B) {
+	// Dealer-related setup (not part of signing being measured)
+	k256 := btcec.S256()
+
+	pk, sharesMap, err := dealer.NewDealerShares(k256, 2, 2, nil)
+	require.NoError(b, err)
+
+	pubSharesMap, err := dealer.PreparePublicShares(sharesMap)
+	require.NoError(b, err)
+
+	keyPrimesArray := genPrimesArray(2)
+	paillier1, err := paillier.NewSecretKey(keyPrimesArray[0].p, keyPrimesArray[0].q)
+	require.NoError(b, err)
+	paillier2, err := paillier.NewSecretKey(keyPrimesArray[1].p, keyPrimesArray[1].q)
+	require.NoError(b, err)
+
+	dealerSetup := &signingSetup{
+		curve:        k256,
+		pk:           pk,
+		sharesMap:    sharesMap,
+		pubSharesMap: pubSharesMap,
+		pubkeys: map[uint32]*paillier.PublicKey{
+			1: &paillier1.PublicKey,
+			2: &paillier2.PublicKey,
+		},
+		privkeys: map[uint32]*paillier.SecretKey{
+			1: paillier1,
+			2: paillier2,
+		},
+		proofParams: &dealer.TrustedDealerKeyGenType{
+			ProofParams: dealerParams,
+		},
+	}
+
+	b.ResetTimer()
+
+	msgMetrics := &msgCounter{}
+	for i := 0; i < b.N; i++ {
+		sign2p(b, msgMetrics, dealerSetup)
+	}
+
+	// Report mean messaging metrics
+	b.ReportMetric(float64(msgMetrics.messages/b.N), "msgs/sign")
+	b.ReportMetric(float64(msgMetrics.bytes/b.N), "bytes/sign")
+}
+
+type signingSetup struct {
+	curve        elliptic.Curve
+	pk           *curves.EcPoint
+	sharesMap    map[uint32]*dealer.Share
+	pubSharesMap map[uint32]*dealer.PublicShare
+	pubkeys      map[uint32]*paillier.PublicKey
+	privkeys     map[uint32]*paillier.SecretKey
+	proofParams  *dealer.TrustedDealerKeyGenType
+}
+
+// Run a 2-party signing protocol and report messaging metrics.
+func sign2p(b *testing.B, bw *msgCounter, setup *signingSetup) {
+	// Hash of message for signature
+	hashBi, err := core.Hash([]byte("I will be brief. Your noble son is mad."), setup.curve)
+	require.NoError(b, err)
+	msgHash := hashBi.Bytes()
+
+	// Create signers
+	p1 := Participant{*setup.sharesMap[1], setup.privkeys[1]}
+	s1, err := p1.PrepareToSign(
+		setup.pk,
+		k256Verifier,
+		setup.curve,
+		setup.proofParams,
+		setup.pubSharesMap,
+		setup.pubkeys)
+	require.NoError(b, err)
+
+	p2 := Participant{*setup.sharesMap[2], setup.privkeys[2]}
+	s2, err := p2.PrepareToSign(
+		setup.pk,
+		k256Verifier,
+		setup.curve,
+		setup.proofParams,
+		setup.pubSharesMap,
+		setup.pubkeys)
+	require.NoError(b, err)
+
+	//
+	// Sign Round 1
+	//
+	r1_s1_bcast, r1_s1_p2p, err := s1.SignRound1()
+	require.NoError(b, err)
+
+	r1_s2_bcast, r1_s2_p2p, err := s2.SignRound1()
+	require.NoError(b, err)
+
+	// Count R1 msgs
+	require.NoError(b,
+		bw.Count(
+			r1_s1_bcast,
+			r1_s1_p2p,
+			r1_s2_bcast,
+			r1_s2_p2p,
+		))
+	b.Log()
+	b.Logf("R1 %#v", bw)
+
+	//
+	// Sign Round 2
+	//
+	r2_s1_p2p, err := s1.SignRound2(
+		map[uint32]*Round1Bcast{2: r1_s2_bcast},
+		map[uint32]*Round1P2PSend{2: r1_s2_p2p[1]},
+	)
+	require.NoError(b, err)
+
+	r2_s2_p2p, err := s2.SignRound2(
+		map[uint32]*Round1Bcast{1: r1_s1_bcast},
+		map[uint32]*Round1P2PSend{1: r1_s1_p2p[2]},
+	)
+	require.NoError(b, err)
+
+	// Count R2 msgs
+	require.NoError(b,
+		bw.Count(
+			r2_s1_p2p,
+			r2_s2_p2p,
+		))
+	b.Logf("R2 %#v", bw)
+
+	//
+	// Sign Round 3
+	//
+	r3_s1_bcast, err := s1.SignRound3(
+		map[uint32]*P2PSend{2: r2_s2_p2p[1]},
+	)
+	require.NoError(b, err)
+
+	r3_s2_bcast, err := s2.SignRound3(
+		map[uint32]*P2PSend{1: r2_s1_p2p[2]},
+	)
+	require.NoError(b, err)
+
+	// Count R3 msgs
+	require.NoError(b,
+		bw.Count(
+			r3_s1_bcast,
+			r3_s2_bcast,
+		))
+	b.Logf("R3 %#v", bw)
+
+	//
+	// Sign Round 4
+	//
+	r4_s1_bcast, err := s1.SignRound4(
+		map[uint32]*Round3Bcast{2: r3_s2_bcast})
+	require.NoError(b, err)
+
+	r4_s2_bcast, err := s2.SignRound4(
+		map[uint32]*Round3Bcast{1: r3_s1_bcast})
+	require.NoError(b, err)
+
+	// Count R4 msgs
+	require.NoError(b,
+		bw.Count(
+			r4_s1_bcast,
+			r4_s2_bcast,
+		))
+	b.Logf("R4 %#v", bw)
+
+	//
+	// Sign Round 5
+	//
+	r5_s1_bcast, r5_s1_p2p, err := s1.SignRound5(
+		map[uint32]*Round4Bcast{2: r4_s2_bcast},
+	)
+	require.NoError(b, err)
+
+	r5_s2_bcast, r5_s2_p2p, err := s2.SignRound5(
+		map[uint32]*Round4Bcast{1: r4_s1_bcast},
+	)
+	require.NoError(b, err)
+
+	// Count R5 msgs
+	require.NoError(b,
+		bw.Count(
+			r5_s1_bcast,
+			r5_s1_p2p,
+			r5_s2_bcast,
+			r5_s2_p2p,
+		))
+	b.Logf("R5 %#v", bw)
+
+	//
+	// Sign Round 6
+	//
+	r6_s1_bcast, err := s1.SignRound6Full(msgHash,
+		map[uint32]*Round5Bcast{2: r5_s2_bcast},
+		map[uint32]*Round5P2PSend{2: r5_s2_p2p[1]},
+	)
+	require.NoError(b, err)
+
+	r6_s2_bcast, err := s2.SignRound6Full(msgHash,
+		map[uint32]*Round5Bcast{1: r5_s1_bcast},
+		map[uint32]*Round5P2PSend{1: r5_s1_p2p[2]},
+	)
+	require.NoError(b, err)
+
+	// Count R6 msgs
+	require.NoError(b,
+		bw.Count(
+			r6_s1_bcast,
+			r6_s2_bcast,
+		))
+	b.Logf("R6 %#v", bw)
+
+	//
+	// Compute signature
+	//
+
+	s1_sig, err := s1.SignOutput(
+		map[uint32]*Round6FullBcast{2: r6_s2_bcast},
+	)
+	require.NoError(b, err)
+
+	s2_sig, err := s2.SignOutput(
+		map[uint32]*Round6FullBcast{1: r6_s1_bcast},
+	)
+	require.NoError(b, err)
+
+	// Verify that both parties compute the same signature
+	assert.Equal(b, s1_sig, s2_sig, "computed ECDSA signature do not match")
+}
+
+// Tracks messaging-related metrics: msg count, serialized total bytes
+type msgCounter struct {
+	bytes    int
+	messages int
+}
+
+// Accumulates message and byte counts
+func (m *msgCounter) Count(msgs ...interface{}) error {
+	for _, msg := range msgs {
+		if msg == nil {
+			continue
+		}
+		// Count a discrete message
+		m.messages++
+
+		// Serialize and count the byte length
+		msgBytes, err := json.Marshal(msg)
+		if err != nil {
+			return err
+		}
+		// fmt.Println(string(msgBytes))
+		m.bytes += len(msgBytes)
+	}
+	return nil
+}
diff --git a/pkg/tecdsa/gg20/participant/dkg_round1.go b/pkg/tecdsa/gg20/participant/dkg_round1.go
new file mode 100644
index 00000000..7cbc078c
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/dkg_round1.go
@@ -0,0 +1,188 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+)
+
+// DkgRound1Bcast contains values to be broadcast to all players after the completion of DKG round 1
+type DkgRound1Bcast struct {
+	Identifier       uint32
+	Ci               core.Commitment
+	Pki              *paillier.PublicKey
+	H1i, H2i, Ni     *big.Int
+	Proof1i, Proof2i *proof.CdlProof
+}
+
+// DkgRound1 performs round 1 distributed key generation operation
+// [spec] fig 5: DistKeyGenRound1
+func (dp *DkgParticipant) DkgRound1(threshold, total uint32) (*DkgRound1Bcast, error) {
+	if total < threshold {
+		return nil, fmt.Errorf("parts cannot be less than threshold")
+	}
+
+	if dp == nil || dp.Curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	if err := dp.verifyDkgRound(1); err != nil {
+		return nil, err
+	}
+
+	// Step 1: choose ui from Z_q randomly
+	ui, err := core.Rand(dp.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 2: Compute [vi0,...,vit], [xi1,...,xin] <- FeldmanShare(g, ui, t, q, [p1...pn])
+	feldman, err := v1.NewFeldman(threshold, total, dp.Curve)
+	if err != nil {
+		return nil, err
+	}
+
+	// V is an array of FeldmanVerifiers, X is an array of ShamirShares
+	V, X, err := feldman.Split(ui.Bytes())
+	if err != nil {
+		return nil, err
+	}
+
+	// Convert V (type []FeldmanVerifier) to a single byteV (type []byte)
+	var byteV []byte
+	for i := 0; i < len(V); i++ {
+		byteV = append(byteV, V[i].Bytes()...)
+	}
+
+	// Step 3: [Ci, Di] = Commit([vi0...vit])
+	Ci, Di, err := core.Commit(byteV)
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 4: ski, pki := PaillierKeyGen(1^k) (generate a 2048-bit Paillier key pair
+	pki, ski, err := paillier.NewKeys()
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 5-6: Choose 1024-bit safe primes Pi, Qi, Pi=2pi+1, Qi=2qi+1 where Pi, Qi, pi, qi are primes
+	values := make(chan *big.Int, 2)
+	errors := make(chan error, 2)
+
+	var Pi, Qi *big.Int
+	for Pi == Qi {
+		for range []int{1, 2} {
+			go func() {
+				value, err := core.GenerateSafePrime(paillier.PaillierPrimeBits)
+				values <- value
+				errors <- err
+			}()
+		}
+
+		for _, err := range []error{<-errors, <-errors} {
+			if err != nil {
+				return nil, err
+			}
+		}
+
+		Pi, Qi = <-values, <-values
+	}
+
+	// Step 7: Compute tildeNi = Pi*Qi
+	tildeNi := new(big.Int).Mul(Pi, Qi)
+
+	// Step 8-9: Sample f, alpha from Z_tildeNi*
+	f, err := core.Rand(tildeNi)
+	if err != nil {
+		return nil, err
+	}
+
+	alpha, err := core.Rand(tildeNi)
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 10: Compute beta = alpha^-1 mod pi*qi
+	// Compute pi = (Pi-1)/2, qi = (Qi-1)/2
+	pi := new(big.Int).Rsh(Pi, 1)
+	qi := new(big.Int).Rsh(Qi, 1)
+
+	// Compute pi*qi
+	pq := new(big.Int).Mul(pi, qi)
+
+	// Compute beta
+	beta := new(big.Int).ModInverse(alpha, pq)
+
+	// Step 11-12: h1i = f^2 mod tildeNi, h2i = h1i^alpha mod tildeNi
+	h1i, err := core.Mul(f, f, tildeNi)
+	if err != nil {
+		return nil, err
+	}
+	h2i := new(big.Int).Exp(h1i, alpha, tildeNi)
+
+	// Step 13-14:
+	cdlParams1 := proof.CdlProofParams{
+		Curve:   dp.Curve,
+		Pi:      pi,
+		Qi:      qi,
+		H1:      h1i,
+		H2:      h2i,
+		ScalarX: alpha,
+		N:       tildeNi,
+	}
+
+	cdlParams2 := proof.CdlProofParams{
+		Curve:   dp.Curve,
+		Pi:      pi,
+		Qi:      qi,
+		H1:      h2i,
+		H2:      h1i,
+		ScalarX: beta,
+		N:       tildeNi,
+	}
+
+	// proof1 <- ProveCompositeDL(g, q, pi, qi, h1i, h2i, alpha, tildeNi)
+	proof1, err := cdlParams1.Prove()
+	if err != nil {
+		return nil, err
+	}
+
+	// proof2 <- ProveCompositeDl(g, q, pi, qi, h2i, h1i, beta, tildeNi)
+	proof2, err := cdlParams2.Prove()
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 16:
+	// Store Di, ski, pki, tildeNi, h1i, h2i, [vi0...vit], [xi1,...xin] locally
+	dp.state.D = Di
+	dp.state.Sk = ski
+	dp.state.Pk = pki
+	dp.state.N = tildeNi
+	dp.state.H1 = h1i
+	dp.state.H2 = h2i
+	dp.state.V = V
+	dp.state.X = X
+	dp.state.Threshold = threshold
+	dp.state.Limit = total
+
+	// used in Round 2
+	dp.Round = 2
+
+	// Step 15: EchoBroadcast Ci, pki, tildeNi, h1i, h2i, proof1, proof2
+	return &DkgRound1Bcast{
+		dp.id, Ci, pki, h1i, h2i, tildeNi, proof1, proof2,
+	}, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/dkg_round2.go b/pkg/tecdsa/gg20/participant/dkg_round2.go
new file mode 100644
index 00000000..984ac0c0
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/dkg_round2.go
@@ -0,0 +1,122 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+)
+
+// DkgRound2Bcast contains value that will be echo broadcast to all other players.
+type DkgRound2Bcast struct {
+	Di *core.Witness
+}
+
+// DkgRound2P2PSend contains value that will be P2PSend to all other player Pj
+type DkgRound2P2PSend struct {
+	xij *v1.ShamirShare
+}
+
+// DkgRound2 implements distributed key generation round 2
+// [spec] fig 5: DistKeyGenRound2
+func (dp *DkgParticipant) DkgRound2(params map[uint32]*DkgRound1Bcast) (*DkgRound2Bcast, map[uint32]*DkgRound2P2PSend, error) {
+	// Make sure dkg participant is not empty
+	if dp == nil || dp.Curve == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+
+	// Check DkgParticipant has the correct dkg round number
+	if err := dp.verifyDkgRound(2); err != nil {
+		return nil, nil, err
+	}
+
+	// Check the total number of parties
+	cnt := 0
+	for id := range params {
+		if params[id] == nil {
+			continue
+		}
+		if id == dp.id {
+			continue
+		}
+		cnt++
+	}
+	if uint32(cnt) != dp.state.Limit-1 {
+		return nil, nil, internal.ErrIncorrectCount
+	}
+
+	// Initiate P2P channel to other parties
+	p2PSend := make(map[uint32]*DkgRound2P2PSend)
+
+	// Initiate two CdlVerifyParams that will be used in CDL verification.
+	cdlParams1 := proof.CdlVerifyParams{
+		Curve: dp.Curve,
+	}
+	cdlParams2 := proof.CdlVerifyParams{
+		Curve: dp.Curve,
+	}
+
+	dp.state.otherParticipantData = make(map[uint32]*dkgParticipantData)
+
+	// For j = [1...n]
+	for id, param := range params {
+		// If i = j, Continue
+		if id == dp.id {
+			continue
+		}
+
+		// If VerifyCompositeDL(pi_1j^CDL, g, q, h1j, h2j, tildeN_j) = False, Abort
+		cdlParams1.H1 = param.H1i
+		cdlParams1.H2 = param.H2i
+		cdlParams1.N = param.Ni
+		if err := param.Proof1i.Verify(&cdlParams1); err != nil {
+			return nil, nil, err
+		}
+
+		// If VerifyCompositeDL(pi_2j^CDL, g, q, h2j, h1j, tildeN_j) = False, Abort
+		// Note the position of h1j and h2j, they are reversed in the second verification!
+		cdlParams2.H1 = param.H2i
+		cdlParams2.H2 = param.H1i
+		cdlParams2.N = param.Ni
+		if err := param.Proof2i.Verify(&cdlParams2); err != nil {
+			return nil, nil, err
+		}
+
+		// P2PSend xij to player Pj
+		if dp.state.X == nil || dp.state.X[id-1] == nil {
+			return nil, nil, fmt.Errorf("Missing Shamir share to P2P send")
+		}
+		p2PSend[id] = &DkgRound2P2PSend{
+			xij: dp.state.X[id-1],
+		}
+
+		// Store other parties data
+		dp.state.otherParticipantData[id] = &dkgParticipantData{
+			PublicKey:  param.Pki,
+			Commitment: param.Ci,
+			ProofParams: &dealer.ProofParams{
+				N:  param.Ni,
+				H1: param.H1i,
+				H2: param.H2i,
+			},
+		}
+	}
+
+	// Assign dkg round to 3
+	dp.Round = 3
+
+	// EchoBroadcast Di to all other players. Also return it with P2PSend
+	return &DkgRound2Bcast{
+		Di: dp.state.D,
+	}, p2PSend, nil
+
+}
diff --git a/pkg/tecdsa/gg20/participant/dkg_round3.go b/pkg/tecdsa/gg20/participant/dkg_round3.go
new file mode 100644
index 00000000..71b7fb53
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/dkg_round3.go
@@ -0,0 +1,183 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// DkgRound3 computes dkg round 3 as shown in
+// [spec] fig. 5: DistKeyGenRoun3
+func (dp *DkgParticipant) DkgRound3(d map[uint32]*core.Witness, x map[uint32]*v1.ShamirShare) (paillier.PsfProof, error) {
+	if len(d) == 0 || len(x) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+	if dp.Round != 3 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Extract the share verifiers from the commitment
+	verifiers := make(map[uint32][]*v1.ShareVerifier, len(d))
+	// NOTE: ID-1 because participant IDs are 1-based
+	verifiers[dp.id] = dp.state.V
+	verifierSize := internal.CalcFieldSize(dp.Curve) * 2
+	feldman, err := v1.NewFeldman(dp.state.Threshold, dp.state.Limit, dp.Curve)
+	if err != nil {
+		return nil, err
+	}
+
+	// 1. set xi = xii
+	xi := dp.state.X[dp.id-1]
+
+	// 2. for j = [1,...,n]
+	for j, wit := range d {
+		// 3. if i == j continue
+		if j == dp.id {
+			continue
+		}
+		// 4. Compute [vj0, . . . , vjt] ←Open(Cj , Dj )
+		if ok, err := core.Open(dp.state.otherParticipantData[j].Commitment, *d[j]); !ok {
+			if err != nil {
+				return nil, err
+			} else {
+				return nil, fmt.Errorf("invalid witness for participant %d", j+1)
+			}
+		}
+
+		verifiers[j], err = unmarshalFeldmanVerifiers(dp.Curve, wit.Msg, verifierSize, int(dp.state.Threshold))
+		if err != nil {
+			return nil, err
+		}
+
+		// 6. If FeldmanVerify(g, q, xji, pi, [vj0, . . . , vjt]) = False, Abort
+		if ok, err := feldman.Verify(x[j], verifiers[j]); !ok {
+			if err != nil {
+				return nil, err
+			} else {
+				return nil, fmt.Errorf("invalid share for participant %d", j+1)
+			}
+		}
+
+		// 7. Compute xi = xi + xji mod q
+		xi.Value = xi.Value.Add(x[j].Value)
+	}
+
+	v := make([]*curves.EcPoint, dp.state.Threshold)
+	// 8. for j = [0,...,t]
+	for j := 0; j < int(dp.state.Threshold); j++ {
+		// 9. Set vj = 1 or identity point
+		v[j], err = curves.NewScalarBaseMult(dp.Curve, big.NewInt(0))
+		if err != nil {
+			return nil, err
+		}
+
+		// 10. for k = [1,...,n]
+		for _, verifier := range verifiers {
+			// 11. Compute vj = vj · vkj in G
+			v[j], err = v[j].Add(verifier[j])
+			if err != nil {
+				return nil, err
+			}
+		}
+	}
+
+	// 12. y = v0 i.e the public key
+	y := v[0]
+
+	// This is a sanity check to make sure nothing went wrong when
+	// computing the public key
+	if !dp.Curve.IsOnCurve(y.X, y.Y) || y.IsIdentity() {
+		return nil, fmt.Errorf("invalid public key")
+	}
+
+	// Xj's
+	publicShares := make([]*curves.EcPoint, dp.state.Limit)
+
+	// 13. for j = [1,...,n]
+	for j := 0; j < int(dp.state.Limit); j++ {
+		id := uint32(j + 1)
+		// 14. Set Xj = y
+		publicShares[j] = &curves.EcPoint{
+			Curve: dp.Curve,
+			X:     new(big.Int).Set(y.X),
+			Y:     new(big.Int).Set(y.Y),
+		}
+		// 15. for k = [1,...,t]
+		for k := 0; k < int(dp.state.Threshold); k++ {
+			// 16. compute ck = pj^k mod q
+			pj := big.NewInt(int64(id))
+			ck, err := core.Mul(pj, big.NewInt(int64(k+1)), dp.Curve.Params().N)
+			if err != nil {
+				return nil, err
+			}
+			// 17. compute Xj = Xj x vk ^ ck in G
+			t, err := v[k].ScalarMult(ck)
+			if err != nil {
+				return nil, err
+			}
+			// Xj = Xj * t in G
+			publicShares[j], err = publicShares[j].Add(t)
+			if err != nil {
+				return nil, err
+			}
+		}
+	}
+
+	// 18. Compute πPSF = ProvePSF(ski.N, ski.φ(N), y, g, q, pi)
+	psfParams := paillier.PsfProofParams{
+		Curve:     dp.Curve,
+		SecretKey: dp.state.Sk,
+		Pi:        dp.id,
+		Y:         y,
+	}
+	psfProof, err := psfParams.Prove()
+	if err != nil {
+		return nil, err
+	}
+
+	dp.Round = 4
+	dp.state.Y = y
+	dp.state.Xi = xi.Value.BigInt()
+	dp.state.PublicShares = publicShares
+
+	return psfProof, nil
+}
+
+// unmarshalFeldmanVerifiers converts a byte sequence into
+// a number of feldman verifiers
+func unmarshalFeldmanVerifiers(curve elliptic.Curve, msg []byte, verifierSize, threshold int) ([]*v1.ShareVerifier, error) {
+	if len(msg)%verifierSize != 0 {
+		return nil, fmt.Errorf("invalid committed verifier shares")
+	}
+	numShares := len(msg) / verifierSize
+
+	// 5. If [vj0,...,vjt] = ⊥, Abort
+	if numShares != threshold {
+		return nil, fmt.Errorf("invalid number of verifier shares")
+	}
+
+	// Extract verifiers from bytes
+	verifiers := make([]*v1.ShareVerifier, numShares)
+	var err error
+	for k := 0; k < numShares; k++ {
+		value := make([]byte, verifierSize)
+		copy(value, msg[k*verifierSize:(k+1)*verifierSize])
+		verifiers[k], err = curves.PointFromBytesUncompressed(curve, value)
+		if err != nil {
+			return nil, err
+		}
+	}
+	return verifiers, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/dkg_round4.go b/pkg/tecdsa/gg20/participant/dkg_round4.go
new file mode 100644
index 00000000..2a38fc7a
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/dkg_round4.go
@@ -0,0 +1,91 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+)
+
+// DkgResult is all the data generated from the DKG
+type DkgResult struct {
+	PublicShares    []*curves.EcPoint
+	VerificationKey *curves.EcPoint
+	SigningKeyShare *big.Int
+	EncryptionKey   *paillier.SecretKey
+	ParticipantData map[uint32]*DkgParticipantData
+}
+
+type DkgParticipantData struct {
+	PublicKey   *paillier.PublicKey
+	ProofParams *dealer.ProofParams
+}
+
+// DkgRound4 computes dkg round 4 as shown in
+// [spec] fig. 5: DistKeyGenRound4
+func (dp *DkgParticipant) DkgRound4(psfProof map[uint32]paillier.PsfProof) (*DkgResult, error) {
+	if len(psfProof) == 0 {
+		return nil, internal.ErrIncorrectCount
+	}
+	if dp.Round != 4 {
+		return nil, internal.ErrInvalidRound
+	}
+	// Make sure all participants sent a proof
+	for id := range dp.state.otherParticipantData {
+		if id == dp.id {
+			continue
+		}
+		if _, ok := psfProof[id]; !ok {
+			return nil, fmt.Errorf("missing proof for participant %d", id)
+		}
+	}
+
+	verifyPsfParams := paillier.PsfVerifyParams{
+		Curve: dp.Curve,
+		Y:     dp.state.Y,
+	}
+	// 1. for j = [1,...,n]
+	for id, p := range psfProof {
+		// 2. if i == j, continue
+		if dp.id == id {
+			continue
+		}
+		verifyPsfParams.PublicKey = dp.state.otherParticipantData[id].PublicKey
+		verifyPsfParams.Pi = id
+		// 3. if VerifyPSF(\pi_j, pk_j.N, y, g, q, pj) = false, abort
+		if err := p.Verify(&verifyPsfParams); err != nil {
+			return nil, err
+		}
+	}
+
+	// Return paillier public keys and proof params
+	// from all participants
+	participantData := make(map[uint32]*DkgParticipantData)
+	for id, data := range dp.state.otherParticipantData {
+		participantData[id] = &DkgParticipantData{
+			PublicKey:   data.PublicKey,
+			ProofParams: data.ProofParams,
+		}
+	}
+
+	// Return all necessary information to complete signing
+	// the proof params, paillier public keys, and public commitments
+	// from other participants, the secret signing key share, and
+	// the public verification key
+	return &DkgResult{
+		VerificationKey: dp.state.Y,
+		SigningKeyShare: dp.state.Xi,
+		PublicShares:    dp.state.PublicShares,
+		EncryptionKey:   dp.state.Sk,
+		ParticipantData: participantData,
+	}, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/dkg_rounds_test.go b/pkg/tecdsa/gg20/participant/dkg_rounds_test.go
new file mode 100644
index 00000000..93d2d40b
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/dkg_rounds_test.go
@@ -0,0 +1,1044 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/elliptic"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+	"testing"
+
+	tt "github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/require"
+)
+
+func setupDkgRound3ParticipantMap(curve elliptic.Curve, t, n int) map[uint32]*DkgParticipant {
+	feldman, _ := v1.NewFeldman(uint32(t), uint32(n), curve)
+	participants := make(map[uint32]*DkgParticipant, n)
+	prime1Idx := 0
+	pIds := make(map[uint32]*dkgParticipantData, n)
+	for j := 1; j <= n; j++ {
+		pIds[uint32(j)] = &dkgParticipantData{}
+	}
+
+	for i := 0; i < n; i++ {
+		u, _ := core.Rand(curve.Params().N)
+		v, x, _ := feldman.Split(u.Bytes())
+		sk, _ := paillier.NewSecretKey(testPrimes[prime1Idx], testPrimes[prime1Idx+1])
+		id := uint32(i + 1)
+		pIds[id].PublicKey = &sk.PublicKey
+		pIds[id].ProofParams = &dealer.ProofParams{}
+		participants[id] = &DkgParticipant{
+			Curve: curve,
+			id:    id,
+			Round: 3,
+			state: &dkgstate{
+				Sk:                   sk,
+				Pk:                   &sk.PublicKey,
+				Threshold:            uint32(t),
+				Limit:                uint32(n),
+				X:                    x,
+				V:                    v,
+				otherParticipantData: pIds,
+			},
+		}
+		prime1Idx++
+	}
+
+	return participants
+}
+
+func setupDkgRound3Commitments(t *testing.T, participants map[uint32]*DkgParticipant, playerCnt int) map[uint32]*core.Witness {
+	var err error
+	// Setup commitments for each player so they can be passed as inputs
+	// normally received from echo broadcast
+	commitments := make(map[uint32]core.Commitment, playerCnt)
+	decommitments := make(map[uint32]*core.Witness, playerCnt)
+	for id, p := range participants {
+		commitments[id], decommitments[id], err = commitVerifiers(participants[id].state.V)
+		p.state.otherParticipantData[id].Commitment = commitments[id]
+		require.NoError(t, err)
+	}
+
+	return decommitments
+}
+
+func commitVerifiers(v []*v1.ShareVerifier) (core.Commitment, *core.Witness, error) {
+	var bytes []byte
+	for _, vi := range v {
+		bytes = append(bytes, vi.Bytes()...)
+	}
+	return core.Commit(bytes)
+}
+
+func TestDkgRound3Works(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	// Actual test
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[1],
+		2: participants[2].state.X[1],
+		3: participants[3].state.X[1],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res2)
+	res3, err := participants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[2],
+		2: participants[2].state.X[2],
+		3: participants[3].state.X[2],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res3)
+	field := curves.NewField(curve.Params().N)
+	shamir, _ := v1.NewShamir(playerMin, playerCnt, field)
+
+	// Check that they all generated the same public key
+	require.Equal(t, participants[1].state.Y, participants[2].state.Y)
+	require.Equal(t, participants[1].state.Y, participants[3].state.Y)
+
+	// Check that they all generated the same public shares
+	for i, e := range participants[1].state.PublicShares {
+		require.Equal(t, e, participants[2].state.PublicShares[i])
+		require.Equal(t, e, participants[3].state.PublicShares[i])
+	}
+	share1 := v1.NewShamirShare(1, participants[1].state.Xi.Bytes(), field)
+	share2 := v1.NewShamirShare(2, participants[2].state.Xi.Bytes(), field)
+	share3 := v1.NewShamirShare(3, participants[3].state.Xi.Bytes(), field)
+	secret12, err := shamir.Combine(share1, share2)
+	require.NoError(t, err)
+	secret13, err := shamir.Combine(share1, share3)
+	require.NoError(t, err)
+	secret23, err := shamir.Combine(share2, share3)
+	require.NoError(t, err)
+
+	require.Equal(t, secret12, secret13)
+	require.Equal(t, secret12, secret23)
+	pk, err := curves.NewScalarBaseMult(curve, new(big.Int).SetBytes(secret12))
+	require.NoError(t, err)
+	require.True(t, participants[1].state.Y.Equals(pk))
+}
+
+func TestDkgRound3RepeatCall(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	// Actual test
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.Error(t, err)
+	require.Nil(t, res2)
+}
+
+func TestDkgRound3InvalidWitnesses(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	decommitments[2].Msg[0] ^= decommitments[1].Msg[0]
+	decommitments[2].Msg[1] ^= decommitments[1].Msg[1]
+
+	// Actual test
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.Error(t, err)
+	require.Nil(t, res1)
+
+	// corrupt 2nd participant
+	decommitments[2].Msg[0] ^= decommitments[1].Msg[0]
+	decommitments[2].Msg[1] ^= decommitments[1].Msg[1]
+
+	// corrupt 3rd participant
+	decommitments[3].Msg[0] ^= decommitments[1].Msg[0]
+	decommitments[3].Msg[1] ^= decommitments[1].Msg[1]
+	res2, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.Error(t, err)
+	require.Nil(t, res2)
+}
+
+func TestDkgRound3InvalidShares(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	// corrupt 2nd participant share
+	temp := participants[2].state.X[0].Value
+	participants[2].state.X[0].Value = curves.NewField(curve.Params().N).NewElement(big.NewInt(1))
+
+	// Actual test
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.Error(t, err)
+	require.Nil(t, res1)
+
+	// restore 2nd participant share
+	participants[2].state.X[0].Value = temp
+
+	// corrupt 3rd participant share
+	participants[3].state.X[0].Value = curves.NewField(curve.Params().N).NewElement(big.NewInt(1))
+
+	res2, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.Error(t, err)
+	require.Nil(t, res2)
+}
+
+func TestDkgRound1Works(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping test in short mode.")
+	}
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+
+	// Initiate a DKG participant
+	dkgParticipant := &DkgParticipant{
+		Curve: curve,
+		id:    uint32(1),
+		Round: 1,
+		state: &dkgstate{
+			Threshold: uint32(threshold),
+			Limit:     uint32(total),
+		},
+	}
+
+	// Run DKG round 1
+	dkgParticipantOut, err := dkgParticipant.DkgRound1(uint32(threshold), uint32(total))
+	tt.AssertNoError(t, err)
+
+	// Checking DkgParticipant's items and stored values
+	if dkgParticipant.Curve == nil {
+		t.Errorf("dkgParticipant curve is nil")
+	}
+
+	if dkgParticipant.id == 0 {
+		t.Errorf("dkgParticipant id is zero")
+	}
+
+	if dkgParticipant.Round != 2 {
+		t.Errorf("Expected round to be 2, found: %d", dkgParticipant.Round)
+	}
+
+	if dkgParticipant.state.D == nil {
+		t.Errorf("dkgstate D is nil")
+	}
+
+	if dkgParticipant.state.Sk == nil {
+		t.Errorf("dkgstate Sk is nil")
+	}
+
+	if dkgParticipant.state.Pk == nil {
+		t.Errorf("dkgstate Pk is nil")
+	}
+
+	tt.AssertNotNil(t, dkgParticipant.state.N)
+	tt.AssertNotNil(t, dkgParticipant.state.H1)
+	tt.AssertNotNil(t, dkgParticipant.state.H2)
+
+	if dkgParticipant.state.V == nil {
+		t.Errorf("dkgstate V is nil")
+	}
+
+	if dkgParticipant.state.X == nil {
+		t.Errorf("dkgstate X is nil")
+	}
+
+	if dkgParticipant.state.Threshold != uint32(threshold) {
+		t.Errorf("dkgstate Threshold mismatch")
+	}
+
+	if dkgParticipant.state.Limit != uint32(total) {
+		t.Errorf("dkgstate Limit mismatch")
+	}
+
+	// Check DKG Round 1 output
+	if dkgParticipantOut.Ci == nil {
+		t.Errorf("DkgRound1Bcast Ci is nil")
+	}
+
+	if dkgParticipantOut.Pki == nil {
+		t.Errorf("DkgRound1Bcast Pki is nil")
+	}
+
+	tt.AssertNotNil(t, dkgParticipantOut.H1i)
+	tt.AssertNotNil(t, dkgParticipantOut.H2i)
+	tt.AssertNotNil(t, dkgParticipantOut.Ni)
+
+	if dkgParticipantOut.Proof1i == nil {
+		t.Errorf("DkgRound1Bcast Proof1i is nil")
+	}
+
+	if dkgParticipantOut.Proof2i == nil {
+		t.Errorf("DkgRound1Bcast Proof2i is nil")
+	}
+}
+
+// Test repeat call for DKG Round 1. There should be some error after repeat call
+func TestDkgRound1RepeatCall(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping test in short mode.")
+	}
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	dkgParticipant := &DkgParticipant{
+		Curve: curve,
+		id:    uint32(1),
+		Round: 1,
+		state: &dkgstate{
+			Threshold: uint32(threshold),
+			Limit:     uint32(total),
+		},
+	}
+
+	// Test repeat call
+	_, err := dkgParticipant.DkgRound1(uint32(threshold), uint32(total))
+	tt.AssertNoError(t, err)
+	_, err = dkgParticipant.DkgRound1(uint32(threshold), uint32(total))
+	tt.AssertSomeError(t, err)
+}
+
+/*
+Tests for DKG Round 2
+*/
+// Setup DKG Round2 parameters for 3 parties.
+func setupDkgRound2Params(curve elliptic.Curve, threshold, total int) (map[uint32]*DkgParticipant, map[uint32]*DkgRound1Bcast) {
+	dkgParticipants := make(map[uint32]*DkgParticipant, total)
+	dpOutputs := make(map[uint32]*DkgRound1Bcast, total)
+	feldman, _ := v1.NewFeldman(uint32(threshold), uint32(total), curve)
+
+	// Setup parameters for player 1
+	u1, _ := core.Rand(curve.Params().N)
+	v1, x1, _ := feldman.Split(u1.Bytes())
+	c1, d1, _ := commitVerifiers(v1)
+	sk1, _ := paillier.NewSecretKey(testPrimes[0], testPrimes[1])
+	pk1 := &sk1.PublicKey
+	p1 := tt.B10("82762378445241041785597416507146490924447650731139897784752935952615188889635739493260515391609009395512012510709694417682987650969620502923818755809286104031313081465573622419369705445472375093283434921189190872945878407680529264737835792880592698668922695556861850401038676208972765968600517704143107930939")
+	q1 := tt.B10("69984280963080064677800727110502274842099368563604158420066520063922637818395160287343267480348823052616167329961701614168083898925612364204117254926526013551734867336492773207372540967720859662663438793769658958121285041708356176137310878638419197674131049677486047662703715583824220317748400146581518805651")
+	N1 := tt.B10("23168262185138042086985251479966140367473901735462054883904158802899264898691745453544888260128845593494180271821344835446388187526575974414101963091834292189789300379762157838980851815082897653013412610189597921830744654589452349113217726909094907934886602336832701591827947839296008075387481044145203853001040451482685799793720746884491540403980953810998121611944634910546812395244563473672734584566589265151370354163653553724356278901340380622401163641562474726319566531912584399552348312976911765268861745938301120268844120841005241592287730934409073936996169212424570979999552686559812737873042697608781537218337")
+	alpha1 := tt.B10("15700848461280380865453593955761108710562895414247363097072882828466191790916811503316377080013948938072225007516727823198461336870478274783583845926904074063193546765645477855455273258274150739378394943431150849983293677107578668862239783392036575043145101427760350638472037576829352497038388585737650687025976060296433989815102965583016771823595419876353838074154404831501616992756987140969613192813913996292033706748510041393036246923312030419247298071079496294307995794672335020365605673661246459738777446284403765226964816958599530935710152502359977024900546418123107827630153113273622448646563626731524890158451")
+	beta1 := tt.B10("4445879341351807551209439241920588140685341448529417529966129370975387582547328611790463864985523049818186588579898273930075299257729508047763338871424268681977630441148158141892066821441561729492103026410192844346284104817705886190143212900488394256716287705027856018936240395625790280151981634907904864178490159409363504387136507125542627454380016748558057005637225625481246654258853972871702501872856487903999341616690584954898272433078686327089310861915148328259913401109993699884551105056353404107220173983671620298275738982057963556561810371192793230372490607557673240894790572775163623912821853064509864539001")
+	h11 := tt.B10("20655589105424284731130950222365942513635708110950343104368669683186013800106942421524347648458254016225036450934479227664921498785561364595133998161005944291950359490505065673829287124165328608814740981967547208784457369473849019618903667437471918601627601044509671230680260942658093024204790610273965477549218656620684879208070965028279550643411998341767974100272557335380738716438934690826564692745348318822199802416149976761047532756651975957242217027025407351894263261364922859598069540698965816588058759437732436981028926328047363612699976563290609364678354605271871488415744707392237965701195336114850923722797")
+	h12 := tt.B10("5496074424480326456967307779978137640059660693996954490061656724729243248263235164326034392211487428145642035897732902987019830534770657265806433471056048721413319683923174766405888321053057575584689236687181096491031182941541387466426725040271572300593534197768598345205731705003156108961982545733171941969970689906713317136842479008121330098952126720386613744001301998221850208337277017663694634040173073680721828995733047624361263114536685654886828447330526802851522697283703748194422611303519895796695954647757152041586980035268266906531329254312878479944233983358807551831572963272582468808462893198641903856921")
+
+	dkgParticipants[1] = &DkgParticipant{
+		Curve: curve,
+		state: &dkgstate{
+			D:         d1,
+			Sk:        sk1,
+			Pk:        pk1,
+			N:         N1,
+			H1:        h11,
+			H2:        h12,
+			V:         v1,
+			X:         x1,
+			Threshold: uint32(threshold),
+			Limit:     uint32(total),
+		},
+		id:    uint32(1),
+		Round: 2,
+	}
+
+	cdlParams11 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p1,
+		Qi:      q1,
+		H1:      h11,
+		H2:      h12,
+		ScalarX: alpha1,
+		N:       N1,
+	}
+
+	cdlParams12 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p1,
+		Qi:      q1,
+		H1:      h12,
+		H2:      h11,
+		ScalarX: beta1,
+		N:       N1,
+	}
+
+	proof11, _ := cdlParams11.Prove()
+	proof12, _ := cdlParams12.Prove()
+
+	dpOutputs[1] = &DkgRound1Bcast{
+		Identifier: uint32(1),
+		Ci:         c1,
+		Pki:        pk1,
+		H1i:        h11,
+		H2i:        h12,
+		Ni:         N1,
+		Proof1i:    proof11,
+		Proof2i:    proof12,
+	}
+
+	// Setup parameters for player 2
+	u2, _ := core.Rand(curve.Params().N)
+	v2, x2, _ := feldman.Split(u2.Bytes())
+	c2, d2, _ := commitVerifiers(v2)
+	sk2, _ := paillier.NewSecretKey(testPrimes[1], testPrimes[2])
+	pk2 := &sk1.PublicKey
+	p2 := tt.B10("80835583194913519255227175491027534116323858942133804957873380964125769952153722872767395985807182088879137751973737195611736535673308039044731251312798604370125595953965575058201727000947562582634872106737658889028847062612351664088766417932577222262750095599375976992110180518474405571076375447630197402683")
+	q2 := tt.B10("69210064501097857725048553909160987839131798505582280831015356795143548214286337962509303315200340351978784326318311835136991907096681964505529171491850250428938993794552587102107113717157628550696163063380650545271668730646004879534943159254419759086140189236571989463830596906364636114340509119890275606391")
+	N2 := tt.B10("22378543707615306836182422597086174059399103708656614542204375941627776221585838908498318709084953151230965854544463050621828248405138252834708522307450445556723033074493621883193914559018381068514705602518576848505473239373873163089017151419401575132561803936035907582328999663685768377599926812681660506565947765011705274480316011005378618472210395471633060565141691029027315925435485138015621760349367644867362058194502904616776430082646477391555516713467661564007827039040130177584810996845324575709856975050152799234612346180661626644267859546152830340382918108278013986195106643466879089206972260629605087406361")
+	alpha2 := tt.B10("8747809298656078157114989950041580286626590365412031159633038987400223139122802354043389770093812959933384823884800254545895685397561553107528285733907902692147578830663267889623620419654128177892824386197392899719125115336150424159662997613720657468185455852362111552218248733267188584474338310030535392696941542304627485792649727961749526294440265425869039626150858630065641704957845214905134230348454532342863016686973803114811617354792880686738003360654735024192014095577237597827622102153977484388829956549425633334294348127208872226835724222353398872450805386968650925346794454105303144753420375228918197233593")
+	beta2 := tt.B10("2176139841560966477022156779585373977084793770032865716611721076366510042072757393725554689134042997574346080091862079219885406368886527384471502222447681728053956990594598338683296079141837969515744306817198519923794261948389920085503550175806501862554903010097757202296695916608707138517580767801026927471661226104627834436167025248795975530399204624851613982839790026616531533724496017750091049160213747834420322575228605441197854900387941711504209396818854405944049291123654264161208369287697015498157320659403403958742767733621289282236149735088305802788340120427685904560051631430226452469729196005350071038518")
+	h21 := tt.B10("20764671747204185805546844344412835044481927072125473833045065236747774267349721315389519959224111151333812652954644659437452036737962436105131388300631676148138552826539738766476333351400257979985612117861193564814347204651099040729052610123152900373393988655139065773685343172546701895310185998055572542743050440648428933844288312054936095897180901779311613028652390789016218147769551951586322205607557428325588069148780794645970025270442590369880171353631398974136157137932221009218128183651414251492625811774178862987122067289458907794177679420398930552955065418080976552272653430571577633578476287756522428963268")
+	h22 := tt.B10("2991008902201630200117440742333338885856080655411619980514782500763526876709985991258228481606315867770547971678709881862150747984560670352917493320985965538437116820977692577161175862284036913093370195901175312261015557101569791088996256635738918121630482035458153294890744961588474194182996060717185759857085915200708530029348920315889833519026946814499142812753189562082593905483951134885775180934941075664930676658614552989873075474332334764420169918779728208107142868874929816807285246855695166118730354329507679528778713169223069037702719361468552001788414665308334859311395962549949565511540980897385271371982")
+
+	dkgParticipants[2] = &DkgParticipant{
+		Curve: curve,
+		state: &dkgstate{
+			D:         d2,
+			Sk:        sk2,
+			Pk:        pk2,
+			N:         N2,
+			H1:        h21,
+			H2:        h22,
+			V:         v2,
+			X:         x2,
+			Threshold: uint32(threshold),
+			Limit:     uint32(total),
+		},
+		id:    uint32(2),
+		Round: 2,
+	}
+
+	cdlParams21 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p2,
+		Qi:      q2,
+		H1:      h21,
+		H2:      h22,
+		ScalarX: alpha2,
+		N:       N2,
+	}
+
+	cdlParams22 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p2,
+		Qi:      q2,
+		H1:      h22,
+		H2:      h21,
+		ScalarX: beta2,
+		N:       N2,
+	}
+
+	proof21, _ := cdlParams21.Prove()
+	proof22, _ := cdlParams22.Prove()
+
+	dpOutputs[2] = &DkgRound1Bcast{
+		Identifier: uint32(2),
+		Ci:         c2,
+		Pki:        pk2,
+		H1i:        h21,
+		H2i:        h22,
+		Ni:         N2,
+		Proof1i:    proof21,
+		Proof2i:    proof22,
+	}
+
+	// Setup parameters for player 3
+	u3, _ := core.Rand(curve.Params().N)
+	v3, x3, _ := feldman.Split(u3.Bytes())
+	c3, d3, _ := commitVerifiers(v3)
+	sk3, _ := paillier.NewSecretKey(testPrimes[2], testPrimes[3])
+	pk3 := &sk1.PublicKey
+	p3 := tt.B10("82762378445241041785597416507146490924447650731139897784752935952615188889635739493260515391609009395512012510709694417682987650969620502923818755809286104031313081465573622419369705445472375093283434921189190872945878407680529264737835792880592698668922695556861850401038676208972765968600517704143107930939")
+	q3 := tt.B10("69984280963080064677800727110502274842099368563604158420066520063922637818395160287343267480348823052616167329961701614168083898925612364204117254926526013551734867336492773207372540967720859662663438793769658958121285041708356176137310878638419197674131049677486047662703715583824220317748400146581518805651")
+	N3 := tt.B10("23168262185138042086985251479966140367473901735462054883904158802899264898691745453544888260128845593494180271821344835446388187526575974414101963091834292189789300379762157838980851815082897653013412610189597921830744654589452349113217726909094907934886602336832701591827947839296008075387481044145203853001040451482685799793720746884491540403980953810998121611944634910546812395244563473672734584566589265151370354163653553724356278901340380622401163641562474726319566531912584399552348312976911765268861745938301120268844120841005241592287730934409073936996169212424570979999552686559812737873042697608781537218337")
+	alpha3 := tt.B10("15700848461280380865453593955761108710562895414247363097072882828466191790916811503316377080013948938072225007516727823198461336870478274783583845926904074063193546765645477855455273258274150739378394943431150849983293677107578668862239783392036575043145101427760350638472037576829352497038388585737650687025976060296433989815102965583016771823595419876353838074154404831501616992756987140969613192813913996292033706748510041393036246923312030419247298071079496294307995794672335020365605673661246459738777446284403765226964816958599530935710152502359977024900546418123107827630153113273622448646563626731524890158451")
+	beta3 := tt.B10("4445879341351807551209439241920588140685341448529417529966129370975387582547328611790463864985523049818186588579898273930075299257729508047763338871424268681977630441148158141892066821441561729492103026410192844346284104817705886190143212900488394256716287705027856018936240395625790280151981634907904864178490159409363504387136507125542627454380016748558057005637225625481246654258853972871702501872856487903999341616690584954898272433078686327089310861915148328259913401109993699884551105056353404107220173983671620298275738982057963556561810371192793230372490607557673240894790572775163623912821853064509864539001")
+	h31 := tt.B10("20655589105424284731130950222365942513635708110950343104368669683186013800106942421524347648458254016225036450934479227664921498785561364595133998161005944291950359490505065673829287124165328608814740981967547208784457369473849019618903667437471918601627601044509671230680260942658093024204790610273965477549218656620684879208070965028279550643411998341767974100272557335380738716438934690826564692745348318822199802416149976761047532756651975957242217027025407351894263261364922859598069540698965816588058759437732436981028926328047363612699976563290609364678354605271871488415744707392237965701195336114850923722797")
+	h32 := tt.B10("5496074424480326456967307779978137640059660693996954490061656724729243248263235164326034392211487428145642035897732902987019830534770657265806433471056048721413319683923174766405888321053057575584689236687181096491031182941541387466426725040271572300593534197768598345205731705003156108961982545733171941969970689906713317136842479008121330098952126720386613744001301998221850208337277017663694634040173073680721828995733047624361263114536685654886828447330526802851522697283703748194422611303519895796695954647757152041586980035268266906531329254312878479944233983358807551831572963272582468808462893198641903856921")
+
+	dkgParticipants[3] = &DkgParticipant{
+		Curve: curve,
+		state: &dkgstate{
+			D:         d3,
+			Sk:        sk3,
+			Pk:        pk3,
+			N:         N3,
+			H1:        h31,
+			H2:        h32,
+			V:         v3,
+			X:         x3,
+			Threshold: uint32(threshold),
+			Limit:     uint32(total),
+		},
+		id:    uint32(3),
+		Round: 2,
+	}
+
+	cdlParams31 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p3,
+		Qi:      q3,
+		H1:      h31,
+		H2:      h32,
+		ScalarX: alpha3,
+		N:       N3,
+	}
+
+	cdlParams32 := proof.CdlProofParams{
+		Curve:   curve,
+		Pi:      p3,
+		Qi:      q3,
+		H1:      h32,
+		H2:      h31,
+		ScalarX: beta3,
+		N:       N3,
+	}
+
+	proof31, _ := cdlParams31.Prove()
+	proof32, _ := cdlParams32.Prove()
+
+	dpOutputs[3] = &DkgRound1Bcast{
+		Identifier: uint32(3),
+		Ci:         c3,
+		Pki:        pk3,
+		H1i:        h31,
+		H2i:        h32,
+		Ni:         N3,
+		Proof1i:    proof31,
+		Proof2i:    proof32,
+	}
+
+	return dkgParticipants, dpOutputs
+}
+
+func TestDkgRound2Works(t *testing.T) {
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	dkgParticipants, dpOutputs := setupDkgRound2Params(curve, threshold, total)
+
+	// Test
+	participant := dkgParticipants[1]
+	bcast, p2psend, err := participant.DkgRound2(dpOutputs)
+	require.NoError(t, err)
+
+	// Verify the outputs
+	// Check echo broadcast
+	if bcast == nil {
+		t.Errorf("DkgRound2Bcast cannot be nil")
+	}
+
+	// Check P2P send
+	if p2psend == nil {
+		t.Errorf("DkgRound2P2PSend cannot be nil")
+	}
+
+	if len(p2psend) != 2 {
+		t.Errorf("DkgRound2P2PSend should have length 2, found: %d", len(p2psend))
+	}
+
+	// Check participant
+	if participant.Round != 3 {
+		t.Errorf("dkg round should be 3, found: %d", participant.Round)
+	}
+}
+
+// Test when the broadcast of Round 1 is tampered
+func TestDkgRound2Tampered(t *testing.T) {
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	dkgParticipants, dpOutputs := setupDkgRound2Params(curve, threshold, total)
+
+	participant := dkgParticipants[1]
+
+	// Tampering player 2 on Ni
+	dpOutputs[2].Ni.Add(dpOutputs[2].Ni, core.One)
+	_, _, err := participant.DkgRound2(dpOutputs)
+	tt.AssertSomeError(t, err)
+
+	// Restore player 2
+	dpOutputs[2].Ni.Sub(dpOutputs[2].Ni, core.One)
+	participant.Round = 2
+
+	// Tamper player 3 on Ni
+	dpOutputs[3].Ni.Add(dpOutputs[3].Ni, core.One)
+	_, _, err = participant.DkgRound2(dpOutputs)
+	tt.AssertSomeError(t, err)
+
+	// Restore player 3
+	dpOutputs[3].Ni.Sub(dpOutputs[3].Ni, core.One)
+	participant.Round = 2
+
+	// Tamper player 2 on h1
+	dpOutputs[2].H1i.Add(dpOutputs[2].H1i, core.One)
+	_, _, err = participant.DkgRound2(dpOutputs)
+	tt.AssertSomeError(t, err)
+}
+
+// Test repeat call of DKG round 2
+func TestDkgRound2RepeatCall(t *testing.T) {
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	dkgParticipants, dpOutputs := setupDkgRound2Params(curve, threshold, total)
+
+	participant := dkgParticipants[1]
+
+	// Actual test
+	bcast, p2psend, err := participant.DkgRound2(dpOutputs)
+	require.NoError(t, err)
+	require.NotNil(t, bcast)
+	require.NotNil(t, p2psend)
+
+	// Repeat
+	bcast, p2psend, err = participant.DkgRound2(dpOutputs)
+	require.Error(t, err)
+	require.Nil(t, bcast)
+	require.Nil(t, p2psend)
+}
+
+// Test the case when the number of received broadcast messages is not enough
+func TestDkgRound2NotEnoughParties(t *testing.T) {
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	dkgParticipants, dpOutputs := setupDkgRound2Params(curve, threshold, total)
+
+	participant := dkgParticipants[1]
+
+	// Remove player 2's broadcast
+	dpOutputs[2] = nil
+
+	// Actual test
+	bcast, p2psend, err := participant.DkgRound2(dpOutputs)
+	require.Error(t, err)
+	require.Nil(t, bcast)
+	require.Nil(t, p2psend)
+}
+
+func TestDkgRound4Works(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[1],
+		2: participants[2].state.X[1],
+		3: participants[3].state.X[1],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res2)
+	res3, err := participants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[2],
+		2: participants[2].state.X[2],
+		3: participants[3].state.X[2],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res3)
+
+	// Actual test
+	out1, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res2,
+		3: res3,
+	})
+	require.NoError(t, err)
+	require.NotNil(t, out1)
+	out2, err := participants[2].DkgRound4(map[uint32]paillier.PsfProof{
+		1: res1,
+		3: res3,
+	})
+	require.NoError(t, err)
+	require.NotNil(t, out2)
+	out3, err := participants[3].DkgRound4(map[uint32]paillier.PsfProof{
+		1: res1,
+		2: res2,
+	})
+	require.NoError(t, err)
+	require.NotNil(t, out3)
+
+	// check that the shares result in valid secret key and public key
+	field := curves.NewField(curve.Params().N)
+
+	shamir, _ := v1.NewShamir(playerMin, playerCnt, field)
+	share1 := v1.NewShamirShare(1, out1.SigningKeyShare.Bytes(), field)
+	share2 := v1.NewShamirShare(2, out2.SigningKeyShare.Bytes(), field)
+	share3 := v1.NewShamirShare(3, out3.SigningKeyShare.Bytes(), field)
+	secret12, err := shamir.Combine(share1, share2)
+	require.NoError(t, err)
+	secret13, err := shamir.Combine(share1, share3)
+	require.NoError(t, err)
+	secret23, err := shamir.Combine(share2, share3)
+	require.NoError(t, err)
+
+	require.Equal(t, secret12, secret13)
+	require.Equal(t, secret12, secret23)
+	pk, err := curves.NewScalarBaseMult(curve, new(big.Int).SetBytes(secret12))
+	require.NoError(t, err)
+	require.True(t, participants[1].state.Y.Equals(pk))
+}
+
+func TestDkgRound4RepeatCall(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[1],
+		2: participants[2].state.X[1],
+		3: participants[3].state.X[1],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res2)
+	res3, err := participants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[2],
+		2: participants[2].state.X[2],
+		3: participants[3].state.X[2],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res3)
+
+	// Actual test
+	out1, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res2,
+		3: res3,
+	})
+	require.NoError(t, err)
+	require.NotNil(t, out1)
+
+	out2, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res2,
+		3: res3,
+	})
+	require.NoError(t, err)
+	require.Equal(t, out1, out2)
+}
+
+func TestDkgRound4NotEnoughProofs(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[1],
+		2: participants[2].state.X[1],
+		3: participants[3].state.X[1],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res2)
+	res3, err := participants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[2],
+		2: participants[2].state.X[2],
+		3: participants[3].state.X[2],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res3)
+
+	// Actual test
+	out1, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res2,
+	})
+	require.Error(t, err)
+	require.Nil(t, out1)
+	out2, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		3: res3,
+	})
+	require.Error(t, err)
+	require.Nil(t, out2)
+}
+
+func TestDkgRound4NoProofs(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+
+	// Actual test
+	out1, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{})
+	require.Error(t, err)
+	require.Nil(t, out1)
+}
+
+func TestDkgRound4WrongProofs(t *testing.T) {
+	// Setup
+	curve := btcec.S256()
+	playerCnt := 3
+	playerMin := 2
+	participants := setupDkgRound3ParticipantMap(curve, playerMin, playerCnt)
+	decommitments := setupDkgRound3Commitments(t, participants, playerCnt)
+
+	res1, err := participants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[0],
+		2: participants[2].state.X[0],
+		3: participants[3].state.X[0],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res1)
+	res2, err := participants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[1],
+		2: participants[2].state.X[1],
+		3: participants[3].state.X[1],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res2)
+	res3, err := participants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: participants[1].state.X[2],
+		2: participants[2].state.X[2],
+		3: participants[3].state.X[2],
+	})
+	require.NoError(t, err)
+	require.NotNil(t, res3)
+
+	// Actual test
+	out1, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res2,
+		3: res1,
+	})
+	require.Error(t, err)
+	require.Nil(t, out1)
+	out2, err := participants[1].DkgRound4(map[uint32]paillier.PsfProof{
+		2: res3,
+		3: res3,
+	})
+	require.Error(t, err)
+	require.Nil(t, out2)
+}
+
+func TestDkgFullRoundsWorks(t *testing.T) {
+	if testing.Short() {
+		t.Skip("skipping test in short mode.")
+	}
+	curve := btcec.S256()
+	total := 3
+	threshold := 2
+	var err error
+
+	// Initiate 3 parties for DKG
+	dkgParticipants := make(map[uint32]*DkgParticipant, total)
+	for i := 1; i <= total; i++ {
+		dkgParticipants[uint32(i)] = &DkgParticipant{
+			Curve: curve,
+			id:    uint32(i),
+			Round: 1,
+			state: &dkgstate{
+				Threshold: uint32(threshold),
+				Limit:     uint32(total),
+			},
+		}
+	}
+
+	// Run Dkg Round 1
+	dkgR1Out := make(map[uint32]*DkgRound1Bcast, total)
+	for i := 1; i <= total; i++ {
+		dkgR1Out[uint32(i)], err = dkgParticipants[uint32(i)].DkgRound1(uint32(threshold), uint32(total))
+		require.NoError(t, err)
+	}
+
+	// Run Dkg Round 2
+	dkgR2Bcast := make(map[uint32]*DkgRound2Bcast, total)
+	dkgR2P2PSend := make(map[uint32]map[uint32]*DkgRound2P2PSend, total)
+	for i := 1; i <= total; i++ {
+		dkgR2Bcast[uint32(i)], dkgR2P2PSend[uint32(i)], err = dkgParticipants[uint32(i)].DkgRound2(dkgR1Out)
+		require.NoError(t, err)
+	}
+
+	// Run Dkg Round 3
+	decommitments := make(map[uint32]*core.Witness, total)
+	dkgR3Out := make(map[uint32]paillier.PsfProof)
+	decommitments[1] = dkgR2Bcast[1].Di
+	decommitments[2] = dkgR2Bcast[2].Di
+	decommitments[3] = dkgR2Bcast[3].Di
+
+	dkgR3Out[1], err = dkgParticipants[1].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: dkgParticipants[1].state.X[0],
+		2: dkgParticipants[2].state.X[0],
+		3: dkgParticipants[3].state.X[0],
+	})
+	require.NoError(t, err)
+
+	dkgR3Out[2], err = dkgParticipants[2].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: dkgParticipants[1].state.X[1],
+		2: dkgParticipants[2].state.X[1],
+		3: dkgParticipants[3].state.X[1],
+	})
+	require.NoError(t, err)
+
+	dkgR3Out[3], err = dkgParticipants[3].DkgRound3(decommitments, map[uint32]*v1.ShamirShare{
+		1: dkgParticipants[1].state.X[2],
+		2: dkgParticipants[2].state.X[2],
+		3: dkgParticipants[3].state.X[2],
+	})
+	require.NoError(t, err)
+
+	// Run Dkg Round 4
+	dkgR4Out := make(map[uint32]*DkgResult, total)
+	for i := 1; i <= total; i++ {
+		dkgR4Out[uint32(i)], err = dkgParticipants[uint32(i)].DkgRound4(dkgR3Out)
+		require.NoError(t, err)
+	}
+
+	// Check that the shares result in valid secret key and public key
+	field := curves.NewField(curve.Params().N)
+
+	shamir, _ := v1.NewShamir(threshold, total, field)
+	share1 := v1.NewShamirShare(1, dkgR4Out[1].SigningKeyShare.Bytes(), field)
+	share2 := v1.NewShamirShare(2, dkgR4Out[2].SigningKeyShare.Bytes(), field)
+	share3 := v1.NewShamirShare(3, dkgR4Out[3].SigningKeyShare.Bytes(), field)
+	secret12, err := shamir.Combine(share1, share2)
+	require.NoError(t, err)
+	secret13, err := shamir.Combine(share1, share3)
+	require.NoError(t, err)
+	secret23, err := shamir.Combine(share2, share3)
+	require.NoError(t, err)
+
+	require.Equal(t, secret12, secret13)
+	require.Equal(t, secret12, secret23)
+
+	// Check the relationship of verification key and signing key is valid
+	pk, err := curves.NewScalarBaseMult(curve, new(big.Int).SetBytes(secret12))
+	require.NoError(t, err)
+	require.True(t, dkgParticipants[1].state.Y.Equals(pk))
+
+	// Check every participant has the same verification key
+	require.Equal(t, dkgParticipants[1].state.Y, dkgParticipants[2].state.Y)
+	require.Equal(t, dkgParticipants[1].state.Y, dkgParticipants[3].state.Y)
+
+	// Testing validity of paillier public key and secret key
+	// Check every participant receives equal paillier public keys from other parties
+	require.Equal(t, dkgParticipants[1].state.otherParticipantData[2].PublicKey, dkgParticipants[3].state.otherParticipantData[2].PublicKey)
+	require.Equal(t, dkgParticipants[1].state.otherParticipantData[3].PublicKey, dkgParticipants[2].state.otherParticipantData[3].PublicKey)
+	require.Equal(t, dkgParticipants[2].state.otherParticipantData[1].PublicKey, dkgParticipants[3].state.otherParticipantData[1].PublicKey)
+
+	// Testing validity of paillier keys of participant 1
+	pk1 := dkgParticipants[2].state.otherParticipantData[1].PublicKey
+	sk1 := dkgParticipants[1].state.Sk
+	msg1, _ := core.Rand(pk1.N)
+	c1, r1, err := pk1.Encrypt(msg1)
+	require.NoError(t, err)
+	require.NotNil(t, c1, r1)
+	m1, err := sk1.Decrypt(c1)
+	require.Equal(t, m1, msg1)
+	require.NoError(t, err)
+
+	// Testing validity of paillier keys of participant 2
+	pk2 := dkgParticipants[1].state.otherParticipantData[2].PublicKey
+	sk2 := dkgParticipants[2].state.Sk
+	msg, _ := core.Rand(pk2.N)
+	c, r, err := pk2.Encrypt(msg)
+	require.NoError(t, err)
+	require.NotNil(t, c, r)
+	m, err := sk2.Decrypt(c)
+	require.Equal(t, m, msg)
+	require.NoError(t, err)
+
+	// Testing validity of paillier keys of participant 3
+	pk3 := dkgParticipants[1].state.otherParticipantData[3].PublicKey
+	sk3 := dkgParticipants[3].state.Sk
+	msg3, _ := core.Rand(pk3.N)
+	c3, r3, err := pk3.Encrypt(msg3)
+	require.NoError(t, err)
+	require.NotNil(t, c3, r3)
+	m3, err := sk3.Decrypt(c3)
+	require.Equal(t, m3, msg3)
+	require.NoError(t, err)
+
+	// Checking public shares are equal
+	require.Equal(t, dkgParticipants[1].state.PublicShares, dkgParticipants[2].state.PublicShares)
+	require.Equal(t, dkgParticipants[1].state.PublicShares, dkgParticipants[3].state.PublicShares)
+
+	// Checking proof params are equal
+	require.Equal(t, dkgR4Out[1].ParticipantData[2].ProofParams, dkgR4Out[3].ParticipantData[2].ProofParams)
+	require.Equal(t, dkgR4Out[1].ParticipantData[3].ProofParams, dkgR4Out[2].ParticipantData[3].ProofParams)
+	require.Equal(t, dkgR4Out[2].ParticipantData[1].ProofParams, dkgR4Out[3].ParticipantData[1].ProofParams)
+}
diff --git a/pkg/tecdsa/gg20/participant/participant.go b/pkg/tecdsa/gg20/participant/participant.go
new file mode 100644
index 00000000..e4d1305f
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/participant.go
@@ -0,0 +1,342 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/elliptic"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+	"reflect"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// Participant is a tECDSA player that receives information from a trusted dealer
+type Participant struct {
+	dealer.Share
+	sk *paillier.SecretKey
+}
+
+// Signer is a tECDSA player that holds the additive shares needed for performing the signing operation
+type Signer struct {
+	sk              *paillier.SecretKey            // paillier secret key assigned to this signer
+	share           *v1.ShamirShare                // secret signing share for this signer
+	publicSharesMap map[uint32]*dealer.PublicShare // public shares of our cosigners
+	id              uint32                         // The ID assigned to this signer's shamir share
+	// This is minimum number of signers required to produce a valid signature,
+	// not the security threshold (as specified in [spec][GG20])
+	threshold uint
+	PublicKey *curves.EcPoint
+	Curve     elliptic.Curve
+	Round     uint   // current signing round in our linear state machine
+	state     *state // Accumulated intermediate values associated with signing
+}
+
+// NewSigner C=creates a new signer from a dealer-provided output and a specific set of co-signers
+func NewSigner(info *dealer.ParticipantData, cosigners []uint32) (*Signer, error) {
+	// Create the participant
+	p := Participant{*info.SecretKeyShare, info.DecryptKey}
+
+	// Skinny down the sharesMap to just the chosen ones
+	chosenOnes := make(map[uint32]*dealer.PublicShare, len(cosigners))
+	for _, id := range cosigners {
+		chosenOnes[id] = info.PublicShares[id]
+	}
+
+	// Convert to additive shares and return the resultx
+	return p.PrepareToSign(
+		info.EcdsaPublicKey,
+		func(*curves.EcPoint, []byte, *curves.EcdsaSignature) bool {
+			return true
+		},
+		info.EcdsaPublicKey.Curve,
+		info.KeyGenType,
+		chosenOnes,
+		info.EncryptKeys)
+}
+
+// verifyStateMap verifies the round is the expected round number and
+// that the set of signers from in.keys() exactly matches the set
+// in state.cosigners.
+func (signer *Signer) verifyStateMap(round uint, in interface{}) error {
+	// Check the expected round against internal state
+	if signer.Round != round {
+		return internal.ErrInvalidRound
+	}
+
+	// If no map was provided, we're done.
+	if in == nil {
+		return nil
+	}
+
+	// Otherwise, verify that the map contains exactly our current
+	// set of cosigners (except for our own ID)
+	v := reflect.ValueOf(in)
+	if v.Kind() != reflect.Map {
+		return fmt.Errorf("parameter `in` must be a map; instead is %v", v.Kind())
+	}
+	// Put these keys into a map for fast lookup
+	inCosignersMap := make(map[uint32]bool, len(v.MapKeys()))
+	for _, id := range v.MapKeys() {
+		inCosignersMap[uint32(id.Uint())] = true
+	}
+
+	// Check for superfluous cosigners in the input
+	for id := range inCosignersMap {
+		if id != signer.id && !signer.state.cosigners[id] {
+			return fmt.Errorf("cosigner id=%v is not valid", id)
+		}
+	}
+
+	// Check for missing cosigners in the input
+	for id := range signer.state.cosigners {
+		if id != signer.id && !inCosignersMap[id] {
+			return fmt.Errorf("missing input from cosigner id=%v", id)
+		}
+	}
+
+	// Success!
+	return nil
+}
+
+// setCosigners establishes the list of cosigner IDs. This may or may not include self ID.
+func (signer *Signer) setCosigners(in []uint32) error {
+	// Ensure the input is exactly the right length
+	if len(in) != int(signer.threshold-1) && len(in) != int(signer.threshold) {
+		return internal.ErrIncorrectCount
+	}
+
+	// Save off this list of signers
+	signer.state.cosigners = make(map[uint32]bool, len(in))
+	for _, id := range in {
+		signer.state.cosigners[id] = true
+	}
+	return nil
+}
+
+// resetSignRound sets the signer to a pre-round1 state.
+func (signer *Signer) resetSignRound() {
+	signer.Round = 1
+	signer.state = nil
+}
+
+// state encapsulates all the values used in the signing rounds state machine
+type state struct {
+	keyGenType dealer.KeyGenType
+	verify     curves.EcdsaVerify
+	msgHash    []byte
+
+	// List of IDs of the other participants that we expect to see in each round
+	cosigners map[uint32]bool
+
+	// Round 1 variables
+	ki     *big.Int
+	gammai *big.Int
+	Gammai *curves.EcPoint
+	Ci     core.Commitment
+	Di     *core.Witness
+	ci     paillier.Ciphertext
+	ri     *big.Int
+
+	// Round 2 variables
+	cj    map[uint32]paillier.Ciphertext
+	Cj    map[uint32]core.Commitment
+	betaj map[uint32]*big.Int
+	vuj   map[uint32]*big.Int
+	pks   map[uint32]*paillier.PublicKey
+
+	// Round 3 variables
+	deltai *big.Int
+	sigmai *big.Int
+
+	// Round 4 variables
+	delta *big.Int
+
+	// Round 5 variables
+	r     *big.Int
+	Rbari *curves.EcPoint
+	Rbark *curves.EcPoint
+	R     *curves.EcPoint
+
+	// Round 6 variables
+	si *big.Int
+}
+
+// convertToAdditive takes all the publicShares and changes them to their additive form
+// for this participant. Only t shares are needed for this step
+// [spec] §4.figure 4: convertToAdditive
+func (p Participant) convertToAdditive(curve elliptic.Curve, publicSharesMap map[uint32]*dealer.PublicShare) (*Signer, error) {
+	if publicSharesMap == nil {
+		return nil, fmt.Errorf("public shares cannot be nil")
+	}
+	if len(publicSharesMap) < 2 {
+		return nil, fmt.Errorf("threshold must be at least 2")
+	}
+	emptyP := Participant{Share: dealer.Share{}}
+	if p == emptyP || p.Value == nil || p.Point == nil {
+		return nil, fmt.Errorf("participant share cannot be nil")
+	}
+
+	field := curves.NewField(curve.Params().N)
+	x, err := makeXMap(curve, publicSharesMap)
+	if err != nil {
+		return nil, err
+	}
+
+	additiveMap := make(map[uint32]*dealer.PublicShare, len(publicSharesMap))
+	var maxIndex uint32 = 0
+	var privateKeyShare *v1.ShamirShare
+
+	// Compute lagrange coefficients
+	for j := range publicSharesMap {
+		// l is our lambda_j
+		l := field.One()
+		for k := range publicSharesMap {
+			// Don't compute lagrange coefficients for self-point
+			if j == k {
+				continue
+			}
+
+			// lambda(j) = \Prod_{j \= k} { x_k / (x_k - x_j) }
+			den := x[k].Sub(x[j])
+			if den.IsEqual(field.Zero()) {
+				return nil, fmt.Errorf("unable to calculate additive shares due to duplicates")
+			}
+			l = l.Mul(x[k].Div(den))
+		}
+
+		// Additive public shares for all signers this round
+		w, err := publicSharesMap[j].Point.ScalarMult(l.BigInt())
+		if err != nil {
+			return nil, err
+		}
+
+		additiveMap[j] = &dealer.PublicShare{Point: w}
+		if j > maxIndex {
+			maxIndex = j
+		}
+
+		// compute additive private share
+		if j == p.Identifier {
+			wI := l.Mul(field.ElementFromBytes(p.Share.Value.Bytes()))
+			privateKeyShare = v1.NewShamirShare(p.Share.Identifier, wI.Bytes(), field)
+		}
+	}
+
+	return &Signer{
+		sk:              p.sk,
+		share:           privateKeyShare,
+		publicSharesMap: additiveMap,
+		Round:           1,
+		state:           &state{},
+	}, nil
+}
+
+// PrepareToSign creates a Signer out of a Participant. The expected co-signers for the signing rounds are
+// expected to be exactly those included in the publicSharesMap
+func (p Participant) PrepareToSign(pubKey *curves.EcPoint,
+	verify curves.EcdsaVerify,
+	curve elliptic.Curve,
+	keyGenType dealer.KeyGenType,
+	publicSharesMap map[uint32]*dealer.PublicShare,
+	pubKeys map[uint32]*paillier.PublicKey) (*Signer, error) {
+	if pubKey == nil || verify == nil || curve == nil || keyGenType == nil || len(publicSharesMap) < 1 {
+		return nil, internal.ErrNilArguments
+	}
+	signer, err := p.convertToAdditive(curve, publicSharesMap)
+	if err != nil {
+		return nil, err
+	}
+	signer.id = signer.share.Identifier
+
+	signer.state.cosigners = make(map[uint32]bool, len(publicSharesMap)-1)
+	for id := range publicSharesMap {
+		if id == p.Identifier {
+			continue
+		}
+		if _, ok := pubKeys[id]; !ok {
+			return nil, fmt.Errorf("missing public key for signer %v", id)
+		}
+		signer.state.cosigners[id] = true
+	}
+	// Store co-signer pubkeys for round 2 and 6
+	signer.PublicKey = pubKey
+	signer.Curve = curve
+	signer.state.pks = pubKeys
+	signer.state.keyGenType = keyGenType
+	signer.state.verify = verify
+	signer.threshold = uint(len(publicSharesMap))
+	return signer, nil
+}
+
+// Creates a map of polynomial x-coordinates that are field elements.
+func makeXMap(curve elliptic.Curve, publicSharesMap map[uint32]*dealer.PublicShare) (map[uint32]*curves.Element, error) {
+	field := curves.NewField(curve.Params().N)
+	x := make(map[uint32]*curves.Element, len(publicSharesMap))
+
+	// Convert identifiers to a field element
+	for i, ps := range publicSharesMap {
+		if ps == nil {
+			return nil, internal.ErrNilArguments
+		}
+
+		x[i] = field.ElementFromBytes([]byte{byte(i)})
+	}
+	return x, nil
+}
+
+// DkgParticipant is a DKG player that contains information needed to perform DKG rounds and finally get info for signing rounds.
+type DkgParticipant struct {
+	Curve elliptic.Curve
+	state *dkgstate
+	id    uint32
+	Round uint
+}
+
+type dkgParticipantData struct {
+	PublicKey   *paillier.PublicKey
+	ProofParams *dealer.ProofParams
+	Commitment  core.Commitment
+}
+
+// dkgstate encapsulates all the values used in the dkg rounds state machine
+type dkgstate struct {
+	// Round 1 variables
+	D  *core.Witness
+	Sk *paillier.SecretKey
+	Pk *paillier.PublicKey
+	N  *big.Int
+	H1 *big.Int
+	H2 *big.Int
+	// This participants verifiers from FeldmanShare
+	V []*v1.ShareVerifier
+	// This participants shares from FeldmanShare
+	X         []*v1.ShamirShare
+	Y         *curves.EcPoint
+	Threshold uint32
+	Limit     uint32
+	// Commitments and paillier public keys received from other participants
+	otherParticipantData map[uint32]*dkgParticipantData
+	// xi returned from Round 3
+	Xi *big.Int
+	// X1,...,Xn returned from Round 3
+	PublicShares []*curves.EcPoint
+}
+
+// Check DKG round number is valid
+func (dp *DkgParticipant) verifyDkgRound(dkground uint) error {
+	if dp.Round != dkground {
+		return internal.ErrInvalidRound
+	}
+	return nil
+}
diff --git a/pkg/tecdsa/gg20/participant/participant_test.go b/pkg/tecdsa/gg20/participant/participant_test.go
new file mode 100644
index 00000000..8d67b395
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/participant_test.go
@@ -0,0 +1,450 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/ecdsa"
+	"crypto/elliptic"
+	"crypto/rand"
+	"encoding/json"
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/stretchr/testify/assert"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+func TestConvertToAdditiveWorks(t *testing.T) {
+	curve := btcec.S256()
+	_, shares, err := dealer.NewDealerShares(curve, 3, 5, nil)
+	if err != nil {
+		t.Errorf("NewDealerShares failed: %v", err)
+	}
+	publicShares, err := dealer.PreparePublicShares(shares)
+	if err != nil {
+		t.Errorf("PreparePublicShares failed: %v", err)
+	}
+
+	for _, s := range shares {
+		pi := Participant{
+			dealer.Share{
+				ShamirShare: s.ShamirShare,
+				Point:       s.Point,
+			},
+			nil,
+		}
+		_, err := pi.convertToAdditive(curve, publicShares)
+		if err != nil {
+			t.Errorf("convertToAdditive failed: %v", err)
+		}
+	}
+}
+
+func TestConvertToAdditiveNil(t *testing.T) {
+	curve := btcec.S256()
+	var publicSharesMap map[uint32]*dealer.PublicShare
+
+	pi := Participant{Share: dealer.Share{}}
+	_, err := pi.convertToAdditive(curve, publicSharesMap)
+	if err == nil {
+		t.Errorf("convertToAdditive should've failed")
+	}
+	_, shares, err := dealer.NewDealerShares(curve, 2, 3, nil)
+	if err != nil {
+		t.Errorf("NewDealerShares failed: %v", err)
+	}
+	publicSharesMap, err = dealer.PreparePublicShares(shares)
+	if err != nil {
+		t.Errorf("PreparePublicShares failed: %v", err)
+	}
+
+	_, err = pi.convertToAdditive(curve, publicSharesMap)
+	if err == nil {
+		t.Errorf("convertToAdditive should've failed")
+	}
+}
+
+func TestConvertToAdditiveNotEnoughShares(t *testing.T) {
+	curve := btcec.S256()
+	_, shares, err := dealer.NewDealerShares(curve, 2, 3, nil)
+	if err != nil {
+		t.Errorf("NewDealerShares failed: %v", err)
+	}
+	publicSharesMap, err := dealer.PreparePublicShares(shares)
+	if err != nil {
+		t.Errorf("PreparePublicShares failed: %v", err)
+	}
+
+	pi := Participant{Share: dealer.Share{}}
+
+	_, err = pi.convertToAdditive(curve, map[uint32]*dealer.PublicShare{})
+	internal.AssertSomeError(t, err)
+
+	_, err = pi.convertToAdditive(curve, map[uint32]*dealer.PublicShare{1: publicSharesMap[1]})
+	internal.AssertSomeError(t, err)
+}
+
+func TestConvertToAdditiveRecombine(t *testing.T) {
+	curve := btcec.S256()
+	pk, sharesMap, err := dealer.NewDealerShares(curve, 3, 5, nil)
+	if err != nil {
+		t.Errorf("NewDealerShares failed: %v", err)
+	}
+
+	// 5*4*3 possible combinations, try them all.
+	for i, s := range sharesMap {
+		pi := Participant{
+			dealer.Share{
+				ShamirShare: s.ShamirShare,
+				Point:       s.Point,
+			}, nil,
+		}
+		for j := range sharesMap {
+			if i == j {
+				continue
+			}
+
+			for k := range sharesMap {
+				if k == i || k == j {
+					continue
+				}
+
+				// Downsize to this particular set of signers
+				signerMap := map[uint32]*dealer.Share{
+					i: sharesMap[i],
+					j: sharesMap[j],
+					k: sharesMap[k],
+				}
+				publicSharesMap, err := dealer.PreparePublicShares(signerMap)
+				if err != nil {
+					t.Errorf("PreparePublicShares failed: %v", err)
+				}
+
+				pss, err := pi.convertToAdditive(curve,
+					map[uint32]*dealer.PublicShare{
+						i: publicSharesMap[i],
+						j: publicSharesMap[j],
+						k: publicSharesMap[k]})
+				if err != nil {
+					t.Errorf("convertToAdditive failed: %v", err)
+				}
+
+				// See if combining works
+				x := new(big.Int)
+				y := new(big.Int)
+				for _, ps := range pss.publicSharesMap {
+					x, y = curve.Add(x, y, ps.Point.X, ps.Point.Y)
+				}
+
+				internal.AssertBigIntEq(t, pk.X, x)
+				internal.AssertBigIntEq(t, pk.Y, y)
+			}
+		}
+	}
+}
+
+// Test that verifyStateMap checks rounds as expected
+func TestVerifyStateMapRoundCheck(t *testing.T) {
+	tests := []struct {
+		name       string
+		stateRound uint
+		roundIn    uint
+		expected   error
+	}{
+		{"positive", 5, 5, nil},
+		{"positive", 6, 6, nil},
+		{"positive", 1, 1, nil},
+		{"positive", 5, 5, nil},
+		{"negative", 5, 0, internal.ErrInvalidRound},
+		{"negative", 1, 2, internal.ErrInvalidRound},
+		{"negative", 3, 5, internal.ErrInvalidRound},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		s := &Signer{}
+
+		t.Run(test.name, func(t *testing.T) {
+			// set the state round
+			s.Round = test.stateRound
+
+			// test
+			err := s.verifyStateMap(test.roundIn, nil)
+
+			// verify the error is as expected
+			if err != test.expected {
+				t.Errorf("unexpected error: want=%v got=%v", test.expected, err)
+			}
+		})
+	}
+}
+
+// Test that verifyStateMap checks rounds as expected
+func TestSetCosigners(t *testing.T) {
+	tests := []struct {
+		name        string
+		cosigners   map[uint32]*Round1Bcast
+		threshold   int
+		expectedErr error
+		expectedLen int
+	}{
+		{
+			name:        "includes-self",
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}, 5: {}},
+			threshold:   3,
+			expectedErr: nil,
+			expectedLen: 3,
+		},
+		{
+			name:        "excludes-self",
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 5: {}},
+			threshold:   3,
+			expectedErr: nil,
+			expectedLen: 2,
+		},
+		{
+			name:        "wrong-length",
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 5: {}},
+			threshold:   4,
+			expectedErr: internal.ErrIncorrectCount,
+			expectedLen: 0,
+		},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		s := &Signer{}
+
+		t.Run(test.name, func(t *testing.T) {
+			// setup
+			s.resetSignRound()
+			s.state = &state{}
+			s.threshold = uint(test.threshold)
+
+			cosigners := make([]uint32, 0)
+			for k := range test.cosigners {
+				cosigners = append(cosigners, k)
+			}
+
+			err := s.setCosigners(cosigners)
+
+			// did we get the expected result?
+			if err != test.expectedErr {
+				t.Errorf("wrong error. want=%v  got=%v", test.expectedErr, err)
+			}
+			if len(s.state.cosigners) != test.expectedLen {
+				t.Errorf("wrong length. want=%v  got=%v", test.expectedErr.Error(), len(test.cosigners))
+			}
+		})
+	}
+}
+
+// Test that verifyStateMap checks rounds as expected
+func TestVerifyStateMapCosigners(t *testing.T) {
+	tests := []struct {
+		name        string
+		self        uint32
+		cosigners   map[uint32]*Round1Bcast
+		testSigners map[uint32]bool
+		expectedOk  bool
+	}{
+		{
+			name:        "positive-1-2-5-with-self",
+			self:        5,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}, 5: {}},
+			testSigners: map[uint32]bool{1: true, 2: false, 5: true},
+			expectedOk:  true,
+		},
+		{
+			name:        "positive-1-2-5-with-self-excluded-from-cosigners",
+			self:        5,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}},
+			testSigners: map[uint32]bool{1: true, 2: false, 5: true},
+			expectedOk:  true,
+		},
+		{
+			name:        "positive-1-2-missing-self",
+			self:        5,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}},
+			testSigners: map[uint32]bool{1: true, 2: false},
+			expectedOk:  true,
+		},
+		{
+			name:        "positive-1-2-10",
+			self:        1,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}, 10: {}},
+			testSigners: map[uint32]bool{1: true, 2: false, 10: false},
+			expectedOk:  true,
+		},
+		{
+			name:        "negative-missing-5",
+			self:        1,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}, 5: {}},
+			testSigners: map[uint32]bool{1: true, 2: false},
+			expectedOk:  false,
+		},
+		{
+			name:        "negative-missing-2",
+			self:        1,
+			cosigners:   map[uint32]*Round1Bcast{1: {}, 2: {}, 5: {}},
+			testSigners: map[uint32]bool{1: true, 5: false},
+			expectedOk:  false,
+		},
+	}
+	// Run all the tests!
+	for _, test := range tests {
+		s := &Signer{}
+
+		t.Run(test.name, func(t *testing.T) {
+			// setup
+			s.resetSignRound()
+			s.state = &state{}
+			s.id = test.self
+			s.threshold = 3
+			cosigners := make([]uint32, 0)
+			for id := range test.cosigners {
+				cosigners = append(cosigners, id)
+			}
+			err := s.setCosigners(cosigners)
+			internal.AssertNoError(t, err)
+
+			// func under test
+			err = s.verifyStateMap(1, test.testSigners)
+			// did we get the expected result?
+			if test.expectedOk {
+				internal.AssertNoError(t, err)
+			} else {
+				internal.AssertSomeError(t, err)
+			}
+		})
+	}
+}
+
+func TestNormalizeSK256(t *testing.T) {
+	// btcec always produces normalized signatures
+	// instead just double check that s gets negated
+	curve := btcec.S256()
+
+	signer := Signer{
+		state: &state{},
+	}
+	signer.Curve = curve
+	qDiv2, ok := new(big.Int).SetString("7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0", 16)
+	if !ok {
+		t.Error("Couldn't convert q/2")
+	}
+	for i := 0; i < 500; i++ {
+		s, err := core.Rand(qDiv2)
+		assert.NoError(t, err)
+
+		sNorm := signer.normalizeS(s)
+
+		assert.Equal(t, s, sNorm)
+	}
+	for i := 0; i < 500; i++ {
+		s, err := core.Rand(qDiv2)
+		s.Add(s, qDiv2)
+		assert.NoError(t, err)
+
+		sNorm := signer.normalizeS(s)
+
+		assert.NotEqual(t, s, sNorm)
+	}
+}
+
+func TestNormalizeSK256Identity(t *testing.T) {
+	curve := btcec.S256()
+
+	signer := Signer{
+		state: &state{},
+	}
+	signer.Curve = curve
+	for i := 0; i < 1000; i++ {
+		msg, err := core.Rand(curve.N)
+		assert.NoError(t, err)
+		sk, err := btcec.NewPrivateKey(curve)
+		assert.NoError(t, err)
+
+		sig, err := sk.Sign(msg.Bytes())
+		assert.NoError(t, err)
+
+		sNorm := signer.normalizeS(sig.S)
+
+		assert.Equal(t, sig.S, sNorm)
+	}
+}
+
+func TestNormalizeSP256(t *testing.T) {
+	p256 := elliptic.P256()
+	signer := Signer{
+		state: &state{},
+	}
+	signer.Curve = p256
+	sk, err := ecdsa.GenerateKey(p256, rand.Reader)
+	assert.NoError(t, err)
+	for i := 0; i < 1000; i++ {
+		msg, err := core.Rand(p256.Params().N)
+		assert.NoError(t, err)
+		r, s, err := ecdsa.Sign(rand.Reader, sk, msg.Bytes())
+		assert.NoError(t, err)
+
+		newS := signer.normalizeS(s)
+		assert.True(t, ecdsa.Verify(&sk.PublicKey, msg.Bytes(), r, newS))
+	}
+}
+
+func TestSerializeParticipantData(t *testing.T) {
+	participants := 5
+	curve := btcec.S256()
+	ecdsaPk, sharesMap, err := dealer.NewDealerShares(curve, 3, uint32(participants), nil)
+	assert.NoError(t, err)
+	pubSharesMap, err := dealer.PreparePublicShares(sharesMap)
+	assert.NoError(t, err)
+	paillierKeys := make(map[uint32]*paillier.SecretKey, participants)
+	encryptKeys := make(map[uint32]*paillier.PublicKey, participants)
+	for i, k := range genPrimesArray(participants) {
+		id := uint32(i + 1)
+		paillierKeys[id], err = paillier.NewSecretKey(k.p, k.q)
+		encryptKeys[id] = paillier.NewPubkey(paillierKeys[id].PublicKey.N)
+		assert.NoError(t, err)
+	}
+
+	keyGenType := dealer.TrustedDealerKeyGenType{
+		ProofParams: dealerParams,
+	}
+
+	p := dealer.ParticipantData{
+		EcdsaPublicKey: ecdsaPk,
+		KeyGenType:     keyGenType,
+		PublicShares:   pubSharesMap,
+		EncryptKeys:    encryptKeys,
+	}
+
+	for i := 0; i < participants; i++ {
+		id := uint32(i + 1)
+		p.Id = id
+		p.DecryptKey = paillierKeys[id]
+		p.SecretKeyShare = sharesMap[id]
+
+		data, err := json.Marshal(p)
+		assert.NoError(t, err)
+
+		p2 := new(dealer.ParticipantData)
+		assert.NoError(t, json.Unmarshal(data, p2))
+		assert.Equal(t, p.Id, p2.Id)
+		assert.Equal(t, p.DecryptKey, p2.DecryptKey)
+		assert.Equal(t, p.SecretKeyShare, p2.SecretKeyShare)
+		assert.Equal(t, p.KeyGenType, p2.KeyGenType)
+		assert.Equal(t, p.EcdsaPublicKey, p2.EcdsaPublicKey)
+		assert.Equal(t, p.EncryptKeys, p2.EncryptKeys)
+		assert.Equal(t, p.PublicShares, p2.PublicShares)
+	}
+}
diff --git a/pkg/tecdsa/gg20/participant/round1.go b/pkg/tecdsa/gg20/participant/round1.go
new file mode 100644
index 00000000..edd3ec91
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round1.go
@@ -0,0 +1,132 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round1Bcast contains values to be broadcast to all players after the completion of singing round 1
+type Round1Bcast struct {
+	Identifier uint32
+	C          core.Commitment
+	Ctxt       *big.Int
+	Proof      *proof.Range1Proof
+}
+
+type Round1P2PSend = proof.Range1Proof
+
+// SignRound1 performs round 1 signing operation
+// Trusted Dealer Mode: see [spec] fig 7: SignRound1
+// DKG Mode: see [spec] fig 8: SignRound1
+// NOTE: Pseudocode shows N~, h1, h2, the curve's g, q, and signer's public key as inputs
+// Since `signer` already knows the paillier secret and public keys, this input is not necessary here
+// `participant.PrepareToSign` receives the other inputs and stores them as state variables.
+func (signer *Signer) SignRound1() (*Round1Bcast, map[uint32]*Round1P2PSend, error) {
+	if signer == nil || signer.Curve == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+
+	if err := signer.verifyStateMap(1, nil); err != nil {
+		return nil, nil, err
+	}
+
+	pk := &signer.sk.PublicKey
+
+	// 1. k_i \getsr Z_q
+	k, err := core.Rand(signer.Curve.Params().N)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 2. \gamma_i \getsr Z_q
+	gamma, err := core.Rand(signer.Curve.Params().N)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 3. \Gamma_i = g^{\gamma_i} in \G
+	Gamma, err := curves.NewScalarBaseMult(signer.Curve, gamma)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 4. C_i, D_i = Commit(\Gamma_i)
+	Ci, Di, err := core.Commit(Gamma.Bytes())
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 5. c_i, r_i = PaillierEncryptAndReturnRandomness(pk_i, k_i)
+	ctxt, r, err := pk.Encrypt(k)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	pp := proof.Proof1Params{
+		Curve: signer.Curve,
+		Pk:    pk,
+		A:     k,
+		C:     ctxt,
+		R:     r,
+	}
+	bcast := Round1Bcast{
+		Identifier: signer.id,
+		C:          Ci,
+		Ctxt:       ctxt,
+	}
+	p2p := make(map[uint32]*Round1P2PSend)
+
+	if signer.state.keyGenType.IsTrustedDealer() {
+		pp.DealerParams = signer.state.keyGenType.GetProofParams(1)
+		// 6. TrustedDealer - \pi_i^{\Range1} = MtAProveRange1(g,q,pk_i,N~,h_1,h_2,k_i,c_i,r_i)
+		bcast.Proof, err = pp.Prove()
+		if err != nil {
+			return nil, nil, err
+		}
+	} else {
+		// 6. (figure 8.)DKG - for j = [1,...,t+1]
+		for id := range signer.state.cosigners {
+			// 7. DKG if i == j, continue
+			if signer.id == id {
+				continue
+			}
+			pp.DealerParams = signer.state.keyGenType.GetProofParams(id)
+			if pp.DealerParams == nil {
+				return nil, nil, fmt.Errorf("no proof params found for cosigner %d", id)
+			}
+			// 8. DKG \pi_ij^{\Range1} = MtAProveRange1(g,q,pk_i,N~j,h_1j,h_2j,k_i,c_i,r_i)
+			pi, err := pp.Prove()
+			if err != nil {
+				return nil, nil, err
+			}
+			// 9. P2PSend
+			p2p[id] = pi
+		}
+	}
+
+	// 8. Stored locally (k_i, \gamma_i, D_i, c_i, r_i)
+	signer.Round = 2
+	signer.state.ki = k
+	signer.state.gammai = gamma
+	signer.state.Gammai = Gamma
+	signer.state.Di = Di
+	signer.state.ci = ctxt
+	signer.state.ri = r
+
+	// (figure 7) 7. Broadcast (C_i, c_i, \pi^{Range1}_i)
+	// (figure 8) 9. P2PSend(\pi^{Range1}_ij)
+	// (figure 8) 10. Broadcast (C_i, c_i)
+	return &bcast, p2p, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/round2.go b/pkg/tecdsa/gg20/participant/round2.go
new file mode 100644
index 00000000..9a8ed47e
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round2.go
@@ -0,0 +1,131 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"encoding/json"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// P2PSend is all the values that need to be sent to each player
+type P2PSend struct {
+	Proof2, Proof3 proof.ResponseFinalizer
+}
+
+// UnmarshalJSON explicitly unmarshals into ResponseProofs instead of ResponsFinalizer interface
+func (p2ps *P2PSend) UnmarshalJSON(bytes []byte) error {
+	// Temporary struct used to explicitly unmarshal into ResponseProofs instead of ResponseFinalizer
+	data := struct {
+		Proof2, Proof3 proof.ResponseProof
+	}{}
+
+	err := json.Unmarshal(bytes, &data)
+	if err != nil {
+		return err
+	}
+
+	p2ps.Proof2 = data.Proof2
+	p2ps.Proof3 = data.Proof3
+
+	return nil
+}
+
+// SignRound2 performs round 2 signing operations for a single signer
+// Trusted Dealer Mode: see [spec] fig 7: SignRound2
+// DKG Mode: see [spec] fig 8: SignRound2
+func (signer *Signer) SignRound2(params map[uint32]*Round1Bcast, p2p map[uint32]*Round1P2PSend) (map[uint32]*P2PSend, error) {
+	if err := signer.verifyStateMap(2, params); err != nil {
+		return nil, err
+	}
+	// In dearlerless version, p2p map must contain one message from each cosigner.
+	if !signer.state.keyGenType.IsTrustedDealer() {
+		if err := signer.verifyStateMap(2, p2p); err != nil {
+			return nil, err
+		}
+	}
+
+	cnt := signer.threshold - 1
+	p2PSend := make(map[uint32]*P2PSend, cnt)
+	signer.state.betaj = make(map[uint32]*big.Int, cnt)
+	signer.state.vuj = make(map[uint32]*big.Int, cnt)
+	signer.state.cj = make(map[uint32]paillier.Ciphertext, cnt)
+	signer.state.Cj = make(map[uint32]core.Commitment, cnt)
+
+	// This is outside the loop for efficiency since the only changing value is the
+	// params ciphertext
+	pp := &proof.Proof1Params{
+		Curve:        signer.Curve,
+		DealerParams: signer.state.keyGenType.GetProofParams(signer.id),
+	}
+	rpp := proof.ResponseProofParams{
+		Curve: signer.Curve,
+		B:     signer.publicSharesMap[signer.id].Point,
+	}
+
+	// 1. For j = [1 ... t+1]
+	for j, param := range params {
+		// 2. if i == j, continue
+		if param == nil || j == signer.id {
+			continue
+		}
+
+		// 3. if MtAVerifyRange(\pi_j^{Range1}, g, q, N~, h1, h2, c_j) == False then Abort
+		pp.Pk = signer.state.pks[j]
+		pp.C = param.Ctxt
+
+		if signer.state.keyGenType.IsTrustedDealer() {
+			if err := param.Proof.Verify(pp); err != nil {
+				return nil, err
+			}
+		} else {
+			// The case using DKG, verify range proof in P2PSend
+			if err := p2p[j].Verify(pp); err != nil {
+				return nil, err
+			}
+		}
+
+		// 4. Compute c^{\gamma}_{ji}, \beta_{ji}, \pi^{Range2}_{ji} = MtaResponse(γ_i,g,q,pk_j,N~,h1,h2,c_j)
+		rpp.C1 = param.Ctxt
+		rpp.DealerParams = signer.state.keyGenType.GetProofParams(j)
+		rpp.SmallB = signer.state.gammai
+		rpp.Pk = signer.state.pks[j]
+		proofGamma, err := rpp.Prove()
+		if err != nil {
+			return nil, err
+		}
+
+		// 5. Compute c^{w}_{ji}, \vu_{ji}, \pi^{Range3}_{ji} = MtaResponse_wc(w_i,W_i,g,q,pk_j,N~,h1,h2,c_j)
+		rpp.SmallB = signer.share.Value.BigInt()
+		proofW, err := rpp.ProveWc()
+		if err != nil {
+			return nil, err
+		}
+
+		// Store the values for later rounds
+		signer.state.cj[j] = param.Ctxt
+		signer.state.betaj[j] = proofGamma.Beta
+		signer.state.vuj[j] = proofW.Beta
+		signer.state.Cj[j] = param.C
+
+		// Beta and vu are not sent to other signers
+		proofGamma.Beta = nil
+		proofW.Beta = nil
+
+		// 6. P2PSend(c^{gamma}_{ji}, c_^{W}_{ji}, \pi^{Range2}_{ji}, \pi^{Range3}_{ji})
+		p2PSend[j] = &P2PSend{
+			Proof2: proofGamma,
+			Proof3: proofW,
+		}
+	}
+	signer.Round = 3
+	return p2PSend, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/round3.go b/pkg/tecdsa/gg20/participant/round3.go
new file mode 100644
index 00000000..36678fae
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round3.go
@@ -0,0 +1,141 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"encoding/json"
+	"fmt"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round3Bcast represents the value to be broadcast to all players
+// at the conclusion of round 3
+type (
+	Round3Bcast struct {
+		// Note that deltaElement is some element of the entire δ vector.
+		// In this round, it's δ_i. For the recepients of this message in the next round
+		// this will be δ_j
+		deltaElement *big.Int
+		// The reason we can't do something straightforward like `type BetterRound3Bcast *big.int`
+		// is that although `big.int` has some methods implementing marshaler,
+		// they won't be accessible to `BetterRound3Bcast`. So the json.Marhsal uses the default methods
+		// and since the two fields of `big.int` are not exported, the data of `BetterRound3Bcast`
+		// won't actually be serialized and its deserialization results in nil.
+	}
+
+	Round3BcastJSON struct {
+		DeltaElement *big.Int
+	}
+)
+
+func (r3b Round3Bcast) MarshalJSON() ([]byte, error) {
+	return json.Marshal(Round3BcastJSON{r3b.deltaElement})
+}
+
+func (r3b *Round3Bcast) UnmarshalJSON(data []byte) error {
+	message := &Round3BcastJSON{}
+	err := json.Unmarshal(data, message)
+	if err != nil {
+		return err
+	}
+	r3b.deltaElement = message.DeltaElement
+	return nil
+}
+
+// SignRound3 performs the round 3 signing operation according to
+// Trusted Dealer Mode: see [spec] fig 7: SignRound3
+// DKG Mode: see [spec] fig 8: SignRound3
+func (s *Signer) SignRound3(in map[uint32]*P2PSend) (*Round3Bcast, error) {
+	if err := s.verifyStateMap(3, in); err != nil {
+		return nil, err
+	}
+
+	// 1. Compute δ_i = k_i γ_i mod q
+	deltai, err := core.Mul(s.state.ki, s.state.gammai, s.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 2. Compute σ_i = k_i w_i mod q
+	sigmai, err := core.Mul(s.state.ki, s.share.Value.BigInt(), s.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 3. For j=[1,...,t+1]
+	verifyParams := &proof.ResponseVerifyParams{
+		Curve:        s.Curve,
+		DealerParams: s.state.keyGenType.GetProofParams(s.id),
+		Sk:           s.sk,
+		C1:           s.state.ci,
+	}
+
+	for j, value := range in {
+
+		// 4. if i == j Continue
+		if j == s.id {
+			continue
+		}
+
+		if value == nil {
+			return nil, fmt.Errorf("P2P message for participant %v cannot be nil", j)
+		}
+
+		// 5. Compute α_ij = MtAFinalize(g,q,sk_i,pk_i,N~,h1,h2,c_i,c_ij,π_ij)
+		alphaij, err := value.Proof2.Finalize(verifyParams)
+
+		// 6. If α_ij = ⊥, Abort
+		if err != nil {
+			return nil, err
+		}
+
+		// 7. Compute μ_ij = MtAFinalize_wc(g,q,sk_i,pk_i,N~,h1,h2,c_i,c_ij,π_ij,W_j)
+		verifyParams.B = s.publicSharesMap[j].Point
+		mu, err := value.Proof3.FinalizeWc(verifyParams)
+
+		// 8. If μ_ij = ⊥, Abort
+		if err != nil {
+			return nil, err
+		}
+
+		// 9. Compute δ_i = δ_i + α_ij + β_ji  mod q
+		deltai, err = core.Add(deltai, alphaij, s.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+		deltai, err = core.Add(deltai, s.state.betaj[j], s.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+
+		// 10. Compute σ_i = σ_i + μ_ij + ν_ji  mod q
+		sigmai, err = core.Add(sigmai, mu, s.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+		sigmai, err = core.Add(sigmai, s.state.vuj[j], s.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+
+	}
+
+	// 12. Return δ_i, σ_i
+	// Store \delta_i, \sigma_i for future rounds
+	s.state.deltai = deltai
+	s.state.sigmai = sigmai
+
+	// Increment the round counter
+	s.Round = 4
+
+	// 11. Broadcast δ_i to all other players
+	return &Round3Bcast{deltai}, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/round4.go b/pkg/tecdsa/gg20/participant/round4.go
new file mode 100644
index 00000000..7afe406d
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round4.go
@@ -0,0 +1,60 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round4Bcast are the values to be broadcast to the other players at the conclusion
+// of signing round 4
+type Round4Bcast struct {
+	Witness *core.Witness
+}
+
+// SignRound4 performs the round 4 signing operation. It takes input
+// the delta_j values broadcast from signers at the conclusion of
+// round 3.
+// Trusted Dealer Mode: see [spec] fig 7: SignRound4
+// DKG Mode: see [spec] fig 8: SignRound4
+func (s *Signer) SignRound4(deltas map[uint32]*Round3Bcast) (*Round4Bcast, error) {
+	var err error
+	if err = s.verifyStateMap(4, deltas); err != nil {
+		return nil, err
+	}
+
+	// 1. Set δ = δ_i
+	delta := new(big.Int).Set(s.state.deltai)
+
+	// 2. For j=[1,...,t+1]
+	for j, deltaj := range deltas {
+		// 3. If i = j, Continue
+		if j == s.id {
+			continue
+		}
+
+		// 4. Compute δ = δ + δ_j mod q
+		delta, err = core.Add(delta, deltaj.deltaElement, s.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	// 6. Return δ
+	// Store δ as signer state
+	s.state.delta = delta
+
+	// Increment our round counter on success
+	s.Round = 5
+
+	// 5. Broadcast D_i to all other players
+	return &Round4Bcast{
+		s.state.Di,
+	}, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/round5.go b/pkg/tecdsa/gg20/participant/round5.go
new file mode 100644
index 00000000..d88d6788
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round5.go
@@ -0,0 +1,151 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+)
+
+// Round5Bcast are the values to be broadcast to the other players at the conclusion
+// of signing round 5
+type Round5Bcast struct {
+	Rbar  *curves.EcPoint
+	Proof *proof.PdlProof
+}
+
+// Round5P2PSend are the values sent to each participant at the conclusion of
+// signing round 5
+type Round5P2PSend = proof.PdlProof
+
+// SignRound5 performs the round 5 signing operation. It takes input
+// the Witness values broadcast from signers at the conclusion of
+// round 4.
+// Trusted Dealer Mode: see [spec] fig 7: SignRound5
+// DKG Mode: see [spec] fig 8: SignRound5
+func (signer *Signer) SignRound5(witnesses map[uint32]*Round4Bcast) (*Round5Bcast, map[uint32]*Round5P2PSend, error) {
+	if err := signer.verifyStateMap(5, witnesses); err != nil {
+		return nil, nil, err
+	}
+
+	// 1. Compute R = g^{γ_i} in G
+	R := signer.state.Gammai
+
+	// 2. For j = [1,...,t+1]
+	for j, d := range witnesses {
+		if d == nil {
+			return nil, nil, fmt.Errorf("input witnesses cannot be nil")
+		}
+		// 3. If i == j, continue
+		if j == signer.id {
+			continue
+		}
+
+		// FUTURE: match commitment with identifier instead of index
+		// 4. Compute Γ_j = Open(C_j , D_j)
+		ok, err := core.Open(signer.state.Cj[j], *d.Witness)
+		if err != nil {
+			return nil, nil, err
+		}
+		if !ok {
+			return nil, nil, fmt.Errorf("commitment couldn't be opened")
+		}
+
+		// 5. If Γ_j = ⊥, Abort
+		Gammaj, err := curves.PointFromBytesUncompressed(signer.Curve, d.Witness.Msg)
+		if err != nil {
+			return nil, nil, err
+		}
+
+		// 6. Compute R = R · Γ_j in G
+		R, err = R.Add(Gammaj)
+		if err != nil {
+			return nil, nil, err
+		}
+	}
+
+	// 7. Compute R= R^{δ^{−1}} in G
+	deltaInv, err := core.Inv(signer.state.delta, signer.Curve.Params().N)
+	if err != nil {
+		return nil, nil, err
+	}
+	R, err = R.ScalarMult(deltaInv)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// 9. Compute \overline{R_i} = R^{k_i}
+	Rbari, err := R.ScalarMult(signer.state.ki)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Sanity check
+	Rbark, err := R.ScalarMult(signer.state.sigmai)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	bcast := &Round5Bcast{Rbari, nil}
+	p2p := make(map[uint32]*Round5P2PSend)
+	pdlParams := proof.PdlProofParams{
+		Curve:   signer.Curve,
+		Pk:      &signer.sk.PublicKey,
+		ScalarX: signer.state.ki,
+		PointX:  Rbari,
+		C:       signer.state.ci,
+		ScalarR: signer.state.ri,
+		PointR:  R,
+	}
+
+	if signer.state.keyGenType.IsTrustedDealer() {
+		// 10. TrustedDealer - Compute π^{kCONSIST}_i = ProvePDL(g, q, R, pk_i, N~, h1, h2, k_i, \overline{R_i}, c_i, r_i)
+		pdlParams.DealerParams = signer.state.keyGenType.GetProofParams(0) //note ID is ignored for trusted dealer
+		bcast.Proof, err = pdlParams.Prove()
+		if err != nil {
+			return nil, nil, err
+		}
+	} else {
+		// 10. DKG - for j = [1,...,t+1]
+		for id := range signer.state.cosigners {
+			// 11. DKG if i == j, continue
+			if signer.id == id {
+				continue
+			}
+			pdlParams.DealerParams = signer.state.keyGenType.GetProofParams(id)
+			if pdlParams.DealerParams == nil {
+				return nil, nil, fmt.Errorf("no proof params found for cosigner %d", id)
+			}
+			// 12. DKG - Compute π^{kCONSIST}_ij = ProvePDL(g, q, R, pk_i, N~_j, h1_j, h2_j, k_i, \overline{R_i}, c_i, r_i)
+			pdl, err := pdlParams.Prove()
+			if err != nil {
+				return nil, nil, err
+			}
+			// 13. P2PSend π^{kCONSIST}_ij to Pj
+			p2p[id] = pdl
+		}
+	}
+
+	// Used in Round 6
+	signer.state.R = R
+
+	// 8. Set r = R_x
+	signer.state.r = R.X
+
+	// 12. Set \overline{R}_i
+	signer.state.Rbari = Rbari
+	signer.state.Rbark = Rbark
+
+	signer.Round = 6
+
+	// 11. TrustedDealer - Broadcast {R_i, π^{kCONSIST}_i} to all other players
+	// 13. DKG - Broadcast R_i to all other players, P2PSend π^{kCONSIST}_ij
+	return bcast, p2p, nil
+}
diff --git a/pkg/tecdsa/gg20/participant/round6.go b/pkg/tecdsa/gg20/participant/round6.go
new file mode 100644
index 00000000..a8b8dd32
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/round6.go
@@ -0,0 +1,244 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"encoding/json"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+
+	"github.com/coinbase/kryptology/pkg/core"
+)
+
+// Round6FullBcast are the values to be broadcast to the other players
+// This is the s_i value from §5.fig 5.SignRound6.step 9
+type (
+	Round6FullBcast struct {
+		// Note that sElement is some element of the entire s vector.
+		// In this round, it's s_i. For the recepients of this message in the final
+		// sign output round, this will be s_j
+		sElement *big.Int
+		// The reason we can't do something straightforward like `type BetterRound6FullBcast *big.int`
+		// is that although `big.int` has some methods implementing marshaler,
+		// they won't be accessible to `BetterRound6FullBcast`. So the json.Marhsal uses the default methods
+		// and since the two fields of `big.int` are not exported, the data of `BetterRound6FullBcast`
+		// won't actually be serialized and its deserialization results in nil.
+	}
+
+	Round6FullBcastJSON struct {
+		SElement *big.Int
+	}
+)
+
+func (r6b Round6FullBcast) MarshalJSON() ([]byte, error) {
+	return json.Marshal(Round6FullBcastJSON{r6b.sElement})
+}
+
+func (r6b *Round6FullBcast) UnmarshalJSON(data []byte) error {
+	message := &Round6FullBcastJSON{}
+	err := json.Unmarshal(data, message)
+	if err != nil {
+		return err
+	}
+	r6b.sElement = message.SElement
+	return nil
+}
+
+// SignRound6Full performs the round 6 signing operation according to
+// Trusted Dealer Mode: see [spec] fig 7: SignRound6
+// DKG Mode: see [spec] fig 8: SignRound6
+func (signer *Signer) SignRound6Full(hash []byte, in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) (*Round6FullBcast, error) {
+	if err := signer.verifyStateMap(6, in); err != nil {
+		return nil, err
+	}
+
+	if !signer.state.keyGenType.IsTrustedDealer() {
+		if err := signer.verifyStateMap(6, p2p); err != nil {
+			return nil, err
+		}
+	}
+
+	// Steps 1-6
+	err := signer.signRound6Offline(in, p2p)
+	if err != nil {
+		return nil, err
+	}
+
+	// Steps 7-10
+	return signer.signRound6Online(hash)
+}
+
+// signRound6Offline performs the round 6 signing operation according to
+// [spec] §6.fig 6
+// Verifies the accumulated computed values before signing the final result
+func (signer *Signer) signRound6Offline(in map[uint32]*Round5Bcast, p2p map[uint32]*Round5P2PSend) error {
+	// FUTURE: determine round state variables to accommodate on/offline modes
+	// before this function is exported
+	var err error
+
+	// 1. Set V = \bar{R}_i
+	v := signer.state.Rbari
+
+	// 2. For j=[1,...,t+1]
+	for j, value := range in {
+		// 3. If i = j, Continue
+		if j == signer.id {
+			continue
+		}
+
+		// 4. TrustedDealer - If VerifyPDL(πkCONSIST,g,q,R,pkj,N,h1,h2,cj,Rj) = False, Abort
+		// 4. DKG - If VerifyPDL(πkCONSIST_j,g,q,R,pkj,Nj,h1j,h2j,cj,Rj) = False, Abort
+		// Pseudocode says i when it should be j
+		verifyProofParams := &proof.PdlVerifyParams{
+			Curve:        signer.Curve,
+			Pk:           signer.state.pks[j],
+			DealerParams: signer.state.keyGenType.GetProofParams(signer.id),
+			PointX:       value.Rbar,
+			PointR:       signer.state.R,
+			C:            signer.state.cj[j],
+		}
+		if signer.state.keyGenType.IsTrustedDealer() {
+			if err := value.Proof.Verify(verifyProofParams); err != nil {
+				return err
+			}
+		} else {
+			if err := p2p[j].Verify(verifyProofParams); err != nil {
+				return err
+			}
+		}
+
+		// 5. Compute V = V · R_j in G
+		v, err = v.Add(value.Rbar)
+		if err != nil {
+			return err
+		}
+	}
+	// 6 If V != g, Abort
+	if !v.IsBasePoint() {
+		return fmt.Errorf("V != g")
+	}
+	// 7. return r, k, \sigma,
+	// These are already stored
+	return nil
+}
+
+// SignRound6Online performs the round 6 signing operation according to
+// [spec] §6.fig 6.SignRound6Online
+// func (p Participant) SignRound6Online(msg []byte, k, r, sigma *big.Int, curve elliptic.Curve) (*Round6FullBcast, *Round6FullOut, error) {
+func (signer *Signer) signRound6Online(hash []byte) (*Round6FullBcast, error) {
+	// FUTURE: check the current round state if allowed to be called separately
+
+	// 7. Compute m = H(M) ∈ Z_q
+	// We receive the message already hashed to allow flexibility for the callers
+	// to hash the message according to the library they use
+	// However, we check the hash is in the field
+	m := new(big.Int).SetBytes(hash)
+	if err := core.In(m, signer.Curve.Params().N); err != nil {
+		return nil, err
+	}
+	signer.state.msgHash = hash
+
+	// 8. Compute s_i = m k_i + r σ_i mod q
+	m, err := core.Mul(m, signer.state.ki, signer.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	rTmp, err := core.Mul(signer.state.r, signer.state.sigmai, signer.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	si, err := core.Add(m, rTmp, signer.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+
+	signer.state.si = si
+	signer.Round = 7
+
+	// 9. Broadcast s_i to all other players
+	// 10. Return s_i
+	return &Round6FullBcast{si}, nil
+}
+
+// SignOutput performs the signature aggregation step in
+// [spec] §5.fig 5
+func (signer *Signer) SignOutput(in map[uint32]*Round6FullBcast) (*curves.EcdsaSignature, error) {
+	var err error
+	if err = signer.verifyStateMap(7, in); err != nil {
+		return nil, err
+	}
+	// 1. Set s = s_i
+	s := new(big.Int).Set(signer.state.si)
+
+	// 2. For j = [1,...,t+1]
+	for j, sj := range in {
+		// 3. If i = j, continue
+		if j == signer.id {
+			continue
+		}
+
+		// 4. Compute s = s + s_j mod q
+		s, err = core.Add(s, sj.sElement, signer.Curve.Params().N)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	sOld := new(big.Int).Set(s)
+	s = signer.normalizeS(s)
+	v := int(signer.state.R.Y.Bit(0))
+
+	if sOld.Cmp(s) != 0 {
+		v ^= 1
+	}
+
+	// 5. Set \sigma = (r, s)
+	sigma := &curves.EcdsaSignature{V: v, R: signer.state.r, S: s}
+
+	// 6. If ECDSAVerify(y, \sigma, M) = False, Abort
+	if !signer.state.verify(signer.PublicKey, signer.state.msgHash, sigma) {
+		return nil, fmt.Errorf("signature is not valid")
+	}
+
+	// 7. Return \sigma
+	return sigma, nil
+}
+
+func (signer Signer) normalizeS(s *big.Int) *big.Int {
+	// Normalize the signature to a "low S" form. In ECDSA, signatures are
+	// of the form (r, s) where r and s are numbers lying in some finite
+	// field. The verification equation will pass for (r, s) iff it passes
+	// for (r, -s), so it is possible to ``modify'' signatures in transit
+	// by flipping the sign of s. This does not constitute a forgery since
+	// the signed message still cannot be changed, but for some applications,
+	// changing even the signature itself can be a problem. Such applications
+	// require a "strong signature". It is believed that ECDSA is a strong
+	// signature except for this ambiguity in the sign of s, so to accommodate
+	// these applications we will only produce signatures for which
+	// s is in the lower half of the field range. This eliminates the
+	// ambiguity.
+	//
+	// However, for some systems, signatures with high s-values are considered
+	// valid. (For example, parsing the historic Bitcoin blockchain requires
+	// this.) We normalize to the low S form which ensures that the s value
+	// lies in the lower half of its range.
+	// See <https://en.bitcoin.it/wiki/BIP_0062#Low_S_values_in_signatures>
+	qDiv2 := new(big.Int)
+	qDiv2 = qDiv2.Div(signer.Curve.Params().N, core.Two)
+
+	// Check whether a scalar is higher than the group order divided
+	// by 2. If true, we negate s.
+	// Not constant time, it would be better to conditionally negate with check in constant time
+	// but since `s` is a public value anyway, this is allowed to be variable time
+	if s.Cmp(qDiv2) == 1 {
+		return new(big.Int).Sub(signer.Curve.Params().N, s)
+	}
+	return new(big.Int).Set(s)
+}
diff --git a/pkg/tecdsa/gg20/participant/rounds_test.go b/pkg/tecdsa/gg20/participant/rounds_test.go
new file mode 100644
index 00000000..3fe387dc
--- /dev/null
+++ b/pkg/tecdsa/gg20/participant/rounds_test.go
@@ -0,0 +1,996 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package participant
+
+import (
+	"crypto/ecdsa"
+	"crypto/elliptic"
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+	"github.com/stretchr/testify/require"
+
+	"github.com/stretchr/testify/assert"
+
+	tt "github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+var (
+	dealerParams = &dealer.ProofParams{
+		N:  tt.B10("135817986946410153263607521492868157288929876347703239389804036854326452848342067707805833332721355089496671444901101084429868705550525577068432132709786157994652561102559125256427177197007418406633665154772412807319781659630513167839812152507439439445572264448924538846645935065905728327076331348468251587961"),
+		H1: tt.B10("130372793360787914947629694846841279927281520987029701609177523587189885120190605946568222485341643012763305061268138793179515860485547361500345083617939280336315872961605437911597699438598556875524679018909165548046362772751058504008161659270331468227764192850055032058007664070200355866555886402826731196521"),
+		H2: tt.B10("44244046835929503435200723089247234648450309906417041731862368762294548874401406999952605461193318451278897748111402857920811242015075045913904246368542432908791195758912278843108225743582704689703680577207804641185952235173475863508072754204128218500376538767731592009803034641269409627751217232043111126391"),
+	}
+	testPrimes = []*big.Int{
+		tt.B10("186141419611617071752010179586510154515933389116254425631491755419216243670159714804545944298892950871169229878325987039840135057969555324774918895952900547869933648175107076399993833724447909579697857041081987997463765989497319509683575289675966710007879762972723174353568113668226442698275449371212397561567"),
+		tt.B10("94210786053667323206442523040419729883258172350738703980637961803118626748668924192069593010365236618255120977661397310932923345291377692570649198560048403943687994859423283474169530971418656709749020402756179383990602363122039939937953514870699284906666247063852187255623958659551404494107714695311474384687"),
+		tt.B10("130291226847076770981564372061529572170236135412763130013877155698259035960569046218348763182598589633420963942796327547969527085797839549642610021986391589746295634536750785366034581957858065740296991986002552598751827526181747791647357767502200771965093659353354985289411489453223546075843993686648576029043"),
+		tt.B10("172938910323633442195852028319756134734590277522945546987913328782597284762767185925315797321999389252040294991952361905020940252121762387957669654615602135429944435719699091344247805645764550860505536884031064967454028383404046221898300153428182409080298694828920944094158777327533157774919783417586902830043"),
+		tt.B10("135841191929788643010555393808775051922265083622266098277752143441294911675705272940799534437169053045878247274810449617960047255023823301284034559807472662111224710158898548617194658983006262996831617082584649612602010680423107108651221824216065228161009680618243402116924511141821829055830713600437589058643"),
+		tt.B10("179677777376220950493907657233669314916823596507009854134559513388779535023958212632715646194917807302098015450071151245496651913873851032302340489007561121851068326577148680474495447007833318066335149850926605897908761267606415610900931306044455332084757793630487163583451178807470499389106913845684353833379"),
+		tt.B10("62649985409697862206708027961094957171873130708493280862148817115812710388878279240372941307490519941098268192630359164091992515623574326498710952492586770923230983753287493884398990474917756375654842939939940915963324175552421981212594421823752854754541693709434365609636589761589816398869727328798680335583"),
+		tt.B10("196576931859098680370388202020086631604584490828609819764890020064880575503817891126703473215983239396058738287255240835101797315137072822716923594188151190460588551553676484461393180135097616711975997391550414447010491794087888246885960280296709672609456539741162207414899687167396008233995214434586323322859"),
+		tt.B10("271336420864746369701165973306090650688066226258594853124089876839120277465060891854507381090238664515950686049792387028144049076707224579184820539700879884119579186284072404459682082855184644444282438298561112002507411996589407330801765394106772460665497195944412067027079123717579308322520985921886949051399"),
+		tt.B10("147653127360336844448178027222853805809444645720500374788954343695331927468524513989671450440433430392339037667457657655958027740671071573403925974795764987870476118984896439440386146680643457835633462311776946902713168513155240275028008685964121441954481847113848701823211862974120297600518927026940189810103"),
+		tt.B10("61539010433774119199101441060312213379096965116494840834113311373246794436251480454630309900106802555812462300777026043563820643373439814989443964169335227347638731691284339678436222951965582264570176875078394338903074717434072995072121221264531723385013005031614327462206339323414428493321384497439106152163"),
+		tt.B10("311771090987243597109711542316907830756641693311804000593662622484722315782429237915515708860530841821213561483232298821623675096481796856960171671330638042763441430256097782130268494276848432981045602236986861083392706904041234926428759947857376161689191720483868111001987710383245853931937989224732484206639"),
+		tt.B10("348545239501897032367950520763624245702184225360238826931782856428685149253861325854706825698843098817604431561258712026020688621010635185480321876001016614912927680387840531641703966894322797491484955817022624047355473480912508041252361257911175397626575812830091471419378132244146077774966527307225203863239"),
+		tt.B10("167562983031509383478485987630533113343120902430985961468758712448125734458812918541051012669749885569679178971612428577288632429606851871845164719448590160530844833425628143996971699662729056519326776907622035340086832629206691942750594912221135787534670122007438859975313187460872690748138136170080913902203"),
+		tt.B10("151715609132228776595716500435665208768897792993205818803431003524953811539898459230192282642811956896879836518212758893685104146944932088195466999437630114129887975508715417094019351746027667352287673763064246395392591213231796089814648654152625331299642171758052545451706130433176935280325874961374276589763"),
+		tt.B10("281712498774102170277967098381151873986368736986748325672760355775943894718315925237789122870763991635031524237638254080973752419302437870447849091185409669906909828874532209010547976564209374430136988588219470076527433259993640332285914706329187116209118972038509278879237122949265824264856530096167843589043"),
+		tt.B10("86882427063713590116032012033991745733440719961931885774819345297872782432110706546175706398857226544896860987721577779470479838062106788873559026307646871133570915480684987993282364698928926188640576189281202695899665555602891606955025957497645420156315890379148794822782242384167644977894987285630058930123"),
+		tt.B10("83303406464212917441403726886711948278716398972782717472384580707071541544369912289531948826578557956123897261910116726555850408667234850301141318443154703778225305104540324875867615851047711871915209458107086347063530255813116254895432804373554367035028329996279513893337862177371103671113527972705508417219"),
+		tt.B10("290829612093510969863838578444630131194824970528125429399090307997156531200557462531776190769158191441614466855963164356672434851525764502180873524299787560160992955274777477308009367164212073773611071813219472273292916120276721541591451163160398750751633065097434700462944540404208636130411713202759646572187"),
+		tt.B10("48881643615473281990659967689574873112454227417010573158578046287415357392674453353386274403945930212163960526780980360358370255117866064326375672959460785974850231208253282115124348836379470403659096433419030132737534978624170609788431758477453270578400762995584298785082853409573009591146163658067217132999"),
+		tt.B10("47818664065019136841944639898604168570191742429107462510943153778085167306149797958497736138014922106778177497683417470713996340979203175236987691632152128071256018368891463388744514315997309312144264057334961479235114340091423812710466596081259537323405527816634204224641066174554915788023121121924554823463"),
+		tt.B10("229695065817346126758526483359337260282925372883465036895664320607569899180246065431164369223444026964554195802821338287119074827091354255558249504915527499047398698041873875019622138440848556549357174461846992529556315682586788137744896985847052668283284231628825924370859640129811142861116994552829398428647"),
+		tt.B10("100501115016957347491693508757253443864758446032047524096020585354104983606736759639044367167134409576092528219013168507381959241052976704837620234061351712684500077849808223040972825725745511581504906610633548112115513604053190610668096089811015493012026572475283305559529666099836493252485826156659750294903"),
+		tt.B10("164941338210872461448879529698900150056451305424623398039343691654768566536491493438826728710972441042226712374570117138883019423322602098706113298908005378303473844839971995715847918643285222217768344335264383514921181158565529236124115589719970140511822410990649549555047928093673140752570788415674868532299"),
+		tt.B10("277037199251333188171108034082127252450960810846571117481542098050121457972964006392527344163695411986229107011168411232117984760439307440561490229321182283823299859836750264962218540927582605520434969388646847458788766216835350519741512353041653865564337457599778511921159510170311560556844284028160928114623"),
+		tt.B10("194450633495795999995837828580097111229016136925345956148788562473415774074431957758705067019578300241653926511426134047652491974620284426575921711048247821582093564387999309993254763749991516361193554847964638949731507356038181346481870018202492098453036116472375750355687853028597643560794156133662678349939"),
+		tt.B10("351287943170075259292767465687447861777186026969543801283411356809391771346213158326614410370157474105344692424346410925411240089238093158848815209147605381454294661108047095253146499393310219242924552687094316959878415907497273176683394122976929775532753961555304244867490393116346360677109958055297215711587"),
+		tt.B10("329970582937843908299463472795994928703202360293919677760100619380642134736439176597341134222679061949935544692834943628667398294307004076774417457697130314341974849843695836050603685013468031012892094273233016929045028941716224648802422408386216033754532303003405690778077639489173685122357063674177077611499"),
+		tt.B10("67751546105580063387575764356375682499165422473383503143930633584920975946879807021875353514236996076344028719391905234977223693643926924731304657199486141030504275775023186923364159168130612275534168246529309247449138607249407760246378829338068736888203134857601657561860157938495777271164458736576560502603"),
+		tt.B10("276043923868350639738966705196129285523536747369492013710841410915407411458158268634302674024358477700030814139419613881758439643092328709376796555454484423864587139181985503560495790018232370315219082876142282958894264284344738294415199758590186234114829175455336589153989920707778566032047921277945163061363"),
+		tt.B10("62028909880050184794454820320289487394141550306616974968340908736543032782344593292214952852576535830823991093496498970213686040280098908204236051130358424961175634703281821899530101130244725435470475135483879784963475148975313832483400747421265545413510460046067002322131902159892876739088034507063542087523"),
+		tt.B10("321804071508183671133831207712462079740282619152225438240259877528712344129467977098976100894625335474509551113902455258582802291330071887726188174124352664849954838358973904505681968878957681630941310372231688127901147200937955329324769631743029415035218057960201863908173045670622969475867077447909836936523"),
+		tt.B10("52495647838749571441531580865340679598533348873590977282663145916368795913408897399822291638579504238082829052094508345857857144973446573810004060341650816108578548997792700057865473467391946766537119012441105169305106247003867011741811274367120479722991749924616247396514197345075177297436299446651331187067"),
+		tt.B10("118753381771703394804894143450628876988609300829627946826004421079000316402854210786451078221445575185505001470635997217855372731401976507648597119694813440063429052266569380936671291883364036649087788968029662592370202444662489071262833666489940296758935970249316300642591963940296755031586580445184253416139"),
+	}
+	dummyVerifier = func(pubKey *curves.EcPoint, hash []byte, signature *curves.EcdsaSignature) bool {
+		return false
+	}
+	ecdsaVerifier = func(verKey *curves.EcPoint, hash []byte, sig *curves.EcdsaSignature) bool {
+		pk := &ecdsa.PublicKey{
+			Curve: verKey.Curve,
+			X:     verKey.X,
+			Y:     verKey.Y,
+		}
+		return ecdsa.Verify(pk, hash, sig.R, sig.S)
+	}
+	k256Verifier = func(pubKey *curves.EcPoint, hash []byte, sig *curves.EcdsaSignature) bool {
+		btcPk := &btcec.PublicKey{
+			Curve: btcec.S256(),
+			X:     pubKey.X,
+			Y:     pubKey.Y,
+		}
+		btcSig := btcec.Signature{
+			R: sig.R,
+			S: sig.S,
+		}
+		return btcSig.Verify(hash, btcPk)
+	}
+)
+
+func genPrimesArray(count int) []struct{ p, q *big.Int } {
+	primesArray := make([]struct{ p, q *big.Int }, 0, count)
+	for len(primesArray) < count {
+		for i := 0; i < len(testPrimes) && len(primesArray) < count; i++ {
+			for j := 0; j < len(testPrimes) && len(primesArray) < count; j++ {
+				if i == j {
+					continue
+				}
+				keyPrime := struct {
+					p, q *big.Int
+				}{
+					testPrimes[i], testPrimes[j],
+				}
+				primesArray = append(primesArray, keyPrime)
+			}
+		}
+	}
+	return primesArray
+}
+
+// Creates a set of signers that are usable for testing
+func setupSignersMap(t *testing.T, curve elliptic.Curve, playerThreshold, playerCnt int,
+	addRound1 bool, verify curves.EcdsaVerify, useDistributed bool) (*curves.EcPoint, map[uint32]*Signer) {
+
+	if playerThreshold > playerCnt {
+		t.Errorf("threshold cannot be larger than count")
+		t.FailNow()
+	}
+
+	pk, sharesMap, err := dealer.NewDealerShares(curve, uint32(playerThreshold), uint32(playerCnt), nil)
+	tt.AssertNoError(t, err)
+
+	// TODO: After the map refactor, we should be able to delete arbitrary signers,
+	// however, for now, the signers' identifiers need to be predictable in array form
+	// Remove non-signers from the shares map
+	for len(sharesMap) > playerThreshold {
+		delete(sharesMap, uint32(len(sharesMap)))
+	}
+
+	// Create public shares
+	pubSharesMap, err := dealer.PreparePublicShares(sharesMap)
+	tt.AssertNoError(t, err)
+
+	// Create player paillier pubkeys
+	playerKeysMap := make(map[uint32]*paillier.SecretKey, playerThreshold)
+	pubkeys := make(map[uint32]*paillier.PublicKey, playerThreshold)
+
+	primesCnt := playerThreshold
+	var proofParams dealer.KeyGenType
+	if useDistributed {
+		primesCnt *= 2
+	}
+
+	primesArray := genPrimesArray(primesCnt)
+	distributedProofParams := make(map[uint32]*dealer.ProofParams, playerCnt)
+	for i := range sharesMap {
+		playerKeysMap[i], err = paillier.NewSecretKey(primesArray[i-1].p, primesArray[i-1].q)
+		tt.AssertNoError(t, err)
+		pubkeys[i] = &playerKeysMap[i].PublicKey
+		if useDistributed {
+			pp := primesArray[int(i)+playerThreshold-1]
+			params, _ := dealer.NewProofParamsWithPrimes(pp.p, pp.q)
+			distributedProofParams[i] = params
+		}
+	}
+
+	if useDistributed {
+		proofParams = &dealer.DistributedKeyGenType{
+			ProofParams: distributedProofParams,
+		}
+	} else {
+		proofParams = &dealer.TrustedDealerKeyGenType{
+			ProofParams: dealerParams,
+		}
+	}
+
+	// Create participants and signers
+	signersMap := make(map[uint32]*Signer, playerThreshold)
+	for i := range playerKeysMap {
+		p := Participant{*sharesMap[i], playerKeysMap[i]}
+		signersMap[i], err = p.PrepareToSign(pk, verify, curve, proofParams, pubSharesMap, pubkeys)
+		tt.AssertNoError(t, err)
+
+		signersMap[i].threshold = uint(playerThreshold)
+
+		// Add the round 1 values if requested
+		if addRound1 {
+			signersMap[i].state = &state{
+				keyGenType: proofParams,
+			}
+		}
+	}
+
+	return pk, signersMap
+}
+
+func TestSignerSignRound1Works(t *testing.T) {
+	curve := btcec.S256()
+	playerCnt := 5
+	playerMin := 3
+	for _, useDistributed := range []bool{false, true} {
+		_, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, dummyVerifier, useDistributed)
+
+		// Sign Round 1 with each player
+		for _, signer := range signers {
+			signerIOut, p2p, err := signer.SignRound1()
+			require.NoError(t, err)
+
+			if signer.state.keyGenType == nil {
+				t.Errorf("dealerParams is nil")
+			}
+			if signer.Curve == nil {
+				t.Errorf("curve is nil")
+			}
+			if signer.state.Gammai == nil {
+				t.Errorf("Gammai is nil")
+			}
+			if signer.state.Di == nil {
+				t.Errorf("Di is nil")
+			}
+			if signer.Round != 2 {
+				t.Errorf("Expected round to be 2, found: %d", signer.Round)
+			}
+			require.NotNil(t, signer.state.ki)
+			require.NotNil(t, signer.state.gammai)
+			require.NotNil(t, signer.state.ci)
+			require.NotNil(t, signer.state.ri)
+
+			if signerIOut.Proof != nil {
+				err = signerIOut.Proof.Verify(&proof.Proof1Params{
+					Curve:        curve,
+					Pk:           &signer.sk.PublicKey,
+					DealerParams: dealerParams,
+					C:            signerIOut.Ctxt,
+				})
+				require.NoError(t, err)
+			} else {
+				for id, pf := range p2p {
+					err = pf.Verify(&proof.Proof1Params{
+						Curve:        curve,
+						Pk:           &signer.sk.PublicKey,
+						DealerParams: signer.state.keyGenType.GetProofParams(id),
+						C:            signerIOut.Ctxt,
+					})
+					require.NoError(t, err)
+				}
+			}
+		}
+	}
+}
+
+func TestSignerSignRound1RepeatCall(t *testing.T) {
+	curve := btcec.S256()
+	playerCnt := 5
+	playerMin := 3
+	_, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, dummyVerifier, false)
+	_, _, err := signers[1].SignRound1()
+	tt.AssertNoError(t, err)
+	_, _, err = signers[1].SignRound1()
+	tt.AssertSomeError(t, err)
+}
+
+func TestSignerSignRound2Works(t *testing.T) {
+	var err error
+	curve := btcec.S256()
+	playerCnt := 5
+	playerMin := 3
+	for _, useDistributed := range []bool{false, true} {
+		_, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, dummyVerifier, useDistributed)
+
+		// Run round 1 with all signers
+		signerOut := make(map[uint32]*Round1Bcast, playerMin)
+		p2pOut := make(map[uint32]map[uint32]*Round1P2PSend, playerMin)
+		for i, s := range signers {
+			signerOut[i], p2pOut[i], err = s.SignRound1()
+			tt.AssertNoError(t, err)
+		}
+
+		// run signing round 2 with player index 0
+		signer := signers[1]
+		require.NoError(t, err)
+		otherSigners := make(map[uint32]*Round1Bcast)
+		otherSigners[2] = signerOut[2]
+		otherSigners[3] = signerOut[3]
+		otherP2p := make(map[uint32]*Round1P2PSend)
+		otherP2p[2] = p2pOut[2][1]
+		otherP2p[3] = p2pOut[3][1]
+		p2pi, err := signer.SignRound2(otherSigners, otherP2p)
+		require.NoError(t, err)
+
+		// Verify the outputs
+		if len(p2pi) != 2 {
+			t.Errorf("expected %d proofs, found %d", 2, len(p2pi))
+		}
+		if signer.Round != 3 {
+			t.Errorf("signer round should be 3, found: %d", signer.Round)
+		}
+		if len(signer.state.betaj) != 2 {
+			t.Errorf("state.betaj should have 2, found: %d", len(signer.state.betaj))
+		}
+		if len(signer.state.vuj) != 2 {
+			t.Errorf("state.vuj should have 2, found: %d", len(signer.state.vuj))
+		}
+		if len(signer.state.cj) != 2 {
+			t.Errorf("state.cj should have 2, found: %d", len(signer.state.cj))
+		}
+		if len(signer.state.Cj) != 2 {
+			t.Errorf("state.Cj should have 2, found: %d", len(signer.state.Cj))
+		}
+
+		// Check that the return values can be finalized without error
+		_, err = p2pi[2].Proof2.Finalize(&proof.ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: signer.state.keyGenType.GetProofParams(2),
+			Sk:           signers[2].sk,
+			C1:           signers[2].state.ci,
+		})
+		require.NoError(t, err)
+
+		_, err = p2pi[3].Proof2.Finalize(&proof.ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: signer.state.keyGenType.GetProofParams(3),
+			Sk:           signers[3].sk,
+			C1:           signers[3].state.ci,
+		})
+		require.NoError(t, err)
+
+		_, err = p2pi[2].Proof3.FinalizeWc(&proof.ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: signer.state.keyGenType.GetProofParams(2),
+			Sk:           signers[2].sk,
+			C1:           signers[2].state.ci,
+			// pubkey of the proof creator which in this case is signer = signers[0]
+			B: signer.publicSharesMap[1].Point,
+		})
+		require.NoError(t, err)
+
+		_, err = p2pi[3].Proof3.FinalizeWc(&proof.ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: signer.state.keyGenType.GetProofParams(3),
+			Sk:           signers[3].sk,
+			C1:           signers[3].state.ci,
+			B:            signer.publicSharesMap[1].Point,
+		})
+		require.NoError(t, err)
+	}
+}
+
+func TestSignerSignRound2RepeatCall(t *testing.T) {
+	curve := btcec.S256()
+	playerCnt := 5
+	playerMin := 3
+	for _, useDistributed := range []bool{false, true} {
+		_, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, dummyVerifier, useDistributed)
+		_, _, err := signers[1].SignRound1()
+		tt.AssertNoError(t, err)
+		out1, p2p1, err := signers[2].SignRound1()
+		tt.AssertNoError(t, err)
+		out2, p2p2, err := signers[3].SignRound1()
+		tt.AssertNoError(t, err)
+
+		tt.AssertNoError(t, err)
+		otherSigners := make(map[uint32]*Round1Bcast)
+		otherP2PSend := make(map[uint32]*Round1P2PSend)
+		otherSigners[2] = out1
+		otherSigners[3] = out2
+		otherP2PSend[2] = p2p1[1]
+		otherP2PSend[3] = p2p2[1]
+
+		_, err = signers[1].SignRound2(otherSigners, otherP2PSend)
+		tt.AssertNoError(t, err)
+		_, err = signers[1].SignRound2(otherSigners, otherP2PSend)
+		assert.Error(t, err)
+	}
+}
+
+// Mocks for response proof
+type responseProofMock struct {
+	finalizeResult, finalizeWcResult *big.Int
+}
+
+// Have the compiler ensure we're meeting our interface requirements
+var _ proof.ResponseFinalizer = (*responseProofMock)(nil)
+
+func (m *responseProofMock) Finalize(vp *proof.ResponseVerifyParams) (*big.Int, error) {
+	return m.finalizeResult, nil
+}
+
+func (m *responseProofMock) FinalizeWc(vp *proof.ResponseVerifyParams) (*big.Int, error) {
+	return m.finalizeWcResult, nil
+}
+
+func TestSignRound3(t *testing.T) {
+	for _, useDistributed := range []bool{false, true} {
+		// Reasonably valid setup for testing round 3
+		_, signers := setupSignersMap(t, btcec.S256(), 3, 5, true, dummyVerifier, useDistributed)
+
+		for _, s := range signers {
+			// Set variables that are expected to be present at the end of round 2
+			s.state.ki = core.One
+			s.state.gammai = core.One
+			s.state.betaj = make(map[uint32]*big.Int)
+			s.state.vuj = make(map[uint32]*big.Int)
+			p2p := make(map[uint32]*P2PSend)
+			th13een := big.NewInt(13)
+			for j := range signers {
+				s.state.betaj[j] = core.One
+				s.state.vuj[j] = core.One
+				p2p[j] = &P2PSend{&responseProofMock{th13een, th13een},
+					&responseProofMock{th13een, th13een},
+				}
+			}
+
+			// Test that invalid signing rounds states are rejected
+			invalid := []uint{0, 1, 2, 5}
+			for _, round := range invalid {
+				t.Run("invalid signing round states are rejected", func(t *testing.T) {
+					s.Round = round
+					_, err := s.SignRound3(p2p)
+					tt.AssertSomeError(t, err)
+				})
+			}
+
+			// Sign
+			s.Round = 3
+			err := s.setCosigners([]uint32{1, 2, 3})
+			tt.AssertNoError(t, err)
+
+			// signing round 3 completes without error
+			bcast, err := s.SignRound3(p2p)
+			if err != nil {
+				t.Errorf("unexpected failure: %v", err)
+				t.FailNow()
+			}
+
+			t.Run("state vars are set", func(t *testing.T) {
+				tt.AssertNotNil(t, s.state.deltai)
+				tt.AssertNotNil(t, s.state.sigmai)
+			})
+
+			t.Run("return value matches state", func(t *testing.T) {
+				tt.AssertBigIntEq(t, bcast.deltaElement, s.state.deltai)
+			})
+
+			t.Run("round variable is updated", func(t *testing.T) {
+				if s.Round != 4 {
+					t.Errorf("round variable != 4")
+				}
+			})
+
+			t.Run("round variable is updated", func(t *testing.T) {
+				if s.Round != 4 {
+					t.Errorf("round variable != 4")
+				}
+			})
+		}
+	}
+}
+
+func TestSignRound4(t *testing.T) {
+	// Reasonably valid setup for testing round 4
+	_, signers := setupSignersMap(t, btcec.S256(), 3, 5, true, dummyVerifier, false)
+
+	for _, s := range signers {
+		// Set variables that are expected to be present at the end of round 3
+		ones := make(map[uint32]*Round3Bcast, 2)
+		s.state.cosigners = make(map[uint32]bool, 2)
+		for j := range signers {
+			if s.id == j {
+				continue
+			}
+			ones[j] = &Round3Bcast{core.One}
+			s.state.cosigners[j] = true
+		}
+		s.state.ki = core.One
+		s.state.gammai = core.One
+		s.state.deltai = core.One
+		s.state.sigmai = core.One
+		s.state.Di = &core.Witness{}
+
+		// Test that invalid signing rounds states are rejected
+		invalid := []uint{0, 1, 2, 3, 5, 6}
+		for _, round := range invalid {
+			t.Run("invalid signing round states are rejected", func(t *testing.T) {
+				s.Round = round
+				_, err := s.SignRound4(ones)
+				tt.AssertSomeError(t, err)
+			})
+		}
+
+		// Sign
+		s.Round = 4
+		bcast, err := s.SignRound4(ones)
+
+		// signing round 4 completes without error
+		if err != nil {
+			t.Errorf("unexpected failure: %v", err)
+			t.FailNow()
+		}
+		if bcast == nil {
+			t.Errorf("bcast should not be nil")
+		}
+
+		t.Run("state vars are set", func(t *testing.T) {
+			tt.AssertNotNil(t, s.state.delta)
+		})
+	}
+}
+
+func TestSignerSignRound5Works(t *testing.T) {
+	var err error
+	curve := btcec.S256()
+	playerCnt := 5
+	playerMin := 3
+	for _, useDistributed := range []bool{false, true} {
+		_, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, dummyVerifier, useDistributed)
+
+		// Sign Round 1
+		round2In := make(map[uint32]*Round1Bcast, playerCnt)
+		r1p2p := make(map[uint32]map[uint32]*Round1P2PSend, playerCnt)
+		for id, s := range signers {
+			round2In[id], r1p2p[id], err = s.SignRound1()
+			if !assert.NoError(t, err) {
+				t.FailNow()
+			}
+		}
+
+		// Sign Round 2
+		err = signers[1].setCosigners([]uint32{1, 2, 3})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+		p2p := make(map[uint32]map[uint32]*P2PSend)
+		if useDistributed {
+			_, err = signers[1].SignRound2(round2In, nil)
+			// check for required P2P round1 params
+			require.Error(t, err)
+			p2pR2In := make(map[uint32]*Round1P2PSend, playerMin)
+			_, err = signers[1].SignRound2(round2In, p2pR2In)
+			require.Error(t, err)
+
+			p2pR2In[2] = r1p2p[2][1]
+			p2pR2In[3] = r1p2p[3][1]
+			p2p[1], err = signers[1].SignRound2(round2In, p2pR2In)
+		} else {
+			p2p[1], err = signers[1].SignRound2(round2In, nil)
+		}
+
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		err = signers[2].setCosigners([]uint32{1, 2, 3})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+		if useDistributed {
+			_, err = signers[2].SignRound2(round2In, nil)
+			// check for required P2P round1 params
+			require.Error(t, err)
+			p2pR2In := make(map[uint32]*Round1P2PSend, playerMin)
+			_, err = signers[2].SignRound2(round2In, p2pR2In)
+			require.Error(t, err)
+
+			p2pR2In[1] = r1p2p[1][2]
+			p2pR2In[3] = r1p2p[3][2]
+			p2p[2], err = signers[2].SignRound2(round2In, p2pR2In)
+		} else {
+			p2p[2], err = signers[2].SignRound2(round2In, nil)
+		}
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		err = signers[3].setCosigners([]uint32{1, 2, 3})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		if useDistributed {
+			_, err = signers[3].SignRound2(round2In, nil)
+			// check for required P2P round1 params
+			require.Error(t, err)
+			p2pR2In := make(map[uint32]*Round1P2PSend, playerMin)
+			_, err = signers[3].SignRound2(round2In, p2pR2In)
+			require.Error(t, err)
+
+			p2pR2In[1] = r1p2p[1][3]
+			p2pR2In[2] = r1p2p[2][3]
+			p2p[3], err = signers[3].SignRound2(round2In, p2pR2In)
+		} else {
+			p2p[3], err = signers[3].SignRound2(round2In, nil)
+		}
+		require.NoError(t, err)
+
+		// Sign Round 3
+		round3Bcast := make(map[uint32]*Round3Bcast, playerMin)
+		round3Bcast[1], err = signers[1].SignRound3(map[uint32]*P2PSend{2: p2p[2][1], 3: p2p[3][1]})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		round3Bcast[2], err = signers[2].SignRound3(map[uint32]*P2PSend{1: p2p[1][2], 3: p2p[3][2]})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		round3Bcast[3], err = signers[3].SignRound3(map[uint32]*P2PSend{1: p2p[1][3], 2: p2p[2][3]})
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		// Sign Round 4
+		round4Bcast := make(map[uint32]*Round4Bcast, playerMin)
+		round4Bcast[1], err = signers[1].SignRound4(round3Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		round4Bcast[2], err = signers[2].SignRound4(round3Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		round4Bcast[3], err = signers[3].SignRound4(round3Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		// Sign Round 5
+		round5Bcast := make(map[uint32]*Round5Bcast, playerMin)
+		round5P2P := make(map[uint32]map[uint32]*Round5P2PSend, playerMin)
+		round5Bcast[1], round5P2P[1], err = signers[1].SignRound5(round4Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		if signers[1].state.Rbari == nil {
+			t.Errorf("Expected Rbari to be set but is nil")
+		}
+		if signers[1].state.r == nil {
+			t.Errorf("Expected Rbari to be set but is nil")
+		}
+		if signers[1].state.R == nil {
+			t.Errorf("Expected R to be set")
+		}
+		if signers[1].state.r.Cmp(signers[1].state.R.X) != 0 {
+			t.Errorf("Expected r == Rx")
+		}
+
+		round5Bcast[2], round5P2P[2], err = signers[2].SignRound5(round4Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		round5Bcast[3], round5P2P[3], err = signers[3].SignRound5(round4Bcast)
+		if !assert.NoError(t, err) {
+			t.FailNow()
+		}
+
+		if useDistributed {
+			require.True(t, len(round5P2P[1]) == 2)
+			require.True(t, len(round5P2P[2]) == 2)
+			require.True(t, len(round5P2P[3]) == 2)
+		}
+	}
+}
+
+func TestSignerSignRound6WorksK256(t *testing.T) {
+	curve := btcec.S256()
+	msg := make([]byte, 32)
+	hash, err := core.Hash(msg, curve)
+	tt.AssertNoError(t, err)
+	fullroundstest3Signers(t, curve, hash.Bytes(), k256Verifier)
+}
+
+func TestSignerSignRound6WorksP256(t *testing.T) {
+	curve := elliptic.P256()
+	msg := make([]byte, 32)
+	hash, err := core.Hash(msg, curve)
+	assert.NoError(t, err)
+	fullroundstest3Signers(t, curve, hash.Bytes(), ecdsaVerifier)
+}
+
+func fullroundstest3Signers(t *testing.T, curve elliptic.Curve, msg []byte, verify curves.EcdsaVerify) {
+	var err error
+	playerCnt := 5
+	playerMin := 3
+	for _, useDistributed := range []bool{false, true} {
+		pk, signers := setupSignersMap(t, curve, playerMin, playerCnt, false, verify, useDistributed)
+
+		sk := signers[1].share.Value.Add(signers[2].share.Value).Add(signers[3].share.Value)
+		_, ppk := btcec.PrivKeyFromBytes(curve, sk.Bytes())
+
+		if ppk.X.Cmp(pk.X) != 0 || ppk.Y.Cmp(pk.Y) != 0 {
+			t.Errorf("Invalid shares")
+			t.FailNow()
+		}
+
+		// Sign Round 1
+		signerOut := make(map[uint32]*Round1Bcast, playerCnt)
+		r1P2P := make(map[uint32]map[uint32]*Round1P2PSend, playerCnt)
+		for i, s := range signers {
+			signerOut[i], r1P2P[i], err = s.SignRound1()
+			require.NoError(t, err)
+		}
+		// Sign Round 2
+
+		err = signers[1].setCosigners([]uint32{2, 3})
+		require.NoError(t, err)
+		p2p := make(map[uint32]map[uint32]*P2PSend)
+		var r1P2pIn map[uint32]*Round1P2PSend
+		if useDistributed {
+			r1P2pIn = make(map[uint32]*Round1P2PSend, 3)
+			r1P2pIn[2] = r1P2P[2][1]
+			r1P2pIn[3] = r1P2P[3][1]
+		}
+		p2p[1], err = signers[1].SignRound2(map[uint32]*Round1Bcast{
+			2: signerOut[2],
+			3: signerOut[3],
+		}, r1P2pIn)
+		require.NoError(t, err)
+
+		err = signers[2].setCosigners([]uint32{1, 3})
+		require.NoError(t, err)
+		if useDistributed {
+			r1P2pIn = make(map[uint32]*Round1P2PSend, 3)
+			r1P2pIn[1] = r1P2P[1][2]
+			r1P2pIn[3] = r1P2P[3][2]
+		}
+		p2p[2], err = signers[2].SignRound2(map[uint32]*Round1Bcast{
+			1: signerOut[1],
+			3: signerOut[3],
+		}, r1P2pIn)
+		require.NoError(t, err)
+
+		err = signers[3].setCosigners([]uint32{1, 2})
+		require.NoError(t, err)
+		if useDistributed {
+			r1P2pIn = make(map[uint32]*Round1P2PSend, 3)
+			r1P2pIn[1] = r1P2P[1][3]
+			r1P2pIn[2] = r1P2P[2][3]
+		}
+		p2p[3], err = signers[3].SignRound2(map[uint32]*Round1Bcast{
+			1: signerOut[1],
+			2: signerOut[2],
+		}, r1P2pIn)
+		require.NoError(t, err)
+
+		// Sign Round 3
+		round3Bcast := make(map[uint32]*Round3Bcast, playerMin)
+		round3Bcast[1], err = signers[1].SignRound3(map[uint32]*P2PSend{2: p2p[2][1], 3: p2p[3][1]})
+		require.NoError(t, err)
+
+		round3Bcast[2], err = signers[2].SignRound3(map[uint32]*P2PSend{1: p2p[1][2], 3: p2p[3][2]})
+		require.NoError(t, err)
+
+		round3Bcast[3], err = signers[3].SignRound3(map[uint32]*P2PSend{1: p2p[1][3], 2: p2p[2][3]})
+		require.NoError(t, err)
+
+		// Sign Round 4
+		round4Bcast := make(map[uint32]*Round4Bcast, playerMin)
+		round4Bcast[1], err = signers[1].SignRound4(map[uint32]*Round3Bcast{2: round3Bcast[2], 3: round3Bcast[3]})
+		require.NoError(t, err)
+
+		round4Bcast[2], err = signers[2].SignRound4(map[uint32]*Round3Bcast{1: round3Bcast[1], 3: round3Bcast[3]})
+		require.NoError(t, err)
+
+		round4Bcast[3], err = signers[3].SignRound4(map[uint32]*Round3Bcast{1: round3Bcast[1], 2: round3Bcast[2]})
+		require.NoError(t, err)
+
+		// Sign Round 5
+		round5Bcast := make(map[uint32]*Round5Bcast, playerMin)
+		r5P2p := make(map[uint32]map[uint32]*Round5P2PSend, playerMin)
+		round5Bcast[1], r5P2p[1], err = signers[1].SignRound5(map[uint32]*Round4Bcast{2: round4Bcast[2], 3: round4Bcast[3]})
+		require.NoError(t, err)
+
+		round5Bcast[2], r5P2p[2], err = signers[2].SignRound5(map[uint32]*Round4Bcast{1: round4Bcast[1], 3: round4Bcast[3]})
+		require.NoError(t, err)
+
+		round5Bcast[3], r5P2p[3], err = signers[3].SignRound5(map[uint32]*Round4Bcast{1: round4Bcast[1], 2: round4Bcast[2]})
+		require.NoError(t, err)
+
+		Rbark, err := signers[1].state.Rbark.Add(signers[2].state.Rbark)
+		require.NoError(t, err)
+
+		Rbark, err = Rbark.Add(signers[3].state.Rbark)
+		require.NoError(t, err)
+
+		Rbark.Y, err = core.Neg(Rbark.Y, curve.Params().P)
+		require.NoError(t, err)
+		Rbark, err = Rbark.Add(pk)
+		require.NoError(t, err)
+
+		if !Rbark.IsIdentity() {
+			t.Errorf("%v != %v", Rbark.X, pk.X)
+			t.FailNow()
+		}
+
+		// Sign Round 6
+		var r6P2pin map[uint32]*Round5P2PSend
+		if useDistributed {
+			// Check failure cases, first with nil input
+			// then with missing participant data
+			_, err = signers[1].SignRound6Full(msg, map[uint32]*Round5Bcast{2: round5Bcast[2], 3: round5Bcast[3]}, r6P2pin)
+			require.Error(t, err)
+
+			r6P2pin = make(map[uint32]*Round5P2PSend, playerMin)
+			_, err = signers[1].SignRound6Full(msg, map[uint32]*Round5Bcast{2: round5Bcast[2], 3: round5Bcast[3]}, r6P2pin)
+
+			require.Error(t, err)
+
+			r6P2pin[2] = r5P2p[2][1]
+			_, err = signers[1].SignRound6Full(msg, map[uint32]*Round5Bcast{2: round5Bcast[2], 3: round5Bcast[3]}, r6P2pin)
+			require.Error(t, err)
+
+			r6P2pin[3] = r5P2p[3][1]
+		}
+		round6FullBcast := make([]*Round6FullBcast, playerMin)
+		round6FullBcast[0], err = signers[1].SignRound6Full(msg, map[uint32]*Round5Bcast{2: round5Bcast[2], 3: round5Bcast[3]}, r6P2pin)
+		assert.Nil(t, err)
+		if useDistributed {
+			r6P2pin = make(map[uint32]*Round5P2PSend, playerMin)
+			r6P2pin[1] = r5P2p[1][2]
+			r6P2pin[3] = r5P2p[3][2]
+		}
+		round6FullBcast[1], err = signers[2].SignRound6Full(msg, map[uint32]*Round5Bcast{1: round5Bcast[1], 3: round5Bcast[3]}, r6P2pin)
+		assert.Nil(t, err)
+		if useDistributed {
+			r6P2pin = make(map[uint32]*Round5P2PSend, playerMin)
+			r6P2pin[1] = r5P2p[1][3]
+			r6P2pin[2] = r5P2p[2][3]
+		}
+		round6FullBcast[2], err = signers[3].SignRound6Full(msg, map[uint32]*Round5Bcast{1: round5Bcast[1], 2: round5Bcast[2]}, r6P2pin)
+		assert.Nil(t, err)
+		tt.AssertNoError(t, err)
+
+		sigs := make([]*curves.EcdsaSignature, 3)
+		sigs[0], err = signers[1].SignOutput(map[uint32]*Round6FullBcast{
+			2: round6FullBcast[1],
+			3: round6FullBcast[2],
+		})
+		tt.AssertNoError(t, err)
+
+		sigs[1], err = signers[2].SignOutput(map[uint32]*Round6FullBcast{
+			1: round6FullBcast[0],
+			3: round6FullBcast[2],
+		})
+		tt.AssertNoError(t, err)
+		sigs[2], err = signers[3].SignOutput(map[uint32]*Round6FullBcast{
+			1: round6FullBcast[0],
+			2: round6FullBcast[1],
+		})
+		tt.AssertNoError(t, err)
+	}
+}
+
+// Ensures that marshal-unmarshal Round1Bcast is the identity function
+func TestMarshalRound1BcastRoundTrip(t *testing.T) {
+	expected := Round1Bcast{
+		Identifier: 1337,
+		C:          []byte("Your name's Lebowski, Lebowski."),
+		Ctxt:       tt.B10("1979"),
+		Proof:      &proof.Range1Proof{},
+	}
+
+	// Marshal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Round1Bcast
+	err = json.Unmarshal(jsonBytes, &actual)
+	assert.NoError(t, err)
+
+	assert.Equal(t, expected, actual)
+}
+
+// Test that P2PSend can be marshaled and unmarshaled correctly
+// Also See TestMarshalResponseProof and TestMarshalJsonRange2Proof
+func TestMarshalP2PSend(t *testing.T) {
+	curve := btcec.S256()
+
+	rpp := proof.ResponseProofParams{
+		Curve: curve,
+		Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+		DealerParams: &dealer.ProofParams{
+			N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+			H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+			H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+		},
+		SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+		C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+		B: &curves.EcPoint{
+			Curve: curve,
+			X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+			Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+		},
+	}
+
+	proofGamma, err := rpp.Prove()
+	assert.NoError(t, err)
+	assert.NotNil(t, proofGamma)
+
+	proofW, err := rpp.ProveWc()
+	assert.NoError(t, err)
+	assert.NotNil(t, proofW)
+
+	initSend := P2PSend{
+		Proof2: *proofGamma,
+		Proof3: *proofW,
+	}
+
+	testJSON, err := json.Marshal(initSend)
+	assert.NoError(t, err)
+	assert.NotNil(t, testJSON)
+
+	var actual P2PSend
+	err = json.Unmarshal(testJSON, &actual)
+	assert.NoError(t, err)
+
+	assert.Equal(t, initSend, actual)
+}
+
+// Ensures that marshal-unmarshal Round3Bcast is the identity function
+func TestMarshalRound3BcastRoundTrip(t *testing.T) {
+	expected := Round3Bcast{
+		deltaElement: tt.B10("22963319250927626464432314334264998185524558636490611781390004531598870711554"),
+	}
+	// Marshal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Round3Bcast
+	err = json.Unmarshal(jsonBytes, &actual)
+	assert.NoError(t, err)
+	assert.Equal(t, expected, actual)
+}
+
+// Ensures that marshal-unmarshal Round4Bcast is the identity function
+func TestMarshalRound4BcastRoundTrip(t *testing.T) {
+	// This is the same test as TestWitnessMarshalRoundTrip
+	expected := Round4Bcast{
+		Witness: &core.Witness{
+			Msg: []byte("test"),
+		},
+	}
+	// Marhal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Round4Bcast
+	assert.NoError(t, json.Unmarshal(jsonBytes, &actual))
+	assert.Equal(t, expected, actual)
+}
+
+// Ensures that marshal-unmarshal Round5Bcast is the identity function
+func TestMarshalRound5BcastRoundTrip(t *testing.T) {
+	expected := Round5Bcast{
+		Rbar: &curves.EcPoint{
+			Curve: btcec.S256(),
+			X:     tt.B10("22963319250927626464432314334264998185524558636490611781390004531598870711554"),
+			Y:     tt.B10("5554841823708042459730720811862682529836762867109252962559124452631448728441"),
+		},
+		Proof: &proof.PdlProof{},
+	}
+
+	// Marshal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Round5Bcast
+	err = json.Unmarshal(jsonBytes, &actual)
+	assert.NoError(t, err)
+
+	assert.Equal(t, expected, actual)
+}
+
+// Ensures that marshal-unmarshal Round3Bcast is the identity function
+func TestMarshalRound6FullBcast(t *testing.T) {
+	expected := Round6FullBcast{
+		sElement: tt.B10("22963319250927626464432314334264998185524558636490611781390004531598870711554"),
+	}
+	// Marshal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Round6FullBcast
+	err = json.Unmarshal(jsonBytes, &actual)
+	assert.NoError(t, err)
+	assert.Equal(t, expected, actual)
+}
diff --git a/pkg/tecdsa/gg20/proof/README.md b/pkg/tecdsa/gg20/proof/README.md
new file mode 100755
index 00000000..b1b9d48f
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/README.md
@@ -0,0 +1,349 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# proof
+
+```go
+import "github.com/coinbase/kryptology/pkg/tecdsa/gg20/proof"
+```
+
+## Index
+
+- [type CdlProof](<#type-cdlproof>)
+  - [func (cdlp CdlProof) MarshalJSON() ([]byte, error)](<#func-cdlproof-marshaljson>)
+  - [func (cdlp *CdlProof) UnmarshalJSON(bytes []byte) error](<#func-cdlproof-unmarshaljson>)
+  - [func (p CdlProof) Verify(cv *CdlVerifyParams) error](<#func-cdlproof-verify>)
+- [type CdlProofParams](<#type-cdlproofparams>)
+  - [func (p CdlProofParams) Prove() (*CdlProof, error)](<#func-cdlproofparams-prove>)
+- [type CdlVerifyParams](<#type-cdlverifyparams>)
+- [type PdlProof](<#type-pdlproof>)
+  - [func (pdlp PdlProof) MarshalJSON() ([]byte, error)](<#func-pdlproof-marshaljson>)
+  - [func (pdlp *PdlProof) UnmarshalJSON(bytes []byte) error](<#func-pdlproof-unmarshaljson>)
+  - [func (p PdlProof) Verify(pv *PdlVerifyParams) error](<#func-pdlproof-verify>)
+- [type PdlProofParams](<#type-pdlproofparams>)
+  - [func (p PdlProofParams) Prove() (*PdlProof, error)](<#func-pdlproofparams-prove>)
+- [type PdlVerifyParams](<#type-pdlverifyparams>)
+- [type Proof1Params](<#type-proof1params>)
+  - [func (pp Proof1Params) Prove() (*Range1Proof, error)](<#func-proof1params-prove>)
+- [type Range1Proof](<#type-range1proof>)
+  - [func (r Range1Proof) MarshalJSON() ([]byte, error)](<#func-range1proof-marshaljson>)
+  - [func (r *Range1Proof) UnmarshalJSON(bytes []byte) error](<#func-range1proof-unmarshaljson>)
+  - [func (pi Range1Proof) Verify(pp *Proof1Params) error](<#func-range1proof-verify>)
+- [type Range2Proof](<#type-range2proof>)
+  - [func (rP2 Range2Proof) MarshalJSON() ([]byte, error)](<#func-range2proof-marshaljson>)
+  - [func (rP2 *Range2Proof) UnmarshalJSON(bytes []byte) error](<#func-range2proof-unmarshaljson>)
+  - [func (pi Range2Proof) Verify(pp *verifyProof2Params) error](<#func-range2proof-verify>)
+  - [func (pi Range2Proof) VerifyWc(pp *verifyProof2Params) error](<#func-range2proof-verifywc>)
+- [type ResponseFinalizer](<#type-responsefinalizer>)
+- [type ResponseProof](<#type-responseproof>)
+  - [func (rp ResponseProof) Finalize(vp *ResponseVerifyParams) (*big.Int, error)](<#func-responseproof-finalize>)
+  - [func (rp ResponseProof) FinalizeWc(vp *ResponseVerifyParams) (*big.Int, error)](<#func-responseproof-finalizewc>)
+- [type ResponseProofParams](<#type-responseproofparams>)
+  - [func (rp ResponseProofParams) Prove() (*ResponseProof, error)](<#func-responseproofparams-prove>)
+  - [func (rp ResponseProofParams) ProveWc() (*ResponseProof, error)](<#func-responseproofparams-provewc>)
+- [type ResponseVerifyParams](<#type-responseverifyparams>)
+
+
+## type [CdlProof](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L31-L33>)
+
+```go
+type CdlProof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(CdlProof\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L40>)
+
+```go
+func (cdlp CdlProof) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*CdlProof\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L48>)
+
+```go
+func (cdlp *CdlProof) UnmarshalJSON(bytes []byte) error
+```
+
+### func \(CdlProof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L121>)
+
+```go
+func (p CdlProof) Verify(cv *CdlVerifyParams) error
+```
+
+Verify checks the CdlProof as specified in \[spec\] §10\.fig 16
+
+## type [CdlProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L26-L29>)
+
+CdlProofParams encapsulates parameters for ProveCompositeDL in Fig\.16 Curve contains EC group generator g and EC group modulus q Pi\, Qi are small p\_i\, q\_i s\.t\. P\_i = 2p\_i\+1\, Q\_i = 2q\_i\+1\, which are Safe Primes ScalarX is a random element from Z\_N\~ and it should be kept as secret N is the field modulus
+
+```go
+type CdlProofParams struct {
+    Curve                      elliptic.Curve
+    Pi, Qi, H1, H2, ScalarX, N *big.Int
+}
+```
+
+### func \(CdlProofParams\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L67>)
+
+```go
+func (p CdlProofParams) Prove() (*CdlProof, error)
+```
+
+Prove generates a CdlProof as specified in \[spec\] §10\.fig 16
+
+## type [CdlVerifyParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/cdl.go#L60-L63>)
+
+```go
+type CdlVerifyParams struct {
+    Curve     elliptic.Curve
+    H1, H2, N *big.Int
+}
+```
+
+## type [PdlProof](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L35-L37>)
+
+PdlProof is the proof generated in \[spec\] fig 14
+
+```go
+type PdlProof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(PdlProof\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L43>)
+
+```go
+func (pdlp PdlProof) MarshalJSON() ([]byte, error)
+```
+
+### func \(\*PdlProof\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L54>)
+
+```go
+func (pdlp *PdlProof) UnmarshalJSON(bytes []byte) error
+```
+
+### func \(PdlProof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L163>)
+
+```go
+func (p PdlProof) Verify(pv *PdlVerifyParams) error
+```
+
+Verify checks the PdlProof as specified in \[spec\] fig 14
+
+## type [PdlProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L25-L31>)
+
+PdlProofParams encapsulates the parameters for ProvePDL in \[spec\] fig 14
+
+```go
+type PdlProofParams struct {
+    Curve               elliptic.Curve
+    DealerParams        *dealer.ProofParams
+    Pk                  *paillier.PublicKey
+    ScalarX, ScalarR, C *big.Int
+    PointX, PointR      *curves.EcPoint
+}
+```
+
+### func \(PdlProofParams\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L88>)
+
+```go
+func (p PdlProofParams) Prove() (*PdlProof, error)
+```
+
+Prove generates a PdlProof as specified in \[spec\] fig 14
+
+## type [PdlVerifyParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/pdl.go#L72-L78>)
+
+PdlVerifyParams encapsulates the parameters for VerifyPDL in \[spec\] fig 14
+
+```go
+type PdlVerifyParams struct {
+    Curve          elliptic.Curve
+    DealerParams   *dealer.ProofParams
+    Pk             *paillier.PublicKey
+    PointX, PointR *curves.EcPoint
+    C              *big.Int
+}
+```
+
+## type [Proof1Params](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L60-L65>)
+
+Proof1Params encapsulates the values over which a range proof \(1\) is computed\. \[spec\] fig 10
+
+```go
+type Proof1Params struct {
+    Curve        elliptic.Curve
+    Pk           *paillier.PublicKey
+    DealerParams *dealer.ProofParams
+    A, C, R      *big.Int
+}
+```
+
+### func \(Proof1Params\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L311>)
+
+```go
+func (pp Proof1Params) Prove() (*Range1Proof, error)
+```
+
+Prove computes a range proof over these parameters \[spec\] fig 10: MtaProveRange1
+
+## type [Range1Proof](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L75-L77>)
+
+Range1Proof encapsulates the results returned in proof \(1\) \[spec\] fig 10
+
+```go
+type Range1Proof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Range1Proof\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L125>)
+
+```go
+func (r Range1Proof) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON converts Range1Proof into JSON
+
+### func \(\*Range1Proof\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L136>)
+
+```go
+func (r *Range1Proof) UnmarshalJSON(bytes []byte) error
+```
+
+UnmarshalJSON converts json into a Range1Proof
+
+### func \(Range1Proof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L440>)
+
+```go
+func (pi Range1Proof) Verify(pp *Proof1Params) error
+```
+
+Verify checks a range \(1\) proof: \[spec\] §7\.fig 7: MtaVerifyRange1
+
+## type [Range2Proof](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L113-L116>)
+
+Range2Proof encapsulates the values over which a range proof \(2\) is computed\. \[spec\] fig 12
+
+```go
+type Range2Proof struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(Range2Proof\) [MarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L152>)
+
+```go
+func (rP2 Range2Proof) MarshalJSON() ([]byte, error)
+```
+
+MarshalJSON converts Range2Proof into JSON format
+
+### func \(\*Range2Proof\) [UnmarshalJSON](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L167>)
+
+```go
+func (rP2 *Range2Proof) UnmarshalJSON(bytes []byte) error
+```
+
+UnmarshalJSON converts json into a Range2Proof
+
+### func \(Range2Proof\) [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L678>)
+
+```go
+func (pi Range2Proof) Verify(pp *verifyProof2Params) error
+```
+
+Verify checks a range \(2\) proof: \[spec\] §7\.fig 9: MtaVerifyRange2
+
+### func \(Range2Proof\) [VerifyWc](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L683>)
+
+```go
+func (pi Range2Proof) VerifyWc(pp *verifyProof2Params) error
+```
+
+VerifyWc checks a range \(2\) proof: \[spec\] §7\.fig 9: MtaVerifyRange2\_wc
+
+## type [ResponseFinalizer](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L45-L48>)
+
+ResponseFinalizer captures the interface provided by a response proof \[spec\] fig 13
+
+```go
+type ResponseFinalizer interface {
+    Finalize(vp *ResponseVerifyParams) (*big.Int, error)
+    FinalizeWc(vp *ResponseVerifyParams) (*big.Int, error)
+}
+```
+
+## type [ResponseProof](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L53-L56>)
+
+ResponseProof encapsulates the values over which a range proof \(2\) is computed and a portion of the random value is encrypted \[spec\] §7\.fig 8
+
+```go
+type ResponseProof struct {
+    R2proof  *Range2Proof
+    C2, Beta *big.Int
+}
+```
+
+### func \(ResponseProof\) [Finalize](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L260>)
+
+```go
+func (rp ResponseProof) Finalize(vp *ResponseVerifyParams) (*big.Int, error)
+```
+
+Finalize checks a range \(2\) proof: \[spec\] fig 13: MtaFinalize and returns the paillier encrypted random value
+
+### func \(ResponseProof\) [FinalizeWc](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L284>)
+
+```go
+func (rp ResponseProof) FinalizeWc(vp *ResponseVerifyParams) (*big.Int, error)
+```
+
+FinalizeWc checks a range \(2\) proof: \[spec\] fig 13: MtaFinalize\_wc and returns the paillier encrypted random value
+
+## type [ResponseProofParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L25-L31>)
+
+ResponseProofParams encapsulates the values over which a range proof \(2\) is computed\. \[spec\] §7\.fig 8
+
+```go
+type ResponseProofParams struct {
+    Curve        elliptic.Curve
+    DealerParams *dealer.ProofParams
+    Pk           *paillier.PublicKey
+    SmallB, C1   *big.Int
+    B            *curves.EcPoint
+}
+```
+
+### func \(ResponseProofParams\) [Prove](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L189>)
+
+```go
+func (rp ResponseProofParams) Prove() (*ResponseProof, error)
+```
+
+Prove computes a range proof over these parameters \[spec\] fig 11: MtaResponse
+
+### func \(ResponseProofParams\) [ProveWc](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L195>)
+
+```go
+func (rp ResponseProofParams) ProveWc() (*ResponseProof, error)
+```
+
+ProveWc computes: \[spec\] fig 11: MtaResponse\_wc
+
+## type [ResponseVerifyParams](<https://github.com/coinbase/kryptology/blob/master/pkg/tecdsa/gg20/proof/mta.go#L35-L41>)
+
+ResponseVerifyParams encapsulates the values over which a range proof \(2\) is verified\. \[spec\] §7\.fig 10
+
+```go
+type ResponseVerifyParams struct {
+    Curve        elliptic.Curve
+    DealerParams *dealer.ProofParams
+    Sk           *paillier.SecretKey
+    C1           *big.Int
+    B            *curves.EcPoint
+}
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/tecdsa/gg20/proof/cdl.go b/pkg/tecdsa/gg20/proof/cdl.go
new file mode 100644
index 00000000..268b0425
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/cdl.go
@@ -0,0 +1,167 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+// Package proof contains the proof of knowledge of a discrete log modulo a composite (fig 16), i.e., ProveCompositeDL and VerifyCompositeDL
+
+package proof
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"fmt"
+	"math/big"
+
+	mod "github.com/coinbase/kryptology/pkg/core"
+)
+
+const ell = 128
+
+// CdlProofParams encapsulates parameters for ProveCompositeDL in Fig.16
+// Curve contains EC group generator g and EC group modulus q
+// Pi, Qi are small p_i, q_i s.t. P_i = 2p_i+1, Q_i = 2q_i+1, which are Safe Primes
+// ScalarX is a random element from Z_N~ and it should be kept as secret
+// N is the field modulus
+type CdlProofParams struct {
+	Curve                      elliptic.Curve
+	Pi, Qi, H1, H2, ScalarX, N *big.Int
+}
+
+type CdlProof struct {
+	u, s []*big.Int
+}
+
+// U, S are small u, s in JSON format
+type cdlProofJSON struct {
+	U, S []*big.Int
+}
+
+func (cdlp CdlProof) MarshalJSON() ([]byte, error) {
+	data := cdlProofJSON{
+		U: cdlp.u,
+		S: cdlp.s,
+	}
+	return json.Marshal(data)
+}
+
+func (cdlp *CdlProof) UnmarshalJSON(bytes []byte) error {
+	data := new(cdlProofJSON)
+
+	err := json.Unmarshal(bytes, &data)
+	if err != nil {
+		return err
+	}
+	cdlp.u = data.U
+	cdlp.s = data.S
+	return nil
+}
+
+type CdlVerifyParams struct {
+	Curve     elliptic.Curve
+	H1, H2, N *big.Int
+}
+
+// Prove generates a CdlProof as specified in
+// [spec] §10.fig 16
+func (p CdlProofParams) Prove() (*CdlProof, error) {
+	if p.Curve == nil || p.H1 == nil || p.H2 == nil || p.Pi == nil || p.Qi == nil || p.ScalarX == nil || p.N == nil {
+		return nil, fmt.Errorf("invalid params")
+	}
+
+	// Step 1
+	// Set ell = 128
+
+	// Step 2-4, create a array of alpha_i, prod = p_i*q_i
+	prod := new(big.Int).Mul(p.Pi, p.Qi)
+	alpha := make([]*big.Int, ell)
+	fsInput := make([]*big.Int, ell+6)
+	fsInput[0] = p.Curve.Params().Gx
+	fsInput[1] = p.Curve.Params().Gy
+	fsInput[2] = p.Curve.Params().N
+	fsInput[3] = p.N
+	fsInput[4] = p.H1
+	fsInput[5] = p.H2
+
+	for i := 6; i < ell+6; i++ {
+		a, err := mod.Rand(prod)
+		if err != nil {
+			return nil, err
+		}
+		alpha[i-6] = a
+		fsInput[i], err = mod.Exp(p.H1, a, p.N) // In the pseudocode, there is a typo which uses h, but it should be h_1 instead
+		if err != nil {
+			return nil, err
+		}
+	}
+	// 5. Compute e = FS-HASH(g,q,N,h_1,h_2,[u_1...u_ell]
+	challenge, err := mod.FiatShamir(fsInput...)
+	if err != nil {
+		return nil, err
+	}
+	e := new(big.Int).SetBytes(challenge)
+	// Step 6-7. For i=[1...ell], compute s_i = alpha_i+x*e_i mod pq
+	s := make([]*big.Int, ell)
+	pq := new(big.Int).Mul(p.Pi, p.Qi)
+	for i := 0; i < ell; i++ {
+		ei := big.NewInt(int64(e.Bit(i)))
+		s[i] = new(big.Int).Mod(new(big.Int).Add(alpha[i], new(big.Int).Mul(ei, p.ScalarX)), pq)
+	}
+
+	// 8. Set \Pi = [(u1,s1),...,(u_ell, s_ell)]
+	// 9. Return \Pi
+	u := fsInput[6:]
+	return &CdlProof{
+		u, s,
+	}, nil
+}
+
+// Verify checks the CdlProof as specified in
+// [spec] §10.fig 16
+func (p CdlProof) Verify(cv *CdlVerifyParams) error {
+	if p.u == nil || p.s == nil {
+		return fmt.Errorf("proof values cannot be nil")
+	}
+
+	if cv == nil || cv.Curve == nil || cv.H1 == nil || cv.H2 == nil || cv.N == nil {
+		return fmt.Errorf("proof verify params cannot be nil")
+	}
+
+	// When you multiply two numbers m and n, the number of bits in the product cannot be less than max(m,n) and cannot be more than (m+n).
+	// (Unless one of the two numbers is a 0).
+	if cv.N.BitLen() < 1024 {
+		return fmt.Errorf("Modulus length is invalid")
+	}
+
+	// Step 1
+	// Set ell = 128
+
+	// 2. Compute e = FS-HASH(g,q,N,h1,h2,[u1,...,u_ell])
+	fsInput := make([]*big.Int, ell+6)
+	fsInput[0] = cv.Curve.Params().Gx
+	fsInput[1] = cv.Curve.Params().Gy
+	fsInput[2] = cv.Curve.Params().N
+	fsInput[3] = cv.N
+	fsInput[4] = cv.H1
+	fsInput[5] = cv.H2
+	copy(fsInput[6:], p.u)
+	challenge, err := mod.FiatShamir(fsInput...)
+	if err != nil {
+		return err
+	}
+
+	e := new(big.Int).SetBytes(challenge)
+
+	// Step 3-4
+	for i := 0; i < ell; i++ {
+		ei := big.NewInt(int64(e.Bit(i)))
+		left := new(big.Int).Exp(cv.H1, p.s[i], cv.N)
+		right := new(big.Int).Mod(new(big.Int).Mul(p.u[i], new(big.Int).Exp(cv.H2, ei, cv.N)), cv.N)
+		if left.Cmp(right) != 0 {
+			return fmt.Errorf("h1^si != ui*h2^ei")
+		}
+	}
+
+	// Step 5
+	return nil
+}
diff --git a/pkg/tecdsa/gg20/proof/cdl_test.go b/pkg/tecdsa/gg20/proof/cdl_test.go
new file mode 100644
index 00000000..428b0091
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/cdl_test.go
@@ -0,0 +1,356 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package proof
+
+import (
+	"encoding/json"
+	"math/big"
+	"testing"
+
+	tt "github.com/coinbase/kryptology/internal"
+	mod "github.com/coinbase/kryptology/pkg/core"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+)
+
+// To test ProveCompositeDL, the input must satisfy the following relationship
+// P = 2Pi+1, Q = 2Qi+1, N = PQ
+// H2 = H1^x mod N
+// P, Q are 1024 bits
+func TestCdlProof(t *testing.T) {
+	curve := btcec.S256()
+	params := []*CdlProofParams{
+		{
+			Curve:   curve,
+			Pi:      tt.B10("69979182966199119672351533979383654499397224507518060735584349051652764492448136547713282139549035562089101777193243018061896970048738918135727018564481835840179068003226387981023729616470203107028273690173680912153598953087314298633621289521741954003727691656981967430921179270576924304274459867142386866233"),
+			Qi:      tt.B10("84424010159268042809195618234668170228427874149211682832595019116005334677981908011739260951914473600143292358100903745699777808120747187820649504013204732464439679512865842249450303793972825236153746944676836172054279530040675313001271469918167027979171285553816301512008832730050650239840859438662619111399"),
+			N:       tt.B10("23631693014702686598491747297681569475877326460812464082819481422202713346211180070062414360449939288078360593861292547953001504075134774288233379964236347153126995445451429330749200073283458248684973345738352066279459449816118837062102541615816746664320639714285376717243575093782737364692876115029953880688277093224947831946660228299342362879622467185199611987459117940187846509287850536067217425664948192994941586900797272776595126412023378302307519372803612686581113206608355719746319871239226865149982986439036498029925509216269045641120927388902686667987841077785466791674964976428828991419580797672404965915133"),
+			H1:      tt.B10("7946425901597611550738413402091207348349673201811011777758041950640367669127591562559941008463663269491315559897208768775232447391501592581877731140164059638274471726341875678455474107814193902512015507251883997545858299492500962124389479454741467013546908266057900991789262148766092771402882570705098310732185565230244188671537946720849813029966760353542287359829173490796747660692731745728903580183343647146866291218790289460250912792371107912019640755966623243965663097337215423829596916087566120282913217797405222525769972767463810191902348082642684555912203247043727191165051070774263967911353607952365245400947"),
+			ScalarX: tt.B10("9060855727394538554280486019975466408154154373013627407948965978243783485406040771639015901954551816313856770333109273827682320951740510817356910069451842815860762800653008008734702455588363782662799763807936814615743776850798351473244971478097357831497231664301656006475400319088867810184234855807442006410165018848767142974822471227021406352580604137332089139556516988505126169997002017833858827496695461902663346560474857016062532738611411777646178283588990177506440466839975300743011477322819000458010731313375502203626231094265141803538312989410050792429290230188104355460623820692518310405901018793614779352365"),
+			H2:      tt.B10("9655716947834799186539374175271253546360574889564941529186887148524811253942671582167482352632019351834566840338079786327815799490180732501072504891516646810008321428562261204389435547506173159604155572508109327801749630580463385051725499673777772465780243560444849344381658998224546017336909884296424486545406973413882945499464570750924583721544332515711367988346291270454498094198508290623057769669971189478287975093769597415578597441391516518992736837455435830471650960836487483840938880704655913775433524618584886395406891877498467764813222176205917831839824829752294548668410502170499760676452530462719513197659"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("67888050747812851425842238967480716528620751828903194145676972894251304673883735098328837590840818877762364813615848817532849830755892212636267607196610651447723752842688900061362287945644919469354026105141182996474829188730844136985148548346048734847454613613006744111959146944241178072643958108055109208669"),
+			Qi:      tt.B10("74028583328840379462079789341032310086933613584606697607428537990913172909197902388422323870097092632268691549460498294185854606703100438377050619092037950146228310525692099718006602293395173980000397794576241083381416571186609861062015966780930151103765006974601121311197135038509984827174382833566361332459"),
+			N:       tt.B10("20102624887268032436385352818309224611522117481187785072762969444240952373977012433059077411520297892283717463008349816277829183652055938423641934427094022881233221976429590801180822524846487163410907356244738306218466738291842021324571650500458383974369353051471917385538473367391737488963462364596813583268975946170601367819464693418426390466501882866808616688082647634542999240442063438027459804109064071267956138187461519377808857618462480066921719138950396485850908712512499459355024531358622117678159829573237832605918882277226089593396668852935983490680149025683860215703874267028152487275463608689386596630541"),
+			H1:      tt.B10("2376518835100800976110377446508048627458382318670199614681941939618957469802074100964557196232832900256536094316139165206461461940284874993903911499340652135862549146228175201825717740466426272093870244464122393235976412050142856096926928069502460776404328490281063237799360068282994265687557447485328660684313615679759719396617374050181308075085809989635946482359863766907954463561844155574462370765003067298540057340699453379534447672507032661473128248596224981515811565065700663734038702396414461854756619095554520442820368266108115668333256283196813050455307108963605317668312367263714220550180930603737069042681"),
+			ScalarX: tt.B10("14488423386509878470589768290899871750691012627125956350082287802110592303459003618093602404322350514916636961391783202847213112161591547267362064786324008087712203131139538157555973305762533116789572682662080915716282021431017132003226801582363966807205962239049864881081267891864101582031208944201226750450293268348489147631715204012459970983233418780535765088312679112283662704474419873686631944623889770749773996675154272528531861252719763116466349018521737163036477417936570219206390064706371039438309462010306171743504615466373920828843322740046857066875757090005851593014487741915608184497652830496479301046101"),
+			H2:      tt.B10("15879604731069180823336489370430079158612574193637569666769343387116241501138672742037225999442092265612857660656553596930640898982694079345286033477972766098595684079264887219808793990685522553437704209214389414396934083563795665724990112792161324509368439824463260812389360700531646699291443828484023663984617896684393589265154610104646989442735621432109976922590169132245891501805740557524118742816342082961519552869452712799863985060370901800328292511999673878319215159254098261935327388754658587343367584404415707368858166863610846433431741855897776292306056157680786291582652749608898679384525696607905677562940"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("76330104306302336171080114522369103577528135517365964316288949628987850291369939487976722362743065903494105959054506903318328806931036907581609818174438335482939721074022473215585686298551052611871769430789160485977457333536557385501363802286842127881913680259737758668074492827574254852970687584896454490369"),
+			Qi:      tt.B10("74680459525723769595192139188749594456005241009599674590157723679305006605114825831746447884821436868201575261183366679755987845338855141692678446759207587562380509454643686288880947446224009212779939349122453707965183148822196568163102099137040033736913880137247777891407945116122572996093120804287262887611"),
+			N:       tt.B10("22801469060964340910128152680947327636805006778962251378289516834550134705056051838162503660322739730617028792712364262429554478015061929184008948187688156605464971916260293876377626719491351669108340778429763083516422879865468816939162564424003743741897912808344473692378164285592107193109403870333748874018903354200950300950333957718176868883093796762281239806732966028756450674690678269159740896623627493650760571188487210844131051548881955675140569772845035538976001671215032881856442978894225575234946453841339285439684649206855675243871163627152506578088434038260704484378510293449583782074426672839352750429797"),
+			H1:      tt.B10("20806111194326574035679672768739736858091819757645346758021785460314376599301419996391552167503230068997416579785272226365650120077000964746008759656721174712277436474112550446553328239712665397967183925836893294379889458489429334367827089024323487828041759547979283434655829287281438497101362147499106999452268149455783225328882973374880831689906754199016227640168040507681655515611153025357280494053341572862736455523226702405927614126963630370765902600152731846620871866239702506880141644695257384096428760156930215724940913719081038961766230182718949910447613483603623677539012295395768844645520397810463957385064"),
+			ScalarX: tt.B10("15680711572265412302063710770100256379142303758183622454827770633536053015410125301746669617168927840582543443640485515259880553994650563353596050406993218267888689674576174291292544181319318290540656134509455403555836349380843917576044782017032252612309396418725437217288341460444014546130837821402423422015544908647599204304517283721877733784155111971303558627174554499877650796086982127066231644058631024937179283400939543733407645999366471982125969899025962517640974247501614047650918073386577048332793677704293299537593243143375588086886366242986351992009685208447912923549964467532904719505360890187205305699459"),
+			H2:      tt.B10("622658591279147036927766482179620016370160116224103009000775777741977746076069841974182622264916996020211240564452627583018818598398927997509249354168351328209433205510046968758622632579900996917482688488998451832822212978905701352270659049839671444956557784505017848150403230178964425529347380297488762918345919142437261093899029818695107925965006069381608544120388500753110329923373348736800348712931341066415725312620621446928469239018646863379711766363968549027231209938338940192298373744505449601807104666477538150562655076590620733447959977455361655346656264899909425757426204005449809320724302574761557419731"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("82883554749339666963586441494337620435893416497294374579482883836972805943324488477506490102969223378939443091658227508760650417478882372581176762787634196217793921803806235447860770523627208770135378072841065094614012362146856770210350489621870309656243783617131413009270202064367777187073091174042668140719"),
+			Qi:      tt.B10("69225815559898813841972197257369214418510039477259267562386576754105996517641287187354271185517091465322957847668322767001848636388632130892875166130086418905967220151161781954791233039810992082584155593127502090379734391611013337128628560799387768620268946450680104840369217258842944810825920588121700493123"),
+			N:       tt.B10("22950726696106252594177150043702726168157075733848228603840197369993285323355022881679851977892612224492713729744126629955665066185266969130231247332745420728832293954467828637032990587597267170802253468024344651848441930746397341359174394464185978358597098005624864548609773709166088442852948437798183551200690008139352012083637986045796225151454930178660324726916856513773213004410369292488865134255536689323311258239790555126688842073858461480933636320357175937577130089085815509252853603516538213035830991253353875279132119189820404992281851244229733861968450581391216339219701593104607616741537835284904160369433"),
+			H1:      tt.B10("16947714733355968353285087150980488488797136017640333340847024527191500632540085135174374838838715006487240699680849864319988293467608752442017432880375482280049463974990082250738962509544799109260352673773363020130912159245439261485567779683327978891270641219826411739866109659592983663828776367898959223055923734598751887123852213233896336740080689174821591168670844378375591715457972908784654711637529831964663980121859709144936543716417104012030317467473498694302940867353074810598697963868975995075238602465887766432955803284002304692712238697582306243591149618478337706345348084669052787889594825614138884254857"),
+			ScalarX: tt.B10("7141254243649730791870594504444361694661965691954862970497207011721889507031355783622099741060773071546652817450619360631529113879924641192639273248901801434686465102669717633914711151251701245166721810172824415155507752247435419525086338189605111924764954431194140203170189796624665041965605014805810747231699659835664794666132438293568877475559274697866641060695899446664193994146827881518532054761256829920204913452337762833840277415230500040020938819338025433474821575450449377841822597092548025041637670944198465638103484247157760932440805627816356173686151826558462387115649657392225680106913427091008986414122"),
+			H2:      tt.B10("8866059999511505016265292876826970660608930702174554980770241858104175572432348371991218071753504427593404759665569189913263950749226807497981103036201156716522101847506433897179982772552762029382294277009511885974503187408175951461864212501193897223537353833041834349069832240822300902557558570805521547512377574784899720538802689603248450763304879728986861357544735140736494322201689579228336939649023190017663290242463120794168012436767474812418152518586579869344956732872664353467783350156896625854233546860497073584838622854905571366278592478526806298651643691717520658141804698488684958703838336892275534751751"),
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("CdlProve failed: #{err}")
+		}
+		cv := &CdlVerifyParams{
+			Curve: curve,
+			H1:    pp.H1,
+			H2:    pp.H2,
+			N:     pp.N,
+		}
+		err = proof.Verify(cv)
+		tt.AssertNoError(t, err)
+	}
+}
+
+func TestCdlProofTampered(t *testing.T) {
+	curve := btcec.S256()
+	params := []*CdlProofParams{
+		{
+			Curve:   curve,
+			Pi:      tt.B10("69979182966199119672351533979383654499397224507518060735584349051652764492448136547713282139549035562089101777193243018061896970048738918135727018564481835840179068003226387981023729616470203107028273690173680912153598953087314298633621289521741954003727691656981967430921179270576924304274459867142386866233"),
+			Qi:      tt.B10("84424010159268042809195618234668170228427874149211682832595019116005334677981908011739260951914473600143292358100903745699777808120747187820649504013204732464439679512865842249450303793972825236153746944676836172054279530040675313001271469918167027979171285553816301512008832730050650239840859438662619111399"),
+			N:       tt.B10("23631693014702686598491747297681569475877326460812464082819481422202713346211180070062414360449939288078360593861292547953001504075134774288233379964236347153126995445451429330749200073283458248684973345738352066279459449816118837062102541615816746664320639714285376717243575093782737364692876115029953880688277093224947831946660228299342362879622467185199611987459117940187846509287850536067217425664948192994941586900797272776595126412023378302307519372803612686581113206608355719746319871239226865149982986439036498029925509216269045641120927388902686667987841077785466791674964976428828991419580797672404965915133"),
+			H1:      tt.B10("7946425901597611550738413402091207348349673201811011777758041950640367669127591562559941008463663269491315559897208768775232447391501592581877731140164059638274471726341875678455474107814193902512015507251883997545858299492500962124389479454741467013546908266057900991789262148766092771402882570705098310732185565230244188671537946720849813029966760353542287359829173490796747660692731745728903580183343647146866291218790289460250912792371107912019640755966623243965663097337215423829596916087566120282913217797405222525769972767463810191902348082642684555912203247043727191165051070774263967911353607952365245400947"),
+			ScalarX: tt.B10("9060855727394538554280486019975466408154154373013627407948965978243783485406040771639015901954551816313856770333109273827682320951740510817356910069451842815860762800653008008734702455588363782662799763807936814615743776850798351473244971478097357831497231664301656006475400319088867810184234855807442006410165018848767142974822471227021406352580604137332089139556516988505126169997002017833858827496695461902663346560474857016062532738611411777646178283588990177506440466839975300743011477322819000458010731313375502203626231094265141803538312989410050792429290230188104355460623820692518310405901018793614779352365"),
+			H2:      tt.B10("9655716947834799186539374175271253546360574889564941529186887148524811253942671582167482352632019351834566840338079786327815799490180732501072504891516646810008321428562261204389435547506173159604155572508109327801749630580463385051725499673777772465780243560444849344381658998224546017336909884296424486545406973413882945499464570750924583721544332515711367988346291270454498094198508290623057769669971189478287975093769597415578597441391516518992736837455435830471650960836487483840938880704655913775433524618584886395406891877498467764813222176205917831839824829752294548668410502170499760676452530462719513197659"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("67888050747812851425842238967480716528620751828903194145676972894251304673883735098328837590840818877762364813615848817532849830755892212636267607196610651447723752842688900061362287945644919469354026105141182996474829188730844136985148548346048734847454613613006744111959146944241178072643958108055109208669"),
+			Qi:      tt.B10("74028583328840379462079789341032310086933613584606697607428537990913172909197902388422323870097092632268691549460498294185854606703100438377050619092037950146228310525692099718006602293395173980000397794576241083381416571186609861062015966780930151103765006974601121311197135038509984827174382833566361332459"),
+			N:       tt.B10("20102624887268032436385352818309224611522117481187785072762969444240952373977012433059077411520297892283717463008349816277829183652055938423641934427094022881233221976429590801180822524846487163410907356244738306218466738291842021324571650500458383974369353051471917385538473367391737488963462364596813583268975946170601367819464693418426390466501882866808616688082647634542999240442063438027459804109064071267956138187461519377808857618462480066921719138950396485850908712512499459355024531358622117678159829573237832605918882277226089593396668852935983490680149025683860215703874267028152487275463608689386596630541"),
+			H1:      tt.B10("2376518835100800976110377446508048627458382318670199614681941939618957469802074100964557196232832900256536094316139165206461461940284874993903911499340652135862549146228175201825717740466426272093870244464122393235976412050142856096926928069502460776404328490281063237799360068282994265687557447485328660684313615679759719396617374050181308075085809989635946482359863766907954463561844155574462370765003067298540057340699453379534447672507032661473128248596224981515811565065700663734038702396414461854756619095554520442820368266108115668333256283196813050455307108963605317668312367263714220550180930603737069042681"),
+			ScalarX: tt.B10("14488423386509878470589768290899871750691012627125956350082287802110592303459003618093602404322350514916636961391783202847213112161591547267362064786324008087712203131139538157555973305762533116789572682662080915716282021431017132003226801582363966807205962239049864881081267891864101582031208944201226750450293268348489147631715204012459970983233418780535765088312679112283662704474419873686631944623889770749773996675154272528531861252719763116466349018521737163036477417936570219206390064706371039438309462010306171743504615466373920828843322740046857066875757090005851593014487741915608184497652830496479301046101"),
+			H2:      tt.B10("15879604731069180823336489370430079158612574193637569666769343387116241501138672742037225999442092265612857660656553596930640898982694079345286033477972766098595684079264887219808793990685522553437704209214389414396934083563795665724990112792161324509368439824463260812389360700531646699291443828484023663984617896684393589265154610104646989442735621432109976922590169132245891501805740557524118742816342082961519552869452712799863985060370901800328292511999673878319215159254098261935327388754658587343367584404415707368858166863610846433431741855897776292306056157680786291582652749608898679384525696607905677562940"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("76330104306302336171080114522369103577528135517365964316288949628987850291369939487976722362743065903494105959054506903318328806931036907581609818174438335482939721074022473215585686298551052611871769430789160485977457333536557385501363802286842127881913680259737758668074492827574254852970687584896454490369"),
+			Qi:      tt.B10("74680459525723769595192139188749594456005241009599674590157723679305006605114825831746447884821436868201575261183366679755987845338855141692678446759207587562380509454643686288880947446224009212779939349122453707965183148822196568163102099137040033736913880137247777891407945116122572996093120804287262887611"),
+			N:       tt.B10("22801469060964340910128152680947327636805006778962251378289516834550134705056051838162503660322739730617028792712364262429554478015061929184008948187688156605464971916260293876377626719491351669108340778429763083516422879865468816939162564424003743741897912808344473692378164285592107193109403870333748874018903354200950300950333957718176868883093796762281239806732966028756450674690678269159740896623627493650760571188487210844131051548881955675140569772845035538976001671215032881856442978894225575234946453841339285439684649206855675243871163627152506578088434038260704484378510293449583782074426672839352750429797"),
+			H1:      tt.B10("20806111194326574035679672768739736858091819757645346758021785460314376599301419996391552167503230068997416579785272226365650120077000964746008759656721174712277436474112550446553328239712665397967183925836893294379889458489429334367827089024323487828041759547979283434655829287281438497101362147499106999452268149455783225328882973374880831689906754199016227640168040507681655515611153025357280494053341572862736455523226702405927614126963630370765902600152731846620871866239702506880141644695257384096428760156930215724940913719081038961766230182718949910447613483603623677539012295395768844645520397810463957385064"),
+			ScalarX: tt.B10("15680711572265412302063710770100256379142303758183622454827770633536053015410125301746669617168927840582543443640485515259880553994650563353596050406993218267888689674576174291292544181319318290540656134509455403555836349380843917576044782017032252612309396418725437217288341460444014546130837821402423422015544908647599204304517283721877733784155111971303558627174554499877650796086982127066231644058631024937179283400939543733407645999366471982125969899025962517640974247501614047650918073386577048332793677704293299537593243143375588086886366242986351992009685208447912923549964467532904719505360890187205305699459"),
+			H2:      tt.B10("622658591279147036927766482179620016370160116224103009000775777741977746076069841974182622264916996020211240564452627583018818598398927997509249354168351328209433205510046968758622632579900996917482688488998451832822212978905701352270659049839671444956557784505017848150403230178964425529347380297488762918345919142437261093899029818695107925965006069381608544120388500753110329923373348736800348712931341066415725312620621446928469239018646863379711766363968549027231209938338940192298373744505449601807104666477538150562655076590620733447959977455361655346656264899909425757426204005449809320724302574761557419731"),
+		},
+		{
+			Curve:   curve,
+			Pi:      tt.B10("82883554749339666963586441494337620435893416497294374579482883836972805943324488477506490102969223378939443091658227508760650417478882372581176762787634196217793921803806235447860770523627208770135378072841065094614012362146856770210350489621870309656243783617131413009270202064367777187073091174042668140719"),
+			Qi:      tt.B10("69225815559898813841972197257369214418510039477259267562386576754105996517641287187354271185517091465322957847668322767001848636388632130892875166130086418905967220151161781954791233039810992082584155593127502090379734391611013337128628560799387768620268946450680104840369217258842944810825920588121700493123"),
+			N:       tt.B10("22950726696106252594177150043702726168157075733848228603840197369993285323355022881679851977892612224492713729744126629955665066185266969130231247332745420728832293954467828637032990587597267170802253468024344651848441930746397341359174394464185978358597098005624864548609773709166088442852948437798183551200690008139352012083637986045796225151454930178660324726916856513773213004410369292488865134255536689323311258239790555126688842073858461480933636320357175937577130089085815509252853603516538213035830991253353875279132119189820404992281851244229733861968450581391216339219701593104607616741537835284904160369433"),
+			H1:      tt.B10("16947714733355968353285087150980488488797136017640333340847024527191500632540085135174374838838715006487240699680849864319988293467608752442017432880375482280049463974990082250738962509544799109260352673773363020130912159245439261485567779683327978891270641219826411739866109659592983663828776367898959223055923734598751887123852213233896336740080689174821591168670844378375591715457972908784654711637529831964663980121859709144936543716417104012030317467473498694302940867353074810598697963868975995075238602465887766432955803284002304692712238697582306243591149618478337706345348084669052787889594825614138884254857"),
+			ScalarX: tt.B10("7141254243649730791870594504444361694661965691954862970497207011721889507031355783622099741060773071546652817450619360631529113879924641192639273248901801434686465102669717633914711151251701245166721810172824415155507752247435419525086338189605111924764954431194140203170189796624665041965605014805810747231699659835664794666132438293568877475559274697866641060695899446664193994146827881518532054761256829920204913452337762833840277415230500040020938819338025433474821575450449377841822597092548025041637670944198465638103484247157760932440805627816356173686151826558462387115649657392225680106913427091008986414122"),
+			H2:      tt.B10("8866059999511505016265292876826970660608930702174554980770241858104175572432348371991218071753504427593404759665569189913263950749226807497981103036201156716522101847506433897179982772552762029382294277009511885974503187408175951461864212501193897223537353833041834349069832240822300902557558570805521547512377574784899720538802689603248450763304879728986861357544735140736494322201689579228336939649023190017663290242463120794168012436767474812418152518586579869344956732872664353467783350156896625854233546860497073584838622854905571366278592478526806298651643691717520658141804698488684958703838336892275534751751"),
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("ProveCompositeDL failed: #{err}")
+		}
+		cv := &CdlVerifyParams{
+			Curve: curve,
+			H1:    pp.H1,
+			H2:    pp.H2,
+			N:     pp.N,
+		}
+
+		proof.u[0].Add(proof.u[0], mod.One)
+		if err := proof.Verify(cv); err == nil {
+			t.Errorf("Expected CdlVerify to fail but succeeded")
+		}
+
+		proof.s[0].Add(proof.s[0], mod.One)
+		if err := proof.Verify(cv); err == nil {
+			t.Errorf("Expected CdlVerify to fail but succeeded")
+		}
+
+		proof.u[0].Sub(proof.u[0], mod.One)
+		proof.s[0].Sub(proof.s[0], mod.One)
+		cv.H1.Add(cv.H1, mod.One).Mod(cv.H1, cv.N)
+		if err := proof.Verify(cv); err == nil {
+			t.Errorf("Expected CdlVerify to fail but succeeded")
+		}
+
+		cv.H2.Add(cv.H2, mod.One).Mod(cv.H2, cv.N)
+		if err := proof.Verify(cv); err == nil {
+			t.Errorf("Expected CdlVerify to fail but succeeded")
+		}
+	}
+}
+
+// Recall that if the input to ProveCompositeDL is correct, h2 must be equal to h1^alpha
+// In this test, we set h1, h2, alpha as random values purposely, which should make the verification incorrect.
+// Pi, Qi and N are generated correctly via a side program and P = 2*Pi+1, Q=2*Qi+1, N = PQ
+func TestCdlProofRandValues(t *testing.T) {
+	curve := btcec.S256()
+	pi := tt.B10("69194751040870458870606183726555435909086788535387699389669514131170791430457074867750473589740101538563709151356299341625165252163443101897409551452286117584229969813571483217371266470819768503264181903858655002445121864855018050830086220605407845379111572386400613256577806622758645652928390261158201056559")
+	qi := tt.B10("82637633161541176464703465424481086073529001916957361226495184953100155149539385427685606853188505515091549850006242891763636582655438360592297819967249750168526728829169019442914966932888398845776455389981984845838757231468840109235034665375458310070782153041383978515298908502237439774363022952285938551943")
+	n := tt.B10("22872361812878489876060907543278948578387147675520825541510527859532146822027982754603729909037595317258111424852220535313592335395829235521522221441210174887876906980298605562656860093862386445954521521259318033327437806280309919241306055629653903861746476630826350344558570927747295219571966411822552470277193572834840982644421834542817903768311471107148331859193087484753051900698022956193382070220395102397179763375245079349836869922078435771068117889295943356668151757001536241849212462656770832021260539449326135398784589973524619988879740444034914415022192221461822737062898569969299902763089827704220688593553")
+	h1, _ := mod.Rand(n)
+	alpha, _ := mod.Rand(new(big.Int).Mul(pi, qi))
+	h2, _ := mod.Rand(n)
+	params := []*CdlProofParams{
+		{
+			Curve:   curve,
+			Pi:      pi,
+			Qi:      qi,
+			H1:      h1,
+			H2:      h2,
+			ScalarX: alpha,
+			N:       n,
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("CdlProve failed: #{err}")
+		}
+		cv := &CdlVerifyParams{
+			Curve: curve,
+			H1:    pp.H1,
+			H2:    pp.H2,
+			N:     pp.N,
+		}
+		err = proof.Verify(cv)
+		tt.AssertSomeError(t, err)
+	}
+}
+
+func TestCdlProofInvalidParams(t *testing.T) {
+	params := CdlProofParams{}
+	if _, err := params.Prove(); err == nil {
+		t.Errorf("CdlProve succeeded but should've failed")
+	}
+
+	curve := btcec.S256()
+	P := tt.B10("165767109498679333927172882988675240871786832994588749158965767673945611886648976955012980205938446757878886183316455017521300834957764745162353525575268392435587843607612470895721541047254417540270756145682130189228024724293713540420700979243740619312487567234262826018540404128735554374146182348085336281439")
+	Q := tt.B10("138451631119797627683944394514738428837020078954518535124773153508211993035282574374708542371034182930645915695336645534003697272777264261785750332260172837811934440302323563909582466079621984165168311186255004180759468783222026674257257121598775537240537892901360209680738434517685889621651841176243400986247")
+	pi := new(big.Int).Div(new(big.Int).Sub(P, big.NewInt(1)), big.NewInt(2))
+	qi := new(big.Int).Div(new(big.Int).Sub(Q, big.NewInt(1)), big.NewInt(2))
+	n := new(big.Int).Mul(P, Q)
+	h1, _ := mod.Rand(n)
+	alpha, _ := mod.Rand(n)
+	h2 := new(big.Int).Exp(h1, alpha, n)
+	params = CdlProofParams{
+		Curve:   curve,
+		Pi:      pi,
+		Qi:      qi,
+		H1:      h1,
+		H2:      h2,
+		ScalarX: alpha,
+		N:       n,
+	}
+	proof, _ := params.Prove()
+	cv := &CdlVerifyParams{}
+	if err := proof.Verify(cv); err == nil {
+		t.Errorf("CdlVerify succeeded but should've failed.")
+	}
+
+	cv.Curve = params.Curve
+	if err := proof.Verify(cv); err == nil {
+		t.Errorf("CdlVerify succeeded but should've failed")
+	}
+
+	cv.H1 = params.H1
+	if err := proof.Verify(cv); err == nil {
+		t.Errorf("CdlVerify succeeded but should've failed")
+	}
+
+	cv.N = params.N
+	if err := proof.Verify(cv); err == nil {
+		t.Errorf("CdlVerify succeeded but should've failed")
+	}
+}
+
+// Numbers in array u and s are randomly generated via a side program
+func TestMarshalJsonCdlProof(t *testing.T) {
+	test := CdlProof{
+		u: []*big.Int{
+			bi(31), bi(38), bi(77), bi(43), bi(27),
+			bi(42), bi(56), bi(36), bi(45), bi(20),
+			bi(81), bi(31), bi(69), bi(36), bi(35),
+			bi(47), bi(44), bi(95), bi(95), bi(79),
+			bi(90), bi(67), bi(90), bi(95), bi(96),
+			bi(73), bi(100), bi(17), bi(26), bi(56),
+			bi(96), bi(66), bi(63), bi(31), bi(12),
+			bi(91), bi(96), bi(83), bi(89), bi(34),
+			bi(91), bi(54), bi(66), bi(46), bi(19),
+			bi(50), bi(30), bi(32), bi(74), bi(17),
+			bi(98), bi(98), bi(56), bi(33), bi(57),
+			bi(55), bi(98), bi(73), bi(31), bi(95),
+			bi(31), bi(26), bi(45), bi(42), bi(59),
+			bi(70), bi(30), bi(10), bi(58), bi(59),
+			bi(47), bi(35), bi(35), bi(74), bi(73),
+			bi(74), bi(38), bi(95), bi(99), bi(12),
+			bi(34), bi(40), bi(64), bi(22), bi(30),
+			bi(31), bi(81), bi(56), bi(20), bi(58),
+			bi(26), bi(16), bi(31), bi(83), bi(29),
+			bi(13), bi(20), bi(29), bi(37), bi(92),
+			bi(10), bi(12), bi(24), bi(15), bi(34),
+			bi(79), bi(54), bi(59), bi(40), bi(18),
+			bi(88), bi(70), bi(10), bi(81), bi(11),
+			bi(13), bi(81), bi(10), bi(66), bi(15),
+			bi(23), bi(39), bi(92), bi(32), bi(78),
+			bi(96), bi(72), bi(23),
+		},
+		s: []*big.Int{
+			bi(58), bi(85), bi(46), bi(71), bi(67),
+			bi(64), bi(15), bi(98), bi(47), bi(22),
+			bi(82), bi(26), bi(40), bi(76), bi(74),
+			bi(15), bi(66), bi(88), bi(77), bi(85),
+			bi(69), bi(18), bi(56), bi(58), bi(16),
+			bi(21), bi(46), bi(61), bi(97), bi(42),
+			bi(85), bi(83), bi(21), bi(69), bi(75),
+			bi(22), bi(97), bi(41), bi(33), bi(75),
+			bi(21), bi(11), bi(15), bi(59), bi(12),
+			bi(21), bi(45), bi(63), bi(94), bi(79),
+			bi(47), bi(92), bi(11), bi(27), bi(77),
+			bi(63), bi(50), bi(25), bi(100), bi(25),
+			bi(48), bi(70), bi(98), bi(26), bi(99),
+			bi(75), bi(23), bi(61), bi(15), bi(23),
+			bi(36), bi(86), bi(73), bi(71), bi(88),
+			bi(38), bi(91), bi(89), bi(65), bi(68),
+			bi(78), bi(23), bi(73), bi(84), bi(71),
+			bi(90), bi(17), bi(13), bi(15), bi(40),
+			bi(49), bi(79), bi(45), bi(40), bi(84),
+			bi(71), bi(50), bi(40), bi(16), bi(94),
+			bi(88), bi(95), bi(77), bi(87), bi(49),
+			bi(62), bi(38), bi(28), bi(20), bi(68),
+			bi(31), bi(87), bi(98), bi(67), bi(91),
+			bi(62), bi(60), bi(91), bi(71), bi(25),
+			bi(44), bi(72), bi(43), bi(19), bi(65),
+			bi(24), bi(16), bi(47),
+		},
+	}
+
+	testJSON, err := json.Marshal(test)
+	assert.NoError(t, err)
+	assert.NotNil(t, testJSON)
+
+	unmarshaled := new(CdlProof)
+	err = json.Unmarshal(testJSON, unmarshaled)
+	assert.NoError(t, err)
+
+	assert.Equal(t, test.u, unmarshaled.u)
+	assert.Equal(t, test.s, unmarshaled.s)
+}
+
+// Set SafePrimes P, Q to 100-bit length instead of 1024-bit length to test small modulus.
+// P and Q are generated using the SafePrime Generator via side program
+// P = 1028783406134480509185302717063
+// Q = 1093599917998934718101903070203
+func TestSmallModulus(t *testing.T) {
+	curve := btcec.S256()
+	pi := tt.B10("514391703067240254592651358531")
+	qi := tt.B10("546799958999467359050951535101")
+	n := tt.B10("1125077448587332637478027734178491491371406782346677534973789")
+	h1 := tt.B10("1044115315550618597679290143551713476694466276523205398373512")
+	x := tt.B10("232563802391440426149543743017793250842498595895226805619115")
+	h2 := tt.B10("47869393962942536914052882363726168408056214230151183601468")
+	params := []*CdlProofParams{
+		{
+			Curve:   curve,
+			Pi:      pi,
+			Qi:      qi,
+			H1:      h1,
+			H2:      h2,
+			ScalarX: x,
+			N:       n,
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("CdlProve failed: #{err}")
+		}
+		cv := &CdlVerifyParams{
+			Curve: curve,
+			H1:    pp.H1,
+			H2:    pp.H2,
+			N:     pp.N,
+		}
+		err = proof.Verify(cv)
+		if err == nil {
+			t.Errorf("CdlVerify should fail but succeeded")
+		}
+	}
+}
diff --git a/pkg/tecdsa/gg20/proof/mta.go b/pkg/tecdsa/gg20/proof/mta.go
new file mode 100644
index 00000000..5059f4d5
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/mta.go
@@ -0,0 +1,905 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+// Package proof contains the multiplicative-to-additive (MtA) subprotocol from [spec] §7
+
+package proof
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// ResponseProofParams encapsulates the values over which a range proof (2) is computed.
+// [spec] §7.fig 8
+type ResponseProofParams struct {
+	Curve        elliptic.Curve
+	DealerParams *dealer.ProofParams
+	Pk           *paillier.PublicKey
+	SmallB, C1   *big.Int
+	B            *curves.EcPoint
+}
+
+// ResponseVerifyParams encapsulates the values over which a range proof (2) is verified.
+// [spec] §7.fig 10
+type ResponseVerifyParams struct {
+	Curve        elliptic.Curve
+	DealerParams *dealer.ProofParams
+	Sk           *paillier.SecretKey
+	C1           *big.Int
+	B            *curves.EcPoint
+}
+
+// ResponseFinalizer captures the interface provided by a response proof
+// [spec] fig 13
+type ResponseFinalizer interface {
+	Finalize(vp *ResponseVerifyParams) (*big.Int, error)
+	FinalizeWc(vp *ResponseVerifyParams) (*big.Int, error)
+}
+
+// ResponseProof encapsulates the values over which a range proof (2) is computed
+// and a portion of the random value is encrypted
+// [spec] §7.fig 8
+type ResponseProof struct {
+	R2proof  *Range2Proof
+	C2, Beta *big.Int
+}
+
+// Proof1Params encapsulates the values over which a range proof (1) is computed.
+// [spec] fig 10
+type Proof1Params struct {
+	Curve        elliptic.Curve
+	Pk           *paillier.PublicKey
+	DealerParams *dealer.ProofParams
+	A, C, R      *big.Int
+}
+
+// randProof1Params encapsulates the random values generated in proof (1)
+// [spec] fig 10
+type randProof1Params struct {
+	alpha, beta, gamma, rho *big.Int
+}
+
+// Range1Proof encapsulates the results returned in proof (1)
+// [spec] fig 10
+type Range1Proof struct {
+	z, e, s, s1, s2 *big.Int
+}
+
+// struct for JSON serialization
+type range1ProofJSON struct {
+	Z, E, S, S1, S2 *big.Int
+}
+
+// proof2Params encapsulates the values over which a range proof (2) is computed.
+// [spec] fig 12
+type proof2Params struct {
+	curve           elliptic.Curve
+	dealerParams    *dealer.ProofParams
+	pk              *paillier.PublicKey
+	y, r, c1, c2, x *big.Int
+	X               *curves.EcPoint
+}
+
+// verifyProof2Params encapsulates the values over which a range proof (2) is computed.
+// [spec] fig 12
+type verifyProof2Params struct {
+	curve        elliptic.Curve
+	dealerParams *dealer.ProofParams
+	pk           *paillier.PublicKey
+	c1, c2       *big.Int
+	X            *curves.EcPoint
+}
+
+// Range2Proof encapsulates the results returned in proof (2)
+// [spec] fig 12
+type randProof2Params struct {
+	randProof1Params
+	rhoTick, sigma, tau *big.Int
+}
+
+// Range2Proof encapsulates the values over which a range proof (2) is computed.
+// [spec] fig 12
+type Range2Proof struct {
+	z, e, s, s1, s2 *big.Int
+	t, t1, t2       *big.Int
+}
+
+// JSON struct for serialization
+type range2ProofJSON struct {
+	Z, E, S, S1, S2 *big.Int
+	T, T1, T2       *big.Int
+}
+
+// MarshalJSON converts Range1Proof into JSON
+func (r Range1Proof) MarshalJSON() ([]byte, error) {
+	return json.Marshal(range1ProofJSON{
+		Z:  r.z,
+		E:  r.e,
+		S:  r.s,
+		S1: r.s1,
+		S2: r.s2,
+	})
+}
+
+// UnmarshalJSON converts json into a Range1Proof
+func (r *Range1Proof) UnmarshalJSON(bytes []byte) error {
+	var proof range1ProofJSON
+	err := json.Unmarshal(bytes, &proof)
+	if err != nil {
+		return err
+	}
+
+	r.z = proof.Z
+	r.e = proof.E
+	r.s = proof.S
+	r.s1 = proof.S1
+	r.s2 = proof.S2
+	return nil
+}
+
+// MarshalJSON converts Range2Proof into JSON format
+func (rP2 Range2Proof) MarshalJSON() ([]byte, error) {
+	data := range2ProofJSON{
+		Z:  rP2.z,
+		E:  rP2.e,
+		S:  rP2.s,
+		S1: rP2.s1,
+		S2: rP2.s2,
+		T:  rP2.t,
+		T1: rP2.t1,
+		T2: rP2.t2,
+	}
+	return json.Marshal(data)
+}
+
+// UnmarshalJSON converts json into a Range2Proof
+func (rP2 *Range2Proof) UnmarshalJSON(bytes []byte) error {
+	data := new(range2ProofJSON)
+
+	err := json.Unmarshal(bytes, &data)
+	if err != nil {
+		return err
+	}
+
+	rP2.z = data.Z
+	rP2.e = data.E
+	rP2.s = data.S
+	rP2.s1 = data.S1
+	rP2.s2 = data.S2
+	rP2.t = data.T
+	rP2.t1 = data.T1
+	rP2.t2 = data.T2
+
+	return nil
+}
+
+// Prove computes a range proof over these parameters
+// [spec] fig 11: MtaResponse
+func (rp ResponseProofParams) Prove() (*ResponseProof, error) {
+	return genResponseProof(rp, false)
+}
+
+// ProveWc computes:
+// [spec] fig 11: MtaResponse_wc
+func (rp ResponseProofParams) ProveWc() (*ResponseProof, error) {
+	return genResponseProof(rp, true)
+}
+
+// genResponseProof computes both
+// [spec] fig 11: MtAResponse and MtAResponse_wc
+func genResponseProof(rp ResponseProofParams, wc bool) (*ResponseProof, error) {
+	// 1. c_b = PaillierMultiply(SmallB, c_1)
+	cb, err := rp.Pk.Mul(rp.SmallB, rp.C1)
+	if err != nil {
+		return nil, err
+	}
+	// 2. Set N = Pk.N
+
+	// 3. \beta' = Z_{\mathbb{N}}
+	betaTick, err := core.Rand(rp.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+	// step 4
+	cBeta, rBeta, err := rp.Pk.Encrypt(betaTick)
+	if err != nil {
+		return nil, err
+	}
+	// step 5
+	c2, err := rp.Pk.Add(cb, cBeta)
+	if err != nil {
+		return nil, err
+	}
+	// step 6
+	beta, err := core.Neg(betaTick, rp.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	// step 7
+	pp := proof2Params{
+		curve:        rp.Curve,
+		pk:           rp.Pk,
+		dealerParams: rp.DealerParams,
+		x:            rp.SmallB,
+		y:            betaTick,
+		r:            rBeta,
+		c1:           rp.C1,
+		c2:           c2,
+		X:            rp.B,
+	}
+	var r2p *Range2Proof
+	if wc {
+		r2p, err = pp.ProveWc()
+	} else {
+		r2p, err = pp.Prove()
+	}
+	if err != nil {
+		return nil, err
+	}
+
+	return &ResponseProof{
+		r2p,
+		c2,
+		beta,
+	}, nil
+}
+
+// Finalize checks a range (2) proof: [spec] fig 13: MtaFinalize
+// and returns the paillier encrypted random value
+func (rp ResponseProof) Finalize(vp *ResponseVerifyParams) (*big.Int, error) {
+	v2Params := verifyProof2Params{
+		curve:        vp.Curve,
+		dealerParams: vp.DealerParams,
+		pk: &paillier.PublicKey{
+			N:  vp.Sk.N,
+			N2: vp.Sk.N2,
+		},
+		c1: vp.C1,
+		c2: rp.C2,
+	}
+	if err := rp.R2proof.Verify(&v2Params); err != nil {
+		return nil, err
+	}
+	alpha, err := vp.Sk.Decrypt(rp.C2)
+	if err != nil {
+		return nil, err
+	}
+
+	return alpha.Mod(alpha, vp.Curve.Params().N), nil
+}
+
+// FinalizeWc checks a range (2) proof: [spec] fig 13: MtaFinalize_wc
+// and returns the paillier encrypted random value
+func (rp ResponseProof) FinalizeWc(vp *ResponseVerifyParams) (*big.Int, error) {
+	v2Params := verifyProof2Params{
+		curve:        vp.Curve,
+		dealerParams: vp.DealerParams,
+		pk: &paillier.PublicKey{
+			N:  vp.Sk.N,
+			N2: vp.Sk.N2,
+		},
+		c1: vp.C1,
+		c2: rp.C2,
+		X:  vp.B,
+	}
+	// 1. If MtaVerifyRange2_wc(...) = False, Return Error
+	if err := rp.R2proof.VerifyWc(&v2Params); err != nil {
+		return nil, err
+	}
+	// 2. Compute \alpha = Decrypt(sk, C2)
+	alpha, err := vp.Sk.Decrypt(rp.C2)
+	if err != nil {
+		return nil, err
+	}
+	// 3. Return \alpha mod q
+	return alpha.Mod(alpha, vp.Curve.Params().N), nil
+}
+
+// Prove computes a range proof over these parameters
+// [spec] fig 10: MtaProveRange1
+func (pp Proof1Params) Prove() (*Range1Proof, error) {
+	if err := core.In(pp.A, pp.Curve.Params().N); err != nil {
+		return nil, err
+	}
+	if err := core.In(pp.R, pp.Pk.N); err != nil {
+		return nil, err
+	}
+	// Fetch our randomized values
+	rp, err := rand1(pp.Pk.N, pp.DealerParams.N, pp.Curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	// Compute and return the proof
+	return genProof1(pp, rp)
+}
+
+// Fetches random values for use in range proof
+// [spec] fig 10: MtaProveRange1
+func rand1(N, Ntilde, q *big.Int) (*randProof1Params, error) {
+	// Rings in which we'll operate
+	// q^3
+	q3, err := core.Exp(q, big.NewInt(3), nil)
+	if err != nil {
+		return nil, err
+	}
+
+	// q^3(N~)
+	q3Ntilde, err := core.Mul(q3, Ntilde, nil)
+	if err != nil {
+		return nil, err
+	}
+
+	// q(N~)
+	qNtilde, err := core.Mul(q, Ntilde, nil)
+	if err != nil {
+		return nil, err
+	}
+
+	// Select initial values
+	// 1: \alpha \getsr Z_{q^3}
+	alpha, err := core.Rand(q3)
+	if err != nil {
+		return nil, err
+	}
+
+	// 2: \beta \getsr Z^*_N
+	beta, err := core.Rand(N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 3: \gamma \getsr Z_{q^3N~}
+	gamma, err := core.Rand(q3Ntilde)
+	if err != nil {
+		return nil, err
+	}
+
+	// 4: \rho \getsr Z_{q^N~}
+	rho, err := core.Rand(qNtilde)
+	if err != nil {
+		return nil, err
+	}
+
+	// Success!
+	return &randProof1Params{
+		alpha, beta, gamma, rho,
+	}, nil
+}
+
+// genProof1 deterministically computes a range proof
+// [spec] fig 10: MtaProveRange1
+func genProof1(in Proof1Params, rp *randProof1Params) (*Range1Proof, error) {
+	// 6: z = h_1^a * h_2^\rho mod N~
+	z, err := pedersen(in.DealerParams.H1, in.DealerParams.H2, in.A, rp.rho, in.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 7: u = (N+1)^alpha * \beta^N  mod N^2
+	u, err := inc(rp.alpha, rp.beta, in.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 8: w = h_1^alpha & h_2^\gamma mod N~
+	w, err := pedersen(in.DealerParams.H1, in.DealerParams.H2, rp.alpha, rp.gamma, in.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 9: e = H(g, q, Pk, N~, h_1, h_2, c, z, u, w)
+	bytes, err := core.FiatShamir(in.Curve.Params().Gx, in.Curve.Params().Gy, in.Curve.Params().N, in.Pk.N, in.DealerParams.N, in.DealerParams.H1, in.DealerParams.H2, in.C, z, u, w)
+	if err != nil {
+		return nil, err
+	}
+	e := new(big.Int).SetBytes(bytes)
+
+	// 10: s = r^e*\beta mod N
+	s, err := pedersen(in.R, rp.beta, e, core.One, in.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 11: s_1 = ea + \alpha
+	s1, err := schnorr(e, in.A, rp.alpha)
+	if err != nil {
+		return nil, err
+	}
+
+	// 12: s_2 = e\rho + \gamma
+	s2, err := schnorr(e, rp.rho, rp.gamma)
+	if err != nil {
+		return nil, err
+	}
+
+	// 13: \Pi = [z,u,w,s,s_1,s_2]
+	pi := &Range1Proof{
+		z:  z,
+		e:  e,
+		s:  s,
+		s1: s1,
+		s2: s2,
+	}
+
+	// 14: return \Pi
+	return pi, nil
+}
+
+// Verify checks a range (1) proof: [spec] §7.fig 7: MtaVerifyRange1
+func (pi Range1Proof) Verify(pp *Proof1Params) error {
+	params := pp.Curve.Params()
+	// Rings in which we'll operate
+	q3, err := core.Exp(params.N, big.NewInt(3), nil) // q^3
+	if err != nil {
+		return err
+	}
+
+	// 1: Set N = pk.N
+
+	// 2: Check range. s_1 > q^3 => return false
+	if pi.s1.Cmp(q3) == 1 {
+		return fmt.Errorf("s1 > q3")
+	}
+
+	// step 3
+	uHat, err := pi.uHatConstruct(pp)
+	if err != nil {
+		return fmt.Errorf("u hat construction error: %s", err)
+	}
+
+	// step 4
+	wHat, err := pi.wHatConstruct(pp)
+	if err != nil {
+		return fmt.Errorf("w hat construction error: %s", err)
+	}
+
+	// 5: Compute e = H(g,q,Pk,N~,h_1,h_2,c,z,uHat,wHat)
+	bytes, err := core.FiatShamir(params.Gx, params.Gy, params.N, pp.Pk.N, pp.DealerParams.N, pp.DealerParams.H1, pp.DealerParams.H2, pp.C, pi.z, uHat, wHat)
+	if err != nil {
+		return err
+	}
+	eHat := new(big.Int).SetBytes(bytes)
+
+	// 6: if e != eHat return false
+	if !core.ConstantTimeEq(pi.e, eHat) {
+		return fmt.Errorf("e != eHat")
+	}
+
+	// 7: return true
+	return nil
+}
+
+func (pi Range1Proof) uHatConstruct(pp *Proof1Params) (*big.Int, error) {
+	// 3: \hat{u} = (N+1)^{s_1}s^{N}c^{-e} mod N^2
+
+	x, err := inc(pi.s1, pi.s, pp.Pk.N) // x = (N+1)^{s_1}(S^N) mod N^2
+	if err != nil {
+		return nil, err
+	}
+	cInv, err := core.Inv(pp.C, pp.Pk.N2) // cInv = c^{-1} mod N^2
+	if err != nil {
+		return nil, err
+	}
+	y, err := core.Exp(cInv, pi.e, pp.Pk.N2) // y = c^{-e} mod N^2
+	if err != nil {
+		return nil, err
+	}
+	uHat, err := core.Mul(x, y, pp.Pk.N2) // u' := xy = ((N+1)^{s_1}(S^N))(c^{-e}) mod N^2
+	if err != nil {
+		return nil, err
+	}
+	return uHat, nil
+}
+
+func (pi Range1Proof) wHatConstruct(pp *Proof1Params) (*big.Int, error) {
+	// 4: \hat{w} = h_1^{s_1}*h_2^{s_2}*z^{-e} mod N~
+
+	a, err := pedersen(pp.DealerParams.H1, pp.DealerParams.H2, pi.s1, pi.s2, pp.DealerParams.N) // a = h_1^{s_1}*h_2^{s_2} mod N~
+	if err != nil {
+		return nil, err
+	}
+	zInv, err := core.Inv(pi.z, pp.DealerParams.N) // zInv = z^{-1} mod N~
+	if err != nil {
+		return nil, err
+	}
+	b, err := core.Exp(zInv, pi.e, pp.DealerParams.N) // SmallB = z^{-e} mod N~
+	if err != nil {
+		return nil, err
+	}
+	wHat, err := core.Mul(a, b, pp.DealerParams.N) // wHat = ab = (h_1^{s_1}*h_2^{s_2})(z^{-e}) mod N~
+	if err != nil {
+		return nil, err
+	}
+	return wHat, nil
+}
+
+// Prove computes a range proof over these parameters
+// [spec] fig 12: MtaProveRange2
+func (pp proof2Params) Prove() (*Range2Proof, error) {
+	randParams, err := rand2(pp.pk.N, pp.dealerParams.N, pp.curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	return genProof2(pp, randParams, false)
+}
+
+// Prove computes a range proof over these parameters
+// [spec] fig 12: MtaProveRange2_wc
+func (pp proof2Params) ProveWc() (*Range2Proof, error) {
+	if pp.X == nil {
+		return nil, fmt.Errorf("X must have a value")
+	}
+	randParams, err := rand2(pp.pk.N, pp.dealerParams.N, pp.curve.Params().N)
+	if err != nil {
+		return nil, err
+	}
+	return genProof2(pp, randParams, true)
+}
+
+// genProof2 creates the proof for MtAProveRange2
+func genProof2(pp proof2Params, rp *randProof2Params, wc bool) (*Range2Proof, error) {
+	curveParams := pp.curve.Params()
+	if err := core.In(pp.x, curveParams.N); err != nil {
+		return nil, fmt.Errorf("x is not in q")
+	}
+	// γi ←$ Zq
+	// calls MtAResponse    (γi,g, q, pkj,nTilde, h1, h2, cj) or
+	// calls MtAResponse_wc (wi,g, q, pkj,nTilde, h1, h2, cj, Wi)
+	// receives MtAResponse (SmallB, g, q, Pk, nTilde, h1, h2, C1)
+	//1. Compute cb = PaillierMultiply(SmallB, C1 )
+	//2. Choose β′ ←$ ZN
+	//3. Compute (cβ,rβ) = PaillierEncryptAndReturnRandomness(Pk,β′)
+	//4. Compute C2 = PaillierAdd(cb , cβ )
+	//5. Compute β = −β′ mod q
+	// calls    MtAProveRange2    (g, q, Pk, nTilde, h1, h2, SmallB, β ,rβ,C1, C2)
+	// receives MtAProveRange2    (g, q, Pk, nTilde, h1, h2, x, y, r, C1, C2)
+	// receives MtAProveRange2_wc (g, q, Pk, nTilde, h1, h2, x, y, r, C1, C2, X)
+
+	var u *curves.EcPoint
+	if wc {
+		// u = g^\alpha
+		ux, uy := pp.curve.ScalarBaseMult(rp.alpha.Bytes())
+		u = &curves.EcPoint{
+			Curve: pp.curve,
+			X:     ux,
+			Y:     uy,
+		}
+	}
+
+	// z = h1^x * h2^rho mod N ̃
+	z, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, pp.x, rp.rho, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// z' = h1^\alpha * h2^rho' mod N ̃
+	zTick, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, rp.alpha, rp.rhoTick, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// t = h1^y * h2^\sigma mod N ̃
+	t, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, pp.y, rp.sigma, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// v = C1^\alpha * (N + 1)^\gamma * \beta^N mod N^2
+	vLhs, err := core.Exp(pp.c1, rp.alpha, pp.pk.N2)
+	if err != nil {
+		return nil, err
+	}
+	vRhs, err := inc(rp.gamma, rp.beta, pp.pk.N)
+	if err != nil {
+		return nil, err
+	}
+	v, err := core.Mul(vLhs, vRhs, pp.pk.N2)
+	if err != nil {
+		return nil, err
+	}
+
+	// w = h1^\gamma & h2^\tau mod N ̃
+	w, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, rp.gamma, rp.tau, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	var challenge []byte
+	if wc {
+		// g || q || Pk || N ̃ || h1 || h2 || X || C1 || C2 || u || z || z' || t || v || w
+		challenge, err = core.FiatShamir(curveParams.Gx, curveParams.Gy, curveParams.N, pp.pk.N, pp.dealerParams.N, pp.dealerParams.H1, pp.dealerParams.H2, pp.X.X, pp.X.Y, pp.c1, pp.c2, u.X, u.Y, z, zTick, t, v, w)
+		if err != nil {
+			return nil, err
+		}
+	} else {
+		// g || q || Pk || N ̃ || h1 || h2 || C1 || C2 || z || z' || t || v || w
+		challenge, err = core.FiatShamir(curveParams.Gx, curveParams.Gy, curveParams.N, pp.pk.N, pp.dealerParams.N, pp.dealerParams.H1, pp.dealerParams.H2, pp.c1, pp.c2, z, zTick, t, v, w)
+		if err != nil {
+			return nil, err
+		}
+	}
+
+	e := new(big.Int).SetBytes(challenge)
+
+	// s = r^e * \beta mod N
+	s, err := pedersen(pp.r, rp.beta, e, core.One, pp.pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// s1 = ex + \alpha
+	s1, err := schnorr(e, pp.x, rp.alpha)
+	if err != nil {
+		return nil, err
+	}
+
+	// s2 = e\rho + \rho'
+	s2, err := schnorr(e, rp.rho, rp.rhoTick)
+	if err != nil {
+		return nil, err
+	}
+
+	// t1 = ey + \gamma
+	t1, err := schnorr(e, pp.y, rp.gamma)
+	if err != nil {
+		return nil, err
+	}
+
+	// t2 = e\sigma + \tau
+	t2, err := schnorr(e, rp.sigma, rp.tau)
+	if err != nil {
+		return nil, err
+	}
+
+	return &Range2Proof{
+		z:  z,
+		e:  e,
+		s:  s,
+		s1: s1,
+		s2: s2,
+		t:  t,
+		t1: t1,
+		t2: t2,
+	}, nil
+}
+
+// Verify checks a range (2) proof: [spec] §7.fig 9: MtaVerifyRange2
+func (pi Range2Proof) Verify(pp *verifyProof2Params) error {
+	return verify2Proof(pi, pp, false)
+}
+
+// VerifyWc checks a range (2) proof: [spec] §7.fig 9: MtaVerifyRange2_wc
+func (pi Range2Proof) VerifyWc(pp *verifyProof2Params) error {
+	return verify2Proof(pi, pp, true)
+}
+
+func verify2Proof(pi Range2Proof, pp *verifyProof2Params, wc bool) error {
+	// 1: Set N = pk.N
+
+	// Rings in which we'll operate
+	q3, err := core.Exp(pp.curve.Params().N, big.NewInt(3), nil) // q^3
+	if err != nil {
+		return err
+	}
+
+	// 2: If s1 > q3, Return False
+	if pi.s1.Cmp(q3) == 1 {
+		return fmt.Errorf("s1 > q3")
+	}
+	// steps 3 and 4 are needed only if wc: we check for X=g^x
+
+	// step 5
+	zHatTick, err := pi.zHatTickConstruct(pp)
+	if err != nil {
+		return fmt.Errorf("z hat tick construction error: %s", err)
+	}
+	// step 6
+	vHat, err := pi.vHatConstruct(pp)
+	if err != nil {
+		return fmt.Errorf("v hat construction error: %s", err)
+	}
+	// step 7
+	wHat, err := pi.wHatConstruct(pp)
+	if err != nil {
+		return fmt.Errorf("w hat construction error: %s", err)
+	}
+
+	var uHat *curves.EcPoint
+	if wc {
+		// steps 3, 4
+		uHat, err = pi.uHatConstruct(pp)
+		if err != nil {
+			return fmt.Errorf("u hat construction error: %s", err)
+		}
+	}
+
+	curveParams := pp.curve.Params()
+	var challenge []byte
+	if wc {
+		// g || q || Pk || N ̃ || h1 || h2 || X || c1 || c2 || uHat || z || zHatTick || t || vHat || wHat
+		challenge, err = core.FiatShamir(curveParams.Gx, curveParams.Gy, curveParams.N, pp.pk.N, pp.dealerParams.N, pp.dealerParams.H1, pp.dealerParams.H2, pp.X.X, pp.X.Y, pp.c1, pp.c2, uHat.X, uHat.Y, pi.z, zHatTick, pi.t, vHat, wHat)
+		if err != nil {
+			return err
+		}
+	} else {
+		// g || q || Pk || N ̃ || h1 || h2 || c1 || c2 || z || zHatTick || t || vHat || wHat
+		challenge, err = core.FiatShamir(curveParams.Gx, curveParams.Gy, curveParams.N, pp.pk.N, pp.dealerParams.N, pp.dealerParams.H1, pp.dealerParams.H2, pp.c1, pp.c2, pi.z, zHatTick, pi.t, vHat, wHat)
+		if err != nil {
+			return err
+		}
+	}
+
+	eHat := new(big.Int).SetBytes(challenge)
+
+	if !core.ConstantTimeEq(pi.e, eHat) {
+		return fmt.Errorf("e != eHat")
+	}
+
+	return nil
+}
+
+func (pi Range2Proof) uHatConstruct(pp *verifyProof2Params) (*curves.EcPoint, error) {
+	// 3. Compute s1' = s1 mod q
+	s1Tick := new(big.Int).Mod(pi.s1, pp.curve.Params().N)
+
+	// 4: \hat{u} = g^{s^\prime_1} . X^{-e} in G
+
+	gS1Tick, err := curves.NewScalarBaseMult(pp.curve, s1Tick)
+	if err != nil {
+		return nil, err
+	}
+
+	negE := new(big.Int).Neg(pi.e)
+
+	XnegE, err := pp.X.ScalarMult(negE)
+	if err != nil {
+		return nil, err
+	}
+
+	uHat, err := gS1Tick.Add(XnegE)
+	if err != nil {
+		return nil, err
+	}
+	return uHat, err
+}
+
+func (pi Range2Proof) zHatTickConstruct(pp *verifyProof2Params) (*big.Int, error) {
+	// 5: \hat{z} = (h_1)^s_1 . (h_2)^{s_2}z^{-e} mod \tilde{N}
+
+	// h_1^s_1 . h_2^s_2 mod \tilde{N}
+	pedersenHS, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, pi.s1, pi.s2, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	zInv, err := core.Inv(pi.z, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	zInvToE := new(big.Int).Exp(zInv, pi.e, pp.dealerParams.N)
+
+	zHat, err := core.Mul(pedersenHS, zInvToE, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	return zHat, err
+}
+
+func (pi Range2Proof) vHatConstruct(pp *verifyProof2Params) (*big.Int, error) {
+	// 6: \hat{v} = (c_1)^s_1 . s^N . (N+1)^t_1 . c^-e_2 mod N^2
+
+	// s^N . (N+1)^t_1
+	pedersenInc, err := inc(pi.t1, pi.s, pp.pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	c2Inv, err := core.Inv(pp.c2, pp.pk.N2)
+	if err != nil {
+		return nil, err
+	}
+
+	// c_1^s_1 . c^-e_2
+	pedersenCSCE, err := pedersen(pp.c1, c2Inv, pi.s1, pi.e, pp.pk.N2)
+	if err != nil {
+		return nil, err
+	}
+
+	vHat, err := core.Mul(pedersenInc, pedersenCSCE, pp.pk.N2)
+	if err != nil {
+		return nil, err
+	}
+	return vHat, nil
+}
+
+func (pi Range2Proof) wHatConstruct(pp *verifyProof2Params) (*big.Int, error) {
+	// 7: \hat{w} = (h_1)^t_1 . (h_2)^t_2 . t^-e mod \tilde{N}
+
+	// h_1^t_1 . h_2^t_2 mod \tilde{N}
+	pedersenHT, err := pedersen(pp.dealerParams.H1, pp.dealerParams.H2, pi.t1, pi.t2, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	tInv, err := core.Inv(pi.t, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	tInvToE := new(big.Int).Exp(tInv, pi.e, pp.dealerParams.N)
+
+	wHat, err := core.Mul(pedersenHT, tInvToE, pp.dealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	return wHat, nil
+}
+
+// Fetches random values for use in range proof
+// [spec] fig 12: MtaProveRange2
+func rand2(N, Ntilde, q *big.Int) (*randProof2Params, error) {
+	// Rings in which we'll operate
+	q3, err := core.Exp(q, big.NewInt(3), nil) // q^3
+	if err != nil {
+		return nil, err
+	}
+	q3Ntilde, err := core.Mul(q3, Ntilde, nil) // q^3(N~)
+	if err != nil {
+		return nil, err
+	}
+	qNtilde, err := core.Mul(q, Ntilde, nil) // q(N~)
+	if err != nil {
+		return nil, err
+	}
+
+	alpha, err := core.Rand(q3)
+	if err != nil {
+		return nil, err
+	}
+	rho, err := core.Rand(qNtilde)
+	if err != nil {
+		return nil, err
+	}
+	rhoTick, err := core.Rand(q3Ntilde)
+	if err != nil {
+		return nil, err
+	}
+	sigma, err := core.Rand(qNtilde)
+	if err != nil {
+		return nil, err
+	}
+	beta, err := core.Rand(N)
+	if err != nil {
+		return nil, err
+	}
+	gamma, err := core.Rand(N)
+	if err != nil {
+		return nil, err
+	}
+	tau, err := core.Rand(qNtilde)
+	if err != nil {
+		return nil, err
+	}
+
+	return &randProof2Params{
+		randProof1Params: randProof1Params{
+			alpha,
+			beta,
+			gamma,
+			rho,
+		},
+		rhoTick: rhoTick,
+		sigma:   sigma,
+		tau:     tau,
+	}, nil
+}
diff --git a/pkg/tecdsa/gg20/proof/mta_test.go b/pkg/tecdsa/gg20/proof/mta_test.go
new file mode 100644
index 00000000..f95d8211
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/mta_test.go
@@ -0,0 +1,1217 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package proof
+
+import (
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	paillier "github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/btcsuite/btcd/btcec"
+
+	tt "github.com/coinbase/kryptology/internal"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestRange1Proof(t *testing.T) {
+	curve := btcec.S256()
+	params := []*Proof1Params{{
+		Curve: curve.CurveParams,
+		Pk:    paillier.NewPubkey(tt.B10("141823146723804727729633738357765828294831142954010692457328076293957505983859895806895734447482792591026897171204062485196286886661302420276834336655587982881158751341502328470707400685538658612981911773025635736943733001923468023720033301313420189810298555472599689752973326558212722047094791724129635174941")),
+		DealerParams: &dealer.ProofParams{
+			N:  tt.B10("135817986946410153263607521492868157288929876347703239389804036854326452848342067707805833332721355089496671444901101084429868705550525577068432132709786157994652561102559125256427177197007418406633665154772412807319781659630513167839812152507439439445572264448924538846645935065905728327076331348468251587961"),
+			H1: tt.B10("130372793360787914947629694846841279927281520987029701609177523587189885120190605946568222485341643012763305061268138793179515860485547361500345083617939280336315872961605437911597699438598556875524679018909165548046362772751058504008161659270331468227764192850055032058007664070200355866555886402826731196521"),
+			H2: tt.B10("44244046835929503435200723089247234648450309906417041731862368762294548874401406999952605461193318451278897748111402857920811242015075045913904246368542432908791195758912278843108225743582704689703680577207804641185952235173475863508072754204128218500376538767731592009803034641269409627751217232043111126391"),
+		},
+		A: tt.B10("69419834349415853894890573917063122307277917076225427448771019868576648260600"),
+		C: tt.B10("18847568264006333380939287985787671948454143538446174819166825848732846525911186304740436914881274338959557435225686813604290193949014624061947647271411133485846391130016894483860450081602884139421405154057523839321239800217322755403591626776618194353121431489530790253985977500301181480604877832198998069341489839600864774760266800069826119409804215007615236664725258674727917968021583387375774570296029692159700158983350777557570591870565786777775317840482767648752436614429480990665662186556252959370410165035210824558411113808153951646950567756832761054357235695768210609602326533352980917662838030713969147577580"),
+		R: tt.B10("51886819834371251006015218788911494248706876016519888346806242851820213680996324974371873475760855517466937827668415006977450699788621663903939308570896707699568767367925269253643717512759597981479828523349172771324686694516983594834820044069638828375581061206377589070672524406557592378617469206619362344334"),
+	},
+		{
+			Curve: curve.CurveParams,
+			Pk:    paillier.NewPubkey(tt.B10("9463658995206843770851525158043255816500680189464439363095520560386614479556714668895588462872126103893747723284862135073561694263269764946949629217223601")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("10273826729942063692697010060060594189312421215159102246808412466917904003223823687218001436152302280389572289298911434937289415755177478451846062468556417"),
+				H1: tt.B10("8167935838771182008182545199994552899088966708202004570505499867215233183293912199558208134810141196561068449078607686456211448067551558116808974484973823"),
+				H2: tt.B10("1970661048433046426977416407106770949147216315571621971821051491584141078795051536868700972508332670892828402361693033635357376943122091647496860229630757"),
+			},
+			A: tt.B10("115526880823597585707678515351506817772182122025200976618245337689911430629189"),
+			C: tt.B10("24863961566325565999591866542173666702673420408697429354806387592500301145340463984188913772103540073904498350983609595088568585339776683627724027187053064389377343283641347948144757981770327556063857980147985583807326240539344503674432544585705881605891637105814844708369139287177428173455597756160905566908"),
+			R: tt.B10("5429643852343163390381887406843848421434905359379877890761970908590486754109980221258199728602735196971674594950794639675145303739445896672634255126793715"),
+		},
+		{
+			Curve: curve.CurveParams,
+			Pk:    paillier.NewPubkey(tt.B10("26509846098969606030666644039648735072473371434396262226628957752776958016920176604138513076285080490756189037154836350358953193044108325638765720332205170853305196270848703082212703922373221666660374795896208650056354982913710298628785967974006931457072686585546613336263077109720447885211641481085196018808984886607748129379016797794987745814597073536482747374479333608767826317573570455719831930309513750297610046842033491846725866000900668533198008806351432839430072881565290122414283921152984764756250407839754767248421661857280750005054466634329774370484024085212040716987194046113511394116210477123260601300881")),
+			DealerParams: &dealer.ProofParams{
+				H1: tt.B10("14992883567326790009834034452774380881734723148422937597913759615616527894329716582094216131278069891754415684125978444772511456388384539478359237139420627595253084679427853969706385560348203106008084518063368655525999918846958064735464480540227040261127629154933497666914570262795996253259552162123968669420229672303143236908906153814910725786469012911748229438005634598038592141662328047446496393313102162064295444876003000587651597062721350331609362965763517981159778802267296421256980684242791310186114847130909958129781491826248268454674630252197299528151229014292276126945753681298480222125140847225297966918532"),
+				H2: tt.B10("14451347439159866238139129172581939135639377298556733244044449026294991997647446913414655524593230026671131401671272904249129277301803851355795175741045874967757624456900503361379054274654925224532323369122476258816285661783355994483540913053432288260800426312310730874341856134640161338601508545687545669401903291225410983268791172255873788692947107839385412427853422631156622058264538604067715438447935043009066210075839028695556578873902786008338985136644998643392979637373322946219799880176559775088371463960865119158841025722295583121063385860131824665408457687782230865745847949240766808890277225700715298320028"),
+				N:  tt.B10("26863522432473035730119731755593267196935542494137223684869105097384908488378699999135799398068117050398327203794264171049568246937359730719602384478980465448464098415665075997352344166791916282650859961543602404343544893507812734906139108639107349334720437496231800511507757697269442530789089480688292170466415570422030582299025027913665235886474942651615736182869373910904226618891682710354700061830476496646926791079185776204186251841370042114552535830831492471396014245114861782301822918098243256413965536851647280940178471906923067287511334834085103114355667173309503520818859537916417500022813080379172002131161"),
+			},
+			A: tt.B10("102024524059200259914515251031129904340184560661551068326674667230176806449506"),
+			C: tt.B10("606905289067344415850202384963927807134074353753762997257139430299812182620789663669753085660750100022719025049769721871852917326438594417966014441377841114473716278535355511853112878357850260859242353337424543205348122482112039398030783631927973189296947834031801759665061597419376410365790909188233494366639644168598330927045472353639926008764761376362372272652870903476621415523086627609902565278681254439749699499964324994947822843344753874646817673194134131040626119618863214379753666656464721612766553737646301416269176254237867925949500933369778301789961143888981155504260520734175430789915153903521880643114178314960870183923188006046608215171306656277401312025824694786889128622248770904521403820097381630141895711830288326748574592831238442924220948599138494415447657546918345399556268360296693801290614871481728134864429369982420396573830325179024969495621348263376326342276471894987989086008604688478904941945515982645748283506996193414153700843150014598669607700805670795651750859589109718155558799860867664043927196730496991416549697032467861774965678794181745578038357826073865504972139863122015040769720633544827076677588868998005770420542433350693915538883714213593428075244047359976923502176166652802828244500743984"),
+			R: tt.B10("4316163330616341786022288762832695381195100634212156354702126474815234684335206120216209492000672992524572068497975715249928730630414020780112556541596959799124749690188860501409819228282255248826297918129804256958220248011547662972248478384023051376285459600289836843197969576018915415705606888468581697804440068058156017301462882709815898624972811614438016468969724947563418144645148725119578732409829110402274538268887921145538190094844077282783611364448423084988722318385383581689504139158759909146950046109199997715092849454619804168861913291000920258829447007487469712233737637494770509169807492681846224392197"),
+		},
+	}
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+		tt.AssertNoError(t, pi.Verify(pp))
+	}
+}
+
+func TestRange1ProofValuesTampered(t *testing.T) {
+	curve := btcec.S256()
+	params := []*Proof1Params{{
+		Curve: curve.CurveParams,
+		Pk:    paillier.NewPubkey(tt.B10("141823146723804727729633738357765828294831142954010692457328076293957505983859895806895734447482792591026897171204062485196286886661302420276834336655587982881158751341502328470707400685538658612981911773025635736943733001923468023720033301313420189810298555472599689752973326558212722047094791724129635174941")),
+		DealerParams: &dealer.ProofParams{
+			N:  tt.B10("135817986946410153263607521492868157288929876347703239389804036854326452848342067707805833332721355089496671444901101084429868705550525577068432132709786157994652561102559125256427177197007418406633665154772412807319781659630513167839812152507439439445572264448924538846645935065905728327076331348468251587961"),
+			H1: tt.B10("130372793360787914947629694846841279927281520987029701609177523587189885120190605946568222485341643012763305061268138793179515860485547361500345083617939280336315872961605437911597699438598556875524679018909165548046362772751058504008161659270331468227764192850055032058007664070200355866555886402826731196521"),
+			H2: tt.B10("44244046835929503435200723089247234648450309906417041731862368762294548874401406999952605461193318451278897748111402857920811242015075045913904246368542432908791195758912278843108225743582704689703680577207804641185952235173475863508072754204128218500376538767731592009803034641269409627751217232043111126391"),
+		},
+		A: tt.B10("69419834349415853894890573917063122307277917076225427448771019868576648260600"),
+		C: tt.B10("18847568264006333380939287985787671948454143538446174819166825848732846525911186304740436914881274338959557435225686813604290193949014624061947647271411133485846391130016894483860450081602884139421405154057523839321239800217322755403591626776618194353121431489530790253985977500301181480604877832198998069341489839600864774760266800069826119409804215007615236664725258674727917968021583387375774570296029692159700158983350777557570591870565786777775317840482767648752436614429480990665662186556252959370410165035210824558411113808153951646950567756832761054357235695768210609602326533352980917662838030713969147577580"),
+		R: tt.B10("51886819834371251006015218788911494248706876016519888346806242851820213680996324974371873475760855517466937827668415006977450699788621663903939308570896707699568767367925269253643717512759597981479828523349172771324686694516983594834820044069638828375581061206377589070672524406557592378617469206619362344334"),
+	},
+	}
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+
+		pi.s.Add(pi.s, crypto.One)
+		err = pi.Verify(pp)
+		if err == nil {
+			t.Errorf("Range1Proof verification passed but should've failed")
+		}
+	}
+}
+
+func TestRange1ProofRandValue(t *testing.T) {
+	curve := btcec.S256()
+	q := tt.B10("115792089237316195423570985008687907852837564279074904382605163141518161494337")
+	pk, _ := crypto.Rand(q)
+	nTilde, _ := crypto.Rand(q)
+	h1, _ := crypto.Rand(q)
+	h2, _ := crypto.Rand(q)
+	a, _ := crypto.Rand(q)
+	c, _ := crypto.Rand(q)
+	r, _ := crypto.Rand(pk)
+	params := []*Proof1Params{{
+		Curve: curve.CurveParams,
+		Pk:    paillier.NewPubkey(pk),
+		DealerParams: &dealer.ProofParams{
+			N:  nTilde,
+			H1: h1,
+			H2: h2,
+		},
+		A: a,
+		C: c,
+		R: r,
+	},
+	}
+
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+
+		err = pi.Verify(pp)
+		if err == nil {
+			t.Errorf("Range1Proof verification passed but should've failed")
+		}
+	}
+}
+
+func TestRange1ProofInvalidInputs(t *testing.T) {
+	q := tt.B10("115792089237316195423570985008687907852837564279074904382605163141518161494337")
+	pk, _ := crypto.Rand(q)
+	nTilde, _ := crypto.Rand(q)
+	h1, _ := crypto.Rand(q)
+	h2, _ := crypto.Rand(q)
+	a, _ := crypto.Rand(q)
+	c, _ := crypto.Rand(q)
+	r := new(big.Int).Add(pk, crypto.One)
+	curve := btcec.S256()
+
+	pp := Proof1Params{
+		Curve: curve.CurveParams,
+		Pk:    paillier.NewPubkey(pk),
+		DealerParams: &dealer.ProofParams{
+			N:  nTilde,
+			H1: h1,
+			H2: h2,
+		},
+		A: a,
+		C: c,
+		R: r,
+	}
+
+	_, err := pp.Prove()
+	if err == nil {
+		t.Errorf("Expected proof to fail but succeeded")
+	}
+	pp.R, _ = crypto.Rand(pk)
+	pp.A.Add(q, crypto.One)
+	_, err = pp.Prove()
+	if err == nil {
+		t.Errorf("Expected proof to fail but succeeded")
+	}
+}
+
+func TestRange2Proof(t *testing.T) {
+	curve := btcec.S256()
+	params := []*proof2Params{
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("10101470169236701307989356288549331324760297732311017474717291556920575008390399360557666841555549459285530036654740758928369671798624054612167588575932381")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("9219281919791721120536299917894003720538003954278079222431314286049931351876006427491931284170862581081845453829013148809004259723778319764538149793497641"),
+				H1: tt.B10("6644196892054206924378867076159386233640761201152351529435080914361042562172198110073851611109267445161412502166236307500486777706747140647390726550075708"),
+				H2: tt.B10("5688591485822699373931740080400822403356782026899259938734839090439486234586917273468710951700668234996427145700773040250733669224784692962885908122139650"),
+			},
+			x:  tt.B10("69816829924976195108406719236630054316602642151744146726591584302591798356879"),
+			y:  tt.B10("6091419963879175825016282184751419224433102581039722555067324512579982829027772376266606470474464178886647266708567804526639019529121691232740502772158395"),
+			r:  tt.B10("2057508414415506856632950455679739628101265359451898937499968640834406996284985079891571080368801894092310083101905560673405285298960212293813512484533243"),
+			c1: tt.B10("77354088856869596047326860655816379899282736592351758252376955959642660833724912873058095618492448830932484717132524379596300316296173378157021077360406566328813261560359655672580394103296273833156212883702975483977364312384187692944453695070505171585703326682734887227351393788925364680581746031838277285466"),
+			c2: tt.B10("62625690358179126259470167549477031595729452083445529618665252599670128159810380715262451914271340539338064221878983094991977027339744473746794751463196253529296039288796638711807366538447194372313357153970305414515194509313903498505159827101743516759038500222068024267206874190242842752012118257578748158935"),
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("12210032433973194713101879401736114046289525026621157295286479630950151870825704771591565830307623853624194868105373425480240786504903455545980711905540733")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("9980343328531824486415926064525896643228568487098332026186422359474742346064230978030493474421691362007851816031135057302846980207789705913115253186949929"),
+				H1: tt.B10("2469673179884483986143806855579592525432144934828258881402734291568845128541228962341595624784892382862940048418684325214631955580804153588960938651100023"),
+				H2: tt.B10("5685075883067849042500523803668918481205783573655253866720026214840936701271228054652129542672137002652385298991713452536323897385839029159489038543618111"),
+			},
+			x:  tt.B10("105977005668720423578092754536102512363464080739402364055701968817880388173564"),
+			y:  tt.B10("10580891309922780663455235282515343025623240093871582757351334419612913975217510679538051246788872785510052073278327271011365532533554403624959069180581073"),
+			r:  tt.B10("9136335827666726813247236926436786672989404553255067682415003421023171372953384600969639069948806408705646121348918941058359753103225314459714441851896890"),
+			c1: tt.B10("3137646227323871093340569416710991921739110531106602992459184319984538323233705778064679266338098210649513203253885987958171516776148995543543874239450894815730651947941578431695081314470146489521545931896062912145090884587761137595453392468669129591664836000059246133095103069755216958353868086703009409007"),
+			c2: tt.B10("117162960239617992288211111570585143841439876387814723449486127427269624507583529452070542802236573762087221934918534435924767110744800267605779648487146533084050398880360218943350553051905824704311237243263432485578052690072578609844333462008562932905463898722374546675589796756376946519865698604982035075860"),
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("24006913232556170743687256926411383572685914178725475584546729266081072560742664682316751513922351492731916830819991652570232108587525710585787212295495042393457532642958235116228331214937916656207743912133379867824263625067181157967173699059101735486321531980561382043427722981553748630204989026528801081173268163768220316884987314169182764807097584743805541115263331414941361031802812537543888741551242018695090519994120080616317331369873231788340089609365466582767729028404412551414411783991423226467702149120924355765283967364974919403961589444957748041302084944730207635344441075632726716283335883554650872391817")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("23860321693243408915285634667126319607029258830310722858616298293090774243853938528516172318323586950359261307782164021512152687506385993022681970597450674643369827412129155830719269633871079399119546887419782449142407872196757762829680911694406871079920722666739220339627194776816161447024512993082597495586758354580607447584695500284641632976305705127500848686700697864168339353722767241861901618702529822855652770760839810911469800714397927519979196161681565110864846050753366224989966372990306678566170613749484781791197178496155518267861948015142128777050453948357016204687631478842990872969865562749504308289321"),
+				H1: tt.B10("18739963062868236055523374223403987299519125465905789112585717097241915094501689476952575752645765949616652320751728118948443965846550107873550298482277861881212384752345824547773084194224498010327383344716012292771833811785400473027252158122724183047497102273824709944530327171103095292901313850904394313756204621107931116195962519595510074637264528286866179535920411663823822050355570037597313507899569727799048016402592869527872094986310414810244530418193835726408360459997193495554207655504488141530377908260277369300355796046620382270308875262484043788069568055471394564032265334439460399732013818519087125209291"),
+				H2: tt.B10("12163400087917683646137489145747822585252103269291951065968363100667845814487256597741255884887916357152485768705079255596283306041038105293053731433242061286760695046099554060517156715815248955428884920797601991295472823198873625504858547757752101542129213721934397771916784953246371682758165236787047386274743475196173219919703931897838802897118179026707936623911659023941810590819891136115782747594034401712796912010250950460753996445790779228196800904305305557513340729372141761372316869712752692253017128388161025717361881141865639873860953634747335447043871369762137568601156584516703599828999624681383424904268"),
+			},
+			x:  tt.B10("1183169060828468438002965363358707918795988635564203608058950247926495168444"),
+			y:  tt.B10("7293911945949010390458324767285044973990376766933756148434784925293433850020940532757951881022757618321061744633083721332134550426910076435396510033963585425552696429667115345073232612562744840167186248507049396229733012483438857042045789124596166171036562118778997431227842385129042847771769687182071724319010909289821645417665264498977305772962006468150887518642140736818354425900118292439282479696823894874913967622594763555647835253420302749102279713541603132333565142505991371129067951473893338055811512136134827753632413214786435767384138288631910921011600701133728447389217785317320101805018751163182406468255"),
+			r:  tt.B10("7277115633059593699842594283205544005606789287205763437225637228748066593006893949270073174884964276552716253205074502736294210158481341005306224069327225246011858354719224071629478444010965094418317631572158089119615004017614950610745842639284941451030180613556468553229283917977108351833535295719351149428921934299360505371202226418621518596417048730228765246349189673850261365511958826980752021218666379299128790765982842644649907192714080776727846821208976399163844571810485997271552038669644288560524148724337682439294331287480204495332352762669535553814001552810108365326941186198150890462960373306336864507735"),
+			c1: tt.B10("464866952852913092347202302187506800006630275997158690576467369160262286832092217254714435237418906716576120732215276581391583436712457855565949230630753226132768820239354111308450355834170036262275041431436393986225764154760441302733054701716360093825803706112674820577220074485830350261966524251280067408732862805269937036694720529361210420785117185393443358654009779898418312191692062264618218091331404395199552849986837424325916403944068685457732760883137533335923883928334180126411574348555187291633923796221856030393195707239688430342076538433037977986334930568865631426380247571396851308386283571803949871075776379134665440737979756269504438503412503367048072728560799164032076778640238976351032285854684893201455404015670413766043037872528549530047318211423151300083425338011538655419126913270418373290547764482868099031758569002021258625813564434869316786643458814202720512927739028875176581438529156378620559783948696214417098710071638985731360204131707639660620459949603823171257582498738788277970562341882508213506138743367776192561855262827993558489205971069614003406633599273081878483679850823958594648825170338189768315766110860686667501703858115667359037267469518222285214580865767971590133972212867800115070126953368"),
+			c2: tt.B10("87054746811998808852750056109819023786671110957815179115900051264949784342635809119831910125419284770492485609549082903423179703744463561163569834515491136663352518336126032974632263674792581836367278021499562100451772533596207842635483356680337833976709510891868134899756376855360834845609165180238776036642063520760473124267720102852673018196357588477924410997706540293465921355167014551128362709936645961409083040863315940847250131054475475902056256228640208391495301996700461783302757908539516329083394794959589562320450655849398458971004648845697279534368242916131585772073908370105312752870580536509251252543234549517636502223982430171411338358101387742547185790223841575969928322674680552415533109012782424923657732851492401156454799145861648550278513023956759591228830652765771616189289750466703399263657155477884193649025885818223829232243010534182019169454495579133314331205842873596879928283271465381113279539118677413311470168563120989509112283274008507717309272957541695858123739357199894271068524097884917020267347009001467460730436391704379761867033238124489154030180080594750319595350447722626278014518750212038735434477954916503424607892883739579417439328783709705164147296137752523228552974616459937563449481724082"),
+		},
+	}
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+
+		vp := &verifyProof2Params{
+			curve:        pp.curve,
+			dealerParams: pp.dealerParams,
+			pk:           pp.pk,
+			c1:           pp.c1,
+			c2:           pp.c2,
+		}
+
+		err = pi.Verify(vp)
+		tt.AssertNoError(t, err)
+	}
+}
+
+func TestRange2ProofValuesTampered(t *testing.T) {
+	curve := btcec.S256()
+	params := []*proof2Params{
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("10101470169236701307989356288549331324760297732311017474717291556920575008390399360557666841555549459285530036654740758928369671798624054612167588575932381")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("9219281919791721120536299917894003720538003954278079222431314286049931351876006427491931284170862581081845453829013148809004259723778319764538149793497641"),
+				H1: tt.B10("6644196892054206924378867076159386233640761201152351529435080914361042562172198110073851611109267445161412502166236307500486777706747140647390726550075708"),
+				H2: tt.B10("5688591485822699373931740080400822403356782026899259938734839090439486234586917273468710951700668234996427145700773040250733669224784692962885908122139650"),
+			},
+			x:  tt.B10("69816829924976195108406719236630054316602642151744146726591584302591798356879"),
+			y:  tt.B10("6091419963879175825016282184751419224433102581039722555067324512579982829027772376266606470474464178886647266708567804526639019529121691232740502772158395"),
+			r:  tt.B10("2057508414415506856632950455679739628101265359451898937499968640834406996284985079891571080368801894092310083101905560673405285298960212293813512484533243"),
+			c1: tt.B10("77354088856869596047326860655816379899282736592351758252376955959642660833724912873058095618492448830932484717132524379596300316296173378157021077360406566328813261560359655672580394103296273833156212883702975483977364312384187692944453695070505171585703326682734887227351393788925364680581746031838277285466"),
+			c2: tt.B10("62625690358179126259470167549477031595729452083445529618665252599670128159810380715262451914271340539338064221878983094991977027339744473746794751463196253529296039288796638711807366538447194372313357153970305414515194509313903498505159827101743516759038500222068024267206874190242842752012118257578748158935"),
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("12210032433973194713101879401736114046289525026621157295286479630950151870825704771591565830307623853624194868105373425480240786504903455545980711905540733")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("9980343328531824486415926064525896643228568487098332026186422359474742346064230978030493474421691362007851816031135057302846980207789705913115253186949929"),
+				H1: tt.B10("2469673179884483986143806855579592525432144934828258881402734291568845128541228962341595624784892382862940048418684325214631955580804153588960938651100023"),
+				H2: tt.B10("5685075883067849042500523803668918481205783573655253866720026214840936701271228054652129542672137002652385298991713452536323897385839029159489038543618111"),
+			},
+			x:  tt.B10("105977005668720423578092754536102512363464080739402364055701968817880388173564"),
+			y:  tt.B10("10580891309922780663455235282515343025623240093871582757351334419612913975217510679538051246788872785510052073278327271011365532533554403624959069180581073"),
+			r:  tt.B10("9136335827666726813247236926436786672989404553255067682415003421023171372953384600969639069948806408705646121348918941058359753103225314459714441851896890"),
+			c1: tt.B10("3137646227323871093340569416710991921739110531106602992459184319984538323233705778064679266338098210649513203253885987958171516776148995543543874239450894815730651947941578431695081314470146489521545931896062912145090884587761137595453392468669129591664836000059246133095103069755216958353868086703009409007"),
+			c2: tt.B10("117162960239617992288211111570585143841439876387814723449486127427269624507583529452070542802236573762087221934918534435924767110744800267605779648487146533084050398880360218943350553051905824704311237243263432485578052690072578609844333462008562932905463898722374546675589796756376946519865698604982035075860"),
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("24006913232556170743687256926411383572685914178725475584546729266081072560742664682316751513922351492731916830819991652570232108587525710585787212295495042393457532642958235116228331214937916656207743912133379867824263625067181157967173699059101735486321531980561382043427722981553748630204989026528801081173268163768220316884987314169182764807097584743805541115263331414941361031802812537543888741551242018695090519994120080616317331369873231788340089609365466582767729028404412551414411783991423226467702149120924355765283967364974919403961589444957748041302084944730207635344441075632726716283335883554650872391817")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("23860321693243408915285634667126319607029258830310722858616298293090774243853938528516172318323586950359261307782164021512152687506385993022681970597450674643369827412129155830719269633871079399119546887419782449142407872196757762829680911694406871079920722666739220339627194776816161447024512993082597495586758354580607447584695500284641632976305705127500848686700697864168339353722767241861901618702529822855652770760839810911469800714397927519979196161681565110864846050753366224989966372990306678566170613749484781791197178496155518267861948015142128777050453948357016204687631478842990872969865562749504308289321"),
+				H1: tt.B10("18739963062868236055523374223403987299519125465905789112585717097241915094501689476952575752645765949616652320751728118948443965846550107873550298482277861881212384752345824547773084194224498010327383344716012292771833811785400473027252158122724183047497102273824709944530327171103095292901313850904394313756204621107931116195962519595510074637264528286866179535920411663823822050355570037597313507899569727799048016402592869527872094986310414810244530418193835726408360459997193495554207655504488141530377908260277369300355796046620382270308875262484043788069568055471394564032265334439460399732013818519087125209291"),
+				H2: tt.B10("12163400087917683646137489145747822585252103269291951065968363100667845814487256597741255884887916357152485768705079255596283306041038105293053731433242061286760695046099554060517156715815248955428884920797601991295472823198873625504858547757752101542129213721934397771916784953246371682758165236787047386274743475196173219919703931897838802897118179026707936623911659023941810590819891136115782747594034401712796912010250950460753996445790779228196800904305305557513340729372141761372316869712752692253017128388161025717361881141865639873860953634747335447043871369762137568601156584516703599828999624681383424904268"),
+			},
+			x:  tt.B10("1183169060828468438002965363358707918795988635564203608058950247926495168444"),
+			y:  tt.B10("7293911945949010390458324767285044973990376766933756148434784925293433850020940532757951881022757618321061744633083721332134550426910076435396510033963585425552696429667115345073232612562744840167186248507049396229733012483438857042045789124596166171036562118778997431227842385129042847771769687182071724319010909289821645417665264498977305772962006468150887518642140736818354425900118292439282479696823894874913967622594763555647835253420302749102279713541603132333565142505991371129067951473893338055811512136134827753632413214786435767384138288631910921011600701133728447389217785317320101805018751163182406468255"),
+			r:  tt.B10("7277115633059593699842594283205544005606789287205763437225637228748066593006893949270073174884964276552716253205074502736294210158481341005306224069327225246011858354719224071629478444010965094418317631572158089119615004017614950610745842639284941451030180613556468553229283917977108351833535295719351149428921934299360505371202226418621518596417048730228765246349189673850261365511958826980752021218666379299128790765982842644649907192714080776727846821208976399163844571810485997271552038669644288560524148724337682439294331287480204495332352762669535553814001552810108365326941186198150890462960373306336864507735"),
+			c1: tt.B10("464866952852913092347202302187506800006630275997158690576467369160262286832092217254714435237418906716576120732215276581391583436712457855565949230630753226132768820239354111308450355834170036262275041431436393986225764154760441302733054701716360093825803706112674820577220074485830350261966524251280067408732862805269937036694720529361210420785117185393443358654009779898418312191692062264618218091331404395199552849986837424325916403944068685457732760883137533335923883928334180126411574348555187291633923796221856030393195707239688430342076538433037977986334930568865631426380247571396851308386283571803949871075776379134665440737979756269504438503412503367048072728560799164032076778640238976351032285854684893201455404015670413766043037872528549530047318211423151300083425338011538655419126913270418373290547764482868099031758569002021258625813564434869316786643458814202720512927739028875176581438529156378620559783948696214417098710071638985731360204131707639660620459949603823171257582498738788277970562341882508213506138743367776192561855262827993558489205971069614003406633599273081878483679850823958594648825170338189768315766110860686667501703858115667359037267469518222285214580865767971590133972212867800115070126953368"),
+			c2: tt.B10("87054746811998808852750056109819023786671110957815179115900051264949784342635809119831910125419284770492485609549082903423179703744463561163569834515491136663352518336126032974632263674792581836367278021499562100451772533596207842635483356680337833976709510891868134899756376855360834845609165180238776036642063520760473124267720102852673018196357588477924410997706540293465921355167014551128362709936645961409083040863315940847250131054475475902056256228640208391495301996700461783302757908539516329083394794959589562320450655849398458971004648845697279534368242916131585772073908370105312752870580536509251252543234549517636502223982430171411338358101387742547185790223841575969928322674680552415533109012782424923657732851492401156454799145861648550278513023956759591228830652765771616189289750466703399263657155477884193649025885818223829232243010534182019169454495579133314331205842873596879928283271465381113279539118677413311470168563120989509112283274008507717309272957541695858123739357199894271068524097884917020267347009001467460730436391704379761867033238124489154030180080594750319595350447722626278014518750212038735434477954916503424607892883739579417439328783709705164147296137752523228552974616459937563449481724082"),
+		},
+	}
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+
+		vp := &verifyProof2Params{
+			curve:        pp.curve,
+			dealerParams: pp.dealerParams,
+			pk:           pp.pk,
+			c1:           pp.c1,
+			c2:           pp.c2,
+		}
+
+		pi.s.Add(pi.s, crypto.One)
+		err = pi.Verify(vp)
+		if err == nil {
+			t.Errorf("Range2Proof verification passed but should've failed")
+		}
+
+		pi.s.Sub(pi.s, crypto.One)
+		pi.s1.Add(pi.s1, crypto.One)
+		err = pi.Verify(vp)
+		if err == nil {
+			t.Errorf("Range2Proof verification passed but should've failed")
+		}
+		pi.s1.Sub(pi.s1, crypto.One)
+
+		pi.t.Add(pi.t, crypto.One)
+		err = pi.Verify(vp)
+		if err == nil {
+			t.Errorf("Range2Proof verification passed but should've failed")
+		}
+		pi.t.Sub(pi.t, crypto.One)
+
+		pp.c2.Add(pp.c2, crypto.One)
+		err = pi.Verify(vp)
+		if err == nil {
+			t.Errorf("Range2Proof verification passed but should've failed")
+		}
+
+		pp.c2.Sub(pp.c2, crypto.One)
+	}
+}
+
+func TestRange2ProofRandValue(t *testing.T) {
+	q := tt.B10("115792089237316195423570985008687907852837564279074904382605163141518161494337")
+	pk, _ := crypto.Rand(q)
+	nTilde, _ := crypto.Rand(q)
+	h1, _ := crypto.Rand(q)
+	h2, _ := crypto.Rand(q)
+	y, _ := crypto.Rand(q)
+	x, _ := crypto.Rand(q)
+	r, _ := crypto.Rand(pk)
+	nn := new(big.Int).Mul(pk, pk)
+	c1, _ := crypto.Rand(nn)
+	c2, _ := crypto.Rand(nn)
+	curve := btcec.S256()
+	params := []*proof2Params{{
+		curve: curve,
+		pk:    paillier.NewPubkey(pk),
+		dealerParams: &dealer.ProofParams{
+			N:  nTilde,
+			H1: h1,
+			H2: h2,
+		},
+		y:  y,
+		x:  x,
+		r:  r,
+		c1: c1,
+		c2: c2,
+	},
+	}
+
+	for _, pp := range params {
+		pi, err := pp.Prove()
+		tt.AssertNoError(t, err)
+
+		vp := &verifyProof2Params{
+			curve:        pp.curve,
+			dealerParams: pp.dealerParams,
+			pk:           pp.pk,
+			c1:           pp.c1,
+			c2:           pp.c2,
+		}
+
+		err = pi.Verify(vp)
+		if err == nil {
+			t.Errorf("Range1Proof verification passed but should've failed")
+		}
+	}
+}
+
+func TestRange2ProofInvalidInputs(t *testing.T) {
+	q := tt.B10("115792089237316195423570985008687907852837564279074904382605163141518161494337")
+	pk, _ := crypto.Rand(q)
+	nTilde, _ := crypto.Rand(q)
+	h1, _ := crypto.Rand(q)
+	h2, _ := crypto.Rand(q)
+	y, _ := crypto.Rand(q)
+	x, _ := crypto.Rand(q)
+	r, _ := crypto.Rand(pk)
+	nn := new(big.Int).Mul(pk, pk)
+	c1, _ := crypto.Rand(nn)
+	c2, _ := crypto.Rand(nn)
+	curve := btcec.S256()
+	pp := proof2Params{
+		curve: curve,
+		pk:    paillier.NewPubkey(pk),
+		dealerParams: &dealer.ProofParams{
+			N:  nTilde,
+			H1: h1,
+			H2: h2,
+		},
+		y:  y,
+		x:  x,
+		r:  r,
+		c1: c1,
+		c2: c2,
+	}
+	pp.x.Add(q, crypto.One)
+
+	_, err := pp.Prove()
+	if err == nil {
+		t.Errorf("Expected proof to fail but succeeded")
+	}
+}
+
+func TestRange2ProofWc(t *testing.T) {
+	curve := btcec.S256()
+	params := []*proof2Params{
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("12454003829785224424909094445321308251642868283898585771126291413816540758580767663318262594367601382376375285059803068275753905283271465428331446633428881")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("10565068081883900157917697460780075318076969969901870528290601230599518987697963206864737177306559344301211791508548333134326255847602343521746041372426881"),
+				H1: tt.B10("7995751561221948028555930079358601302030574855166341757560091202406660630455075618838456965406208797281104787963327486869802618778764549164875103578199469"),
+				H2: tt.B10("7656532047837282735662605356869379560760308364231923312709699220273737479894881594867882898131984223682773313158428858357773402466278427550311109701486213"),
+			},
+			x:  tt.B10("105065309678071150133793653554043899106789496891962463467003002461969456301937"),
+			y:  tt.B10("5492702923972299127390337572417062993980668847185989290093492369744698001785552062798957147644205248651717016835329378738252704422952664489273869210714003"),
+			r:  tt.B10("1479534906543044211837231294218146026461926193132920007306744928145282345504037584342904362659217507974835202601777094522405553436698892393763885061388478"),
+			c1: tt.B10("143139889611903589791816262441353094495263441207310098132338003158492847002109314489881492343532425133051402774239042571452064034364626727430154115486293525771026058106095404307844006484693932483119088608294103884465173259538644991990959041058781505906814834658717310198971570959147449328032151332111925175205"),
+			c2: tt.B10("118850417101393756978218229112645750124529443709777802628131640767910204536747768079123339300198360815481275960898822338743893982286509338811075702711051016050016330207766224111849625677925169769209362045134781493418045321274455428812004395599285384603402897485645035555320943199972214345978870565639942564875"),
+			X: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("22963319250927626464432314334264998185524558636490611781390004531598870711554"),
+				Y:     tt.B10("5554841823708042459730720811862682529836762867109252962559124452631448728441"),
+			},
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("1060646492933110030733036957140437117778853920088720844678695121930416862871848281832311778181619020077402392416415062286117610417982744789370366578341399268003467505720475646331195973509120599160516265415812314251530320408372372861")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("1092329328730104790080891116775013322627506771460114583079604278592390501361457437165424061010231921145619588453126221328435382425114836966113840506851641980212559859014884518613814057080788292341006461503638915697811040968629875229"),
+				H1: tt.B10("475106144368109368621647223376250922203280347957986484537098262925547265747101998903429384389406883704682638887286062550314246547956114040038314931266705139797302692613495472203652050545575197911638917386795821397986672973442649852"),
+				H2: tt.B10("908892396653303011912973312306706584315788720901361712520264106930695316871113623418118614676353709160818322009456857252848481098273083048966416012141843137572088979329467889633963130784228334674862715752823932989133005328963465921"),
+			},
+			x:  tt.B10("114417606410524292427506997399265920033404253984170300302370946490808825962924"),
+			y:  tt.B10("586816447123619771693988881257330494370346272001223238279252817311920204333999184633265849434212686066242756673492928992862563865831830233746655248409845773739878931473780870549350098937875929793807478594218009388204837185459737919"),
+			r:  tt.B10("330796414466337649065998673127317227360488458860671793045378311254259977988638646931493464453961100514867885866715451182650164536723136385570701713383150450958075548521851688567562997612982503922174169456503934892101537752875664649"),
+			c1: tt.B10("1053114622466963003050574957242008810794692807386408905242320867953216982016919832662798802583673970059568892771139314303098776240720837149047157440593394428053903998661246679248461257929216872492254813539989922056355923322352092748537060888144046806888646757812380709971001358158052219367381617739549374202298322532799430177580147769298175501100566420263545685855762900224502196330893960190794093573840711343202150393882356493072497241709222593553058376990428749"),
+			c2: tt.B10("282995671708572882191803929476857983442165614546789410443055590075997541079154885531091807745001380120084162515695562607280881887478831579446043490216567197486587119564058767144606070291657542062162477471067951023117132942298078062925825801742646118533360633918755222208006077148644571685345834096390060463136244486213068755867539693534078580249641605131209859196033291820646392678019396035155273950379122353511299942804484747778762777455190997200340374025210604"),
+			X: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("50876597730608100062498311383044640512079694460924904618750291323486830041462"),
+				Y:     tt.B10("44752679645488452545460727493390458766430770231868115695935742857907083404094"),
+			},
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("174153312534089570851525899271032113589979275411880883678905382495482218200069318069066709881321340381727078580248641402176174621811075736768090255011847709291394451539546906653608626836448448020222398750360809711536150952843601595213887853850370357766230989289426170056175863362575474454013936944961991616917")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("172651933488426286000131404169487588322431008522303036264382503852354196099850367973622481590491253503822918355198554197718452410956377207564832063926424629148712821482012770717310191205998337495810553384655519767643630533417620146481480034022054172027443937693269900872590795674430004269196692532205568992797"),
+				H1: tt.B10("118590594397995715752759118478489421665301876966360944695255662546217438576754007990572612412558112202779477174654578819656999557709637501325095444942727570178523420463669183588227929688886106825223816617633684958293667006462159268928157372520994885081158859164577709896423981522572434717430302992428297563136"),
+				H2: tt.B10("134670168222115720330617018933117329706043690406511938007555183497088606773771086397373341514464452199836099436095879891995241553734608283972469208903671070619142587047785148969236848204481295341629735981076134200060203874731519195293356672742761698767188091288714798209580414829549336877389345746546623854646"),
+			},
+			x:  tt.B10("11065870426263357752715666130320313833735406355792717575097984439586884032490"),
+			y:  tt.B10("36464645647514715867413937854145462127810804862931420694577018890822787594932079309954871457301931984778444696726176574946509910582711607744028602737288692165282404593451931849565140473027081137199772297679431922499599098994970030882523537693592951861149846509591964489120526188688486708871270663194198803163"),
+			r:  tt.B10("114439245405242865335314672675720680989637705396425491762165178333134035260749078520020316475929191564774865391197965293635562898561745706704763887963876472856962358482497951850804996026147471193879252222078520701059462538863234597127144547181963762391829067919378195246296446543044324051501773342909764067556"),
+			c1: tt.B10("10775808173033770984516167593505365443783752555324100755349598877836047307677011637063063086315464238435942493513507939945317658034289026591317406423694552504425405748691173106069124708756001018953795030004747650666979352069544640241341341634464323746030746804743164353982891624309639357226399617037483637891422140507649333375651193920153187885728755575682029759253435182307427668124884893428171790688719491734746237016553855965720036356784163356580399681227692884720048765980707977190599610039433157123735266679615119769970198124644524904227106442303993553933698710757937136567369366989575579828638106312021244735576"),
+			c2: tt.B10("30081032099130121042979418502314732490719753473424114269077343447566818310706174779202648249698139639476385455155651247417793442942854649358361924495597693091703669083361687546974413521594367983286798808990237196724019455528529345219738461830504687825927374179734750899960456788631962603677555569952144233741180806147699428820186187816960868351869404694066944962203753659515738157649329707123134540498621853203568711230375538669203190295243319306416180550940998013971867657559561764692136675632632802099489800529591165607293978221436761361588014597480442011722111700291203977932301875940605359806382399923838597144621"),
+			X: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47084789480364327168510770945852899215890777561128851891780884017450025060230"),
+				Y:     tt.B10("51817703111792417794557488019866663167938515271909049389156243599051715526516"),
+			},
+		},
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("21343818843614709778423937467108011341949327450311182535762771398497610046006056929783583120189923419499898117106346564723970688957902489020760820401098919871682075861931799235066903163746901354170019434386796757961110772586542136098473272723261983749356990793919918143337029627426527223682816946912414305615650546812211977749178634879531473845018271907797786434001508143575303841556331835005538916568952225221288873486059556819320279715818032087600078162347990319903724428078162246887152420651155875072990694535614688712113234073038424857000481868713031907767238817547353122272824696372544813541777562757422452703389")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("21440609852763007138735819899427806271414854462185275004105464455197604028063646788155856601369873449136102779324764141381374061363107493235913636137967294095523840220584234845218424429287340200522460522857569274189388148014800027306925331046969787804744347172513704978733300054228429317388724036765350349009865056654594809086359543736284803700478627750549030595336332998309598246755011660697153809128912586862548974075788304443681642756309026939544472534183771013135688836883808280586469385349750553135584076915837689561368338280498868185703287861527010800344946216746545759790109259487926065269704130409284767429177"),
+				H1: tt.B10("16082635924491180859892052103348669817831264904927338842878735505605620083836951511324620211235252509887724382590329701187323154406501073390714214519796783889250963354564148094242739350419652368817226620967931116172473952600520718782740615687485618371096717393827640715223390036730088624516780108618713553389032163184056235335558973728431463388816701504113051515919433765055909706322416878748025691541271134753796299366797197495449817911629608648248034133751449416402345897196052605688982385924866769136480343090234200198250957774538326561070317488121335369054416364814254940990819583076364003690898899394819454633098"),
+				H2: tt.B10("14581575636264039655004935624295665826821662670021192681449849898952812734812533416341722319273085643584616068165596471926906706017999808980633056192835003414324093106336680886193782067021903503846628520391128045160570365359689255780975718001105668028170355680197829874604770103036088371504694876566679319280638385262068207480704484804089815241036119191122828877958876654866902642083194300482531632717542525621225069688599520378773108909949351788022723435884261787275644523174797781228241972164905878355557210473408688766653679471890512201620009709897132423036276837599483769590210914062571174776497975951152604861909"),
+			},
+			x:  tt.B10("8750392648567976522956319619137607006114258896023630967546640616198856173726"),
+			y:  tt.B10("18514950016402011364856738069185973263573668938655713951878101224620475463654594476052229843255158572976230514682023959519940322543142809152791591239229560830161242933660100090403615237790904170566122483876823815824883487186433813630025550831286728242139087984528338135469743069319708820862657693434427713556907042286156802653833457143628131843981622956009453554840126029887277400824931655621757965664714723702031714992339685404183589750609938552715628719275090046676551011043639556782182524866474591844193422887744052604695933670596126789247839852218746997248277319591694382650165057957709932713486988304450923675169"),
+			r:  tt.B10("7413993536311990938185363447591674123090498279011518110530459679826505226842315567225447966136772813354380874216337993625731894208173620227576059773605455100525699149077963620155949930982645602807982410870840178869228214289984614787137438697125088675307673132503799184337485473063337977691388528865511930911615069717911764298852791123820414152746682198972700664631157433225157132581988251670394901587709237320936324359651495290814362610131883393180776817054519048519945827745509527633704961289024312648874849430623550895600046463196591224795799125593480551703200134016544000687466864662987123101979601157886397711803"),
+			c1: tt.B10("390111299656227329049911645962500049392377387594152457668485483110800144720345180158229237161842828307254342803083379655054467517296523210675130263404686580646992792502830916302607437160813512962532146963059202294210687402129360020946526304905339187636229176261028993936810993006653314076335851074005727014314790162490593160207216642747021985552411284433670026363853068691081342083837886029591829540186654863374285161120653539204838867832932794810504576871885290319716389567292694319143715930162553277300961962282646376301436460212705495080036300372011810745765622016658529618697349936654020519012125853508298624943295528382686465797342272133086342053444730761082595522615614885422356326860879270969967076748246605215181659738839204838987139706656213356349676893722627421667492378370979872311805729149448736645369425823598900065737429573410247512812271614068171292075691207858929206060218031819070034607110062687579951509005561963770102163971963284714329558342723034716742547265888594343447182501412167939138160985186539850524487166372948687703793947452682996182101681482493637159856664957425454529042197760223673798097694156006735908818858773992720569533879034557981434329714599172480672498298131329669845732971041195290211843618632"),
+			c2: tt.B10("414087322628778402052959871377634400860248171375261792193144317672300614724281086753475884955098749530245517666626070220023837866083495805270132399813304329252689077343468337707206098232075158608771732248133557071475694837741409195765164074997213805914716339977051463942457350793538324515833385944508770700664326460035329168418037159052366329523249559273078751143884242025833162097387231202870641959939732293302387535340888655961847675311628622867627210584641057626409220755786650508201240444516063051609479239783655873029341585766046078627874459278839410413907919155641132604960419572061051554199366136670190861016711564259967824430385720014590007708922089334725408148434521574752769123778588354362776275486871150115492580224894993397625084784531194257887612938916463009330046882110591904397780495603613183257020623566136447191271492858669730549102508120617247346893119719597165329952921576745462349408389606590821498410192408490984668453385335803103990707065772580336758620783567149166236290386033908327151705445208775711918923753061831564281672808588018264175270521545096269242721341581645386390246637994933601094434633774176728776076349417726483624629605791700004811923881810302845629521698242170650586675551125725410099894092551"),
+			X: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("88095946520726762438892505977255012182736220056004178905714021421963837809351"),
+				Y:     tt.B10("66969024082335057813279558085339750203065011944255927129083411560465715907117"),
+			},
+		},
+	}
+	for _, pp := range params {
+		pi, err := pp.ProveWc()
+		tt.AssertNoError(t, err)
+
+		vp := &verifyProof2Params{
+			curve:        pp.curve,
+			dealerParams: pp.dealerParams,
+			pk:           pp.pk,
+			c1:           pp.c1,
+			c2:           pp.c2,
+			X:            pp.X,
+		}
+
+		err = pi.VerifyWc(vp)
+		tt.AssertNoError(t, err)
+	}
+}
+
+func TestRange2ProofWcInvalidInputs(t *testing.T) {
+	q := tt.B10("115792089237316195423570985008687907852837564279074904382605163141518161494337")
+	pk, _ := crypto.Rand(q)
+	nTilde, _ := crypto.Rand(q)
+	h1, _ := crypto.Rand(q)
+	h2, _ := crypto.Rand(q)
+	y, _ := crypto.Rand(q)
+	x, _ := crypto.Rand(q)
+	r, _ := crypto.Rand(pk)
+	nn := new(big.Int).Mul(pk, pk)
+	c1, _ := crypto.Rand(nn)
+	c2, _ := crypto.Rand(nn)
+	curve := btcec.S256()
+	pp := proof2Params{
+		curve: curve,
+		pk:    paillier.NewPubkey(pk),
+		dealerParams: &dealer.ProofParams{
+			N:  nTilde,
+			H1: h1,
+			H2: h2,
+		},
+		y:  y,
+		x:  x,
+		r:  r,
+		c1: c1,
+		c2: c2,
+	}
+
+	_, err := pp.ProveWc()
+	// Expect bigX check
+	if err == nil {
+		t.Errorf("Expected proof to fail but succeeded")
+	}
+	pp.X = &curves.EcPoint{
+		Curve: curve,
+		X:     crypto.One,
+		Y:     crypto.One,
+	}
+
+	pp.x.Add(q, crypto.One)
+
+	_, err = pp.ProveWc()
+	// Expect smallX check
+	if err == nil {
+		t.Errorf("Expected proof to fail but succeeded")
+	}
+}
+
+func TestRange2ProofWcTampered(t *testing.T) {
+	curve := btcec.S256()
+	params := []*proof2Params{
+		{
+			curve: curve,
+			pk:    paillier.NewPubkey(tt.B10("12454003829785224424909094445321308251642868283898585771126291413816540758580767663318262594367601382376375285059803068275753905283271465428331446633428881")),
+			dealerParams: &dealer.ProofParams{
+				N:  tt.B10("10565068081883900157917697460780075318076969969901870528290601230599518987697963206864737177306559344301211791508548333134326255847602343521746041372426881"),
+				H1: tt.B10("7995751561221948028555930079358601302030574855166341757560091202406660630455075618838456965406208797281104787963327486869802618778764549164875103578199469"),
+				H2: tt.B10("7656532047837282735662605356869379560760308364231923312709699220273737479894881594867882898131984223682773313158428858357773402466278427550311109701486213"),
+			},
+			x:  tt.B10("105065309678071150133793653554043899106789496891962463467003002461969456301937"),
+			y:  tt.B10("5492702923972299127390337572417062993980668847185989290093492369744698001785552062798957147644205248651717016835329378738252704422952664489273869210714003"),
+			r:  tt.B10("1479534906543044211837231294218146026461926193132920007306744928145282345504037584342904362659217507974835202601777094522405553436698892393763885061388478"),
+			c1: tt.B10("143139889611903589791816262441353094495263441207310098132338003158492847002109314489881492343532425133051402774239042571452064034364626727430154115486293525771026058106095404307844006484693932483119088608294103884465173259538644991990959041058781505906814834658717310198971570959147449328032151332111925175205"),
+			c2: tt.B10("118850417101393756978218229112645750124529443709777802628131640767910204536747768079123339300198360815481275960898822338743893982286509338811075702711051016050016330207766224111849625677925169769209362045134781493418045321274455428812004395599285384603402897485645035555320943199972214345978870565639942564875"),
+			X: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("22963319250927626464432314334264998185524558636490611781390004531598870711554"),
+				Y:     tt.B10("5554841823708042459730720811862682529836762867109252962559124452631448728441"),
+			},
+		},
+	}
+
+	for _, pp := range params {
+		pi, _ := pp.ProveWc()
+		vp := &verifyProof2Params{
+			curve:        pp.curve,
+			dealerParams: pp.dealerParams,
+			pk:           pp.pk,
+			c1:           pp.c1,
+			c2:           pp.c2,
+			X:            pp.X,
+		}
+		if err := pi.VerifyWc(vp); err != nil {
+			t.Errorf("RangeProof2Wc failed: %v", err)
+		}
+		pi.z, _ = crypto.Add(pi.z, pi.z, pp.dealerParams.N)
+		if err := pi.VerifyWc(vp); err == nil {
+			t.Errorf("RangeProof2Wc Succeeded but should've failed")
+		}
+	}
+}
+
+func TestMtaResponse(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687")
+	q := tt.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("111958869483513815922567059983360120902124751080912197360754574997487631638823")
+	q = tt.B10("95481433573633164229505151253229736602852797329141344427447414443810362028219")
+
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+				H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+				H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+			},
+			SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+			C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+				Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10689993359569189584971133266138347482779112503958068052786133618081233424519509554592362492412511708066911136948775161899463259225741593724792361141946237")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("11199860387109154020980079861224590064747847360780224770239565392448675561193234585575766622953310666489181959737787534900201619335359226299004761248037869"),
+				H1: tt.B10("8420237019599021198189250566368868058512091420199113722789430631818946591995096516958967513657607083740933414708568490783103184892513468965472217352417370"),
+				H2: tt.B10("4410824807618073391238885878571676086100288528709400551944741057952927655556136509257979472810321794801624633615860035610145462010641568995471021245619215"),
+			},
+			SmallB: tt.B10("35757537348996621957461215098882730872747662393337533981591895725421179051196"),
+			C1:     tt.B10("92352588588873729555430055172430595475910468157254446887005633321086645506984959001356424661276448180525800287366079400461958418643751933701277823127881543396640181010723902113675414173812412486759363992283619394596611725910844787234817793297468668543716260158106119514868237915982895111931557116755302785277"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47119159900193871131301454349459631159900055770279833902936369018055039407305"),
+				Y:     tt.B10("115146922864592374131907157924472992158066770148954896711377713046850262233029"),
+			},
+		},
+	}
+
+	for i, pp := range params {
+		rp, err := pp.Prove()
+		if err != nil {
+			t.Errorf("MtAResponse failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+		alpha, err := rp.Finalize(vp)
+		if err != nil {
+			t.Errorf("MtAFinalize failed: %v", err)
+		}
+		if err := crypto.In(alpha, curve.N); err != nil {
+			t.Errorf("MtAFinalize failed. alpha is not in q")
+		}
+	}
+}
+
+func TestMtaResponseTampered(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687")
+	q := tt.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("111958869483513815922567059983360120902124751080912197360754574997487631638823")
+	q = tt.B10("95481433573633164229505151253229736602852797329141344427447414443810362028219")
+
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+				H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+				H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+			},
+			SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+			C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+				Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10689993359569189584971133266138347482779112503958068052786133618081233424519509554592362492412511708066911136948775161899463259225741593724792361141946237")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("11199860387109154020980079861224590064747847360780224770239565392448675561193234585575766622953310666489181959737787534900201619335359226299004761248037869"),
+				H1: tt.B10("8420237019599021198189250566368868058512091420199113722789430631818946591995096516958967513657607083740933414708568490783103184892513468965472217352417370"),
+				H2: tt.B10("4410824807618073391238885878571676086100288528709400551944741057952927655556136509257979472810321794801624633615860035610145462010641568995471021245619215"),
+			},
+			SmallB: tt.B10("35757537348996621957461215098882730872747662393337533981591895725421179051196"),
+			C1:     tt.B10("92352588588873729555430055172430595475910468157254446887005633321086645506984959001356424661276448180525800287366079400461958418643751933701277823127881543396640181010723902113675414173812412486759363992283619394596611725910844787234817793297468668543716260158106119514868237915982895111931557116755302785277"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47119159900193871131301454349459631159900055770279833902936369018055039407305"),
+				Y:     tt.B10("115146922864592374131907157924472992158066770148954896711377713046850262233029"),
+			},
+		},
+	}
+
+	for i, pp := range params {
+		rp, err := pp.Prove()
+		if err != nil {
+			t.Errorf("MtAResponse failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+		vp.C1.Add(vp.C1, crypto.One)
+		alpha, err := rp.Finalize(vp)
+		if err == nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+		if alpha != nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+	}
+}
+
+func TestMtaResponseWrongSk(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("109928870258914484332246736086443528668845422515353017331132578048644419715903")
+	q := tt.B10("111833762805904019963656115671572366535325687950926082867211892127281860836163")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("95269679274361747243452342896385486502483333138266248958026102399010319729739")
+	q = tt.B10("112602195828184040143541749000556013737317259050057140690946494035359955461307")
+
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+				H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+				H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+			},
+			SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+			C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+				Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10689993359569189584971133266138347482779112503958068052786133618081233424519509554592362492412511708066911136948775161899463259225741593724792361141946237")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("11199860387109154020980079861224590064747847360780224770239565392448675561193234585575766622953310666489181959737787534900201619335359226299004761248037869"),
+				H1: tt.B10("8420237019599021198189250566368868058512091420199113722789430631818946591995096516958967513657607083740933414708568490783103184892513468965472217352417370"),
+				H2: tt.B10("4410824807618073391238885878571676086100288528709400551944741057952927655556136509257979472810321794801624633615860035610145462010641568995471021245619215"),
+			},
+			SmallB: tt.B10("35757537348996621957461215098882730872747662393337533981591895725421179051196"),
+			C1:     tt.B10("92352588588873729555430055172430595475910468157254446887005633321086645506984959001356424661276448180525800287366079400461958418643751933701277823127881543396640181010723902113675414173812412486759363992283619394596611725910844787234817793297468668543716260158106119514868237915982895111931557116755302785277"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47119159900193871131301454349459631159900055770279833902936369018055039407305"),
+				Y:     tt.B10("115146922864592374131907157924472992158066770148954896711377713046850262233029"),
+			},
+		},
+	}
+
+	for i, pp := range params {
+		rp, err := pp.Prove()
+		if err != nil {
+			t.Errorf("MtAResponse failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+
+		alpha, err := rp.Finalize(vp)
+		if err == nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+		if alpha != nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+	}
+}
+
+func TestMtaResponseWc(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("109274773745638923845891746843821104418395321621977125174407642049279000707627")
+	q := tt.B10("89126345888070631866058676691750589235695184917280127558036280089888607061483")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("110815904968740611416753240686541004240868069636504134412941867250037339746203")
+	q = tt.B10("95305040696076266863383164332348929709699372932895253104818242887250802699023")
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("9739261281694474339427833205775587535140226500608473457279620904321187569177296563924547185701059893472319006449953695720569246692958491636426106096030841")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9039439634444824307508960751383917494860453859140486800804377263935631222453614752524890446026796441312472278432791555840405344583483734720495411403245341"),
+				H1: tt.B10("175854216774129343007276239448395891168112696535680488272500883809002629028020863635719402934930695093869431279518728877092436324149259536576325085223306"),
+				H2: tt.B10("6307050187956924667864766848371197144510791412166574989883457690848742178406996950362636692594817895627086478115929251619995169388211920572432371440432347"),
+			},
+			SmallB: tt.B10("52267911369760448083721726508303370554429030131465579507196814348877287376175"),
+			C1:     tt.B10("93754185865506539900146251138967028050138438425830227162734497980682090590177901823650921334915913917868690888765728438724497317559474386038306965827476012034259085194788921672874210195001360283191491538466572357948080845312295163017659705576708240686678523086913486497655485353079002424965875207215069433398"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("46954861409208447737222535381893412230292203379578782164747089670087262529053"),
+				Y:     tt.B10("27561307727226443248314925239745475174755673899477133056173695085314410311303"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10561314332818344160426522481555121082766474200972362425484359311030065087872679231901544552512335365773466347074637755559792307623751725613939546216059669")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9643670778755502087821511421601217246607541351131474488232424192369802750396732907390248701851324825725530822397546546505555733008152836274165662480740417"),
+				H1: tt.B10("7843381716533908821162161041946908084554884986407926815754661446302558744899453613400103510283205209464285840290645719613059411061767360623582068930361898"),
+				H2: tt.B10("8675621642889082921911159451182831584536536604341004981762562955656958762259322285123115196323048509747676814279953111100389711921780293874360929010502564"),
+			},
+			SmallB: tt.B10("96239849653450913364080147788247184659137655804206953534092167696450698926934"),
+			C1:     tt.B10("83665058672718242257733172987490955606067969188309375700725991273542909812324380350060502232466695592442821671447507874987206896988955864837869918873659407684672821529999047344427388923843813425378165980734381968601276897393925133091718868356318532966891511178329432381215866238662246512828543244610787501373"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("73152511031340534294337476499647134418743213468977810079263243542061796393179"),
+				Y:     tt.B10("37239378704657125612907515682572196819463356277616280533808406179170645816253"),
+			},
+		},
+	}
+	for i, pp := range params {
+		rp, err := pp.ProveWc()
+		if err != nil {
+			t.Errorf("MtAResponseWc failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+		alpha, err := rp.FinalizeWc(vp)
+		if err != nil {
+			t.Errorf("MtAFinalizeWc failed: %v", err)
+		}
+		if err := crypto.In(alpha, curve.N); err != nil {
+			t.Errorf("MtAFinalizeWc failed. alpha is not in q")
+		}
+	}
+}
+
+func TestMtaResponseWcTampered(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("110045198697022997120409435651962875820936327127306040565577217116705932648687")
+	q := tt.B10("95848033199746534486927143950536999279071340697368502822602282152563330640779")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("111958869483513815922567059983360120902124751080912197360754574997487631638823")
+	q = tt.B10("95481433573633164229505151253229736602852797329141344427447414443810362028219")
+
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+				H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+				H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+			},
+			SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+			C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+				Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10689993359569189584971133266138347482779112503958068052786133618081233424519509554592362492412511708066911136948775161899463259225741593724792361141946237")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("11199860387109154020980079861224590064747847360780224770239565392448675561193234585575766622953310666489181959737787534900201619335359226299004761248037869"),
+				H1: tt.B10("8420237019599021198189250566368868058512091420199113722789430631818946591995096516958967513657607083740933414708568490783103184892513468965472217352417370"),
+				H2: tt.B10("4410824807618073391238885878571676086100288528709400551944741057952927655556136509257979472810321794801624633615860035610145462010641568995471021245619215"),
+			},
+			SmallB: tt.B10("35757537348996621957461215098882730872747662393337533981591895725421179051196"),
+			C1:     tt.B10("92352588588873729555430055172430595475910468157254446887005633321086645506984959001356424661276448180525800287366079400461958418643751933701277823127881543396640181010723902113675414173812412486759363992283619394596611725910844787234817793297468668543716260158106119514868237915982895111931557116755302785277"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47119159900193871131301454349459631159900055770279833902936369018055039407305"),
+				Y:     tt.B10("115146922864592374131907157924472992158066770148954896711377713046850262233029"),
+			},
+		},
+	}
+
+	for i, pp := range params {
+		rp, err := pp.ProveWc()
+		if err != nil {
+			t.Errorf("MtAResponse failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+		vp.C1.Add(vp.C1, crypto.One)
+		alpha, err := rp.FinalizeWc(vp)
+		if err == nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+		if alpha != nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+		vp.C1.Sub(vp.C1, crypto.One)
+		vp.B.X, vp.B.Y = curve.Add(vp.B.X, vp.B.Y, crypto.One, crypto.Zero)
+		alpha, err = rp.FinalizeWc(vp)
+		if err == nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+		if alpha != nil {
+			t.Errorf("MtAFinalize succeeded but should've failed")
+		}
+	}
+}
+
+func TestMtaResponseWcWrongSk(t *testing.T) {
+	curve := btcec.S256()
+	p := tt.B10("109928870258914484332246736086443528668845422515353017331132578048644419715903")
+	q := tt.B10("111833762805904019963656115671572366535325687950926082867211892127281860836163")
+	sk1, _ := paillier.NewSecretKey(p, q)
+
+	p = tt.B10("95269679274361747243452342896385486502483333138266248958026102399010319729739")
+	q = tt.B10("112602195828184040143541749000556013737317259050057140690946494035359955461307")
+
+	sk2, _ := paillier.NewSecretKey(p, q)
+
+	sks := []*paillier.SecretKey{
+		sk1,
+		sk2,
+	}
+	params := []*ResponseProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+				H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+				H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+			},
+			SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+			C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+				Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10689993359569189584971133266138347482779112503958068052786133618081233424519509554592362492412511708066911136948775161899463259225741593724792361141946237")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("11199860387109154020980079861224590064747847360780224770239565392448675561193234585575766622953310666489181959737787534900201619335359226299004761248037869"),
+				H1: tt.B10("8420237019599021198189250566368868058512091420199113722789430631818946591995096516958967513657607083740933414708568490783103184892513468965472217352417370"),
+				H2: tt.B10("4410824807618073391238885878571676086100288528709400551944741057952927655556136509257979472810321794801624633615860035610145462010641568995471021245619215"),
+			},
+			SmallB: tt.B10("35757537348996621957461215098882730872747662393337533981591895725421179051196"),
+			C1:     tt.B10("92352588588873729555430055172430595475910468157254446887005633321086645506984959001356424661276448180525800287366079400461958418643751933701277823127881543396640181010723902113675414173812412486759363992283619394596611725910844787234817793297468668543716260158106119514868237915982895111931557116755302785277"),
+			B: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("47119159900193871131301454349459631159900055770279833902936369018055039407305"),
+				Y:     tt.B10("115146922864592374131907157924472992158066770148954896711377713046850262233029"),
+			},
+		},
+	}
+
+	for i, pp := range params {
+		rp, err := pp.ProveWc()
+		if err != nil {
+			t.Errorf("MtAResponseWc failed: %v", err)
+			return
+		}
+		vp := &ResponseVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Sk:           sks[i],
+			C1:           pp.C1,
+			B:            pp.B,
+		}
+
+		alpha, err := rp.FinalizeWc(vp)
+		if err == nil {
+			t.Errorf("MtAFinalizeWc succeeded but should've failed")
+		}
+		if alpha != nil {
+			t.Errorf("MtAFinalizeWc succeeded but should've failed")
+		}
+	}
+}
+
+// Convenience function for making a big.Int
+func bi(x int64) *big.Int {
+	return big.NewInt(x)
+}
+
+// Small number known answer tests for inc
+func TestInc(t *testing.T) {
+	tests := []struct {
+		alpha, beta, n, expected *big.Int
+	}{
+		// (N+1)^alpha * Beta^N  mod N^2
+		// Tests in Z_{3^2}
+		{bi(9), bi(2), bi(3), bi(8)},
+		{bi(7), bi(3), bi(3), bi(0)},
+		{bi(2), bi(2), bi(3), bi(2)},
+		{bi(7), bi(0), bi(3), bi(0)},
+		{bi(5), bi(1), bi(3), bi(7)},
+		{bi(4), bi(8), bi(3), bi(5)},
+	}
+
+	// Run all the tests!
+	for _, test := range tests {
+		actual, err := inc(test.alpha, test.beta, test.n)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// Small number known answer tests for pedersen
+func TestPedersen(t *testing.T) {
+	tests := []struct {
+		g, alpha, h, beta, n, expected *big.Int
+	}{
+		// g^alpha * h*Beta  (mod n)
+		// Tests in Z_{13}
+		{bi(9), bi(8), bi(2), bi(1), bi(13), bi(6)},
+		{bi(9), bi(9), bi(5), bi(0), bi(13), bi(1)},
+		{bi(3), bi(4), bi(4), bi(3), bi(13), bi(10)},
+		{bi(1), bi(5), bi(6), bi(5), bi(13), bi(2)},
+		{bi(6), bi(3), bi(5), bi(6), bi(13), bi(5)},
+		{bi(0), bi(7), bi(6), bi(7), bi(13), bi(0)},
+	}
+
+	// Run all the tests!
+	for _, test := range tests {
+		actual, err := pedersen(test.g, test.h, test.alpha, test.beta, test.n)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// Small number known answer tests for schnorr
+func TestSchnorr(t *testing.T) {
+	tests := []struct {
+		x, y, z, expected *big.Int
+	}{
+		// xy + z
+		{bi(98), bi(2), bi(59), bi(255)},
+		{bi(99), bi(304), bi(65), bi(30161)},
+		{bi(168), bi(0), bi(13), bi(13)},
+		{bi(70), bi(21), bi(8), bi(1478)},
+		{bi(19), bi(23), bi(36), bi(473)},
+	}
+
+	// Run all the tests!
+	for _, test := range tests {
+		actual, err := schnorr(test.x, test.y, test.z)
+		tt.AssertNoError(t, err)
+		tt.AssertBigIntEq(t, test.expected, actual)
+	}
+}
+
+// Test that Range2Proof can be marshaled and unmarshaled correctly
+func TestMarshalJsonRange2Proof(t *testing.T) {
+	hello := "test"
+	assert.NotNil(t, hello)
+	test := Range2Proof{
+		z:  bi(12),
+		e:  bi(44),
+		s:  bi(56),
+		s1: bi(23),
+		s2: bi(14),
+		t:  bi(49),
+		t1: bi(99),
+		t2: bi(67),
+	}
+
+	testJSON, err := json.Marshal(test)
+	assert.NoError(t, err)
+	assert.NotNil(t, testJSON)
+
+	unmarshaled := new(Range2Proof)
+	err = json.Unmarshal(testJSON, unmarshaled)
+	assert.NoError(t, err)
+
+	assert.Equal(t, test.z, unmarshaled.z)
+	assert.Equal(t, test.e, unmarshaled.e)
+	assert.Equal(t, test.s, unmarshaled.s)
+	assert.Equal(t, test.s1, unmarshaled.s1)
+	assert.Equal(t, test.s2, unmarshaled.s2)
+	assert.Equal(t, test.t, unmarshaled.t)
+	assert.Equal(t, test.t1, unmarshaled.t1)
+	assert.Equal(t, test.t2, unmarshaled.t2)
+}
+
+// Test that ResponseProof can be marshaled and unmarshaled correctly
+func TestMarshalJsonResponseProof(t *testing.T) {
+	curve := btcec.S256()
+
+	rpp := ResponseProofParams{
+		Curve: curve,
+		Pk:    paillier.NewPubkey(tt.B10("10547615858184964306411562661985243216511226462060029912418561431293350513994423138528642902287903466486042818341097441827086959649889826199119664403007173")),
+		DealerParams: &dealer.ProofParams{
+			N:  tt.B10("9972886211275433070035994662048032853531452341596222874944455730406324093082012471095835489777525666656101689703091272431312190038636973920385309846023861"),
+			H1: tt.B10("9645317246937167948100761846052703931860463997240776753358695432123565805217588763869923227018453085470821139033044893014220360494788858157967288186449376"),
+			H2: tt.B10("2050268247938630669991905733361921562776155620188477492052136889909625145533819588548316645784225045947395506721263124727029028420360795789170536034891820"),
+		},
+		SmallB: tt.B10("3672791578831700453156064277674396724953117514808181048561503554767812240270"),
+		C1:     tt.B10("77752317560568208206364290265071376718942102730865626173881960000095692236560274288202792728825652824950440213334665539641290999004150367191954333808152149418358084240829193835628503450268249050991899350405972770791757133533190107036510955688542448103156155740141942033820625257531299610966919367173008180688"),
+		B: &curves.EcPoint{
+			Curve: curve,
+			X:     tt.B10("1404866900921975962487332641664497649570820021171040875292185052444634265070"),
+			Y:     tt.B10("22517056746740517460185947144352325511166429596179017818627772864271597116261"),
+		},
+	}
+
+	test, err := rpp.Prove()
+	assert.NoError(t, err)
+	assert.NotNil(t, test)
+
+	testJSON, err := json.Marshal(test)
+	assert.NoError(t, err)
+	assert.NotNil(t, testJSON)
+
+	unmarshaled := new(ResponseProof)
+	err = json.Unmarshal(testJSON, unmarshaled)
+	assert.NoError(t, err)
+	assert.NotNil(t, unmarshaled)
+
+	assert.Equal(t, test.C2, unmarshaled.C2)
+	assert.Equal(t, test.Beta, unmarshaled.Beta)
+	assert.Equal(t, test.R2proof.z, unmarshaled.R2proof.z)
+	assert.Equal(t, test.R2proof.s, unmarshaled.R2proof.s)
+	assert.Equal(t, test.R2proof.s1, unmarshaled.R2proof.s1)
+	assert.Equal(t, test.R2proof.t, unmarshaled.R2proof.t)
+	assert.Equal(t, test.R2proof.t1, unmarshaled.R2proof.t1)
+}
+
+// Ensures that marshal-unmarshal Range1Proof is the identity function
+func TestMarshalRange1ProofRoundTrip(t *testing.T) {
+	expected := Range1Proof{
+		bi(-1),
+		bi(0),
+		bi(1),
+		bi(2),
+		bi(3),
+	}
+
+	// Marshal and test
+	jsonBytes, err := json.Marshal(expected)
+	assert.NoError(t, err)
+	assert.NotNil(t, jsonBytes)
+
+	// Unmarshal and test
+	var actual Range1Proof
+	err = json.Unmarshal(jsonBytes, &actual)
+	assert.NoError(t, err)
+
+	assert.Equal(t, expected.z, actual.z)
+	assert.Equal(t, expected.e, actual.e)
+	assert.Equal(t, expected.s, actual.s)
+	assert.Equal(t, expected.s1, actual.s1)
+	assert.Equal(t, expected.s2, actual.s2)
+}
diff --git a/pkg/tecdsa/gg20/proof/pdl.go b/pkg/tecdsa/gg20/proof/pdl.go
new file mode 100644
index 00000000..0f0ae736
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/pdl.go
@@ -0,0 +1,317 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+// Package proof contains the proof of discrete logarithm (PDL) subprotocol from [spec] §8
+
+package proof
+
+import (
+	"crypto/elliptic"
+	"encoding/json"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	paillier "github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// PdlProofParams encapsulates the parameters for ProvePDL in
+// [spec] fig 14
+type PdlProofParams struct {
+	Curve               elliptic.Curve
+	DealerParams        *dealer.ProofParams
+	Pk                  *paillier.PublicKey
+	ScalarX, ScalarR, C *big.Int
+	PointX, PointR      *curves.EcPoint
+}
+
+// PdlProof is the proof generated in
+// [spec] fig 14
+type PdlProof struct {
+	z, e, s, s1, s2 *big.Int
+}
+
+type pdlProofJSON struct {
+	Z, E, S, S1, S2 *big.Int
+}
+
+func (pdlp PdlProof) MarshalJSON() ([]byte, error) {
+	data := pdlProofJSON{
+		Z:  pdlp.z,
+		E:  pdlp.e,
+		S:  pdlp.s,
+		S1: pdlp.s1,
+		S2: pdlp.s2,
+	}
+	return json.Marshal(data)
+}
+
+func (pdlp *PdlProof) UnmarshalJSON(bytes []byte) error {
+	data := new(pdlProofJSON)
+
+	err := json.Unmarshal(bytes, &data)
+	if err != nil {
+		return err
+	}
+	pdlp.z = data.Z
+	pdlp.e = data.E
+	pdlp.s = data.S
+	pdlp.s1 = data.S1
+	pdlp.s2 = data.S2
+
+	return nil
+}
+
+// PdlVerifyParams encapsulates the parameters for VerifyPDL in
+// [spec] fig 14
+type PdlVerifyParams struct {
+	Curve          elliptic.Curve
+	DealerParams   *dealer.ProofParams
+	Pk             *paillier.PublicKey
+	PointX, PointR *curves.EcPoint
+	C              *big.Int
+}
+
+// randPdlParams are the random values generated in
+// [spec] fig 14
+type randPdlParams struct {
+	alpha, beta, gamma, rho *big.Int
+}
+
+// Prove generates a PdlProof as specified in
+// [spec] fig 14
+func (p PdlProofParams) Prove() (*PdlProof, error) {
+	if p.C == nil || p.DealerParams == nil || p.PointR == nil || p.PointX == nil ||
+		p.Pk == nil || p.Curve == nil || p.ScalarX == nil || p.ScalarR == nil {
+		return nil, fmt.Errorf("invalid params")
+	}
+	// step 1
+	// set N=pk.N
+
+	// steps 2-5
+	randParams, err := randPdl(p)
+	if err != nil {
+		return nil, err
+	}
+
+	// 6. Compute u=R^α in G
+	u, err := p.PointR.ScalarMult(randParams.alpha)
+	if err != nil {
+		return nil, err
+	}
+
+	// 7. Compute z=h1^x h2^ρ mod N ̃
+	z, err := pedersen(p.DealerParams.H1, p.DealerParams.H2, p.ScalarX, randParams.rho, p.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 8. Compute v=(N+1)^α β^N mod N^2
+	v, err := inc(randParams.alpha, randParams.beta, p.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 9. Compute w = h1^α h2^γ mod N ̃
+	w, err := pedersen(p.DealerParams.H1, p.DealerParams.H2, randParams.alpha, randParams.gamma, p.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 10. Compute e = H(pk,N~,h1,h2,g,q,R,X,c,u,z,v,w)
+	challenge, err := crypto.FiatShamir(p.Pk.N, p.DealerParams.N, p.DealerParams.H1,
+		p.DealerParams.H2, p.Curve.Params().Gx, p.Curve.Params().Gy,
+		p.Curve.Params().N, p.PointR.X, p.PointR.Y, p.PointX.X, p.PointX.Y, p.C,
+		u.X, u.Y, z, v, w)
+	if err != nil {
+		return nil, err
+	}
+	e := new(big.Int).SetBytes(challenge)
+
+	// 11. Computes s = r^e β mod N
+	s, err := pedersen(p.ScalarR, randParams.beta, e, crypto.One, p.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	// 12. Compute s1 = ex + α
+	s1, err := schnorr(e, p.ScalarX, randParams.alpha)
+	if err != nil {
+		return nil, err
+	}
+
+	// 13. Compute s2 = eρ + γ
+	s2, err := schnorr(e, randParams.rho, randParams.gamma)
+	if err != nil {
+		return nil, err
+	}
+
+	// 14. set \Pi = [u, z, v, w, s, s1, s2]
+	// 15. return \Pi
+	return &PdlProof{
+		z, e, s, s1, s2,
+	}, nil
+}
+
+// Verify checks the PdlProof as specified in
+// [spec] fig 14
+func (p PdlProof) Verify(pv *PdlVerifyParams) error {
+	if p.z == nil || p.e == nil || p.s1 == nil || p.s2 == nil || p.s == nil {
+		return fmt.Errorf("proof values cannot be nil")
+	}
+	if pv == nil || pv.Curve == nil || pv.C == nil || pv.Pk == nil ||
+		pv.PointX == nil || pv.PointR == nil || pv.DealerParams == nil {
+		return fmt.Errorf("proof verify params cannot be nil")
+	}
+	// step 1
+	// Set N = pk.N
+	// ----
+
+	q3, err := crypto.Exp(pv.Curve.Params().N, big.NewInt(3), nil)
+	if err != nil {
+		return err
+	}
+
+	// 2. If s1 > q3, Return False
+	if p.s1.Cmp(q3) == 1 {
+		return fmt.Errorf("s1 > q3")
+	}
+
+	// Steps 3 & 4
+	uHat, err := p.uHatConstruct(pv)
+	if err != nil {
+		return fmt.Errorf("u hat construction error: %s", err)
+	}
+
+	// step 5
+	vHat, err := p.vHatConstruct(pv)
+	if err != nil {
+		return fmt.Errorf("v hat construction error: %s", err)
+	}
+
+	// step 6
+	wHat, err := p.wHatConstruct(pv)
+	if err != nil {
+		return fmt.Errorf("w hat construction error: %s", err)
+	}
+
+	// step 7
+	challenge, err := crypto.FiatShamir(
+		pv.Pk.N, pv.DealerParams.N, pv.DealerParams.H1, pv.DealerParams.H2,
+		pv.Curve.Params().Gx, pv.Curve.Params().Gy, pv.Curve.Params().N,
+		pv.PointR.X, pv.PointR.Y, pv.PointX.X, pv.PointX.Y, pv.C, uHat.X,
+		uHat.Y, p.z, vHat, wHat)
+	if err != nil {
+		return err
+	}
+	eHat := new(big.Int).SetBytes(challenge)
+	if !crypto.ConstantTimeEq(p.e, eHat) {
+		return fmt.Errorf("e != eHat")
+	}
+
+	return nil
+}
+
+func (p PdlProof) uHatConstruct(pv *PdlVerifyParams) (*curves.EcPoint, error) {
+	// 3. Compute s1' = s1 mod q
+	s1Tick := new(big.Int).Mod(p.s1, pv.Curve.Params().N)
+
+	// 4. \hat{u} = R^{s^\prime_1} . X^-e in G
+	pointRtoS1Tick, err := pv.PointR.ScalarMult(s1Tick)
+	if err != nil {
+		return nil, err
+	}
+	negE := new(big.Int).Neg(p.e)
+	pointXtoNegE, err := pv.PointX.ScalarMult(negE)
+	if err != nil {
+		return nil, err
+	}
+	uHat, err := pointRtoS1Tick.Add(pointXtoNegE)
+	if err != nil {
+		return nil, err
+	}
+	return uHat, err
+}
+
+func (p PdlProof) vHatConstruct(pv *PdlVerifyParams) (*big.Int, error) {
+	// 5. \hat{v} = s^N . (N + 1)^s_1 . c^-e mod N^2
+
+	// s^N . (N + 1)^s_1 mod N^2
+	pedersenInc, err := inc(p.s1, p.s, pv.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+
+	cInv, err := crypto.Inv(pv.C, pv.Pk.N2)
+	if err != nil {
+		return nil, err
+	}
+	cInvToE := new(big.Int).Exp(cInv, p.e, pv.Pk.N2)
+	vHat, err := crypto.Mul(pedersenInc, cInvToE, pv.Pk.N2)
+	if err != nil {
+		return nil, err
+	}
+	return vHat, nil
+}
+
+func (p PdlProof) wHatConstruct(pv *PdlVerifyParams) (*big.Int, error) {
+	// 6. \hat{w} = h_1^s_1 . h_2^s_2 . z^-e mod \tilde{N}
+
+	// h_1^s_1 . h_2^s_2 mod \tilde{N}
+	pedersenHS, err := pedersen(pv.DealerParams.H1, pv.DealerParams.H2, p.s1, p.s2, pv.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+
+	zInv, err := crypto.Inv(p.z, pv.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	zInvToE := new(big.Int).Exp(zInv, p.e, pv.DealerParams.N)
+	wHat, err := crypto.Mul(pedersenHS, zInvToE, pv.DealerParams.N)
+	if err != nil {
+		return nil, err
+	}
+	return wHat, nil
+}
+
+// randPdl computes the random values for Prove in
+// [spec] fig 14
+func randPdl(p PdlProofParams) (*randPdlParams, error) {
+	// The rings in which to operate
+	q3, err := crypto.Exp(p.Curve.Params().N, big.NewInt(3), nil)
+	if err != nil {
+		return nil, err
+	}
+	q3Ntilde := new(big.Int).Mul(q3, p.DealerParams.N)
+	qNtilde := new(big.Int).Mul(p.Curve.Params().N, p.DealerParams.N)
+
+	// 1. \alpha \getsr \Z_{q^3}
+	alpha, err := crypto.Rand(q3)
+	if err != nil {
+		return nil, err
+	}
+	// 2. \beta \getsr \Z_{N*}
+	beta, err := crypto.Rand(p.Pk.N)
+	if err != nil {
+		return nil, err
+	}
+	// 3. \gamma \getsr \Z_{q^3N~}
+	gamma, err := crypto.Rand(q3Ntilde)
+	if err != nil {
+		return nil, err
+	}
+	// 4. \rho \getsr \Z_{qN~}
+	rho, err := crypto.Rand(qNtilde)
+	if err != nil {
+		return nil, err
+	}
+	return &randPdlParams{
+		alpha, beta, gamma, rho,
+	}, nil
+}
diff --git a/pkg/tecdsa/gg20/proof/pdl_test.go b/pkg/tecdsa/gg20/proof/pdl_test.go
new file mode 100644
index 00000000..30e9de66
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/pdl_test.go
@@ -0,0 +1,393 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package proof
+
+import (
+	"encoding/json"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"testing"
+
+	"github.com/coinbase/kryptology/pkg/tecdsa/gg20/dealer"
+
+	tt "github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	paillier "github.com/coinbase/kryptology/pkg/paillier"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/stretchr/testify/assert"
+)
+
+func TestPdlProof(t *testing.T) {
+	curve := btcec.S256()
+	params := []*PdlProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10453436341595661308638945160744691461102262556435425363472041530426551492325701856213450266088099390020182300308521148275956201847403116901822304716109601")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529"),
+				H1: tt.B10("443981490668637266429687390297201088749634563003174874283715634327157954734001973842075142869362000048454124614775810849589137797362291307830836093830666"),
+				H2: tt.B10("552007421234219533984419815258072687324527963891381405280348833912665473111875648095851026421775527483650971365690299261791177376686729651798107556750986"),
+			},
+			C:       tt.B10("4664726001400863462852903463489684025203539312043087122435633780307370116923286498286011073893114770129124053266553951568210161226338715793626006742280222408787817580104395413260066838171514476835074847117030809020314721196250676941071342943510687061594910173132843733171341122020444569560262354325159459786"),
+			ScalarR: tt.B10("6318180506937413445377662339737616688323403611418981231506634960717709610306639938046692771174821698278861338843502933136372971219816146088826194073514165"),
+			ScalarX: tt.B10("8895158955508830352755492106542967678464513230702348453977370181840454571559"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("76094108851287611405923621794156813263013115318084984186541038825106228865281"),
+				Y:     tt.B10("87411113406201178695670215615289769677595073686246590331802071626605210109743"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("8378869356347693656335563305413627471884674848153157571999293829483801014921"),
+				Y:     tt.B10("80919981448100403067082012436084777199105270046135069091255381624902461382599"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("9831275438511106164565495760001688549814922646898355340010126520876442274445536039860446430205527149090890589584611773573077190211427866931337457355561521")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9088113599264300599673127970260964968548172499135862549023291658586581399335917789448267260706627437027412917124323038435336668655448406702348643933116273"),
+				H1: tt.B10("3164162665053366372408698072382121962273229838328732316301891025388141817123845974331611131026458919634038930316963586876688464406529778828717460449177018"),
+				H2: tt.B10("3613863840368443617288882496207460760567029482693254218641355501439683045686086084409356221053813720993545273087552792708369718290403270154193540852884387"),
+			},
+			C:       tt.B10("22945662658826687122951524609605390162419018623016094527985190729136533122138237274890476792343375181731556056387967150127382752299222119038995116814564676335308780927745023238367652917410224228904840247506797913269791009050330669049148699546893290523696971497415351124890632011355109852928076331069242976047"),
+			ScalarR: tt.B10("1456346843273107174185972100354877067846031294442486303631964113650903606327961364695375229133208501529871889372266089869069469359943307589956370077023244"),
+			ScalarX: tt.B10("102510244919994967843708738855867526851165091005601348643599270378342008853277"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("12444758997853784844785736093813953015213016988344585020934721604959711243454"),
+				Y:     tt.B10("41081235245407629494159229858676719985037195350871196150228771571530041697953"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("113704516018493703928170894572168412753803734325704651734551489944526965122231735113871864832368647984131374540170765278144857407900385316781049514749390883049421840883231007361862310299873591131872921717370699215293767892030993383657270453785323881620589052736661635699834501407565652575588677113465300661621")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("161396156400645198270315630211459947895162204967589557653128434044198146712972763644757188404750507699935523771400075723099627628687570310827922128423806613342745876762453195372210790970822267868149576881285953130288404538709228773231419065929483466982712730393834391664915100319075913286488970166494745830629"),
+				H1: tt.B10("18618690214530067135386407378679435235583632518707852129591131476248349544570233992907989023204083131551404048200303628056048157230120466117628669672695188523977903126491955422473754106558050545355882619327085128114452064455293234627361539242255070012976950034765738988611881073014271066763434146268126349086"),
+				H2: tt.B10("160470932600623889076430120482349695585923700506879108611495379697022889537530614221288183210040855444777056432425669107186536229798598233974027384740387767556408392083678883280773977871278647204040220814095879080051573171911139398073589016379401657293154896951331808925184453340679765040425291638017214591731"),
+			},
+			C:       tt.B10("4896957344081721172301761558878471817093957186883505910055484342858487410780344086015815560906271262760225544259435128094000760341287151463805517048421021266091498903664022813965524626993319004586190337532327563453628353189636257770661887076638254789941394875768438354317008447900448371463627310758169649159129081536916678375894293541030505690802142053594972076696842850896392543134018313744617812407507540361629152950683990975258614557530404228537967408981617289478956979359018250290787402363698811959464011054735419841399680079109795365937107391761037923382540359217859416039274471453061333934384874194680103175375"),
+			ScalarR: tt.B10("71432491042795891026819073612920634365551967354604700070651069540194938209260355758675443987816023583431255584159007910956894102538667454292922436540633732978863886218440548882671875019295174919761937584083905373135768543476976716116826486377526415911236104646671272094245775861150495950556869225179514569498"),
+			ScalarX: tt.B10("29086759249526442678185238367636452309232548742213292674117516677478809708340"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("35373660716694800516809670505588645945109927020371800385493928646782619107408"),
+				Y:     tt.B10("93831376976173894628926808190406953951928006489246828107520931318493467317132"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("28389942534630501102482806139823952974111741690036242604042106439862886603688619267610452037222335475089537679295217755530571580626593285091009558531437945110816976195615021869354989046297137202661162264019525351295566584078998072196727905609637713692910458139555157767778141986605896692381096982746996945671616038237894860009730511432701694170671434630558138362258739746798822701440188845001261413779109525471954002454448797337162405307543709201259184397280458098930135776625337988818635617003108990612812385905691812906155358822153859313442892052035130822740985323920091265835286687462996096274931487719072325610177")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("24261699812894468219236852581962158941171546437127926412539821233148323141430665993557279634858451367749742151236664137456393535021164507932299356327658537600664706925498605224953136885130321375799440215429053090822764789891420452788542049702159277693971272237364975365363501274233385233018279005201887745841750070431152586842339528464629058292767675162224332893682681806584690404282462350130622536519356745051558971274796817643519111513887645688237884295068403256342873438983575942322642554660401209713049218828676032196860400247288848285743977850167317265395686177332360511824206274530781460468391577465417929720801"),
+				H1: tt.B10("17657026647294223687309814976205454222798511294827726675315818303244321015282806894016959804822128590945638885512531773391303086945935616064555312507516711837306890638145180820603885391837297676456752054799643739324722052274736234615797408820276188727496193858254442729685055042577087166691843975492210965633375571812076567425573659274242387855645934243075788600138838255585659176549887756643115277634101423586780449892508521439191012182963941322615448360177625994713792119421184181502278161950043424758607370569862562496188656239924691950965423857119024515492868495595715338851989018661609371457796231769498336259942"),
+				H2: tt.B10("23979964903511705755956518552835814554887788458101934011645738984289256815028997364100177641818315274085279710938880812881865338614102252653491843844747319033943655887178975358186429206512358407551818424689996649740298507695877144746406055658538582677662812963918275966732889580926799957382537995554279850611600698693796312231842307725821392566915849737659700063491348941930277735161335382722598575316473065306523191514953001778020716355562889584062417653273306819064551443565311996996530777393328559492161868722813868345420478163731017090977798561095759196393924713008544722136500375754011856471264672596599640334270"),
+			},
+			C:       tt.B10("312072118059655464479623752896370931287580695147558967175370385693010851904602632704190780873037853776949002099920910929454906746297000764022883262339810373530190503057275803212082490648752402411014710837921985963414326996430994445745103595174798048796872071058757782900936657543421311350819518047263143986520258140347967846766008789950384655455533378645886309519148467471177056605854541459719525084429218454218213528571466092270319677971542765590930957717305827486734849822346435125175072130311484595478227013437950067433362331207479003306966751040290017607880331032857536340225782113656911961520425583296868974183306576630007254668037105123599321810686598872455495139523140221304146923992336080310963429648303646680527705397398978349770824945433952717955829331451943599927661217135182414690477094098800503935476443441681845234327088836940113610943548236652767504866712759845009489949232476510935796276956643665275622378791333366356819315458176981133159815798879989329421090265495234364154899918069686655261893245095558625642862189807914671729788023888722841227953770641754100300708912019242483762170421213715045277109343120955558835679335136820251570631374672604143498438152345107896404355150794115568555566877217881851216716202636"),
+			ScalarR: tt.B10("12900317669231902409891919243971118700371339340973561350358176269148021513243084734168439199346596288634953438481056037867044379527349847448380560153748923321339676070090389745139441984141990380824035678411732060617869487616828715411492104244485577512780240110853142143842539932038847998591353405830524617088326337057091796898754978001112967800124945178039660843489033360568972462506417939839595757327089284304802004150446809871851916545282806087722771656348015818813850000672740747971701015100804323897662661550498524602873193812403530774371979198086396784333450586513136371130153973494143884071046170273825540295768"),
+			ScalarX: tt.B10("70007072993875354057337439998121157887778082743724503170686544130591021558682"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("69223975912566247908360773758405000717925830486569659950886484171255446147778"),
+				Y:     tt.B10("32579403683948471182574476344537350186238230569150920925924612041995719512988"),
+			},
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("PdlProve failed: %v", err)
+		}
+		pv := &PdlVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Pk:           pp.Pk,
+			PointX:       pp.PointX,
+			PointR:       pp.PointR,
+			C:            pp.C,
+		}
+		err = proof.Verify(pv)
+		tt.AssertNoError(t, err)
+	}
+}
+
+func TestPdlProofTampered(t *testing.T) {
+	curve := btcec.S256()
+	params := []*PdlProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10453436341595661308638945160744691461102262556435425363472041530426551492325701856213450266088099390020182300308521148275956201847403116901822304716109601")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529"),
+				H1: tt.B10("443981490668637266429687390297201088749634563003174874283715634327157954734001973842075142869362000048454124614775810849589137797362291307830836093830666"),
+				H2: tt.B10("552007421234219533984419815258072687324527963891381405280348833912665473111875648095851026421775527483650971365690299261791177376686729651798107556750986"),
+			},
+			C:       tt.B10("4664726001400863462852903463489684025203539312043087122435633780307370116923286498286011073893114770129124053266553951568210161226338715793626006742280222408787817580104395413260066838171514476835074847117030809020314721196250676941071342943510687061594910173132843733171341122020444569560262354325159459786"),
+			ScalarR: tt.B10("6318180506937413445377662339737616688323403611418981231506634960717709610306639938046692771174821698278861338843502933136372971219816146088826194073514165"),
+			ScalarX: tt.B10("8895158955508830352755492106542967678464513230702348453977370181840454571559"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("76094108851287611405923621794156813263013115318084984186541038825106228865281"),
+				Y:     tt.B10("87411113406201178695670215615289769677595073686246590331802071626605210109743"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("8378869356347693656335563305413627471884674848153157571999293829483801014921"),
+				Y:     tt.B10("80919981448100403067082012436084777199105270046135069091255381624902461382599"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("9831275438511106164565495760001688549814922646898355340010126520876442274445536039860446430205527149090890589584611773573077190211427866931337457355561521")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("9088113599264300599673127970260964968548172499135862549023291658586581399335917789448267260706627437027412917124323038435336668655448406702348643933116273"),
+				H1: tt.B10("3164162665053366372408698072382121962273229838328732316301891025388141817123845974331611131026458919634038930316963586876688464406529778828717460449177018"),
+				H2: tt.B10("3613863840368443617288882496207460760567029482693254218641355501439683045686086084409356221053813720993545273087552792708369718290403270154193540852884387"),
+			},
+			C:       tt.B10("22945662658826687122951524609605390162419018623016094527985190729136533122138237274890476792343375181731556056387967150127382752299222119038995116814564676335308780927745023238367652917410224228904840247506797913269791009050330669049148699546893290523696971497415351124890632011355109852928076331069242976047"),
+			ScalarR: tt.B10("1456346843273107174185972100354877067846031294442486303631964113650903606327961364695375229133208501529871889372266089869069469359943307589956370077023244"),
+			ScalarX: tt.B10("102510244919994967843708738855867526851165091005601348643599270378342008853277"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("12444758997853784844785736093813953015213016988344585020934721604959711243454"),
+				Y:     tt.B10("41081235245407629494159229858676719985037195350871196150228771571530041697953"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("113704516018493703928170894572168412753803734325704651734551489944526965122231735113871864832368647984131374540170765278144857407900385316781049514749390883049421840883231007361862310299873591131872921717370699215293767892030993383657270453785323881620589052736661635699834501407565652575588677113465300661621")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("161396156400645198270315630211459947895162204967589557653128434044198146712972763644757188404750507699935523771400075723099627628687570310827922128423806613342745876762453195372210790970822267868149576881285953130288404538709228773231419065929483466982712730393834391664915100319075913286488970166494745830629"),
+				H1: tt.B10("18618690214530067135386407378679435235583632518707852129591131476248349544570233992907989023204083131551404048200303628056048157230120466117628669672695188523977903126491955422473754106558050545355882619327085128114452064455293234627361539242255070012976950034765738988611881073014271066763434146268126349086"),
+				H2: tt.B10("160470932600623889076430120482349695585923700506879108611495379697022889537530614221288183210040855444777056432425669107186536229798598233974027384740387767556408392083678883280773977871278647204040220814095879080051573171911139398073589016379401657293154896951331808925184453340679765040425291638017214591731"),
+			},
+			C:       tt.B10("4896957344081721172301761558878471817093957186883505910055484342858487410780344086015815560906271262760225544259435128094000760341287151463805517048421021266091498903664022813965524626993319004586190337532327563453628353189636257770661887076638254789941394875768438354317008447900448371463627310758169649159129081536916678375894293541030505690802142053594972076696842850896392543134018313744617812407507540361629152950683990975258614557530404228537967408981617289478956979359018250290787402363698811959464011054735419841399680079109795365937107391761037923382540359217859416039274471453061333934384874194680103175375"),
+			ScalarR: tt.B10("71432491042795891026819073612920634365551967354604700070651069540194938209260355758675443987816023583431255584159007910956894102538667454292922436540633732978863886218440548882671875019295174919761937584083905373135768543476976716116826486377526415911236104646671272094245775861150495950556869225179514569498"),
+			ScalarX: tt.B10("29086759249526442678185238367636452309232548742213292674117516677478809708340"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("35373660716694800516809670505588645945109927020371800385493928646782619107408"),
+				Y:     tt.B10("93831376976173894628926808190406953951928006489246828107520931318493467317132"),
+			},
+		},
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("28389942534630501102482806139823952974111741690036242604042106439862886603688619267610452037222335475089537679295217755530571580626593285091009558531437945110816976195615021869354989046297137202661162264019525351295566584078998072196727905609637713692910458139555157767778141986605896692381096982746996945671616038237894860009730511432701694170671434630558138362258739746798822701440188845001261413779109525471954002454448797337162405307543709201259184397280458098930135776625337988818635617003108990612812385905691812906155358822153859313442892052035130822740985323920091265835286687462996096274931487719072325610177")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("24261699812894468219236852581962158941171546437127926412539821233148323141430665993557279634858451367749742151236664137456393535021164507932299356327658537600664706925498605224953136885130321375799440215429053090822764789891420452788542049702159277693971272237364975365363501274233385233018279005201887745841750070431152586842339528464629058292767675162224332893682681806584690404282462350130622536519356745051558971274796817643519111513887645688237884295068403256342873438983575942322642554660401209713049218828676032196860400247288848285743977850167317265395686177332360511824206274530781460468391577465417929720801"),
+				H1: tt.B10("17657026647294223687309814976205454222798511294827726675315818303244321015282806894016959804822128590945638885512531773391303086945935616064555312507516711837306890638145180820603885391837297676456752054799643739324722052274736234615797408820276188727496193858254442729685055042577087166691843975492210965633375571812076567425573659274242387855645934243075788600138838255585659176549887756643115277634101423586780449892508521439191012182963941322615448360177625994713792119421184181502278161950043424758607370569862562496188656239924691950965423857119024515492868495595715338851989018661609371457796231769498336259942"),
+				H2: tt.B10("23979964903511705755956518552835814554887788458101934011645738984289256815028997364100177641818315274085279710938880812881865338614102252653491843844747319033943655887178975358186429206512358407551818424689996649740298507695877144746406055658538582677662812963918275966732889580926799957382537995554279850611600698693796312231842307725821392566915849737659700063491348941930277735161335382722598575316473065306523191514953001778020716355562889584062417653273306819064551443565311996996530777393328559492161868722813868345420478163731017090977798561095759196393924713008544722136500375754011856471264672596599640334270"),
+			},
+			C:       tt.B10("312072118059655464479623752896370931287580695147558967175370385693010851904602632704190780873037853776949002099920910929454906746297000764022883262339810373530190503057275803212082490648752402411014710837921985963414326996430994445745103595174798048796872071058757782900936657543421311350819518047263143986520258140347967846766008789950384655455533378645886309519148467471177056605854541459719525084429218454218213528571466092270319677971542765590930957717305827486734849822346435125175072130311484595478227013437950067433362331207479003306966751040290017607880331032857536340225782113656911961520425583296868974183306576630007254668037105123599321810686598872455495139523140221304146923992336080310963429648303646680527705397398978349770824945433952717955829331451943599927661217135182414690477094098800503935476443441681845234327088836940113610943548236652767504866712759845009489949232476510935796276956643665275622378791333366356819315458176981133159815798879989329421090265495234364154899918069686655261893245095558625642862189807914671729788023888722841227953770641754100300708912019242483762170421213715045277109343120955558835679335136820251570631374672604143498438152345107896404355150794115568555566877217881851216716202636"),
+			ScalarR: tt.B10("12900317669231902409891919243971118700371339340973561350358176269148021513243084734168439199346596288634953438481056037867044379527349847448380560153748923321339676070090389745139441984141990380824035678411732060617869487616828715411492104244485577512780240110853142143842539932038847998591353405830524617088326337057091796898754978001112967800124945178039660843489033360568972462506417939839595757327089284304802004150446809871851916545282806087722771656348015818813850000672740747971701015100804323897662661550498524602873193812403530774371979198086396784333450586513136371130153973494143884071046170273825540295768"),
+			ScalarX: tt.B10("70007072993875354057337439998121157887778082743724503170686544130591021558682"),
+			PointX: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("86918276961810349294276103416548851884759982251107"),
+				Y:     tt.B10("87194829221142880348582938487511785107150118762739500766654458540580527283772"),
+			},
+			PointR: &curves.EcPoint{
+				Curve: curve,
+				X:     tt.B10("69223975912566247908360773758405000717925830486569659950886484171255446147778"),
+				Y:     tt.B10("32579403683948471182574476344537350186238230569150920925924612041995719512988"),
+			},
+		},
+	}
+
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("ProvePDL failed: %v", err)
+		}
+		pv := &PdlVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Pk:           pp.Pk,
+			PointX:       pp.PointX,
+			PointR:       pp.PointR,
+			C:            pp.C,
+		}
+		proof.z.Add(proof.z, crypto.One)
+		if err := proof.Verify(pv); err == nil {
+			t.Errorf("Expected PdlVerify to fail but succeeded.")
+		}
+		pv.C.Add(pv.C, crypto.One)
+		if err := proof.Verify(pv); err == nil {
+			t.Errorf("Expected PdlVerify to fail but succeeded.")
+		}
+		pv.C.Sub(pv.C, crypto.One)
+		proof.s1.Add(proof.s1, crypto.One)
+		if err := proof.Verify(pv); err == nil {
+			t.Errorf("Expected PdlVerify to fail but succeeded.")
+		}
+		proof.s1.Sub(proof.s1, crypto.One)
+		proof.e.Add(proof.e, crypto.One)
+		if err := proof.Verify(pv); err == nil {
+			t.Errorf("Expected PdlVerify to fail but succeeded.")
+		}
+	}
+}
+
+func TestPdlProofRandValues(t *testing.T) {
+	curve := btcec.S256()
+	n := tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529")
+	c, _ := crypto.Rand(n)
+	r, _ := crypto.Rand(curve.Params().N)
+	x, _ := crypto.Rand(curve.Params().N)
+	pointX, _ := curves.NewScalarBaseMult(curve, x)
+	pointR, _ := curves.NewScalarBaseMult(curve, r)
+	params := []*PdlProofParams{
+		{
+			Curve: curve,
+			Pk:    paillier.NewPubkey(tt.B10("10453436341595661308638945160744691461102262556435425363472041530426551492325701856213450266088099390020182300308521148275956201847403116901822304716109601")),
+			DealerParams: &dealer.ProofParams{
+				N:  tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529"),
+				H1: tt.B10("443981490668637266429687390297201088749634563003174874283715634327157954734001973842075142869362000048454124614775810849589137797362291307830836093830666"),
+				H2: tt.B10("552007421234219533984419815258072687324527963891381405280348833912665473111875648095851026421775527483650971365690299261791177376686729651798107556750986"),
+			},
+			C:       c,
+			ScalarR: r,
+			ScalarX: x,
+			PointX:  pointX,
+			PointR:  pointR,
+		},
+	}
+	for _, pp := range params {
+		proof, err := pp.Prove()
+		if err != nil {
+			t.Errorf("PdlProve failed: %v", err)
+		}
+		pv := &PdlVerifyParams{
+			Curve:        curve,
+			DealerParams: pp.DealerParams,
+			Pk:           pp.Pk,
+			PointX:       pp.PointX,
+			PointR:       pp.PointR,
+			C:            pp.C,
+		}
+		err = proof.Verify(pv)
+		tt.AssertSomeError(t, err)
+	}
+}
+
+func TestPdlProofInvalidParams(t *testing.T) {
+	params := PdlProofParams{}
+	if _, err := params.Prove(); err == nil {
+		t.Errorf("PdlProve succeeded but should've failed.")
+	}
+	curve := btcec.S256()
+	n := tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529")
+	c, _ := crypto.Rand(n)
+	r, _ := crypto.Rand(curve.Params().N)
+	x, _ := crypto.Rand(curve.Params().N)
+	pointX, _ := curves.NewScalarBaseMult(curve, x)
+	pointR, _ := curves.NewScalarBaseMult(curve, r)
+	params = PdlProofParams{
+		Curve: curve,
+		Pk:    paillier.NewPubkey(tt.B10("10453436341595661308638945160744691461102262556435425363472041530426551492325701856213450266088099390020182300308521148275956201847403116901822304716109601")),
+		DealerParams: &dealer.ProofParams{
+			N:  tt.B10("10963150595205830129496851796933410785873564590065350533653414494671353802134199060973898221372286631263311589006105573391294835324596497070909690030594529"),
+			H1: tt.B10("443981490668637266429687390297201088749634563003174874283715634327157954734001973842075142869362000048454124614775810849589137797362291307830836093830666"),
+			H2: tt.B10("552007421234219533984419815258072687324527963891381405280348833912665473111875648095851026421775527483650971365690299261791177376686729651798107556750986"),
+		},
+		C:       c,
+		ScalarR: r,
+		ScalarX: x,
+		PointX:  pointX,
+		PointR:  pointR,
+	}
+	proof, _ := params.Prove()
+	pv := &PdlVerifyParams{}
+	if err := proof.Verify(pv); err == nil {
+		t.Errorf("PdlVerify succeeded but should've failed.")
+	}
+	pv.DealerParams = params.DealerParams
+	if err := proof.Verify(pv); err == nil {
+		t.Errorf("PdlVerify succeeded but should've failed.")
+	}
+	pv.Curve = params.Curve
+	if err := proof.Verify(pv); err == nil {
+		t.Errorf("PdlVerify succeeded but should've failed.")
+	}
+	pv.C = params.C
+	if err := proof.Verify(pv); err == nil {
+		t.Errorf("PdlVerify succeeded but should've failed.")
+	}
+	pv.PointR = params.PointR
+	if err := proof.Verify(pv); err == nil {
+		t.Errorf("PdlVerify succeeded but should've failed.")
+	}
+}
+
+func TestMarshalJsonPdlProof(t *testing.T) {
+	test := PdlProof{
+		z:  bi(12),
+		e:  bi(44),
+		s:  bi(49),
+		s1: bi(23),
+		s2: bi(14),
+	}
+
+	testJSON, err := json.Marshal(test)
+	assert.NoError(t, err)
+	assert.NotNil(t, testJSON)
+
+	unmarshaled := new(PdlProof)
+	err = json.Unmarshal(testJSON, unmarshaled)
+	assert.NoError(t, err)
+
+	assert.Equal(t, test.z, unmarshaled.z)
+	assert.Equal(t, test.e, unmarshaled.e)
+	assert.Equal(t, test.s, unmarshaled.s)
+	assert.Equal(t, test.s1, unmarshaled.s1)
+	assert.Equal(t, test.s2, unmarshaled.s2)
+}
+
+func TestStaticJsonPdlProof(t *testing.T) {
+	data := []byte(`{"Z":3666989406396256123443963142985320937042278632959430370804934299019701626404330930982847513018767734929278689417846246084124902745912477152349523658654602,"E":3115659271069276958682456068359865660696804370282039638783994681427792171677730593932305448178477745644721625256350270361466861753117055063398718073289695633908136229937717022554402500027743733983898897089676208130222278623864865543290659787169815752947365811271471278892825689889603560622879862341389394279,"S":77224884563607684241444406580257773576818651261464273214366432750766155500256211748871610535423213421390789952149378028436013126188776980935340867863856,"S1":739639048952431062486848243847124327050670851742270761995498294062920488651825727546170911992310856903527646746418983923284199570016337142789932710740405633070420584221244436733666126335959078297768150519780944901453061578676852438,"S2":7537969855339005139292750311314807059221711841400740408031810786514882275608436934507859710115709241956762803680015803927128791793177304895160503061938017049910995658419493513094195497328210909069904843769371376987211938248938850632714083738247153801422079209854600831288816219564593004239147913299330262096355556066672661530438723980217508272395618739481901662008216639924596404726636}`)
+	expected := PdlProof{
+		z:  tt.B10("3666989406396256123443963142985320937042278632959430370804934299019701626404330930982847513018767734929278689417846246084124902745912477152349523658654602"),
+		e:  tt.B10("3115659271069276958682456068359865660696804370282039638783994681427792171677730593932305448178477745644721625256350270361466861753117055063398718073289695633908136229937717022554402500027743733983898897089676208130222278623864865543290659787169815752947365811271471278892825689889603560622879862341389394279"),
+		s:  tt.B10("77224884563607684241444406580257773576818651261464273214366432750766155500256211748871610535423213421390789952149378028436013126188776980935340867863856"),
+		s1: tt.B10("739639048952431062486848243847124327050670851742270761995498294062920488651825727546170911992310856903527646746418983923284199570016337142789932710740405633070420584221244436733666126335959078297768150519780944901453061578676852438"),
+		s2: tt.B10("7537969855339005139292750311314807059221711841400740408031810786514882275608436934507859710115709241956762803680015803927128791793177304895160503061938017049910995658419493513094195497328210909069904843769371376987211938248938850632714083738247153801422079209854600831288816219564593004239147913299330262096355556066672661530438723980217508272395618739481901662008216639924596404726636"),
+	}
+	reconstructed := new(PdlProof)
+	err := json.Unmarshal(data, reconstructed)
+	assert.NoError(t, err)
+	assert.Equal(t, expected.z, reconstructed.z)
+	assert.Equal(t, expected.e, reconstructed.e)
+	assert.Equal(t, expected.s, reconstructed.s)
+	assert.Equal(t, expected.s1, reconstructed.s1)
+	assert.Equal(t, expected.s2, reconstructed.s2)
+}
diff --git a/pkg/tecdsa/gg20/proof/util.go b/pkg/tecdsa/gg20/proof/util.go
new file mode 100644
index 00000000..9083bc64
--- /dev/null
+++ b/pkg/tecdsa/gg20/proof/util.go
@@ -0,0 +1,64 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package proof
+
+import (
+	"math/big"
+
+	"github.com/coinbase/kryptology/internal"
+	core "github.com/coinbase/kryptology/pkg/core"
+)
+
+// inc computes the incremented commitment in the extension ring:
+// (N+1)^\alpha * \beta^N  mod N^2
+func inc(alpha, beta, n *big.Int) (*big.Int, error) {
+	if core.AnyNil(n, alpha, beta) {
+		return nil, internal.ErrNilArguments
+	}
+	np1 := new(big.Int).Add(n, core.One) // (N+1)
+	nn, err := core.Mul(n, n, nil)       // N^2
+	if err != nil {
+		return nil, err
+	}
+
+	// It's pedersen commits all the way down :)
+	return pedersen(np1, beta, alpha, n, nn) // (N+1)^\alpha * \beta^N  mod N^2
+}
+
+// Computes Pedersen's commitment: g^\alpha * h^beta (mod N~)
+func pedersen(g, h, alpha, beta, n *big.Int) (*big.Int, error) {
+	// Don't accept nil inputs
+	if core.AnyNil(g, h, alpha, beta, n) {
+		return nil, internal.ErrNilArguments
+	}
+
+	gAlpha, err := core.Exp(g, alpha, n) // g^alpha
+	if err != nil {
+		return nil, err
+	}
+	hBeta, err := core.Exp(h, beta, n) // h^beta
+	if err != nil {
+		return nil, err
+	}
+
+	// g^\alpha * h^beta (mod N)
+	return core.Mul(gAlpha, hBeta, n)
+}
+
+// Computes Claus Schnorr's proof: xy+z \in Z
+func schnorr(x, y, z *big.Int) (*big.Int, error) {
+	// Don't accept nil inputs
+	if core.AnyNil(x, y, z) {
+		return nil, internal.ErrNilArguments
+	}
+
+	r, err := core.Mul(x, y, nil) // r = xy
+	if err != nil {
+		return nil, err
+	}
+	return r.Add(r, z), nil // r+z = xy+z
+}
diff --git a/pkg/ted25519/frost/README.md b/pkg/ted25519/frost/README.md
new file mode 100755
index 00000000..9692d424
--- /dev/null
+++ b/pkg/ted25519/frost/README.md
@@ -0,0 +1,116 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# frost
+
+```go
+import "github.com/coinbase/kryptology/pkg/ted25519/frost"
+```
+
+## Index
+
+- [type ChallengeDerive](<#type-challengederive>)
+- [type Ed25519ChallengeDeriver](<#type-ed25519challengederiver>)
+  - [func (ed Ed25519ChallengeDeriver) DeriveChallenge(msg []byte, pubKey curves.Point, r curves.Point) (curves.Scalar, error)](<#func-ed25519challengederiver-derivechallenge>)
+- [type Round1Bcast](<#type-round1bcast>)
+- [type Round2Bcast](<#type-round2bcast>)
+- [type Round3Bcast](<#type-round3bcast>)
+- [type Signer](<#type-signer>)
+  - [func NewSigner(info *frost.DkgParticipant, id, thresh uint32, lcoeffs map[uint32]curves.Scalar, cosigners []uint32, challengeDeriver ChallengeDerive) (*Signer, error)](<#func-newsigner>)
+  - [func (signer *Signer) SignRound1() (*Round1Bcast, error)](<#func-signer-signround1>)
+  - [func (signer *Signer) SignRound2(msg []byte, round2Input map[uint32]*Round1Bcast) (*Round2Bcast, error)](<#func-signer-signround2>)
+  - [func (signer *Signer) SignRound3(round3Input map[uint32]*Round2Bcast) (*Round3Bcast, error)](<#func-signer-signround3>)
+
+
+## type [ChallengeDerive](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/challenge_derive.go#L14-L16>)
+
+```go
+type ChallengeDerive interface {
+    DeriveChallenge(msg []byte, pubKey curves.Point, r curves.Point) (curves.Scalar, error)
+}
+```
+
+## type [Ed25519ChallengeDeriver](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/challenge_derive.go#L18>)
+
+```go
+type Ed25519ChallengeDeriver struct{}
+```
+
+### func \(Ed25519ChallengeDeriver\) [DeriveChallenge](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/challenge_derive.go#L20>)
+
+```go
+func (ed Ed25519ChallengeDeriver) DeriveChallenge(msg []byte, pubKey curves.Point, r curves.Point) (curves.Scalar, error)
+```
+
+## type [Round1Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round1.go#L16-L18>)
+
+Round1Bcast contains values to be broadcast to all players after the completion of signing round 1\.
+
+```go
+type Round1Bcast struct {
+    Di, Ei curves.Point
+}
+```
+
+## type [Round2Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round2.go#L16-L19>)
+
+Round2Bcast contains values that will be broadcast to other signers after completion of round 2\.
+
+```go
+type Round2Bcast struct {
+    // contains filtered or unexported fields
+}
+```
+
+## type [Round3Bcast](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round3.go#L17-L21>)
+
+Round3Bcast contains the output of FROST signature\, i\.e\.\, it contains FROST signature \(z\,c\) and the corresponding message msg\.
+
+```go
+type Round3Bcast struct {
+    R    curves.Point
+    Z, C curves.Scalar
+    // contains filtered or unexported fields
+}
+```
+
+## type [Signer](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/participant.go#L17-L29>)
+
+Signer is a tSchnorr player performing the signing operation\.
+
+```go
+type Signer struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewSigner](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/participant.go#L47>)
+
+```go
+func NewSigner(info *frost.DkgParticipant, id, thresh uint32, lcoeffs map[uint32]curves.Scalar, cosigners []uint32, challengeDeriver ChallengeDerive) (*Signer, error)
+```
+
+NewSigner create a signer from a dkg participant Note that we can pre\-assign Lagrange coefficients lcoeffs of each cosigner\. This optimizes performance\. See paragraph 3 of section 3 in the draft \- https://tools.ietf.org/pdf/draft-komlo-frost-00.pdf
+
+### func \(\*Signer\) [SignRound1](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round1.go#L20>)
+
+```go
+func (signer *Signer) SignRound1() (*Round1Bcast, error)
+```
+
+### func \(\*Signer\) [SignRound2](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round2.go#L22>)
+
+```go
+func (signer *Signer) SignRound2(msg []byte, round2Input map[uint32]*Round1Bcast) (*Round2Bcast, error)
+```
+
+SignRound2 implements FROST signing round 2\.
+
+### func \(\*Signer\) [SignRound3](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/frost/round3.go#L23>)
+
+```go
+func (signer *Signer) SignRound3(round3Input map[uint32]*Round2Bcast) (*Round3Bcast, error)
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/ted25519/frost/challenge_derive.go b/pkg/ted25519/frost/challenge_derive.go
new file mode 100644
index 00000000..11758ccc
--- /dev/null
+++ b/pkg/ted25519/frost/challenge_derive.go
@@ -0,0 +1,26 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"crypto/sha512"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+type ChallengeDerive interface {
+	DeriveChallenge(msg []byte, pubKey curves.Point, r curves.Point) (curves.Scalar, error)
+}
+
+type Ed25519ChallengeDeriver struct{}
+
+func (ed Ed25519ChallengeDeriver) DeriveChallenge(msg []byte, pubKey curves.Point, r curves.Point) (curves.Scalar, error) {
+	h := sha512.New()
+	_, _ = h.Write(r.ToAffineCompressed())
+	_, _ = h.Write(pubKey.ToAffineCompressed())
+	_, _ = h.Write(msg)
+	return new(curves.ScalarEd25519).SetBytesWide(h.Sum(nil))
+}
diff --git a/pkg/ted25519/frost/participant.go b/pkg/ted25519/frost/participant.go
new file mode 100644
index 00000000..04b4231b
--- /dev/null
+++ b/pkg/ted25519/frost/participant.go
@@ -0,0 +1,81 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/dkg/frost"
+)
+
+// Signer is a tSchnorr player performing the signing operation.
+type Signer struct {
+	skShare          curves.Scalar // secret signing share for this signer
+	vkShare          curves.Point  // store verification key share
+	verificationKey  curves.Point  // verification key
+	id               uint32        // The ID assigned to this signer's shamir share
+	threshold        uint32
+	curve            *curves.Curve
+	round            uint
+	lCoeffs          map[uint32]curves.Scalar // lCoeffs are Lagrange coefficients of each cosigner.
+	cosigners        []uint32
+	state            *state // Accumulated intermediate values associated with signing
+	challengeDeriver ChallengeDerive
+}
+
+type state struct {
+	// Round 1
+	capD, capE     curves.Point  // capD, capE are commitments this signer generates in signing round 1
+	smallD, smallE curves.Scalar // smallD, smallE are scalars this signer generates in signing round 1
+
+	// Round 2
+	commitments map[uint32]*Round1Bcast // Store commitments broadcast after signing round 1
+	msg         []byte
+	c           curves.Scalar
+	capRs       map[uint32]curves.Point
+	sumR        curves.Point
+}
+
+// NewSigner create a signer from a dkg participant
+// Note that we can pre-assign Lagrange coefficients lcoeffs of each cosigner. This optimizes performance.
+// See paragraph 3 of section 3 in the draft - https://tools.ietf.org/pdf/draft-komlo-frost-00.pdf
+func NewSigner(info *frost.DkgParticipant, id, thresh uint32, lcoeffs map[uint32]curves.Scalar, cosigners []uint32, challengeDeriver ChallengeDerive) (*Signer, error) {
+	if info == nil || len(cosigners) == 0 || len(lcoeffs) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	if thresh > uint32(len(cosigners)) {
+		return nil, fmt.Errorf("threshold is higher than number of signers")
+	}
+
+	if len(lcoeffs) != len(cosigners) {
+		return nil, fmt.Errorf("expected coefficients to be equal to number of cosigners")
+	}
+
+	// Check if cosigners and lcoeffs contain the same IDs
+	for i := 0; i < len(cosigners); i++ {
+		id := cosigners[i]
+		if _, ok := lcoeffs[id]; !ok {
+			return nil, fmt.Errorf("lcoeffs and cosigners have inconsistent ID")
+		}
+	}
+
+	return &Signer{
+		skShare:          info.SkShare,
+		vkShare:          info.VkShare,
+		verificationKey:  info.VerificationKey,
+		id:               id,
+		threshold:        thresh,
+		curve:            info.Curve,
+		round:            1,
+		lCoeffs:          lcoeffs,
+		cosigners:        cosigners,
+		state:            &state{},
+		challengeDeriver: challengeDeriver,
+	}, nil
+}
diff --git a/pkg/ted25519/frost/round1.go b/pkg/ted25519/frost/round1.go
new file mode 100644
index 00000000..c8ae9a62
--- /dev/null
+++ b/pkg/ted25519/frost/round1.go
@@ -0,0 +1,53 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	crand "crypto/rand"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Round1Bcast contains values to be broadcast to all players after the completion of signing round 1.
+type Round1Bcast struct {
+	Di, Ei curves.Point
+}
+
+func (signer *Signer) SignRound1() (*Round1Bcast, error) {
+	// Make sure signer is not empty
+	if signer == nil || signer.curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Make sure round number is correct
+	if signer.round != 1 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Step 1 - Sample di, ei
+	di := signer.curve.Scalar.Random(crand.Reader)
+
+	ei := signer.curve.Scalar.Random(crand.Reader)
+
+	// Step 2 - Compute Di, Ei
+	Di := signer.curve.ScalarBaseMult(di)
+
+	Ei := signer.curve.ScalarBaseMult(ei)
+
+	// Update round number
+	signer.round = 2
+
+	// Store di, ei, Di, Ei locally and broadcast Di, Ei
+	signer.state.capD = Di
+	signer.state.capE = Ei
+	signer.state.smallD = di
+	signer.state.smallE = ei
+	return &Round1Bcast{
+		Di,
+		Ei,
+	}, nil
+}
diff --git a/pkg/ted25519/frost/round2.go b/pkg/ted25519/frost/round2.go
new file mode 100644
index 00000000..64f7503d
--- /dev/null
+++ b/pkg/ted25519/frost/round2.go
@@ -0,0 +1,156 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Round2Bcast contains values that will be broadcast to other signers after completion of round 2.
+type Round2Bcast struct {
+	zi  curves.Scalar
+	vki curves.Point
+}
+
+// SignRound2 implements FROST signing round 2.
+func (signer *Signer) SignRound2(msg []byte, round2Input map[uint32]*Round1Bcast) (*Round2Bcast, error) {
+	// Make sure necessary items of signer are not empty
+	if signer == nil || signer.curve == nil || signer.state == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Make sure those private d is not empty and not zero
+	if signer.state.smallD == nil || signer.state.smallD.IsZero() {
+		return nil, fmt.Errorf("empty d or d is zero")
+	}
+
+	// Make sure those private e is not empty and not zero
+	if signer.state.smallE == nil || signer.state.smallE.IsZero() {
+		return nil, fmt.Errorf("empty e or e is zero")
+	}
+
+	// Make sure msg is not empty
+	if len(msg) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Make sure the round number is correct
+	if signer.round != 2 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Check length of round2Input
+	if uint32(len(round2Input)) != signer.threshold {
+		return nil, fmt.Errorf("Invalid length of round2Input")
+	}
+
+	// Step 2 - Check Dj, Ej on the curve and Store round2Input
+	for id, input := range round2Input {
+		if input == nil || input.Di == nil || input.Ei == nil {
+			return nil, fmt.Errorf("round2Input is nil from participant with id %d\n", id)
+		}
+		if !input.Di.IsOnCurve() || input.Di.IsIdentity() {
+			return nil, fmt.Errorf("commitment Di is not on the curve with id %d\n", id)
+		}
+		if !input.Ei.IsOnCurve() || input.Ei.IsIdentity() {
+			return nil, fmt.Errorf("commitment Ei is not on the curve with id %d\n", id)
+		}
+	}
+	// Store Dj, Ej for further usage.
+	signer.state.commitments = round2Input
+
+	// Step 3-6
+	R := signer.curve.NewIdentityPoint()
+	var ri curves.Scalar
+	Rs := make(map[uint32]curves.Point, signer.threshold)
+	for id, data := range round2Input {
+		// Construct the blob (j, m, {Dj, Ej})
+		blob := concatHashArray(id, msg, round2Input, signer.cosigners)
+
+		// Step 4 - rj = H(j,m,{Dj,Ej}_{j in [1...t]})
+		rj := signer.curve.Scalar.Hash(blob)
+		if signer.id == id {
+			ri = rj
+		}
+
+		// Step 5 - R_j = D_j + r_j*E_j
+		rjEj := data.Ei.Mul(rj)
+		Rj := rjEj.Add(data.Di)
+		// assign Rj
+		Rs[id] = Rj
+
+		// Step 6 - R = R+Rj
+		R = R.Add(Rj)
+	}
+
+	// Step 7 - c = H(m, R)
+	c, err := signer.challengeDeriver.DeriveChallenge(msg, signer.verificationKey, R)
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 8 - Record c, R, Rjs
+	signer.state.c = c
+	signer.state.capRs = Rs
+	signer.state.sumR = R
+
+	// Step 9 - zi = di + ei*ri + Li*ski*c
+	Li := signer.lCoeffs[signer.id]
+	Liski := Li.Mul(signer.skShare)
+
+	Liskic := Liski.Mul(c)
+
+	if R.IsNegative() {
+		signer.state.smallE = signer.state.smallE.Neg()
+		signer.state.smallD = signer.state.smallD.Neg()
+	}
+
+	eiri := signer.state.smallE.Mul(ri)
+
+	// Compute zi = di+ei*ri+Li*ski*c
+	zi := Liskic.Add(eiri)
+	zi = zi.Add(signer.state.smallD)
+
+	// Update round number and store message
+	signer.round = 3
+	signer.state.msg = msg
+
+	// set smallD and smallE to zero since they are one-time use
+	signer.state.smallD = signer.curve.NewScalar()
+	signer.state.smallE = signer.curve.NewScalar()
+
+	// Step 10 - Broadcast zi, vki to other participants
+	return &Round2Bcast{
+		zi,
+		signer.vkShare,
+	}, nil
+}
+
+// concatHashArray puts id, msg and (Dj,Ej), j=1...t into a byte array
+func concatHashArray(id uint32, msg []byte, round2Input map[uint32]*Round1Bcast, cosigners []uint32) []byte {
+	var blob []byte
+	// Append identity id
+	blob = append(blob, byte(id))
+
+	// Append message msg
+	blob = append(blob, msg...)
+
+	// Append (Dj, Ej) for all j in [1...t]
+	for i := 0; i < len(cosigners); i++ {
+		id := cosigners[i]
+		bytesDi := round2Input[id].Di.ToAffineCompressed()
+		bytesEi := round2Input[id].Ei.ToAffineCompressed()
+
+		// Following the spec, we should add each party's identity.
+		blob = append(blob, byte(id))
+		blob = append(blob, bytesDi...)
+		blob = append(blob, bytesEi...)
+	}
+	return blob
+}
diff --git a/pkg/ted25519/frost/round3.go b/pkg/ted25519/frost/round3.go
new file mode 100644
index 00000000..1ae36304
--- /dev/null
+++ b/pkg/ted25519/frost/round3.go
@@ -0,0 +1,124 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"fmt"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// Round3Bcast contains the output of FROST signature, i.e., it contains FROST signature (z,c) and the
+// corresponding message msg.
+type Round3Bcast struct {
+	R    curves.Point
+	Z, C curves.Scalar
+	msg  []byte
+}
+
+func (signer *Signer) SignRound3(round3Input map[uint32]*Round2Bcast) (*Round3Bcast, error) {
+	// Make sure signer is not empty
+	if signer == nil || signer.curve == nil {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Make sure signer's smallD and smallE are zero
+	if !signer.state.smallD.IsZero() || !signer.state.smallE.IsZero() {
+		return nil, fmt.Errorf("signer's private smallD and smallE should be zero since one-time use")
+	}
+
+	// Make sure the signer has had the msg
+	if len(signer.state.msg) == 0 {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Validate Round3Input
+	if round3Input == nil {
+		return nil, internal.ErrNilArguments
+	}
+	for _, data := range round3Input {
+		if data == nil {
+			return nil, internal.ErrNilArguments
+		}
+	}
+
+	// Make sure the signer has commitments stored at the end of round 1.
+	if signer.state.commitments == nil || len(signer.state.commitments) != len(round3Input) {
+		return nil, internal.ErrNilArguments
+	}
+
+	// Make sure the round number is correct
+	if signer.round != 3 {
+		return nil, internal.ErrInvalidRound
+	}
+
+	// Round2 Input has different length of threshold
+	if uint32(len(round3Input)) != signer.threshold {
+		return nil, fmt.Errorf("invalid length of round3Input")
+	}
+
+	// Step 1-3
+	// Step 1: For j in [1...t]
+	z := signer.curve.NewScalar()
+	negate := signer.state.sumR.IsNegative()
+	for id, data := range round3Input {
+		zj := data.zi
+		vkj := data.vki
+
+		// Step 2: Verify zj*G = Rj + c*Lj*vkj
+		// zj*G
+		zjG := signer.curve.ScalarBaseMult(zj)
+
+		// c*Lj
+		cLj := signer.state.c.Mul(signer.lCoeffs[id])
+
+		// cLjvkj
+		cLjvkj := vkj.Mul(cLj)
+
+		// Rj + c*Lj*vkj
+		Rj := signer.state.capRs[id]
+		if negate {
+			Rj = Rj.Neg()
+		}
+		right := cLjvkj.Add(Rj)
+
+		// Check equation
+		if !zjG.Equal(right) {
+			return nil, fmt.Errorf("zjG != right with participant id %d\n", id)
+		}
+
+		// Step 3 - z = z+zj
+		z = z.Add(zj)
+	}
+
+	// Step 4 - 7: Self verify the signature (z, c)
+	// Step 5 - R' = z*G + (-c)*vk
+	zG := signer.curve.ScalarBaseMult(z)
+	cvk := signer.verificationKey.Mul(signer.state.c.Neg())
+	tempR := zG.Add(cvk)
+	// Step 6 - c' = H(m, R')
+	tempC, err := signer.challengeDeriver.DeriveChallenge(signer.state.msg, signer.verificationKey, tempR)
+	if err != nil {
+		return nil, err
+	}
+
+	// Step 7 - Check c = c'
+	if tempC.Cmp(signer.state.c) != 0 {
+		return nil, fmt.Errorf("invalid signature: c != c'")
+	}
+
+	// Updating round number
+	signer.round = 4
+
+	// Step 8 - Broadcast signature and message
+	return &Round3Bcast{
+		signer.state.sumR,
+		z,
+		signer.state.c,
+		signer.state.msg,
+	}, nil
+}
diff --git a/pkg/ted25519/frost/rounds_test.go b/pkg/ted25519/frost/rounds_test.go
new file mode 100644
index 00000000..3d142d54
--- /dev/null
+++ b/pkg/ted25519/frost/rounds_test.go
@@ -0,0 +1,403 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package frost
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	dkg "github.com/coinbase/kryptology/pkg/dkg/frost"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+var (
+	testCurve = curves.ED25519()
+	ctx       = "string to prevent replay attack"
+)
+
+// Create two DKG participants.
+func PrepareDkgOutput(t *testing.T) (*dkg.DkgParticipant, *dkg.DkgParticipant) {
+	// Initiate two participants and running DKG round 1
+	p1, err := dkg.NewDkgParticipant(1, 2, ctx, testCurve, 2)
+	require.NoError(t, err)
+	p2, err := dkg.NewDkgParticipant(2, 2, ctx, testCurve, 1)
+	require.NoError(t, err)
+	bcast1, p2psend1, _ := p1.Round1(nil)
+	bcast2, p2psend2, _ := p2.Round1(nil)
+	bcast := make(map[uint32]*dkg.Round1Bcast)
+	p2p1 := make(map[uint32]*sharing.ShamirShare)
+	p2p2 := make(map[uint32]*sharing.ShamirShare)
+	bcast[1] = bcast1
+	bcast[2] = bcast2
+	p2p1[2] = p2psend2[1]
+	p2p2[1] = p2psend1[2]
+
+	// Running DKG round 2
+	_, _ = p1.Round2(bcast, p2p1)
+	_, _ = p2.Round2(bcast, p2p2)
+	return p1, p2
+}
+
+// Test FROST signing round 1
+func TestSignRound1Works(t *testing.T) {
+	p1, p2 := PrepareDkgOutput(t)
+	require.NotNil(t, p1)
+	require.NotNil(t, p2)
+
+	scheme, _ := sharing.NewShamir(2, 2, testCurve)
+	lCoeffs, _ := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		p1.Id: {Id: p1.Id, Value: p1.SkShare.Bytes()},
+		p2.Id: {Id: p2.Id, Value: p2.SkShare.Bytes()},
+	})
+
+	signer1, err := NewSigner(p1, 1, 2, lCoeffs, []uint32{1, 2}, &Ed25519ChallengeDeriver{})
+	require.NoError(t, err)
+	round1Out, _ := signer1.SignRound1()
+	require.NotNil(t, round1Out.Ei)
+	require.NotNil(t, round1Out.Di)
+	require.NotNil(t, signer1.state.smallE)
+	require.NotNil(t, signer1.state.smallD)
+	require.NotNil(t, signer1.state.capD)
+	require.NotNil(t, signer1.state.capE)
+	require.Equal(t, signer1.round, uint(2))
+	require.Equal(t, signer1.cosigners, []uint32{1, 2})
+}
+
+func TestSignRound1RepeatCall(t *testing.T) {
+	p1, p2 := PrepareDkgOutput(t)
+	scheme, _ := sharing.NewShamir(2, 2, testCurve)
+	lCoeffs, _ := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		p1.Id: {Id: p1.Id, Value: p1.SkShare.Bytes()},
+		p2.Id: {Id: p2.Id, Value: p2.SkShare.Bytes()},
+	})
+	signer1, _ := NewSigner(p1, 1, 2, lCoeffs, []uint32{1, 2}, &Ed25519ChallengeDeriver{})
+	_, err := signer1.SignRound1()
+	require.NoError(t, err)
+	_, err = signer1.SignRound1()
+	require.Error(t, err)
+}
+
+func PrepareNewSigners(t *testing.T) (*Signer, *Signer) {
+	threshold := uint32(2)
+	limit := uint32(2)
+	p1, p2 := PrepareDkgOutput(t)
+	require.Equal(t, p1.VerificationKey, p2.VerificationKey)
+	scheme, err := sharing.NewShamir(threshold, limit, testCurve)
+	// field = sharing.NewField(p1.curve.Params().N)
+	require.NotNil(t, scheme)
+	require.NoError(t, err)
+	lCoeffs, err := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		p1.Id: {Id: p1.Id, Value: p1.SkShare.Bytes()},
+		p2.Id: {Id: p2.Id, Value: p2.SkShare.Bytes()},
+	})
+	require.NotNil(t, lCoeffs[1])
+	require.NotNil(t, lCoeffs[2])
+	require.NoError(t, err)
+	signer1, err := NewSigner(p1, p1.Id, threshold, lCoeffs, []uint32{p1.Id, p2.Id}, &Ed25519ChallengeDeriver{})
+	require.NotNil(t, signer1)
+	require.NoError(t, err)
+	signer2, err := NewSigner(p2, p2.Id, threshold, lCoeffs, []uint32{p1.Id, p2.Id}, &Ed25519ChallengeDeriver{})
+	require.NotNil(t, signer2)
+	require.NoError(t, err)
+	return signer1, signer2
+}
+
+func TestSignRound2Works(t *testing.T) {
+	// Preparing round 2 inputs
+	signer1, signer2 := PrepareNewSigners(t)
+	require.Equal(t, signer1.verificationKey, signer2.verificationKey)
+	require.NotNil(t, signer1)
+	require.NotNil(t, signer2)
+	round1Out1, _ := signer1.SignRound1()
+	round1Out2, _ := signer2.SignRound1()
+	round2Input := make(map[uint32]*Round1Bcast)
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+
+	// Actual Test
+	msg := []byte("message")
+	round2Out, err := signer1.SignRound2(msg, round2Input)
+	require.NotNil(t, round2Out)
+	require.NoError(t, err)
+	require.Equal(t, signer1.round, uint(3))
+	require.NotNil(t, signer1.state.commitments)
+	require.Equal(t, signer1.state.msg, msg)
+	require.True(t, signer1.state.smallD.IsZero())
+	require.True(t, signer1.state.smallE.IsZero())
+}
+
+func TestSignRound2RepeatCall(t *testing.T) {
+	// Preparing round 2 inputs
+	signer1, signer2 := PrepareNewSigners(t)
+	require.NotNil(t, signer1)
+	require.NotNil(t, signer2)
+	round1Out1, _ := signer1.SignRound1()
+	round1Out2, _ := signer2.SignRound1()
+	round2Input := make(map[uint32]*Round1Bcast)
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+
+	// Actual Test
+	msg := []byte("message")
+	_, err := signer1.SignRound2(msg, round2Input)
+	require.NoError(t, err)
+	_, err = signer1.SignRound2(msg, round2Input)
+	require.Error(t, err)
+}
+
+func TestSignRound2BadInput(t *testing.T) {
+	// Preparing round 2 inputs
+	signer1, signer2 := PrepareNewSigners(t)
+	_, _ = signer1.SignRound1()
+	round1Out2, _ := signer2.SignRound1()
+	round2Input := make(map[uint32]*Round1Bcast)
+
+	// Actual Test: Set an input to nil
+	round2Input[signer1.id] = nil
+	round2Input[signer2.id] = round1Out2
+	msg := []byte("message")
+	_, err := signer1.SignRound2(msg, round2Input)
+	require.Error(t, err)
+
+	// Preparing round 2 inputs
+	signer1, signer2 = PrepareNewSigners(t)
+	round1Out1, _ := signer1.SignRound1()
+	round1Out2, _ = signer2.SignRound1()
+	round2Input = make(map[uint32]*Round1Bcast)
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+	// Actual Test: Nil message
+	_, err = signer1.SignRound2(nil, round2Input)
+	require.Error(t, err)
+
+	// Preparing round 2 inputs
+	signer1, signer2 = PrepareNewSigners(t)
+	round1Out1, _ = signer1.SignRound1()
+	round1Out2, _ = signer2.SignRound1()
+	round2Input = make(map[uint32]*Round1Bcast)
+
+	// Actual Test: Set invalid round2Input length
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+	round2Input[3] = round1Out2
+	_, err = signer1.SignRound2(msg, round2Input)
+	require.Error(t, err)
+
+	// Preparing round 2 inputs
+	signer1, signer2 = PrepareNewSigners(t)
+	round1Out1, _ = signer1.SignRound1()
+	round1Out2, _ = signer2.SignRound1()
+	round2Input = make(map[uint32]*Round1Bcast)
+
+	// Actual Test: Set invalid round2Input length
+	round1Out2.Ei = nil
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+	_, err = signer1.SignRound2(msg, round2Input)
+	require.Error(t, err)
+
+	// Preparing round 2 inputs
+	signer1, signer2 = PrepareNewSigners(t)
+	round1Out1, _ = signer1.SignRound1()
+	round1Out2, _ = signer2.SignRound1()
+	round2Input = make(map[uint32]*Round1Bcast)
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+
+	// Actual Test: Set nil smallD and smallE
+	signer1.state.smallD = testCurve.NewScalar()
+	signer1.state.smallE = nil
+	_, err = signer1.SignRound2(msg, round2Input)
+	require.Error(t, err)
+}
+
+func PrepareRound3Input(t *testing.T) (*Signer, *Signer, map[uint32]*Round2Bcast) {
+	// Running sign round 1
+	threshold := uint32(2)
+	limit := uint32(2)
+	p1, p2 := PrepareDkgOutput(t)
+	require.Equal(t, p1.VerificationKey, p2.VerificationKey)
+	scheme, err := sharing.NewShamir(threshold, limit, testCurve)
+	require.NotNil(t, scheme)
+	require.NoError(t, err)
+	lCoeffs, err := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		p1.Id: {Id: p1.Id, Value: p1.SkShare.Bytes()},
+		p2.Id: {Id: p2.Id, Value: p2.SkShare.Bytes()},
+	})
+	require.NotNil(t, lCoeffs[1])
+	require.NotNil(t, lCoeffs[2])
+	require.NoError(t, err)
+
+	signer1, err := NewSigner(p1, p1.Id, threshold, lCoeffs, []uint32{p1.Id, p2.Id}, &Ed25519ChallengeDeriver{})
+	require.NotNil(t, signer1)
+	require.NoError(t, err)
+	signer2, err := NewSigner(p2, p2.Id, threshold, lCoeffs, []uint32{p1.Id, p2.Id}, &Ed25519ChallengeDeriver{})
+	require.NotNil(t, signer2)
+	require.NoError(t, err)
+
+	round1Out1, _ := signer1.SignRound1()
+	round1Out2, _ := signer2.SignRound1()
+	round2Input := make(map[uint32]*Round1Bcast, threshold)
+	round2Input[signer1.id] = round1Out1
+	round2Input[signer2.id] = round1Out2
+
+	// Running sign round 2
+	msg := []byte("message")
+	round2Out1, _ := signer1.SignRound2(msg, round2Input)
+	round2Out2, _ := signer2.SignRound2(msg, round2Input)
+	round3Input := make(map[uint32]*Round2Bcast, threshold)
+	round3Input[signer1.id] = round2Out1
+	round3Input[signer2.id] = round2Out2
+	return signer1, signer2, round3Input
+}
+
+func TestSignRound3Works(t *testing.T) {
+	signer1, signer2, round3Input := PrepareRound3Input(t)
+	round3Out1, err := signer1.SignRound3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out1)
+	round3Out2, err := signer2.SignRound3(round3Input)
+	require.NoError(t, err)
+	require.NotNil(t, round3Out2)
+	// signer1 and signer2 outputs the same signature
+	require.Equal(t, round3Out1.Z, round3Out2.Z)
+	require.Equal(t, round3Out1.C, round3Out2.C)
+}
+
+func TestSignRound3RepeatCall(t *testing.T) {
+	signer1, _, round3Input := PrepareRound3Input(t)
+	_, err := signer1.SignRound3(round3Input)
+	require.NoError(t, err)
+	_, err = signer1.SignRound3(round3Input)
+	require.Error(t, err)
+}
+
+func TestSignRound3BadInput(t *testing.T) {
+	signer1, _, round3Input := PrepareRound3Input(t)
+
+	// Actual test: nil input
+	round3Input[signer1.id] = nil
+	_, err := signer1.SignRound3(round3Input)
+	require.Error(t, err)
+	round3Input = nil
+	_, err = signer1.SignRound3(round3Input)
+	require.Error(t, err)
+
+	// Actual test: set invalid length of round3Input
+	signer1, _, round3Input = PrepareRound3Input(t)
+	round3Input[100] = round3Input[signer1.id]
+	_, err = signer1.SignRound3(round3Input)
+	require.Error(t, err)
+
+	// Actual test: maul the round3Input
+	signer1, _, round3Input = PrepareRound3Input(t)
+	round3Input[signer1.id].zi = round3Input[signer1.id].zi.Add(testCurve.Scalar.New(2))
+	_, err = signer1.SignRound3(round3Input)
+	require.Error(t, err)
+
+	// Actual test: set non-zero smallD and smallE
+	signer1, _, round3Input = PrepareRound3Input(t)
+	signer1.state.smallD = testCurve.Scalar.New(1)
+	_, err = signer1.SignRound3(round3Input)
+	require.Error(t, err)
+}
+
+func TestFullRoundsWorks(t *testing.T) {
+	// Give a full-round test (FROST DKG + FROST Signing) with threshold = 3 and limit = 5, same as the test of tECDSA
+	threshold := 3
+	limit := 5
+
+	// Prepare DKG participants
+	participants := make(map[uint32]*dkg.DkgParticipant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewDkgParticipant(uint32(i), uint32(threshold), ctx, testCurve, otherIds...)
+		require.NoError(t, err)
+		participants[uint32(i)] = p
+	}
+
+	// FROST DKG round 1
+	rnd1Bcast := make(map[uint32]*dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		bcast, p2psend, err := p.Round1(nil)
+		require.NoError(t, err)
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+
+	// FROST DKG round 2
+	for id := range rnd1Bcast {
+		rnd1P2pForP := make(map[uint32]*sharing.ShamirShare)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		_, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		require.NoError(t, err)
+	}
+
+	// Prepare Lagrange coefficients
+	scheme, _ := sharing.NewShamir(uint32(threshold), uint32(limit), testCurve)
+	lCoeffs, _ := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		participants[1].Id: {Id: participants[1].Id, Value: participants[1].SkShare.Bytes()},
+		participants[2].Id: {Id: participants[2].Id, Value: participants[2].SkShare.Bytes()},
+		participants[3].Id: {Id: participants[3].Id, Value: participants[3].SkShare.Bytes()},
+	})
+
+	// Using signer 1, 2 and 3 as cosigners
+	var err error
+	signers := make(map[uint32]*Signer, threshold)
+	for i := 1; i <= threshold; i++ {
+		signers[uint32(i)], err = NewSigner(participants[uint32(i)], uint32(i), uint32(threshold), lCoeffs, []uint32{1, 2, 3}, &Ed25519ChallengeDeriver{})
+		require.NoError(t, err)
+		require.NotNil(t, signers[uint32(i)].skShare)
+	}
+
+	// Running sign round 1
+	round2Input := make(map[uint32]*Round1Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		round1Out, err := signers[uint32(i)].SignRound1()
+		require.NoError(t, err)
+		round2Input[signers[uint32(i)].id] = round1Out
+	}
+
+	// Running sign round 2
+	msg := []byte("message")
+	round3Input := make(map[uint32]*Round2Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		round2Out, err := signers[uint32(i)].SignRound2(msg, round2Input)
+		require.NoError(t, err)
+		round3Input[signers[uint32(i)].id] = round2Out
+	}
+
+	// Running sign round 3
+	result := make(map[uint32]*Round3Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		round3Out, err := signers[uint32(i)].SignRound3(round3Input)
+		require.NoError(t, err)
+		result[signers[uint32(i)].id] = round3Out
+	}
+
+	// Every signer has the same output Schnorr signature
+	z := result[1].Z
+	require.Equal(t, z, result[2].Z)
+	require.Equal(t, z, result[3].Z)
+	c := result[1].C
+	require.Equal(t, c, result[2].C)
+	require.Equal(t, c, result[3].C)
+}
diff --git a/pkg/ted25519/ted25519/README.md b/pkg/ted25519/ted25519/README.md
new file mode 100755
index 00000000..3774935f
--- /dev/null
+++ b/pkg/ted25519/ted25519/README.md
@@ -0,0 +1,382 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# ted25519
+
+```go
+import "github.com/coinbase/kryptology/pkg/ted25519/ted25519"
+```
+
+## Index
+
+- [Constants](<#constants>)
+- [func ExpandSeed(seed []byte) []byte](<#func-expandseed>)
+- [func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error)](<#func-generatekey>)
+- [func GenerateSharedKey(config *ShareConfiguration) (PublicKey, []*KeyShare, Commitments, error)](<#func-generatesharedkey>)
+- [func GenerateSharedNonce(config *ShareConfiguration, s *KeyShare, p PublicKey, m Message) (PublicKey, []*NonceShare, Commitments, error)](<#func-generatesharednonce>)
+- [func PublicKeyFromBytes(bytes []byte) ([]byte, error)](<#func-publickeyfrombytes>)
+- [func Reconstruct(keyShares []*KeyShare, config *ShareConfiguration) ([]byte, error)](<#func-reconstruct>)
+- [func Sign(privateKey PrivateKey, message []byte) ([]byte, error)](<#func-sign>)
+- [func ThresholdSign(expandedSecretKeyShare []byte, publicKey PublicKey, message []byte, rShare []byte, R PublicKey) []byte](<#func-thresholdsign>)
+- [func Verify(publicKey PublicKey, message, sig []byte) (bool, error)](<#func-verify>)
+- [type Commitments](<#type-commitments>)
+  - [func CommitmentsFromBytes(bytes [][]byte) (Commitments, error)](<#func-commitmentsfrombytes>)
+  - [func (commitments Commitments) CommitmentsToBytes() [][]byte](<#func-commitments-commitmentstobytes>)
+- [type KeyShare](<#type-keyshare>)
+  - [func KeyShareFromBytes(bytes []byte) *KeyShare](<#func-keysharefrombytes>)
+  - [func NewKeyShare(identifier byte, secret []byte) *KeyShare](<#func-newkeyshare>)
+  - [func (share *KeyShare) VerifyVSS(commitments Commitments, config *ShareConfiguration) (bool, error)](<#func-keyshare-verifyvss>)
+- [type Message](<#type-message>)
+  - [func (m Message) String() string](<#func-message-string>)
+- [type NonceShare](<#type-nonceshare>)
+  - [func NewNonceShare(identifier byte, secret []byte) *NonceShare](<#func-newnonceshare>)
+  - [func NonceShareFromBytes(bytes []byte) *NonceShare](<#func-noncesharefrombytes>)
+  - [func (n NonceShare) Add(other *NonceShare) *NonceShare](<#func-nonceshare-add>)
+- [type PartialSignature](<#type-partialsignature>)
+  - [func NewPartialSignature(identifier byte, sig []byte) *PartialSignature](<#func-newpartialsignature>)
+  - [func TSign(message Message, key *KeyShare, pub PublicKey, nonce *NonceShare, noncePub PublicKey) *PartialSignature](<#func-tsign>)
+  - [func (sig *PartialSignature) Bytes() []byte](<#func-partialsignature-bytes>)
+  - [func (sig *PartialSignature) R() []byte](<#func-partialsignature-r>)
+  - [func (sig *PartialSignature) S() []byte](<#func-partialsignature-s>)
+- [type PrivateKey](<#type-privatekey>)
+  - [func NewKeyFromSeed(seed []byte) (PrivateKey, error)](<#func-newkeyfromseed>)
+  - [func (priv PrivateKey) Public() crypto.PublicKey](<#func-privatekey-public>)
+  - [func (priv PrivateKey) Seed() []byte](<#func-privatekey-seed>)
+  - [func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error)](<#func-privatekey-sign>)
+- [type PublicKey](<#type-publickey>)
+  - [func GeAdd(a PublicKey, b PublicKey) PublicKey](<#func-geadd>)
+  - [func (p PublicKey) Bytes() []byte](<#func-publickey-bytes>)
+- [type ShareConfiguration](<#type-shareconfiguration>)
+- [type Signature](<#type-signature>)
+  - [func Aggregate(sigs []*PartialSignature, config *ShareConfiguration) (Signature, error)](<#func-aggregate>)
+
+
+## Constants
+
+```go
+const (
+    // PublicKeySize is the size, in bytes, of public keys as used in this package.
+    PublicKeySize = 32
+    // PrivateKeySize is the size, in bytes, of private keys as used in this package.
+    PrivateKeySize = 64
+    // SignatureSize is the size, in bytes, of signatures generated and verified by this package.
+    SignatureSize = 64
+    // SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032.
+    SeedSize = 32
+)
+```
+
+## func [ExpandSeed](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ext.go#L32>)
+
+```go
+func ExpandSeed(seed []byte) []byte
+```
+
+ExpandSeed applies the standard Ed25519 transform to the seed to turn it into the real private key that is used for signing\. It returns the expanded seed\.
+
+## func [GenerateKey](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L87>)
+
+```go
+func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error)
+```
+
+GenerateKey generates a public/private key pair using entropy from rand\. If rand is nil\, crypto/rand\.Reader will be used\.
+
+## func [GenerateSharedKey](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L119>)
+
+```go
+func GenerateSharedKey(config *ShareConfiguration) (PublicKey, []*KeyShare, Commitments, error)
+```
+
+GenerateSharedKey generates a random key\, splits it\, and returns the public key\, shares\, and VSS commitments\.
+
+## func [GenerateSharedNonce](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/noncegen.go#L68-L73>)
+
+```go
+func GenerateSharedNonce(config *ShareConfiguration, s *KeyShare, p PublicKey, m Message) (PublicKey, []*NonceShare, Commitments, error)
+```
+
+GenerateSharedNonce generates a random nonce\, splits it\, and returns the nonce pubkey\, nonce shares\, and VSS commitments\.
+
+## func [PublicKeyFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L17>)
+
+```go
+func PublicKeyFromBytes(bytes []byte) ([]byte, error)
+```
+
+PublicKeyFromBytes converts byte array into PublicKey byte array
+
+## func [Reconstruct](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L179>)
+
+```go
+func Reconstruct(keyShares []*KeyShare, config *ShareConfiguration) ([]byte, error)
+```
+
+Reconstruct recovers the secret from a set of secret shares\.
+
+## func [Sign](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L149>)
+
+```go
+func Sign(privateKey PrivateKey, message []byte) ([]byte, error)
+```
+
+Sign signs the message with privateKey and returns a signature\. It will panic if len\(privateKey\) is not PrivateKeySize\.
+
+## func [ThresholdSign](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ext.go#L57-L61>)
+
+```go
+func ThresholdSign(expandedSecretKeyShare []byte, publicKey PublicKey, message []byte, rShare []byte, R PublicKey) []byte
+```
+
+ThresholdSign is used for creating signatures for threshold protocols that replace the values of the private key and nonce with shamir shares instead\. Because of this we must have a custom signing implementation that accepts arguments for values that cannot be derived anymore and removes the extended key generation since that should be done before the secret is shared\.
+
+expandedSecretKeyShare and rShare must be little\-endian\.
+
+## func [Verify](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L236>)
+
+```go
+func Verify(publicKey PublicKey, message, sig []byte) (bool, error)
+```
+
+Verify reports whether sig is a valid signature of message by publicKey\. It will panic if len\(publicKey\) is not PublicKeySize\. Previously publicKey is of type PublicKey
+
+## type [Commitments](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L37>)
+
+Commitments is a collection of public keys with each coefficient of a polynomial as the secret keys\.
+
+```go
+type Commitments []curves.Point
+```
+
+### func [CommitmentsFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L51>)
+
+```go
+func CommitmentsFromBytes(bytes [][]byte) (Commitments, error)
+```
+
+CommitmentsFromBytes converts bytes to commitments
+
+### func \(Commitments\) [CommitmentsToBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L40>)
+
+```go
+func (commitments Commitments) CommitmentsToBytes() [][]byte
+```
+
+CommitmentsToBytes converts commitments to bytes
+
+## type [KeyShare](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L26-L28>)
+
+KeyShare represents a share of a generated key\.
+
+```go
+type KeyShare struct {
+    *v1.ShamirShare
+}
+```
+
+### func [KeyShareFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L67>)
+
+```go
+func KeyShareFromBytes(bytes []byte) *KeyShare
+```
+
+KeyShareFromBytes converts byte array into KeyShare type
+
+### func [NewKeyShare](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L31>)
+
+```go
+func NewKeyShare(identifier byte, secret []byte) *KeyShare
+```
+
+NewKeyShare is a KeyShare constructor\.
+
+### func \(\*KeyShare\) [VerifyVSS](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L197>)
+
+```go
+func (share *KeyShare) VerifyVSS(commitments Commitments, config *ShareConfiguration) (bool, error)
+```
+
+VerifyVSS validates that a Share represents a solution to a Shamir polynomial in which len\(commitments\) \+ 1 solutions are required to construct the private key for the public key at commitments\[0\]\.
+
+## type [Message](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L11>)
+
+```go
+type Message []byte
+```
+
+### func \(Message\) [String](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L13>)
+
+```go
+func (m Message) String() string
+```
+
+## type [NonceShare](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/noncegen.go#L18-L20>)
+
+NonceShare represents a share of a generated nonce\.
+
+```go
+type NonceShare struct {
+    *KeyShare
+}
+```
+
+### func [NewNonceShare](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/noncegen.go#L23>)
+
+```go
+func NewNonceShare(identifier byte, secret []byte) *NonceShare
+```
+
+NewNonceShare is a NonceShare construction
+
+### func [NonceShareFromBytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/noncegen.go#L28>)
+
+```go
+func NonceShareFromBytes(bytes []byte) *NonceShare
+```
+
+NonceShareFromBytes unmashals a NonceShare from its bytes representation
+
+### func \(NonceShare\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/noncegen.go#L91>)
+
+```go
+func (n NonceShare) Add(other *NonceShare) *NonceShare
+```
+
+Add returns the sum of two NonceShares\.
+
+## type [PartialSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L19-L22>)
+
+```go
+type PartialSignature struct {
+    ShareIdentifier byte   // x-coordinate of which signer produced signature
+    Sig             []byte // 64-byte signature: R || s
+}
+```
+
+### func [NewPartialSignature](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L25>)
+
+```go
+func NewPartialSignature(identifier byte, sig []byte) *PartialSignature
+```
+
+NewPartialSignature creates a new PartialSignature
+
+### func [TSign](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L48>)
+
+```go
+func TSign(message Message, key *KeyShare, pub PublicKey, nonce *NonceShare, noncePub PublicKey) *PartialSignature
+```
+
+TSign generates a signature that can later be aggregated with others to produce a signature valid under the provided public key and nonce pair\.
+
+### func \(\*PartialSignature\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L42>)
+
+```go
+func (sig *PartialSignature) Bytes() []byte
+```
+
+### func \(\*PartialSignature\) [R](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L33>)
+
+```go
+func (sig *PartialSignature) R() []byte
+```
+
+R returns the R component of the signature
+
+### func \(\*PartialSignature\) [S](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/partialsig.go#L38>)
+
+```go
+func (sig *PartialSignature) S() []byte
+```
+
+S returns the s component of the signature
+
+## type [PrivateKey](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L46>)
+
+PrivateKey is the type of Ed25519 private keys\. It implements crypto\.Signer\.
+
+```go
+type PrivateKey []byte
+```
+
+### func [NewKeyFromSeed](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L111>)
+
+```go
+func NewKeyFromSeed(seed []byte) (PrivateKey, error)
+```
+
+NewKeyFromSeed calculates a private key from a seed\. It will panic if len\(seed\) is not SeedSize\. This function is provided for interoperability with RFC 8032\. RFC 8032's private keys correspond to seeds in this package\.
+
+### func \(PrivateKey\) [Public](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L54>)
+
+```go
+func (priv PrivateKey) Public() crypto.PublicKey
+```
+
+Public returns the PublicKey corresponding to priv\.
+
+### func \(PrivateKey\) [Seed](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L63>)
+
+```go
+func (priv PrivateKey) Seed() []byte
+```
+
+Seed returns the private key seed corresponding to priv\. It is provided for interoperability with RFC 8032\. RFC 8032's private keys correspond to seeds in this package\.
+
+### func \(PrivateKey\) [Sign](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L74>)
+
+```go
+func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error)
+```
+
+Sign signs the given message with priv\. Ed25519 performs two passes over messages to be signed and therefore cannot handle pre\-hashed messages\. Thus opts\.HashFunc\(\) must return zero to indicate the message hasn't been hashed\. This can be achieved by passing crypto\.Hash\(0\) as the value for opts\.
+
+## type [PublicKey](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L43>)
+
+PublicKey is the type of Ed25519 public keys\.
+
+```go
+type PublicKey []byte
+```
+
+### func [GeAdd](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ext.go#L16>)
+
+```go
+func GeAdd(a PublicKey, b PublicKey) PublicKey
+```
+
+GeAdd returns the sum of two public keys\, a and b\.
+
+### func \(PublicKey\) [Bytes](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/ed25519.go#L49>)
+
+```go
+func (p PublicKey) Bytes() []byte
+```
+
+Bytes returns the publicKey in byte array
+
+## type [ShareConfiguration](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/keygen.go#L77-L80>)
+
+ShareConfiguration sets threshold and limit for the protocol
+
+```go
+type ShareConfiguration struct {
+    T   int // threshold
+    N   int // total shares
+}
+```
+
+## type [Signature](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/sigagg.go#L16>)
+
+```go
+type Signature = []byte
+```
+
+### func [Aggregate](<https://github.com/coinbase/kryptology/blob/master/pkg/ted25519/ted25519/sigagg.go#L18>)
+
+```go
+func Aggregate(sigs []*PartialSignature, config *ShareConfiguration) (Signature, error)
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/ted25519/ted25519/ed25519.go b/pkg/ted25519/ted25519/ed25519.go
new file mode 100644
index 00000000..b527354f
--- /dev/null
+++ b/pkg/ted25519/ted25519/ed25519.go
@@ -0,0 +1,291 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// This file implements the Ed25519 signature algorithm. See
+// https://ed25519.cr.yp.to/.
+//
+// These functions are also compatible with the “Ed25519” function defined in
+// RFC 8032. However, unlike RFC 8032's formulation, this package's private key
+// representation includes a public key suffix to make multiple signing
+// operations with the same key more efficient. This package refers to the RFC
+// 8032 private key as the “seed”.
+// This code is a port of the public domain, “ref10” implementation of ed25519
+// from SUPERCOP.
+
+package ted25519
+
+import (
+	"bytes"
+	"crypto"
+	cryptorand "crypto/rand"
+	"crypto/sha512"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"io"
+	"strconv"
+)
+
+const (
+	// PublicKeySize is the size, in bytes, of public keys as used in this package.
+	PublicKeySize = 32
+	// PrivateKeySize is the size, in bytes, of private keys as used in this package.
+	PrivateKeySize = 64
+	// SignatureSize is the size, in bytes, of signatures generated and verified by this package.
+	SignatureSize = 64
+	// SeedSize is the size, in bytes, of private key seeds. These are the private key representations used by RFC 8032.
+	SeedSize = 32
+)
+
+// PublicKey is the type of Ed25519 public keys.
+type PublicKey []byte
+
+// PrivateKey is the type of Ed25519 private keys. It implements crypto.Signer.
+type PrivateKey []byte
+
+// Bytes returns the publicKey in byte array
+func (p PublicKey) Bytes() []byte {
+	return p
+}
+
+// Public returns the PublicKey corresponding to priv.
+func (priv PrivateKey) Public() crypto.PublicKey {
+	publicKey := make([]byte, PublicKeySize)
+	copy(publicKey, priv[32:])
+	return PublicKey(publicKey)
+}
+
+// Seed returns the private key seed corresponding to priv. It is provided for
+// interoperability with RFC 8032. RFC 8032's private keys correspond to seeds
+// in this package.
+func (priv PrivateKey) Seed() []byte {
+	seed := make([]byte, SeedSize)
+	copy(seed, priv[:32])
+	return seed
+}
+
+// Sign signs the given message with priv.
+// Ed25519 performs two passes over messages to be signed and therefore cannot
+// handle pre-hashed messages. Thus opts.HashFunc() must return zero to
+// indicate the message hasn't been hashed. This can be achieved by passing
+// crypto.Hash(0) as the value for opts.
+func (priv PrivateKey) Sign(rand io.Reader, message []byte, opts crypto.SignerOpts) (signature []byte, err error) {
+	if opts.HashFunc() != crypto.Hash(0) {
+		return nil, fmt.Errorf("ed25519: cannot sign hashed message")
+	}
+	sig, err := Sign(priv, message)
+	if err != nil {
+		return nil, err
+	}
+	return sig, nil
+}
+
+// GenerateKey generates a public/private key pair using entropy from rand.
+// If rand is nil, crypto/rand.Reader will be used.
+func GenerateKey(rand io.Reader) (PublicKey, PrivateKey, error) {
+	if rand == nil {
+		rand = cryptorand.Reader
+	}
+
+	seed := make([]byte, SeedSize)
+	if _, err := io.ReadFull(rand, seed); err != nil {
+		return nil, nil, err
+	}
+
+	privateKey, err := NewKeyFromSeed(seed)
+	if err != nil {
+		return nil, nil, err
+	}
+	publicKey := make([]byte, PublicKeySize)
+	copy(publicKey, privateKey[32:])
+
+	return publicKey, privateKey, nil
+}
+
+// NewKeyFromSeed calculates a private key from a seed. It will panic if
+// len(seed) is not SeedSize. This function is provided for interoperability
+// with RFC 8032. RFC 8032's private keys correspond to seeds in this
+// package.
+func NewKeyFromSeed(seed []byte) (PrivateKey, error) {
+	// Outline the function body so that the returned key can be stack-allocated.
+	privateKey := make([]byte, PrivateKeySize)
+	err := newKeyFromSeed(privateKey, seed)
+	if err != nil {
+		return nil, err
+	}
+	return privateKey, nil
+}
+
+func newKeyFromSeed(privateKey, seed []byte) error {
+	if l := len(seed); l != SeedSize {
+		return fmt.Errorf("ed25519: bad seed length: " + strconv.Itoa(l))
+	}
+
+	digest := sha512.Sum512(seed)
+	digest[0] &= 248
+	digest[31] &= 127
+	digest[31] |= 64
+
+	var hBytes [32]byte
+	copy(hBytes[:], digest[:])
+
+	h, err := new(curves.ScalarEd25519).SetBytesClamping(hBytes[:])
+	if err != nil {
+		return err
+	}
+	ed25519 := curves.ED25519()
+	A := ed25519.ScalarBaseMult(h)
+
+	publicKeyBytes := A.ToAffineCompressed()
+	copy(privateKey, seed)
+	copy(privateKey[32:], publicKeyBytes[:])
+	return nil
+}
+
+// Sign signs the message with privateKey and returns a signature. It will
+// panic if len(privateKey) is not PrivateKeySize.
+func Sign(privateKey PrivateKey, message []byte) ([]byte, error) {
+	// Outline the function body so that the returned signature can be
+	// stack-allocated.
+	signature := make([]byte, SignatureSize)
+	err := sign(signature, privateKey, message)
+	if err != nil {
+		return nil, err
+	}
+	return signature, nil
+}
+
+func sign(signature, privateKey, message []byte) error {
+	if l := len(privateKey); l != PrivateKeySize {
+		return fmt.Errorf("ed25519: bad private key length: " + strconv.Itoa(l))
+	}
+
+	var err error
+	h := sha512.New()
+	_, err = h.Write(privateKey[:32])
+	if err != nil {
+		return err
+	}
+
+	var digest1, messageDigest, hramDigest [64]byte
+	var expandedSecretKey [32]byte
+	_ = h.Sum(digest1[:0])
+	copy(expandedSecretKey[:], digest1[:])
+	expandedSecretKey[0] &= 248
+	expandedSecretKey[31] &= 63
+	expandedSecretKey[31] |= 64
+
+	h.Reset()
+	_, err = h.Write(digest1[32:])
+	if err != nil {
+		return err
+	}
+	_, _ = h.Write(message)
+	if err != nil {
+		return err
+	}
+	_ = h.Sum(messageDigest[:0])
+
+	r, err := new(curves.ScalarEd25519).SetBytesWide(messageDigest[:])
+	if err != nil {
+		return err
+	}
+
+	// R = r * G
+	R := curves.ED25519().Point.Generator().Mul(r)
+	encodedR := R.ToAffineCompressed()
+
+	h.Reset()
+	_, err = h.Write(encodedR[:])
+	if err != nil {
+		return err
+	}
+	_, err = h.Write(privateKey[32:])
+	if err != nil {
+		return err
+	}
+	_, err = h.Write(message)
+	if err != nil {
+		return err
+	}
+	_ = h.Sum(hramDigest[:0])
+
+	// Set k and s
+	k, err := new(curves.ScalarEd25519).SetBytesWide(hramDigest[:])
+	if err != nil {
+		return err
+	}
+
+	s, err := new(curves.ScalarEd25519).SetBytesClamping(expandedSecretKey[:])
+	if err != nil {
+		return err
+	}
+
+	// S = k*s + r
+	S := k.MulAdd(s, r)
+	copy(signature[:], encodedR[:])
+	copy(signature[32:], S.Bytes()[:])
+	return nil
+}
+
+// Verify reports whether sig is a valid signature of message by publicKey. It
+// will panic if len(publicKey) is not PublicKeySize.
+// Previously publicKey is of type PublicKey
+func Verify(publicKey PublicKey, message, sig []byte) (bool, error) {
+	if l := len(publicKey); l != PublicKeySize {
+		return false, fmt.Errorf("ed25519: bad public key length: " + strconv.Itoa(l))
+	}
+
+	if len(sig) != SignatureSize || sig[63]&224 != 0 {
+		return false, fmt.Errorf("ed25519: bad signature size: " + strconv.Itoa(len(sig)))
+	}
+
+	var publicKeyBytes [32]byte
+	copy(publicKeyBytes[:], publicKey)
+
+	A, err := new(curves.PointEd25519).FromAffineCompressed(publicKeyBytes[:])
+	if err != nil {
+		return false, err
+	}
+
+	// Negate sets A = -A, and returns A. It actually negates X and T but keep Y and Z
+	negA := A.Neg()
+
+	h := sha512.New()
+	_, err = h.Write(sig[:32])
+	if err != nil {
+		panic(err)
+	}
+
+	_, err = h.Write(publicKey[:])
+	if err != nil {
+		return false, err
+	}
+
+	_, err = h.Write(message)
+	if err != nil {
+		return false, err
+	}
+
+	var digest [64]byte
+	_ = h.Sum(digest[:0])
+
+	hReduced, err := new(curves.ScalarEd25519).SetBytesWide(digest[:])
+	if err != nil {
+		return false, err
+	}
+
+	var s [32]byte
+	copy(s[:], sig[32:])
+	sScalar, err := new(curves.ScalarEd25519).SetBytesCanonical(s[:])
+	if err != nil {
+		return false, err
+	}
+
+	// R' = hash * A + s * BasePoint
+	R := new(curves.PointEd25519).VarTimeDoubleScalarBaseMult(hReduced, negA, sScalar)
+	// Check R == R'
+	return bytes.Equal(sig[:32], R.ToAffineCompressed()), nil
+}
diff --git a/pkg/ted25519/ted25519/ed25519_test.go b/pkg/ted25519/ted25519/ed25519_test.go
new file mode 100644
index 00000000..7a908df9
--- /dev/null
+++ b/pkg/ted25519/ted25519/ed25519_test.go
@@ -0,0 +1,241 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Copyright 2016 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package ted25519
+
+import (
+	"bufio"
+	"bytes"
+	"compress/gzip"
+	"crypto"
+	"crypto/rand"
+	"encoding/hex"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"os"
+	"strings"
+	"testing"
+)
+
+// sign.input.gz is a selection of test cases from
+// https://ed25519.cr.yp.to/python/sign.input
+const testVectorPath = "../../../test/data/sign.input.gz"
+
+type zeroReader struct{}
+
+func (zeroReader) Read(buf []byte) (int, error) {
+	for i := range buf {
+		buf[i] = 0
+	}
+	return len(buf), nil
+}
+
+func TestUnmarshalMarshal(t *testing.T) {
+	pub, _, err := GenerateKey(rand.Reader)
+	require.NoError(t, err)
+
+	var publicKeyBytes [32]byte
+	copy(publicKeyBytes[:], pub)
+
+	A, err := new(curves.PointEd25519).FromAffineCompressed(publicKeyBytes[:])
+	require.NoError(t, err)
+	var pub2 [32]byte
+	copy(pub2[:], A.ToAffineCompressed())
+
+	if publicKeyBytes != pub2 {
+		t.Errorf("FromBytes(%v)->ToBytes does not round-trip, got %x\n", publicKeyBytes, pub2)
+	}
+}
+
+func TestSignVerify(t *testing.T) {
+	var zero zeroReader
+	public, private, err := GenerateKey(zero)
+	require.NoError(t, err)
+
+	message := []byte("test message")
+	sig, err := Sign(private, message)
+	require.NoError(t, err)
+	ok, _ := Verify(public, message, sig)
+	require.True(t, ok)
+
+	wrongMessage := []byte("wrong message")
+	ok, _ = Verify(public, wrongMessage, sig)
+	require.True(t, !ok)
+}
+
+func TestCryptoSigner(t *testing.T) {
+	var zero zeroReader
+	public, private, _ := GenerateKey(zero)
+
+	signer := crypto.Signer(private)
+
+	publicInterface := signer.Public()
+	public2, ok := publicInterface.(PublicKey)
+	if !ok {
+		t.Fatalf("expected PublicKey from Public() but got %T", publicInterface)
+	}
+
+	if !bytes.Equal(public, public2) {
+		t.Errorf("public keys do not match: original:%x vs Public():%x", public, public2)
+	}
+
+	message := []byte("message")
+	var noHash crypto.Hash
+	signature, err := signer.Sign(zero, message, noHash)
+	if err != nil {
+		t.Fatalf("error from Sign(): %s", err)
+	}
+
+	ok, _ = Verify(public, message, signature)
+	if !ok {
+		t.Errorf("Verify failed on signature from Sign()")
+	}
+}
+
+func TestMalleability(t *testing.T) {
+	// https://tools.ietf.org/html/rfc8032#section-5.1.7 adds an additional test
+	// that s be in [0, order). This prevents someone from adding a multiple of
+	// order to s and obtaining a second valid signature for the same message.
+	msg := []byte{0x54, 0x65, 0x73, 0x74}
+	sig := []byte{
+		0x7c, 0x38, 0xe0, 0x26, 0xf2, 0x9e, 0x14, 0xaa, 0xbd, 0x05, 0x9a,
+		0x0f, 0x2d, 0xb8, 0xb0, 0xcd, 0x78, 0x30, 0x40, 0x60, 0x9a, 0x8b,
+		0xe6, 0x84, 0xdb, 0x12, 0xf8, 0x2a, 0x27, 0x77, 0x4a, 0xb0, 0x67,
+		0x65, 0x4b, 0xce, 0x38, 0x32, 0xc2, 0xd7, 0x6f, 0x8f, 0x6f, 0x5d,
+		0xaf, 0xc0, 0x8d, 0x93, 0x39, 0xd4, 0xee, 0xf6, 0x76, 0x57, 0x33,
+		0x36, 0xa5, 0xc5, 0x1e, 0xb6, 0xf9, 0x46, 0xb3, 0x1d,
+	}
+	publicKey := []byte{
+		0x7d, 0x4d, 0x0e, 0x7f, 0x61, 0x53, 0xa6, 0x9b, 0x62, 0x42, 0xb5,
+		0x22, 0xab, 0xbe, 0xe6, 0x85, 0xfd, 0xa4, 0x42, 0x0f, 0x88, 0x34,
+		0xb1, 0x08, 0xc3, 0xbd, 0xae, 0x36, 0x9e, 0xf5, 0x49, 0xfa,
+	}
+
+	ok, _ := Verify(publicKey, msg, sig)
+	if ok {
+		t.Fatal("non-canonical signature accepted")
+	}
+}
+
+func TestGolden(t *testing.T) {
+	testDataZ, err := os.Open(testVectorPath)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer testDataZ.Close()
+	testData, err := gzip.NewReader(testDataZ)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer testData.Close()
+
+	scanner := bufio.NewScanner(testData)
+	lineNo := 0
+
+	for scanner.Scan() {
+		lineNo++
+
+		line := scanner.Text()
+		parts := strings.Split(line, ":")
+		if len(parts) != 5 {
+			t.Fatalf("bad number of parts on line %d", lineNo)
+		}
+
+		privBytes, _ := hex.DecodeString(parts[0])
+		pubKey, _ := hex.DecodeString(parts[1])
+		msg, _ := hex.DecodeString(parts[2])
+		sig, _ := hex.DecodeString(parts[3])
+		// The signatures in the test vectors also include the message
+		// at the end, but we just want R and S.
+		sig = sig[:SignatureSize]
+
+		if l := len(pubKey); l != PublicKeySize {
+			t.Fatalf("bad public key length on line %d: got %d bytes", lineNo, l)
+		}
+
+		var priv [PrivateKeySize]byte
+		copy(priv[:], privBytes)
+		copy(priv[32:], pubKey)
+
+		sig2, err := Sign(priv[:], msg)
+		require.NoError(t, err)
+		if !bytes.Equal(sig, sig2[:]) {
+			t.Errorf("different signature result on line %d: %x vs %x", lineNo, sig, sig2)
+		}
+
+		ok, _ := Verify(pubKey, msg, sig2)
+		if !ok {
+			t.Errorf("signature failed to verify on line %d", lineNo)
+		}
+
+		priv2, err := NewKeyFromSeed(priv[:32])
+		require.NoError(t, err)
+		if !bytes.Equal(priv[:], priv2) {
+			t.Errorf("recreating key pair gave different private key on line %d: %x vs %x", lineNo, priv[:], priv2)
+		}
+
+		if pubKey2 := priv2.Public().(PublicKey); !bytes.Equal(pubKey, pubKey2) {
+			t.Errorf("recreating key pair gave different public key on line %d: %x vs %x", lineNo, pubKey, pubKey2)
+		}
+
+		if seed := priv2.Seed(); !bytes.Equal(priv[:32], seed) {
+			t.Errorf("recreating key pair gave different seed on line %d: %x vs %x", lineNo, priv[:32], seed)
+		}
+	}
+
+	if err := scanner.Err(); err != nil {
+		t.Fatalf("error reading test data: %s", err)
+	}
+}
+
+func BenchmarkKeyGeneration(b *testing.B) {
+	var zero zeroReader
+	for i := 0; i < b.N; i++ {
+		if _, _, err := GenerateKey(zero); err != nil {
+			b.Fatal(err)
+		}
+	}
+}
+
+func BenchmarkNewKeyFromSeed(b *testing.B) {
+	seed := make([]byte, SeedSize)
+	b.ReportAllocs()
+	for i := 0; i < b.N; i++ {
+		_, _ = NewKeyFromSeed(seed)
+	}
+}
+
+func BenchmarkSigning(b *testing.B) {
+	var zero zeroReader
+	_, priv, err := GenerateKey(zero)
+	if err != nil {
+		b.Fatal(err)
+	}
+	message := []byte("Hello, world!")
+	b.ReportAllocs()
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		_, _ = Sign(priv, message)
+	}
+}
+
+func BenchmarkVerification(b *testing.B) {
+	var zero zeroReader
+	pub, priv, err := GenerateKey(zero)
+	if err != nil {
+		b.Fatal(err)
+	}
+	message := []byte("Hello, world!")
+	signature, _ := Sign(priv, message)
+	b.ResetTimer()
+	for i := 0; i < b.N; i++ {
+		_, _ = Verify(pub, message, signature)
+	}
+}
diff --git a/pkg/ted25519/ted25519/ext.go b/pkg/ted25519/ted25519/ext.go
new file mode 100644
index 00000000..f5cec14f
--- /dev/null
+++ b/pkg/ted25519/ted25519/ext.go
@@ -0,0 +1,122 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"crypto/sha512"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"strconv"
+)
+
+// GeAdd returns the sum of two public keys, a and b.
+func GeAdd(a PublicKey, b PublicKey) PublicKey {
+	aPoint, err := new(curves.PointEd25519).FromAffineCompressed(a)
+	if err != nil {
+		panic("attempted to add invalid point: a")
+	}
+	bPoint, err := new(curves.PointEd25519).FromAffineCompressed(b)
+	if err != nil {
+		panic("attempted to add invalid point: b")
+	}
+
+	sum := aPoint.Add(bPoint)
+	return sum.ToAffineCompressed()
+}
+
+// ExpandSeed applies the standard Ed25519 transform to the seed to turn it into the real private
+// key that is used for signing. It returns the expanded seed.
+func ExpandSeed(seed []byte) []byte {
+	digest := sha512.Sum512(seed)
+	digest[0] &= 248
+	digest[31] &= 127
+	digest[31] |= 64
+	return digest[:32]
+}
+
+// reverseBytes returns a new slice of the input bytes reversed
+func reverseBytes(inBytes []byte) []byte {
+	outBytes := make([]byte, len(inBytes))
+
+	for i, j := 0, len(inBytes)-1; j >= 0; i, j = i+1, j-1 {
+		outBytes[i] = inBytes[j]
+	}
+
+	return outBytes
+}
+
+// ThresholdSign is used for creating signatures for threshold protocols that replace the values of
+// the private key and nonce with shamir shares instead. Because of this we must have a custom
+// signing implementation that accepts arguments for values that cannot be derived anymore and
+// removes the extended key generation since that should be done before the secret is shared.
+//
+// expandedSecretKeyShare and rShare must be little-endian.
+func ThresholdSign(
+	expandedSecretKeyShare []byte, publicKey PublicKey,
+	message []byte,
+	rShare []byte, R PublicKey, // nolint:gocritic
+) []byte {
+	// These length checks are are sanity checks where we panic if a provided value falls outside of the expected range.
+	// These should never fail in practice but serve to protect us from some bug that would cause us to produce
+	// signatures using a zero value or clipping off extra bytes unintentionally.
+	//
+	// We don't specifically check for 32 byte values as any value within the subgroup field could show up here. This is
+	// different than the upstream Ed25519 which does, but this seems to be a result of how they initialize their byte
+	// slices to constants and does not guarantee the value itself is 32 bytes without padding.
+	if l := len(expandedSecretKeyShare); l == 0 || l > 32 {
+		panic("ed25519: bad key share length: " + strconv.Itoa(l))
+	}
+	if l := len(rShare); l == 0 || l > 32 {
+		panic("ed25519: bad nonce share length: " + strconv.Itoa(l))
+	}
+
+	var expandedSecretKey, rBytes [32]byte
+	copy(expandedSecretKey[:], expandedSecretKeyShare)
+	copy(rBytes[:], rShare)
+
+	// c = H(R || A || m) mod q
+	var hramDigest [64]byte
+	var err error
+	h := sha512.New()
+	_, err = h.Write(R[:])
+	if err != nil {
+		panic(err)
+	}
+	_, err = h.Write(publicKey[:])
+	if err != nil {
+		panic(err)
+	}
+	_, err = h.Write(message)
+	if err != nil {
+		panic(err)
+	}
+	_ = h.Sum(hramDigest[:0])
+
+	// Set c, x and r
+	c, err := new(curves.ScalarEd25519).SetBytesWide(hramDigest[:])
+	if err != nil {
+		panic(err)
+	}
+
+	x, err := new(curves.ScalarEd25519).SetBytesCanonical(expandedSecretKey[:])
+	if err != nil {
+		panic(err)
+	}
+
+	r, err := new(curves.ScalarEd25519).SetBytesCanonical(rBytes[:])
+	if err != nil {
+		panic(err)
+	}
+
+	// s = cx+r
+	s := c.MulAdd(x, r)
+
+	signature := make([]byte, SignatureSize)
+	copy(signature, R[:])
+	copy(signature[32:], s.Bytes()[:])
+
+	return signature
+}
diff --git a/pkg/ted25519/ted25519/ext_test.go b/pkg/ted25519/ted25519/ext_test.go
new file mode 100644
index 00000000..5f779983
--- /dev/null
+++ b/pkg/ted25519/ted25519/ext_test.go
@@ -0,0 +1,110 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"crypto/rand"
+	"encoding/hex"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+	"math/big"
+	"testing"
+)
+
+const expectedSeedHex = "9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60"
+const expectedPrivKeyHex = "307c83864f2833cb427a2ef1c00a013cfdff2768d980c0a3a520f006904de94f"
+
+func TestExpandSeed(t *testing.T) {
+	seedBytes, err := hex.DecodeString(expectedSeedHex)
+	require.NoError(t, err)
+	privKeyHex := hex.EncodeToString(ExpandSeed(seedBytes))
+	require.Equal(t, expectedPrivKeyHex, privKeyHex)
+}
+
+func TestThresholdSign(t *testing.T) {
+	pub, priv, err := generateKey()
+	require.NoError(t, err)
+	field := curves.NewField(curves.Ed25519Order())
+	keyShare := v1.NewShamirShare(0, priv, field)
+	r := big.NewInt(123456789).Bytes()
+	nonceShare := v1.NewShamirShare(0, r, field)
+
+	r = reverseBytes(r)
+	var rInput [32]byte
+	copy(rInput[:], r)
+	scalar, err := new(curves.ScalarEd25519).SetBytesCanonical(rInput[:])
+	require.NoError(t, err)
+	noncePub := curves.ED25519().Point.Generator().Mul(scalar)
+
+	message := []byte("fnord!")
+	wrongMessage := []byte("23")
+	sig := ThresholdSign(reverseBytes(keyShare.Value.Bytes()), pub, message, reverseBytes(nonceShare.Value.Bytes()), noncePub.ToAffineCompressed())
+
+	ok, _ := Verify(pub, message, sig)
+	require.True(t, ok)
+	ok, _ = Verify(pub, wrongMessage, sig)
+	require.False(t, ok)
+}
+
+func TestThresholdSign_invalid_secrets(t *testing.T) {
+	message := []byte("fnord!")
+
+	secret := []byte{0x02}
+	secret = reverseBytes(secret)
+	var sInput [32]byte
+	copy(sInput[:], secret)
+	scalar, err := new(curves.ScalarEd25519).SetBytesCanonical(sInput[:])
+	require.NoError(t, err)
+	pub := curves.ED25519().Point.Generator().Mul(scalar)
+
+	nonce := []byte{0x03}
+	nonce = reverseBytes(nonce)
+	var nInput [32]byte
+	copy(nInput[:], nonce)
+	nScalar, err := new(curves.ScalarEd25519).SetBytesCanonical(nInput[:])
+	require.NoError(t, err)
+	noncePub := curves.ED25519().Point.Generator().Mul(nScalar)
+
+	assert.PanicsWithValue(t, "ed25519: bad key share length: 0",
+		func() {
+			ThresholdSign(make([]byte, 0), pub.ToAffineCompressed(), message, nonce, noncePub.ToAffineCompressed())
+		},
+	)
+
+	assert.PanicsWithValue(t, "ed25519: bad key share length: 33",
+		func() {
+			ThresholdSign(make([]byte, 33), pub.ToAffineCompressed(), message, nonce, noncePub.ToAffineCompressed())
+		},
+	)
+
+	assert.PanicsWithValue(t, "ed25519: bad nonce share length: 0",
+		func() {
+			ThresholdSign(secret, pub.ToAffineCompressed(), message, make([]byte, 0), noncePub.ToAffineCompressed())
+		},
+	)
+
+	assert.PanicsWithValue(t, "ed25519: bad nonce share length: 33",
+		func() {
+			ThresholdSign(secret, pub.ToAffineCompressed(), message, make([]byte, 33), noncePub.ToAffineCompressed())
+		},
+	)
+}
+
+// generateKey is the same as generateSharableKey, but used only for testing
+func generateKey() (PublicKey, []byte, error) {
+	pub, priv, err := GenerateKey(rand.Reader)
+	if err != nil {
+		return nil, nil, err
+	}
+	seed := priv.Seed()
+	expandedSeed := reverseBytes(ExpandSeed(seed))
+	field := &curves.Field{Int: curves.Ed25519Order()}
+	expandedSeedReduced := field.ReducedElementFromBytes(expandedSeed)
+	return pub, expandedSeedReduced.Bytes(), nil
+}
diff --git a/pkg/ted25519/ted25519/keygen.go b/pkg/ted25519/ted25519/keygen.go
new file mode 100644
index 00000000..f4cfd6ff
--- /dev/null
+++ b/pkg/ted25519/ted25519/keygen.go
@@ -0,0 +1,239 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"encoding/binary"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+)
+
+// PublicKeyFromBytes converts byte array into PublicKey byte array
+func PublicKeyFromBytes(bytes []byte) ([]byte, error) {
+	if l := len(bytes); l != PublicKeySize {
+		return nil, fmt.Errorf("invalid public key size: %d", l)
+	}
+
+	return bytes, nil
+}
+
+// KeyShare represents a share of a generated key.
+type KeyShare struct {
+	*v1.ShamirShare
+}
+
+// NewKeyShare is a KeyShare constructor.
+func NewKeyShare(identifier byte, secret []byte) *KeyShare {
+	field := curves.NewField(curves.Ed25519Order())
+	return &KeyShare{v1.NewShamirShare(uint32(identifier), secret, field)}
+}
+
+// Commitments is a collection of public keys with each coefficient of a polynomial as the secret keys.
+type Commitments []curves.Point
+
+// CommitmentsToBytes converts commitments to bytes
+func (commitments Commitments) CommitmentsToBytes() [][]byte {
+	bytes := make([][]byte, len(commitments))
+
+	for i, c := range commitments {
+		bytes[i] = c.ToAffineCompressed()
+	}
+
+	return bytes
+}
+
+// CommitmentsFromBytes converts bytes to commitments
+func CommitmentsFromBytes(bytes [][]byte) (Commitments, error) {
+	comms := make([]curves.Point, len(bytes))
+	for i, pubKeyBytes := range bytes {
+		pubKey, err := PublicKeyFromBytes(pubKeyBytes)
+		if err != nil {
+			return nil, err
+		}
+		comms[i], err = new(curves.PointEd25519).FromAffineCompressed(pubKey)
+		if err != nil {
+			return nil, err
+		}
+	}
+	return comms, nil
+}
+
+// KeyShareFromBytes converts byte array into KeyShare type
+func KeyShareFromBytes(bytes []byte) *KeyShare {
+	field := curves.NewField(curves.Ed25519Order())
+	element := field.ElementFromBytes(bytes[4:])
+
+	// We set first 4 bytes as identifier
+	identifier := binary.BigEndian.Uint32(bytes[:4])
+	return &KeyShare{&v1.ShamirShare{Identifier: identifier, Value: element}}
+}
+
+// ShareConfiguration sets threshold and limit for the protocol
+type ShareConfiguration struct {
+	T int // threshold
+	N int // total shares
+}
+
+// generateSharableKey generates a random key and returns the public key and private key in
+// big-endian encoding. It returns an error if it cannot acquire sufficient randomness.
+func generateSharableKey() (PublicKey, []byte, error) {
+	pub, priv, err := GenerateKey(nil)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Internally the PrivateKey type is represented as the seed || public key, but we want to pull
+	// out seed to share which is the actual private key.
+	seed := priv.Seed()
+
+	// We must apply the key expansion to the seed before splitting the key.
+	// Ed25519 signing by default will apply this during signature generation, but since it involves
+	// a hash function, it breaks the relationship between shares and breaks aggregating signatures.
+	// Our signature generation does not apply this mutation at signing time.
+	//
+	// As per anything that comes from the ed25519 library this value should be treated as
+	// little-endian so we reverse it before using it.
+	expandedSeed := reverseBytes(ExpandSeed(seed))
+
+	// Lastly we must reduce this value into the size of the field so we can share it. This diverges
+	// from how the standard implementation treats this because their scalar multiplication accepts
+	// values up to the curve order but we must constrain it to be able to split it and aggregate.
+	//
+	// If you read the documentation for the ReducedElementFromBytes function we call below, it
+	// includes a big warning about how it will return non-uniform outputs depending on the input.
+	// This is true, but not a concern for keygen specifically because the value we are providing it
+	// has been generated as the ed25519 spec requires, which has a slight bias by definition of how
+	// the ExpandSeed operation works.
+	field := &curves.Field{Int: curves.Ed25519Order()}
+	expandedSeedReduced := field.ReducedElementFromBytes(expandedSeed)
+
+	return pub, expandedSeedReduced.Bytes(), nil
+}
+
+// GenerateSharedKey generates a random key, splits it, and returns the public key, shares, and VSS commitments.
+func GenerateSharedKey(config *ShareConfiguration) (PublicKey, []*KeyShare, Commitments, error) {
+	pub, priv, err := generateSharableKey()
+	//pub, priv, err := ed25519.GenerateKey(nil)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+
+	keyShares, commitments, err := splitPrivateKey(config, priv)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+
+	return pub, keyShares, commitments, nil
+}
+
+// splitPrivateKey splits the secret into a set of secret shares and creates a set of commitments of them.
+func splitPrivateKey(config *ShareConfiguration, priv []byte) ([]*KeyShare, Commitments, error) {
+	commitments, shares, err := split(priv, config)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	keyShares := make([]*KeyShare, len(shares))
+	for i, s := range shares {
+		keyShares[i] = &KeyShare{s}
+	}
+	return keyShares, commitments, nil
+}
+
+// split contains core operations to split the secret and generate commitments.
+func split(secret []byte, config *ShareConfiguration) ([]curves.Point, []*v1.ShamirShare, error) {
+	field := curves.NewField(curves.Ed25519Order())
+	shamir, err := v1.NewShamir(config.T, config.N, field)
+	if err != nil {
+		return nil, nil, fmt.Errorf("Error in NewShamir")
+	}
+	shares, poly, err := shamir.GetSharesAndPolynomial(secret)
+	if err != nil {
+		return nil, nil, fmt.Errorf("Error in GetSharesAndPolynomial")
+	}
+
+	// Generate the verifiable commitments to the polynomial for the shares
+	verifiers := make([]curves.Point, len(poly.Coefficients))
+	// curve := sharing.Ed25519()
+	for i, c := range poly.Coefficients {
+		// We have to reverse each coefficient, which is different than the method sharing.Split
+		reverseC := reverseBytes(c.Bytes())
+		var reverseInput [32]byte
+		copy(reverseInput[:], reverseC)
+		cScalar, err := new(curves.ScalarEd25519).SetBytesCanonical(reverseInput[:])
+		if err != nil {
+			return nil, nil, fmt.Errorf("Error in SetBytesCanonical reverseC")
+		}
+		v := curves.ED25519().Point.Generator().Mul(cScalar)
+		verifiers[i] = v
+	}
+	return verifiers, shares, nil
+}
+
+// Reconstruct recovers the secret from a set of secret shares.
+func Reconstruct(keyShares []*KeyShare, config *ShareConfiguration) ([]byte, error) {
+	curve := v1.Ed25519()
+	field := curves.NewField(curve.Params().N)
+	shamir, err := v1.NewShamir(config.T, config.N, field)
+	if err != nil {
+		return nil, err
+	}
+
+	shares := make([]*v1.ShamirShare, len(keyShares))
+	for i, s := range keyShares {
+		shares[i] = s.ShamirShare
+	}
+	return shamir.Combine(shares...)
+}
+
+// VerifyVSS validates that a Share represents a solution to a Shamir polynomial
+// in which len(commitments) + 1 solutions are required to construct the private
+// key for the public key at commitments[0].
+func (share *KeyShare) VerifyVSS(commitments Commitments, config *ShareConfiguration) (bool, error) {
+	if len(commitments) < config.T {
+		return false, fmt.Errorf("not enough verifiers to check")
+	}
+	field := curves.NewField(curves.Ed25519Order())
+	xBytes := make([]byte, 4)
+	binary.BigEndian.PutUint32(xBytes, share.Identifier)
+	x := field.ElementFromBytes(xBytes)
+	i := share.Value.Modulus.One()
+
+	// c_0
+	rhs := commitments[0]
+
+	// Compute the sum of products
+	// c_0 * c_1^i * c_2^{i^2} *c_3^{i^3}
+	for j := 1; j < len(commitments); j++ {
+		// i *= x
+		i = i.Mul(x)
+
+		var iBytes [32]byte
+		copy(iBytes[:], i.Bytes()[:])
+		iScalar, err := new(curves.ScalarEd25519).SetBytesCanonical(iBytes[:])
+		if err != nil {
+			return false, fmt.Errorf("Error in SetBytesCanonical iBytes")
+		}
+		c := commitments[j].Mul(iScalar)
+
+		// ...* c_j^{i^j}
+		rhs = rhs.Add(c)
+	}
+
+	vValue := reverseBytes(share.Value.Bytes())
+	var vInput [32]byte
+	copy(vInput[:], vValue)
+	vScalar, err := new(curves.ScalarEd25519).SetBytes(vInput[:])
+	if err != nil {
+		return false, err
+	}
+	lhs := curves.ED25519().ScalarBaseMult(vScalar)
+
+	// Check if lhs == rhs
+	return lhs.Equal(rhs), nil
+}
diff --git a/pkg/ted25519/ted25519/keygen_test.go b/pkg/ted25519/ted25519/keygen_test.go
new file mode 100644
index 00000000..c333334d
--- /dev/null
+++ b/pkg/ted25519/ted25519/keygen_test.go
@@ -0,0 +1,126 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestGenerateEd25519Key(t *testing.T) {
+	config := ShareConfiguration{T: 2, N: 3}
+
+	// Generate and verify correct number of shares are produced
+	pub, shares, _, err := GenerateSharedKey(&config)
+	require.NoError(t, err)
+	assert.Equal(t, config.N, len(shares))
+
+	// Verify reconstuction works for all permutations of shares
+	shareVec := make([]*KeyShare, 2)
+	shareVec[0] = shares[0]
+	shareVec[1] = shares[1]
+	secret1, err := Reconstruct(shareVec, &config)
+	assert.Nil(t, err)
+	shareVec[0] = shares[1]
+	shareVec[1] = shares[2]
+	secret2, err := Reconstruct(shareVec, &config)
+	assert.Nil(t, err)
+	shareVec[0] = shares[0]
+	shareVec[1] = shares[2]
+	secret3, err := Reconstruct(shareVec, &config)
+	assert.Nil(t, err)
+	assert.Equal(t, secret1, secret2)
+	assert.Equal(t, secret2, secret3)
+
+	// Need to reverse secret1
+	secret1 = reverseBytes(secret1)
+	var secret1Bytes [32]byte
+	copy(secret1Bytes[:], secret1)
+	scalar1, err := new(curves.ScalarEd25519).SetBytesCanonical(secret1Bytes[:])
+	require.NoError(t, err)
+	ed25519 := curves.ED25519()
+	pubFromSeed := ed25519.Point.Generator().Mul(scalar1)
+
+	require.NoError(t, err)
+	assert.Equal(t, pubFromSeed.ToAffineCompressed(), pub.Bytes())
+}
+
+func TestGenerateEd25519KeyInvalidConfig(t *testing.T) {
+	invalidConfig := ShareConfiguration{T: 1, N: 1}
+	_, _, _, err := GenerateSharedKey(&invalidConfig)
+	assert.NotNil(t, err)
+	assert.Error(t, err)
+
+	invalidConfig = ShareConfiguration{T: 2, N: 1}
+	_, _, _, err = GenerateSharedKey(&invalidConfig)
+	assert.NotNil(t, err)
+	assert.Error(t, err)
+}
+
+func TestVerifyVSSEd25519(t *testing.T) {
+
+	config := ShareConfiguration{T: 2, N: 3}
+	pubKey1, shares1, commitments1, err := GenerateSharedKey(&config)
+	require.NoError(t, err)
+	pubKey2, shares2, commitments2, err := GenerateSharedKey(&config)
+	require.NoError(t, err)
+
+	assert.Equal(t, pubKey1.Bytes(), commitments1[0].ToAffineCompressed())
+	assert.Equal(t, pubKey2.Bytes(), commitments2[0].ToAffineCompressed())
+
+	for _, s := range shares1 {
+		ok, err := s.VerifyVSS(commitments1, &config)
+		require.NoError(t, err)
+		require.True(t, ok)
+		ok, _ = s.VerifyVSS(commitments2, &config)
+		require.True(t, !ok)
+	}
+
+	for _, s := range shares2 {
+		ok, err := s.VerifyVSS(commitments2, &config)
+		require.NoError(t, err)
+		require.True(t, ok)
+		ok, _ = s.VerifyVSS(commitments1, &config)
+		require.True(t, !ok)
+	}
+}
+
+func TestCommitmentsFromBytes(t *testing.T) {
+	config := ShareConfiguration{T: 2, N: 3}
+	_, _, comms, err := GenerateSharedKey(&config)
+	require.NoError(t, err)
+
+	recoveredComms, err := CommitmentsFromBytes(comms.CommitmentsToBytes())
+	require.NoError(t, err)
+	require.Equal(t, len(comms), len(recoveredComms))
+	for i := range comms {
+		require.True(t, comms[i].Equal(recoveredComms[i]))
+	}
+	_, err = CommitmentsFromBytes([][]byte{{0x01}})
+	require.Error(t, err)
+}
+
+func TestPublicKeyFromBytes(t *testing.T) {
+	_, err := PublicKeyFromBytes([]byte{0x01})
+	require.EqualError(t, err, "invalid public key size: 1")
+}
+
+func TestKeyShareFromBytes(t *testing.T) {
+	field := curves.NewField(curves.Ed25519Order())
+	share := &v1.ShamirShare{
+		Identifier: 2,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	shareBytes := share.Bytes()
+	recoveredShare := KeyShareFromBytes(shareBytes)
+	require.Equal(t, recoveredShare.ShamirShare, share)
+}
diff --git a/pkg/ted25519/ted25519/noncegen.go b/pkg/ted25519/ted25519/noncegen.go
new file mode 100644
index 00000000..f557eede
--- /dev/null
+++ b/pkg/ted25519/ted25519/noncegen.go
@@ -0,0 +1,121 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"crypto/rand"
+	"crypto/sha256"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"golang.org/x/crypto/hkdf"
+	"io"
+)
+
+// NonceShare represents a share of a generated nonce.
+type NonceShare struct {
+	*KeyShare
+}
+
+// NewNonceShare is a NonceShare construction
+func NewNonceShare(identifier byte, secret []byte) *NonceShare {
+	return &NonceShare{NewKeyShare(identifier, secret)}
+}
+
+// NonceShareFromBytes unmashals a NonceShare from its bytes representation
+func NonceShareFromBytes(bytes []byte) *NonceShare {
+	return &NonceShare{KeyShareFromBytes(bytes)}
+}
+
+func generateSharableNonce(s *KeyShare, p PublicKey, m Message) (PublicKey, []byte, error) {
+	// Create an HKDF reader that produces random bytes that we will use to create a nonce
+	hkdf, err := generateRandomHkdf(s, p, m)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Generate a random nonce that is within the field range so that we can share it.
+	//
+	// This diverges from how the standard implementation treats it because their scalar
+	// multiplication accepts values up to the curve order, but we must constrain it to be able to
+	// split it and aggregate.
+	//
+	// WARN: This operation is not constant time and we are dealing with a secret value
+	nonce, err := curves.NewField(curves.Ed25519Order()).RandomElement(hkdf)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	nonceBytes := nonce.Bytes()
+	reverseBytes := reverseBytes(nonceBytes)
+	var reverseInput [32]byte
+	copy(reverseInput[:], reverseBytes)
+	scalar, err := new(curves.ScalarEd25519).SetBytesCanonical(reverseInput[:])
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// Generate the nonce pubkey by multiplying it by the base point.
+	noncePubkey := curves.ED25519().Point.Generator().Mul(scalar)
+
+	return noncePubkey.ToAffineCompressed(), nonceBytes, nil
+}
+
+// GenerateSharedNonce generates a random nonce, splits it, and returns the nonce pubkey, nonce shares, and
+// VSS commitments.
+func GenerateSharedNonce(config *ShareConfiguration, s *KeyShare, p PublicKey, m Message) (
+	PublicKey,
+	[]*NonceShare,
+	Commitments,
+	error,
+) {
+	noncePubkey, nonce, err := generateSharableNonce(s, p, m)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+	keyShares, vssCommitments, err := splitPrivateKey(config, nonce)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+
+	nonceShares := make([]*NonceShare, len(keyShares))
+	for i, k := range keyShares {
+		nonceShares[i] = &NonceShare{k}
+	}
+	return noncePubkey, nonceShares, vssCommitments, nil
+}
+
+// Add returns the sum of two NonceShares.
+func (n NonceShare) Add(other *NonceShare) *NonceShare {
+	return &NonceShare{
+		&KeyShare{
+			// use Add method from the shamir.Share type to sum the shares
+			// WARN: This is not constant time and deals with secrets
+			n.ShamirShare.Add(other.ShamirShare),
+		},
+	}
+}
+
+// generateRandomHkdf returns an HMAC-based extract-and-expand Key Derivation Function (see RFC 5869).
+func generateRandomHkdf(s *KeyShare, p PublicKey, m Message) (io.Reader, error) {
+	// We _must_ introduce randomness to the HKDF to make the output non-deterministic because deterministic nonces open
+	// up threshold schemes to potential nonce-reuse attacks. We continue to use the HKDF that takes in context about
+	// what is going to be signed as it adds some protection against bad local randomness.
+	randNonce := make([]byte, SeedSize)
+	if _, err := io.ReadFull(rand.Reader, randNonce); err != nil {
+		return nil, err
+	}
+
+	var secret []byte
+	secret = append(secret, s.Bytes()...)
+	secret = append(secret, randNonce...)
+
+	info := []byte("ted25519nonce")
+	// We use info for non-secret inputs to limit an attacker's ability to influence the key.
+	info = append(info, p.Bytes()...)
+	info = append(info, m...)
+
+	return hkdf.New(sha256.New, secret, nil, info), nil
+}
diff --git a/pkg/ted25519/ted25519/noncegen_test.go b/pkg/ted25519/ted25519/noncegen_test.go
new file mode 100644
index 00000000..16caa1b5
--- /dev/null
+++ b/pkg/ted25519/ted25519/noncegen_test.go
@@ -0,0 +1,105 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+	"math/big"
+	"testing"
+)
+
+func TestNonceShareFromBytes(t *testing.T) {
+	field := curves.NewField(curves.Ed25519Order())
+	share := &v1.ShamirShare{
+		Identifier: 2,
+		Value:      field.NewElement(big.NewInt(3)),
+	}
+	shareBytes := share.Bytes()
+	recoveredShare := NonceShareFromBytes(shareBytes)
+	require.Equal(t, recoveredShare.ShamirShare, share)
+	require.Equal(t, share.Identifier, uint32(2))
+}
+
+func TestGenerateSharedNonce_congruence(t *testing.T) {
+	config := &ShareConfiguration{T: 2, N: 3}
+	message := []byte("fnord!")
+	pubKey, keyShares, _, err := GenerateSharedKey(config)
+	require.NoError(t, err)
+	nonceCommitment, nonceShares, _, err := GenerateSharedNonce(config, keyShares[0], pubKey, message)
+	require.NoError(t, err)
+	field := curves.NewField(curves.Ed25519Order())
+	shamir, err := v1.NewShamir(config.T, config.N, field)
+	require.NoError(t, err)
+	nonce, err := shamir.Combine(toShamirShare(nonceShares)...)
+	require.NoError(t, err)
+
+	nonce = reverseBytes(nonce)
+	var nonceBytes [32]byte
+	copy(nonceBytes[:], nonce)
+	nonceScalar, err := new(curves.ScalarEd25519).SetBytesCanonical(nonceBytes[:])
+	require.NoError(t, err)
+	ed25519 := curves.ED25519()
+	recoveredCommitment := ed25519.Point.Generator().Mul(nonceScalar)
+	require.Equal(t, recoveredCommitment.ToAffineCompressed(), nonceCommitment.Bytes())
+}
+
+func TestGenerateNonce_non_determinism(t *testing.T) {
+	config := &ShareConfiguration{T: 2, N: 3}
+	message := []byte("fnord!")
+	pubKey, keyShares, _, err := GenerateSharedKey(config)
+	require.NoError(t, err)
+
+	_, nonceShares1, _, err := GenerateSharedNonce(config, keyShares[0], pubKey, message)
+	require.NoError(t, err)
+	field := curves.NewField(curves.Ed25519Order())
+	shamir, err := v1.NewShamir(config.T, config.N, field)
+	require.NoError(t, err)
+	nonce1, err := shamir.Combine(toShamirShare(nonceShares1)...)
+	require.NoError(t, err)
+
+	_, nonceShares2, _, err := GenerateSharedNonce(config, keyShares[1], pubKey, message)
+	require.NoError(t, err)
+	nonce2, err := shamir.Combine(toShamirShare(nonceShares2)...)
+	require.NoError(t, err)
+
+	_, nonceShares3, _, err := GenerateSharedNonce(config, keyShares[0], pubKey, message)
+	require.NoError(t, err)
+	nonce3, err := shamir.Combine(toShamirShare(nonceShares3)...)
+	require.NoError(t, err)
+
+	require.NotEqual(t, nonce1, nonce2)
+	require.NotEqual(t, nonce1, nonce3)
+}
+
+func TestNonceSharesAdd(t *testing.T) {
+	one := NewNonceShare(0, []byte{0x01})
+	two := NewNonceShare(0, []byte{0x02})
+
+	// basic addition
+	sum := one.Add(two)
+	assert.Equal(t, uint32(0), sum.Identifier)
+	assert.Equal(t, []byte{0x03}, sum.Value.Bytes())
+}
+
+func TestNonceSharesAdd_errors(t *testing.T) {
+	one := NewNonceShare(0, []byte{0x01})
+	two := NewNonceShare(1, []byte{0x02})
+	assert.PanicsWithValue(t, "identifiers must match for valid addition", func() {
+		one.Add(two)
+	})
+}
+
+func toShamirShare(nonceShares []*NonceShare) []*v1.ShamirShare {
+	shamirShares := make([]*v1.ShamirShare, len(nonceShares))
+	for i, n := range nonceShares {
+		shamirShares[i] = n.ShamirShare
+	}
+	return shamirShares
+}
diff --git a/pkg/ted25519/ted25519/partialsig.go b/pkg/ted25519/ted25519/partialsig.go
new file mode 100644
index 00000000..91b39d7d
--- /dev/null
+++ b/pkg/ted25519/ted25519/partialsig.go
@@ -0,0 +1,55 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import "strconv"
+
+type Message []byte
+
+func (m Message) String() string {
+	return string(m)
+}
+
+const signatureLength = 64
+
+type PartialSignature struct {
+	ShareIdentifier byte   // x-coordinate of which signer produced signature
+	Sig             []byte // 64-byte signature: R || s
+}
+
+// NewPartialSignature creates a new PartialSignature
+func NewPartialSignature(identifier byte, sig []byte) *PartialSignature {
+	if l := len(sig); l != signatureLength {
+		panic("ted25519: invalid partial signature length: " + strconv.Itoa(l))
+	}
+	return &PartialSignature{ShareIdentifier: identifier, Sig: sig}
+}
+
+// R returns the R component of the signature
+func (sig *PartialSignature) R() []byte {
+	return sig.Sig[:32]
+}
+
+// S returns the s component of the signature
+func (sig *PartialSignature) S() []byte {
+	return sig.Sig[32:]
+}
+
+func (sig *PartialSignature) Bytes() []byte {
+	return sig.Sig
+}
+
+// TSign generates a signature that can later be aggregated with others to produce a signature valid
+// under the provided public key and nonce pair.
+func TSign(message Message, key *KeyShare, pub PublicKey, nonce *NonceShare, noncePub PublicKey) *PartialSignature {
+	sig := ThresholdSign(
+		reverseBytes(key.Value.Bytes()), pub,
+		message,
+		reverseBytes(nonce.Value.Bytes()), noncePub,
+	)
+	return NewPartialSignature(byte(key.ShamirShare.Identifier), sig)
+}
diff --git a/pkg/ted25519/ted25519/partialsig_test.go b/pkg/ted25519/ted25519/partialsig_test.go
new file mode 100644
index 00000000..1992591b
--- /dev/null
+++ b/pkg/ted25519/ted25519/partialsig_test.go
@@ -0,0 +1,55 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+	"math/big"
+	"testing"
+)
+
+func TestPartialSignNormalSignature(t *testing.T) {
+	pub, priv, err := generateSharableKey()
+	require.NoError(t, err)
+	keyShare := NewKeyShare(0, priv)
+	r := big.NewInt(123456789).Bytes()
+	nonceShare := NewNonceShare(0, r)
+
+	r = reverseBytes(r)
+	var rInput [32]byte
+	copy(rInput[:], r)
+	scalar, err := new(curves.ScalarEd25519).SetBytesCanonical(rInput[:])
+	require.NoError(t, err)
+	noncePub := curves.ED25519().Point.Generator().Mul(scalar)
+
+	message := []byte("test message")
+	wrongMessage := []byte("wrong message")
+	sig := TSign(message, keyShare, pub, nonceShare, noncePub.ToAffineCompressed())
+
+	ok, _ := Verify(pub, message, sig.Sig)
+	require.True(t, ok)
+	ok, _ = Verify(pub, wrongMessage, sig.Sig)
+	require.False(t, ok)
+}
+
+func TestNewPartialSignature(t *testing.T) {
+	s := []byte("11111111111111111111111111111111")
+	r := []byte("22222222222222222222222222222222")
+	sigBytes := []byte("2222222222222222222222222222222211111111111111111111111111111111")
+	sig := NewPartialSignature(1, sigBytes)
+
+	require.Equal(t, byte(1), sig.ShareIdentifier)
+	require.Equal(t, s, sig.S())
+	require.Equal(t, r, sig.R())
+	require.Equal(t, sigBytes, sig.Bytes())
+
+	assert.PanicsWithValue(t, "ted25519: invalid partial signature length: 3", func() {
+		NewPartialSignature(1, []byte("sig"))
+	})
+}
diff --git a/pkg/ted25519/ted25519/sigagg.go b/pkg/ted25519/ted25519/sigagg.go
new file mode 100644
index 00000000..e6d7af43
--- /dev/null
+++ b/pkg/ted25519/ted25519/sigagg.go
@@ -0,0 +1,61 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"bytes"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+)
+
+type Signature = []byte
+
+func Aggregate(sigs []*PartialSignature, config *ShareConfiguration) (Signature, error) {
+	if len(sigs) == 0 {
+		return nil, fmt.Errorf("ted25519: sigs must be non-empty")
+	}
+
+	// Verify all nonce pubKeys are the same by checking they all match the first one.
+	noncePubkey := sigs[0].R()
+	for i := 1; i < len(sigs); i++ {
+		if !bytes.Equal(sigs[i].R(), noncePubkey) {
+			return nil, fmt.Errorf(
+				"ted25519: unexpected nonce pubkey. got: %x expected: %x",
+				sigs[i].R(),
+				noncePubkey,
+			)
+		}
+	}
+
+	// Convert signatures to a Shamir share representation so we can recombine them
+	sigShares := make([]*v1.ShamirShare, len(sigs))
+	field := curves.NewField(curves.Ed25519Order())
+	shamir, err := v1.NewShamir(config.T, config.N, field)
+	if err != nil {
+		return nil, err
+	}
+
+	for i, sig := range sigs {
+		sigShares[i] = v1.NewShamirShare(
+			uint32(sig.ShareIdentifier),
+			reverseBytes(sig.S()),
+			field,
+		)
+	}
+
+	sigS, err := shamir.Combine(sigShares...)
+	if err != nil {
+		return nil, err
+	}
+
+	sig := make([]byte, signatureLength)
+	copy(sig[:32], noncePubkey)        // R is the same on all sigs
+	copy(sig[32:], reverseBytes(sigS)) // be-to-le
+
+	return sig, nil
+}
diff --git a/pkg/ted25519/ted25519/sigagg_test.go b/pkg/ted25519/ted25519/sigagg_test.go
new file mode 100644
index 00000000..079a6d6a
--- /dev/null
+++ b/pkg/ted25519/ted25519/sigagg_test.go
@@ -0,0 +1,93 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package ted25519
+
+import (
+	"encoding/hex"
+	"fmt"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestSigAgg(t *testing.T) {
+	config := ShareConfiguration{T: 2, N: 3}
+	pub, secretShares, _, err := GenerateSharedKey(&config)
+	require.NoError(t, err)
+
+	message := []byte("test message")
+
+	// Each party generates a nonce and we combine them together into an aggregate one
+	noncePub1, nonceShares1, _, err := GenerateSharedNonce(&config, secretShares[0], pub, message)
+	require.NoError(t, err)
+	noncePub2, nonceShares2, _, err := GenerateSharedNonce(&config, secretShares[1], pub, message)
+	require.NoError(t, err)
+	noncePub3, nonceShares3, _, err := GenerateSharedNonce(&config, secretShares[2], pub, message)
+	require.NoError(t, err)
+	nonceShares := []*NonceShare{
+		nonceShares1[0].Add(nonceShares2[0]).Add(nonceShares3[0]),
+		nonceShares1[1].Add(nonceShares2[1]).Add(nonceShares3[1]),
+		nonceShares1[2].Add(nonceShares2[2]).Add(nonceShares3[2]),
+	}
+
+	noncePub := GeAdd(GeAdd(noncePub1, noncePub2), noncePub3)
+
+	sig1 := TSign(message, secretShares[0], pub, nonceShares[0], noncePub)
+	sig2 := TSign(message, secretShares[1], pub, nonceShares[1], noncePub)
+	sig3 := TSign(message, secretShares[2], pub, nonceShares[2], noncePub)
+
+	// Test signer 1&2 verification
+	sig, err := Aggregate([]*PartialSignature{sig1, sig2}, &config)
+	require.NoError(t, err)
+	assertSignatureVerifies(t, pub, message, sig)
+
+	// Test signer 2&3 verification
+	sig, err = Aggregate([]*PartialSignature{sig2, sig3}, &config)
+	require.NoError(t, err)
+	assertSignatureVerifies(t, pub, message, sig)
+
+	// Test signer 1&3 verification
+	sig, err = Aggregate([]*PartialSignature{sig1, sig3}, &config)
+	require.NoError(t, err)
+	assertSignatureVerifies(t, pub, message, sig)
+}
+
+func TestSigAgg_validations(t *testing.T) {
+	config := ShareConfiguration{T: 2, N: 3}
+	_, err := Aggregate([]*PartialSignature{}, &config)
+	require.EqualError(t, err, "ted25519: sigs must be non-empty")
+
+	sig1bytes, _ := hex.DecodeString(
+		"e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e06522490155" +
+			"5fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b",
+	)
+	sig2bytes, _ := hex.DecodeString(
+		"92a009a9f0d4cab8720e820b5f642540a2b27b5416503f8fb3762223ebdb69da" +
+			"085ac1e43e15996e458f3613d0f11d8c387b2eaeb4302aeeb00d291612bb0c00",
+	)
+	sig1 := NewPartialSignature(1, sig1bytes)
+	sig2 := NewPartialSignature(2, sig2bytes)
+
+	_, err = Aggregate([]*PartialSignature{sig1, sig2}, &config)
+	assert.EqualError(
+		t,
+		err,
+		fmt.Sprintf("ted25519: unexpected nonce pubkey. got: %x expected: %x", sig2bytes[:32], sig1bytes[:32]),
+	)
+}
+
+func assertSignatureVerifies(t *testing.T, pub, message, sig []byte) {
+	ok, _ := Verify(pub, message, sig)
+	if !ok {
+		t.Errorf("valid signature rejected")
+	}
+	wrongMessage := []byte("wrong message")
+	ok, _ = Verify(pub, wrongMessage, sig)
+	if ok {
+		t.Errorf("signature of different message accepted")
+	}
+}
diff --git a/pkg/ted25519/ted25519/twobytwo_test.go b/pkg/ted25519/ted25519/twobytwo_test.go
new file mode 100644
index 00000000..8a64f908
--- /dev/null
+++ b/pkg/ted25519/ted25519/twobytwo_test.go
@@ -0,0 +1,53 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+/*
+* This is a simple example of a 2x2 signature scheme to prove out a simpler case than the threshold
+* variants. We don't intend to use it and it is not modeled off of any specific known protocol.
+ */
+package ted25519
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/assert"
+	"testing"
+)
+
+func AggregateSignatures(sig1, sig2 *PartialSignature) []byte {
+	field := curves.NewField(curves.Ed25519Order())
+	sig1s := field.ElementFromBytes(reverseBytes(sig1.S()))
+	sig2s := field.ElementFromBytes(reverseBytes(sig2.S()))
+	sigS := sig1s.Add(sig2s)
+
+	// Create signature as R || s. The R is the same so we use the same one
+	sig := make([]byte, SignatureSize)
+	copy(sig, sig1.R())
+	copy(sig[32:], reverseBytes(sigS.Bytes()))
+	return sig
+}
+
+func TestTwoByTwoSigning(t *testing.T) {
+	// generate shared pubkey
+	pub1, priv1, _ := generateSharableKey()
+	pub2, priv2, _ := generateSharableKey()
+	pub := GeAdd(pub1, pub2)
+
+	// generate shared nonce
+	pubr1, r1, _ := generateSharableKey()
+	pubr2, r2, _ := generateSharableKey()
+	noncePub := GeAdd(pubr1, pubr2)
+
+	// generate partial sigs
+	msg := []byte("test message")
+	sig1 := TSign(msg, NewKeyShare(0, priv1), pub, NewNonceShare(0, r1), noncePub)
+	sig2 := TSign(msg, NewKeyShare(0, priv2), pub, NewNonceShare(0, r2), noncePub)
+
+	// add sigs (s+s)
+	sig := AggregateSignatures(sig1, sig2)
+
+	ok, _ := Verify(pub, msg, sig)
+	assert.True(t, ok, "signature failed verification")
+}
diff --git a/pkg/verenc/camshoup/README.md b/pkg/verenc/camshoup/README.md
new file mode 100755
index 00000000..2ad9651b
--- /dev/null
+++ b/pkg/verenc/camshoup/README.md
@@ -0,0 +1,361 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# camshoup
+
+```go
+import "github.com/coinbase/kryptology/pkg/verenc/camshoup"
+```
+
+### Verifiable encryption
+
+Verifiable encryption addresses a problem about proving statements for encrypted data\. Verifiable encryption allows a prover to convince a verifier that a given ciphertext is an encryption under a given public key\. A verifiable encryption scheme proves that a ciphertext encrypts a plaintext satisfying a certain relation\. Our implementation is a non\-interactive zero\-knowledge proof \(NIZK\) i\.e\. the prover creates the proof and sends it to the verifier with no further interaction\. A verifiable encryption is transferred to a verifier and possibly to a trusted party for decryption\. It does not need to be stored at the prover’s side as it usually is not repeatedly needed\.
+
+Why? Think of scenarios that allow signers or provers to remain anonymous but where some information about the prover needs to be known and is put into escrow\. The escrow service can be a trusted third party or the verifier themselves\. The prover encrypts an attribute to a specific public key and creates a NIZK proof of knowledge of the attribute for the resulting ciphertext\. To recover the attribute\, the opener simply decrypts the ciphertext\. It is recommended that a trusted escrow service serve this purpose and not the verifier such that only the trusted authority can actually recover the attribute\. The attribute can be anything including a secret key\. Another term for this can be a Verifiable Escrow Service\.
+
+Note that a key escrow scheme cannot prevent parties from double\-encrypting messages under a non\-escrowed key\, or applying steganography to hide the fact that they are communicating altogether\. The goal\, therefore\, is rather to prevent “dishonest” usage of public\-key infrastructures\, e\.g\.\, by using it to certify non\-escrowed keys\.
+
+### How it works
+
+Camenisch\-Shoup Verifiable encryption is similar to RSA and based on Paillier's Decision Composite Residuosity http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf\. A group of unknown order is created from two safe primes p\, q where p = 2p'\+1\, q = 2q'\+1 and p'\, q' are also prime and p &ne; q\.
+
+The group parameters are computed as follows:
+
+```
+1. Set n = p * q
+2. Sample a random g' < n^2
+3. Set g = g'^2n
+4. Set h = n + 1
+```
+
+### Secret keys are computed as follows
+
+```
+1. Sample three random values x_1,x_2,x_3 < n^2/4
+2. The secret key is {x_1,x_2,x_3}
+```
+
+### Public keys are computed as follows
+
+```
+1. Compute y_1 = g^x1
+2. Compute y_2 = g^x2
+3. Compute y_3 = g^x3
+4. The public key is {y_1, y_2, y_3}
+```
+
+The group parameters can be stored separate or together with each key\.
+
+### Proving
+
+Verifiable encryption not only produces a ciphertext that can be decrypted\, but also yields a proof that the plaintext is encrypted to a specific public key\. The ciphertext is represented as the triplet \{u\, e\, v\}\, the proof is represented as the Schnorr proof challenge c with responses m\, r\.
+
+### References
+
+Practical Verifiable Encryption and Decryption of Discrete Logarithms \- Jan Camenisch and Victor Shoup 2003\. https://eprint.iacr.org/2002/161.pdf
+
+Specification of the Identity Mixer Cryptographic Library \- IBM Zurich 2009\. https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf
+
+Public\-Key Cryptosystems Based on Composite Degree Residuosity Classes \- Pascall Paillier 1999\. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf
+
+## Index
+
+- [func NewKeys(numMsgs uint, group *PaillierGroup) (*EncryptionKey, *DecryptionKey, error)](<#func-newkeys>)
+- [type CipherText](<#type-ciphertext>)
+  - [func (c CipherText) MarshalBinary() ([]byte, error)](<#func-ciphertext-marshalbinary>)
+  - [func (c *CipherText) UnmarshalBinary(data []byte) error](<#func-ciphertext-unmarshalbinary>)
+- [type DecryptionKey](<#type-decryptionkey>)
+  - [func (dk DecryptionKey) Decrypt(domain []byte, cipherText *CipherText) ([]*big.Int, error)](<#func-decryptionkey-decrypt>)
+  - [func (dk DecryptionKey) EncryptionKey() *EncryptionKey](<#func-decryptionkey-encryptionkey>)
+  - [func (dk DecryptionKey) MarshalBinary() ([]byte, error)](<#func-decryptionkey-marshalbinary>)
+  - [func (dk *DecryptionKey) UnmarshalBinary(data []byte) error](<#func-decryptionkey-unmarshalbinary>)
+- [type EncryptionKey](<#type-encryptionkey>)
+  - [func (ek EncryptionKey) Encrypt(domain []byte, msgs []*big.Int) (*CipherText, error)](<#func-encryptionkey-encrypt>)
+  - [func (ek EncryptionKey) EncryptAndProve(nonce []byte, msgs []*big.Int) (*CipherText, *ProofVerEnc, error)](<#func-encryptionkey-encryptandprove>)
+  - [func (ek EncryptionKey) EncryptAndProveBlindings(nonce []byte, msgs []*big.Int, blindings []*big.Int) (*CipherText, *ProofVerEnc, error)](<#func-encryptionkey-encryptandproveblindings>)
+  - [func (ek EncryptionKey) MarshalBinary() ([]byte, error)](<#func-encryptionkey-marshalbinary>)
+  - [func (ek *EncryptionKey) UnmarshalBinary(data []byte) error](<#func-encryptionkey-unmarshalbinary>)
+  - [func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error](<#func-encryptionkey-verifyencryptproof>)
+- [type PaillierGroup](<#type-pailliergroup>)
+  - [func NewPaillierGroup() (*PaillierGroup, error)](<#func-newpailliergroup>)
+  - [func NewPaillierGroupWithPrimes(p, q *big.Int) (*PaillierGroup, error)](<#func-newpailliergroupwithprimes>)
+  - [func (pg PaillierGroup) Abs(a *big.Int) *big.Int](<#func-pailliergroup-abs>)
+  - [func (pg PaillierGroup) Exp(base, exp *big.Int) *big.Int](<#func-pailliergroup-exp>)
+  - [func (pg PaillierGroup) Gexp(exp *big.Int) *big.Int](<#func-pailliergroup-gexp>)
+  - [func (pg PaillierGroup) Hash(u *big.Int, e []*big.Int, data []byte) (*big.Int, error)](<#func-pailliergroup-hash>)
+  - [func (pg PaillierGroup) Hexp(exp *big.Int) *big.Int](<#func-pailliergroup-hexp>)
+  - [func (pg PaillierGroup) Inv(val *big.Int) *big.Int](<#func-pailliergroup-inv>)
+  - [func (pg PaillierGroup) MarshalBinary() ([]byte, error)](<#func-pailliergroup-marshalbinary>)
+  - [func (pg PaillierGroup) Mul(lhs, rhs *big.Int) *big.Int](<#func-pailliergroup-mul>)
+  - [func (pg PaillierGroup) Rand() (*big.Int, error)](<#func-pailliergroup-rand>)
+  - [func (pg PaillierGroup) RandForEncrypt() (*big.Int, error)](<#func-pailliergroup-randforencrypt>)
+  - [func (pg *PaillierGroup) UnmarshalBinary(data []byte) error](<#func-pailliergroup-unmarshalbinary>)
+- [type ProofVerEnc](<#type-proofverenc>)
+  - [func (pf ProofVerEnc) MarshalBinary() ([]byte, error)](<#func-proofverenc-marshalbinary>)
+  - [func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error](<#func-proofverenc-unmarshalbinary>)
+
+
+## func [NewKeys](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/encryption_key.go#L34>)
+
+```go
+func NewKeys(numMsgs uint, group *PaillierGroup) (*EncryptionKey, *DecryptionKey, error)
+```
+
+## type [CipherText](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/ciphertext.go#L17-L20>)
+
+CipherText represents verifiably encrypted ciphertext as described in section 3\.2 in \<https://shoup.net/papers/verenc.pdf\>\.
+
+```go
+type CipherText struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(CipherText\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/ciphertext.go#L28>)
+
+```go
+func (c CipherText) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*CipherText\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/ciphertext.go#L40>)
+
+```go
+func (c *CipherText) UnmarshalBinary(data []byte) error
+```
+
+## type [DecryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/decryption_key.go#L27-L31>)
+
+DecryptionKey decrypts verifiable ciphertext as described in section 3\.2 in \<https://shoup.net/papers/verenc.pdf\>
+
+```go
+type DecryptionKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(DecryptionKey\) [Decrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/decryption_key.go#L85>)
+
+```go
+func (dk DecryptionKey) Decrypt(domain []byte, cipherText *CipherText) ([]*big.Int, error)
+```
+
+Decrypt as described in section 3\.2 in \<https://shoup.net/papers/verenc.pdf\>
+
+### func \(DecryptionKey\) [EncryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/decryption_key.go#L34>)
+
+```go
+func (dk DecryptionKey) EncryptionKey() *EncryptionKey
+```
+
+EncryptionKey returns the corresponding encryption key for this decryption key
+
+### func \(DecryptionKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/decryption_key.go#L47>)
+
+```go
+func (dk DecryptionKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary serializes a key to bytes
+
+### func \(\*DecryptionKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/decryption_key.go#L64>)
+
+```go
+func (dk *DecryptionKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary deserializes a key from bytes
+
+## type [EncryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/encryption_key.go#L28-L32>)
+
+EncryptionKey encrypts a message to a ciphertext from which zero\-knowledge proofs can be derived as described in section 3\.2 in \<https://shoup.net/papers/verenc.pdf\>\. n\, g are stored in the \`PaillierGroup\` struct
+
+```go
+type EncryptionKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(EncryptionKey\) [Encrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/encryption_key.go#L108>)
+
+```go
+func (ek EncryptionKey) Encrypt(domain []byte, msgs []*big.Int) (*CipherText, error)
+```
+
+Encrypt multiple messages as described in \<https://shoup.net/papers/verenc.pdf\> \`domain\` represents a domain separation tag or nonce
+
+### func \(EncryptionKey\) [EncryptAndProve](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L64>)
+
+```go
+func (ek EncryptionKey) EncryptAndProve(nonce []byte, msgs []*big.Int) (*CipherText, *ProofVerEnc, error)
+```
+
+EncryptAndProve is a NIZK where the ciphertext and commitments are computed \(t values\)\. The blindings are generated as part of calling this function Return ciphertext and proof created during encryption\. "The protocol" from section 5\.2 in \<https://shoup.net/papers/verenc.pdf\> Not using t = g^m\*h^s as the idemix protocol does not use it\. Guess is that since the knowledge of m is proved in the credential attribute proving protocol\. Use this function if the proof is by itself and not part of a bigger composite proof\.
+
+### func \(EncryptionKey\) [EncryptAndProveBlindings](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L83>)
+
+```go
+func (ek EncryptionKey) EncryptAndProveBlindings(nonce []byte, msgs []*big.Int, blindings []*big.Int) (*CipherText, *ProofVerEnc, error)
+```
+
+EncryptAndProveBlindings is a NIZK where the ciphertext and commitments are computed \(t values\)\. The blindings are generated prior to calling this function Return ciphertext and proof created during encryption\. "The protocol" from section 5\.2 in \<https://shoup.net/papers/verenc.pdf\> Not using t = g^m\*h^s as the idemix protocol does not use it\. Guess is that since the knowledge of m is proved in the credential attribute proving protocol\. Use this function if the proof will be part of more proofs\.
+
+### func \(EncryptionKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/encryption_key.go#L69>)
+
+```go
+func (ek EncryptionKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary serializes a key to bytes
+
+### func \(\*EncryptionKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/encryption_key.go#L86>)
+
+```go
+func (ek *EncryptionKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary deserializes a key from bytes
+
+### func \(EncryptionKey\) [VerifyEncryptProof](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L202>)
+
+```go
+func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error
+```
+
+VerifyEncryptProof a Proof of Verifiable Encryption See section 6\.2\.19 in \<https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf\>
+
+## type [PaillierGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L30-L32>)
+
+PaillierGroup holds public values for Verifiable Encryption g and h correspond to the symbols with the same name in the paper\. n = p \* q\, where p = 2p' \+ 1\, q = 2q' \+ 1\, p\, q\, p'\, q' are all prime See section 3\.1 and 3\.2 in verenc\.pdf\. nd4 = n / 4 integer division n2 = n^2 nd4 = n^2 / 4 integer division
+
+```go
+type PaillierGroup struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func [NewPaillierGroup](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L41>)
+
+```go
+func NewPaillierGroup() (*PaillierGroup, error)
+```
+
+NewPaillierGroup creates a new Paillier group for verifiable encryption and generates safe primes for p and q\.
+
+### func [NewPaillierGroupWithPrimes](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L47>)
+
+```go
+func NewPaillierGroupWithPrimes(p, q *big.Int) (*PaillierGroup, error)
+```
+
+NewPaillierGroupWithPrimes create a new Paillier group for verifiable encryption Order n^2 where n = p \* q
+
+### func \(PaillierGroup\) [Abs](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L99>)
+
+```go
+func (pg PaillierGroup) Abs(a *big.Int) *big.Int
+```
+
+Abs computes a mod n^2 where 0 \< a \< n^2 or \(n^2 \- a\) mod n^2 if a \> n^2/2 See section 3\.2
+
+### func \(PaillierGroup\) [Exp](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L111>)
+
+```go
+func (pg PaillierGroup) Exp(base, exp *big.Int) *big.Int
+```
+
+Exp computes base^exp mod n^2
+
+### func \(PaillierGroup\) [Gexp](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L126>)
+
+```go
+func (pg PaillierGroup) Gexp(exp *big.Int) *big.Int
+```
+
+Gexp computes g^exp mod n^2
+
+### func \(PaillierGroup\) [Hash](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L176>)
+
+```go
+func (pg PaillierGroup) Hash(u *big.Int, e []*big.Int, data []byte) (*big.Int, error)
+```
+
+Hash computes h\(u\, e\, L\) for encryption/decryption
+
+### func \(PaillierGroup\) [Hexp](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L131>)
+
+```go
+func (pg PaillierGroup) Hexp(exp *big.Int) *big.Int
+```
+
+Hexp computes h^exp mod n^2
+
+### func \(PaillierGroup\) [Inv](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L121>)
+
+```go
+func (pg PaillierGroup) Inv(val *big.Int) *big.Int
+```
+
+Inv computes val^\-1 mod n^2
+
+### func \(PaillierGroup\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L146>)
+
+```go
+func (pg PaillierGroup) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary serializes a paillier group to a byte sequence
+
+### func \(PaillierGroup\) [Mul](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L115>)
+
+```go
+func (pg PaillierGroup) Mul(lhs, rhs *big.Int) *big.Int
+```
+
+### func \(PaillierGroup\) [Rand](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L136>)
+
+```go
+func (pg PaillierGroup) Rand() (*big.Int, error)
+```
+
+Rand returns a random v ∈ \[1\, n^2 / 4\)
+
+### func \(PaillierGroup\) [RandForEncrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L141>)
+
+```go
+func (pg PaillierGroup) RandForEncrypt() (*big.Int, error)
+```
+
+RandForEncrypt returns a random v ∈ \[1\, n / 4\)
+
+### func \(\*PaillierGroup\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/paillier_group.go#L157>)
+
+```go
+func (pg *PaillierGroup) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary deserializes a paillier group from a byte sequence
+
+## type [ProofVerEnc](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L19-L22>)
+
+ProofVerEnc is a proof of verifiable encryption for a discrete log
+
+```go
+type ProofVerEnc struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(ProofVerEnc\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L30>)
+
+```go
+func (pf ProofVerEnc) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ProofVerEnc\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/camshoup/proof_enc.go#L42>)
+
+```go
+func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/verenc/camshoup/ciphertext.go b/pkg/verenc/camshoup/ciphertext.go
new file mode 100644
index 00000000..65a27175
--- /dev/null
+++ b/pkg/verenc/camshoup/ciphertext.go
@@ -0,0 +1,53 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"math/big"
+
+	"git.sr.ht/~sircmpwn/go-bare"
+)
+
+// CipherText represents verifiably encrypted ciphertext
+// as described in section 3.2 in <https://shoup.net/papers/verenc.pdf>.
+type CipherText struct {
+	u, v *big.Int
+	e    []*big.Int
+}
+
+type cipherTextMarshal struct {
+	E [][]byte `bare:"e"`
+	U []byte   `bare:"u"`
+	V []byte   `bare:"v"`
+}
+
+func (c CipherText) MarshalBinary() ([]byte, error) {
+	tv := new(cipherTextMarshal)
+	tv.U = c.u.Bytes()
+	tv.V = c.v.Bytes()
+	tv.E = make([][]byte, len(c.e))
+	for i, e := range c.e {
+		tv.E[i] = e.Bytes()
+	}
+
+	return bare.Marshal(tv)
+}
+
+func (c *CipherText) UnmarshalBinary(data []byte) error {
+	tv := new(cipherTextMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	c.u = new(big.Int).SetBytes(tv.U)
+	c.v = new(big.Int).SetBytes(tv.V)
+	c.e = make([]*big.Int, len(tv.E))
+	for i, e := range tv.E {
+		c.e[i] = new(big.Int).SetBytes(e)
+	}
+	return nil
+}
diff --git a/pkg/verenc/camshoup/ciphertext_test.go b/pkg/verenc/camshoup/ciphertext_test.go
new file mode 100644
index 00000000..1cd10490
--- /dev/null
+++ b/pkg/verenc/camshoup/ciphertext_test.go
@@ -0,0 +1,39 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestCipherTextMarshal(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestCipherTextMarshal")
+
+	ek, _, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	msg := big.NewInt(1)
+	cs, err := ek.Encrypt(domain, []*big.Int{msg})
+	require.NoError(t, err)
+
+	bin, err := cs.MarshalBinary()
+	require.NoError(t, err)
+	dup := new(CipherText)
+	err = dup.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.Equal(t, 0, cs.u.Cmp(dup.u))
+	require.Equal(t, 0, cs.v.Cmp(dup.v))
+	for i, e := range cs.e {
+		require.Equal(t, 0, e.Cmp(dup.e[i]))
+	}
+}
diff --git a/pkg/verenc/camshoup/decryption_key.go b/pkg/verenc/camshoup/decryption_key.go
new file mode 100644
index 00000000..a84e5836
--- /dev/null
+++ b/pkg/verenc/camshoup/decryption_key.go
@@ -0,0 +1,151 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"fmt"
+	"math/big"
+
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	mod "github.com/coinbase/kryptology/pkg/core"
+)
+
+type decryptionKeyMarshal struct {
+	X1    [][]byte `bare:"x1"`
+	X2    []byte   `bare:"x2"`
+	X3    []byte   `bare:"x3"`
+	Group []byte   `bare:"group"`
+}
+
+// DecryptionKey decrypts verifiable ciphertext
+// as described in section 3.2 in <https://shoup.net/papers/verenc.pdf>
+type DecryptionKey struct {
+	x1     []*big.Int
+	x2, x3 *big.Int
+	group  *PaillierGroup
+}
+
+// EncryptionKey returns the corresponding encryption key for this decryption key
+func (dk DecryptionKey) EncryptionKey() *EncryptionKey {
+	y2 := dk.group.Gexp(dk.x2)
+	y3 := dk.group.Gexp(dk.x3)
+	y1 := make([]*big.Int, len(dk.x1))
+	for i, x := range dk.x1 {
+		y1[i] = dk.group.Gexp(x)
+	}
+	return &EncryptionKey{
+		y1, y2, y3, dk.group,
+	}
+}
+
+// MarshalBinary serializes a key to bytes
+func (dk DecryptionKey) MarshalBinary() ([]byte, error) {
+	tv := new(decryptionKeyMarshal)
+	var err error
+	tv.Group, err = dk.group.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	tv.X3 = dk.x3.Bytes()
+	tv.X2 = dk.x2.Bytes()
+	tv.X1 = make([][]byte, len(dk.x1))
+	for i, y := range dk.x1 {
+		tv.X1[i] = y.Bytes()
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary deserializes a key from bytes
+func (dk *DecryptionKey) UnmarshalBinary(data []byte) error {
+	tv := new(decryptionKeyMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	dk.group = new(PaillierGroup)
+	err = dk.group.UnmarshalBinary(tv.Group)
+	if err != nil {
+		return err
+	}
+	dk.x2 = new(big.Int).SetBytes(tv.X2)
+	dk.x3 = new(big.Int).SetBytes(tv.X3)
+	dk.x1 = make([]*big.Int, len(tv.X1))
+	for i, b := range tv.X1 {
+		dk.x1[i] = new(big.Int).SetBytes(b)
+	}
+	return nil
+}
+
+// Decrypt as described in section 3.2 in <https://shoup.net/papers/verenc.pdf>
+func (dk DecryptionKey) Decrypt(domain []byte, cipherText *CipherText) ([]*big.Int, error) {
+	if cipherText == nil {
+		return nil, internal.ErrNilArguments
+	}
+	if cipherText.v == nil || cipherText.u == nil || cipherText.e == nil {
+		return nil, internal.ErrNilArguments
+	}
+	if len(cipherText.e) > len(dk.x1) {
+		return nil, fmt.Errorf("number of messages %d is more than supported by this key %d", len(cipherText.e), len(dk.x1))
+	}
+	if cipherText.u.Cmp(mod.Zero) == 0 || cipherText.v.Cmp(mod.Zero) == 0 {
+		return nil, internal.ErrZeroValue
+	}
+	for _, e := range cipherText.e {
+		if e.Cmp(mod.Zero) == 0 {
+			return nil, internal.ErrZeroValue
+		}
+	}
+
+	// Check if abs(v) == v
+	if cipherText.v.Cmp(dk.group.Abs(cipherText.v)) != 0 {
+		return nil, fmt.Errorf("absolute check failed")
+	}
+
+	// h(u, e, L)
+	hs, err := dk.group.Hash(cipherText.u, cipherText.e, domain)
+	if err != nil {
+		return nil, err
+	}
+
+	// h(u, e, L) * x3
+	hsX3 := new(big.Int).Mul(hs, dk.x3)
+	twoHsX3PlusX2 := new(big.Int).Add(hsX3, dk.x2)
+	// 2 * (h(u, e, L) * x3 + x2)
+	twoHsX3PlusX2.Lsh(twoHsX3PlusX2, 1)
+
+	uSqr := dk.group.Exp(cipherText.u, twoHsX3PlusX2)
+	vSqr := dk.group.Exp(cipherText.v, big.NewInt(2))
+
+	if uSqr.Cmp(vSqr) != 0 {
+		return nil, fmt.Errorf("u^2 != v^2")
+	}
+
+	msgs := make([]*big.Int, len(cipherText.e))
+	for i, ee := range cipherText.e {
+		// u^{x_1}
+		uX1 := dk.group.Exp(cipherText.u, dk.x1[i])
+		// 1/u^{x_1}
+		uX1Inv := dk.group.Inv(uX1)
+		// e/u^{x_1}
+		eUX1Inv := dk.group.Mul(ee, uX1Inv)
+
+		// m_hat = (e/u^{x_1})^2t
+		mHat := dk.group.Exp(eUX1Inv, dk.group.twoInvTwo)
+		test := new(big.Int).Mod(mHat, dk.group.n)
+		if test.Cmp(big.NewInt(1)) != 0 {
+			return nil, fmt.Errorf("decryption failed for message %d", i)
+		}
+
+		m := new(big.Int).Mod(mHat, dk.group.n2)
+		m.Sub(m, big.NewInt(1))
+		m.Div(m, dk.group.n)
+		msgs[i] = m
+	}
+
+	return msgs, nil
+}
diff --git a/pkg/verenc/camshoup/decryption_key_test.go b/pkg/verenc/camshoup/decryption_key_test.go
new file mode 100644
index 00000000..7b53bbaa
--- /dev/null
+++ b/pkg/verenc/camshoup/decryption_key_test.go
@@ -0,0 +1,69 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestDecryptionKeyMarshal(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+	_, dk, err := NewKeys(3, group)
+	require.NoError(t, err)
+	bin, err := dk.MarshalBinary()
+	require.NoError(t, err)
+	dup := new(DecryptionKey)
+	err = dup.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.Equal(t, 0, dk.x3.Cmp(dup.x3))
+	require.Equal(t, 0, dk.x2.Cmp(dup.x2))
+	for i, x := range dk.x1 {
+		require.Equal(t, 0, x.Cmp(dup.x1[i]))
+	}
+}
+
+func TestDecryptionKeyDecryptBadCiphertext(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+	_, dk, err := NewKeys(3, group)
+	require.NoError(t, err)
+
+	_, err = dk.Decrypt([]byte{}, nil)
+	require.Error(t, err)
+
+	_, err = dk.Decrypt([]byte{}, new(CipherText))
+	require.Error(t, err)
+
+	cs := new(CipherText)
+	cs.v = big.NewInt(1)
+	cs.u = big.NewInt(1)
+	cs.e = []*big.Int{big.NewInt(1), big.NewInt(1), big.NewInt(1), big.NewInt(1)}
+
+	_, err = dk.Decrypt([]byte{}, cs)
+	require.Error(t, err)
+	// all 1s are valid ciphertexts, so we pick other random values
+	cs.e = []*big.Int{big.NewInt(2), big.NewInt(2), big.NewInt(2)}
+
+	_, err = dk.Decrypt([]byte{}, cs)
+	require.Error(t, err)
+
+	cs.v = big.NewInt(0)
+	cs.u = big.NewInt(0)
+	cs.e = []*big.Int{big.NewInt(0), big.NewInt(0), big.NewInt(0)}
+	_, err = dk.Decrypt([]byte{}, cs)
+	require.Error(t, err)
+
+	cs.u = big.NewInt(1)
+	cs.e = []*big.Int{big.NewInt(1), big.NewInt(1), big.NewInt(1)}
+	cs.v = new(big.Int).Add(group.n2, big.NewInt(1))
+	_, err = dk.Decrypt([]byte{}, cs)
+	require.Error(t, err)
+}
diff --git a/pkg/verenc/camshoup/doc.go b/pkg/verenc/camshoup/doc.go
new file mode 100644
index 00000000..31bb2d99
--- /dev/null
+++ b/pkg/verenc/camshoup/doc.go
@@ -0,0 +1,55 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+// Verifiable encryption
+//
+// Verifiable encryption addresses a problem about proving statements for encrypted data. Verifiable encryption allows a prover to convince a verifier that a given ciphertext is an encryption under a given public key. A verifiable encryption scheme proves that a ciphertext encrypts a plaintext satisfying a certain relation. Our implementation is a non-interactive zero-knowledge proof (NIZK) i.e. the prover creates the proof and sends it to the verifier with no further interaction.
+// A verifiable encryption is transferred to a verifier and possibly to a trusted party for decryption. It does not need to be stored at the prover’s side as it usually is not repeatedly needed.
+//
+// Why?
+// Think of scenarios that allow signers or provers to remain anonymous but where some information about the prover needs to be known and is put into escrow. The escrow service can be a trusted third party or the verifier themselves. The prover encrypts an attribute to a specific public key and creates a NIZK proof of knowledge of the attribute for the resulting ciphertext. To recover the attribute, the opener simply decrypts the ciphertext. It is recommended that a trusted escrow service serve this purpose and not the verifier such that only the trusted authority can actually recover the attribute. The attribute can be anything including a secret key. Another term for this can be a Verifiable Escrow Service.
+//
+// Note that a key escrow scheme cannot prevent parties from double-encrypting messages under a non-escrowed key, or applying steganography to hide the fact that they are communicating altogether. The goal, therefore, is rather to prevent “dishonest” usage of public-key infrastructures, e.g., by using it to certify non-escrowed keys.
+//
+// How it works
+//
+// Camenisch-Shoup Verifiable encryption is similar to RSA and based on
+// Paillier's Decision Composite Residuosity http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf. A group of unknown order is created from two safe primes p, q where p = 2p'+1, q = 2q'+1 and p', q' are also prime and p &ne; q.
+//
+// The group parameters are computed as follows:
+//
+// 	1. Set n = p * q
+// 	2. Sample a random g' < n^2
+// 	3. Set g = g'^2n
+// 	4. Set h = n + 1
+//
+// Secret keys are computed as follows
+//
+// 		1. Sample three random values x_1,x_2,x_3 < n^2/4
+// 		2. The secret key is {x_1,x_2,x_3}
+//
+// Public keys are computed as follows
+//
+// 		1. Compute y_1 = g^x1
+// 		2. Compute y_2 = g^x2
+// 		3. Compute y_3 = g^x3
+// 		4. The public key is {y_1, y_2, y_3}
+//
+// The group parameters can be stored separate or together with each key.
+//
+// Proving
+//
+// Verifiable encryption not only produces a ciphertext that can be decrypted, but also yields a proof that the plaintext is encrypted to a specific public key.
+// The ciphertext is represented as the triplet {u, e, v}, the proof is represented as the Schnorr proof challenge c with responses m, r.
+//
+// References
+//
+// Practical Verifiable Encryption and Decryption of Discrete Logarithms - Jan Camenisch and Victor Shoup 2003. https://eprint.iacr.org/2002/161.pdf
+//
+// Specification of the Identity Mixer Cryptographic Library - IBM Zurich 2009. https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf
+//
+// Public-Key Cryptosystems Based on Composite Degree Residuosity Classes - Pascall Paillier 1999. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.112.4035&rep=rep1&type=pdf
+package camshoup
diff --git a/pkg/verenc/camshoup/encryption_key.go b/pkg/verenc/camshoup/encryption_key.go
new file mode 100644
index 00000000..050871ce
--- /dev/null
+++ b/pkg/verenc/camshoup/encryption_key.go
@@ -0,0 +1,167 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"fmt"
+	"math/big"
+
+	"git.sr.ht/~sircmpwn/go-bare"
+	mod "github.com/coinbase/kryptology/pkg/core"
+)
+
+type encryptionKeyMarshal struct {
+	Y1    [][]byte `bare:"y1"`
+	Y2    []byte   `bare:"y2"`
+	Y3    []byte   `bare:"y3"`
+	Group []byte   `bare:"group"`
+}
+
+// EncryptionKey encrypts a message to a ciphertext from which
+// zero-knowledge proofs can be derived
+// as described in section 3.2 in <https://shoup.net/papers/verenc.pdf>.
+// n, g are stored in the `PaillierGroup` struct
+type EncryptionKey struct {
+	y1     []*big.Int
+	y2, y3 *big.Int
+	group  *PaillierGroup
+}
+
+func NewKeys(numMsgs uint, group *PaillierGroup) (*EncryptionKey, *DecryptionKey, error) {
+	if numMsgs < 1 {
+		return nil, nil, fmt.Errorf("number of messages should be greater than 0")
+	}
+
+	x1 := make([]*big.Int, numMsgs)
+	y1 := make([]*big.Int, numMsgs)
+	for i := range x1 {
+		x, err := mod.Rand(group.n2d4)
+		if err != nil {
+			return nil, nil, err
+		}
+		x1[i] = x
+		y1[i] = group.Gexp(x)
+	}
+	x2, err := mod.Rand(group.n2d4)
+	if err != nil {
+		return nil, nil, err
+	}
+	y2 := group.Gexp(x2)
+	x3, err := mod.Rand(group.n2d4)
+	if err != nil {
+		return nil, nil, err
+	}
+	y3 := group.Gexp(x3)
+	dk := &DecryptionKey{
+		x1, x2, x3, group,
+	}
+	ek := &EncryptionKey{
+		y1, y2, y3, group,
+	}
+	return ek, dk, nil
+}
+
+// MarshalBinary serializes a key to bytes
+func (ek EncryptionKey) MarshalBinary() ([]byte, error) {
+	tv := new(encryptionKeyMarshal)
+	var err error
+	tv.Group, err = ek.group.MarshalBinary()
+	if err != nil {
+		return nil, err
+	}
+	tv.Y3 = ek.y3.Bytes()
+	tv.Y2 = ek.y2.Bytes()
+	tv.Y1 = make([][]byte, len(ek.y1))
+	for i, y := range ek.y1 {
+		tv.Y1[i] = y.Bytes()
+	}
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary deserializes a key from bytes
+func (ek *EncryptionKey) UnmarshalBinary(data []byte) error {
+	tv := new(encryptionKeyMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	ek.group = new(PaillierGroup)
+	err = ek.group.UnmarshalBinary(tv.Group)
+	if err != nil {
+		return err
+	}
+	ek.y2 = new(big.Int).SetBytes(tv.Y2)
+	ek.y3 = new(big.Int).SetBytes(tv.Y3)
+	ek.y1 = make([]*big.Int, len(tv.Y1))
+	for i, b := range tv.Y1 {
+		ek.y1[i] = new(big.Int).SetBytes(b)
+	}
+	return nil
+}
+
+// Encrypt multiple messages as described in <https://shoup.net/papers/verenc.pdf>
+// `domain` represents a domain separation tag or nonce
+func (ek EncryptionKey) Encrypt(domain []byte, msgs []*big.Int) (*CipherText, error) {
+	if len(msgs) > len(ek.y1) {
+		return nil, fmt.Errorf("number of messages %d is more than supported by this key %d", len(msgs), len(ek.y1))
+	}
+	for i, m := range msgs {
+		if m == nil || m.Cmp(ek.group.n) == 1 {
+			return nil, fmt.Errorf("message %d is not valid", i)
+		}
+	}
+	r, err := ek.group.RandForEncrypt()
+	if err != nil {
+		return nil, err
+	}
+	return ek.encryptWithR(domain, msgs, r)
+}
+
+func (ek EncryptionKey) encryptWithR(domain []byte, msgs []*big.Int, r *big.Int) (*CipherText, error) {
+	u := ek.computeU(r)
+	e := ek.computeE(msgs, r)
+
+	hs, err := ek.group.Hash(u, e, domain)
+	if err != nil {
+		return nil, err
+	}
+	v := ek.computeV(r, hs, true)
+	return &CipherText{u, v, e}, nil
+}
+
+func (ek EncryptionKey) computeE(msgs []*big.Int, r *big.Int) []*big.Int {
+	e := make([]*big.Int, len(msgs))
+	for i, m := range msgs {
+		y := ek.group.Exp(ek.y1[i], r)
+		hM := ek.group.Hexp(m)
+		e[i] = ek.group.Mul(y, hM)
+	}
+	return e
+}
+
+func (ek EncryptionKey) computeU(r *big.Int) *big.Int {
+	return ek.group.Gexp(r)
+}
+
+// computeV computes the `v` value during encryption
+// abs is present for code reuse as during the proof of encryption
+// in the commitment step absolute value is not taken.
+func (ek EncryptionKey) computeV(r, hash *big.Int, abs bool) *big.Int {
+	// y3 ^ h(u, e, L)
+	y3hs := ek.group.Exp(ek.y3, hash)
+
+	// y2 * (y3^h(u, e, L))
+	y2y3hs := ek.group.Mul(ek.y2, y3hs)
+
+	// (y2y3^h(u, e, L))^r
+	y2y3hsr := ek.group.Exp(y2y3hs, r)
+	if abs {
+		return ek.group.Abs(y2y3hsr)
+	} else {
+		return y2y3hsr
+	}
+}
diff --git a/pkg/verenc/camshoup/encryption_key_test.go b/pkg/verenc/camshoup/encryption_key_test.go
new file mode 100644
index 00000000..d2f3d9f7
--- /dev/null
+++ b/pkg/verenc/camshoup/encryption_key_test.go
@@ -0,0 +1,119 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"fmt"
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestEncryptionKeyEncryptSingleMessage(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptSingleMessage")
+
+	ek, dk, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	testMsgs := []*big.Int{
+		big.NewInt(0),
+		big.NewInt(10),
+		big.NewInt(20),
+		big.NewInt(30),
+		big.NewInt(40),
+		big.NewInt(50),
+		big.NewInt(100),
+		big.NewInt(1000),
+		big.NewInt(10000),
+		big.NewInt(100000),
+		big.NewInt(1000000),
+	}
+
+	for _, msg := range testMsgs {
+		cs, err := ek.Encrypt(domain, []*big.Int{msg})
+		require.NoError(t, err)
+		msgs, err := dk.Decrypt(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, msgs[0].Cmp(msg), 0)
+	}
+}
+
+func TestEncryptionKeyEncryptMultipleMessages(t *testing.T) {
+	const NumMsgs = 10
+
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptMultipleMessages")
+
+	ek, dk, err := NewKeys(NumMsgs, group)
+	require.NoError(t, err)
+
+	msgs := make([]*big.Int, NumMsgs)
+	for i := 0; i < NumMsgs; i++ {
+		msgs[i] = new(big.Int).SetBytes([]byte(fmt.Sprintf("msgs_%d", i+1)))
+	}
+
+	cs, err := ek.Encrypt(domain, msgs)
+	require.NoError(t, err)
+	dmsgs, err := dk.Decrypt(domain, cs)
+	require.NoError(t, err)
+	for i, m := range msgs {
+		require.Equal(t, m.Cmp(dmsgs[i]), 0)
+	}
+}
+
+func TestEncryptionKeyEncryptInvalidMessages(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptInvalidMessages")
+
+	ek, dk, err := NewKeys(1, group)
+	require.NoError(t, err)
+	// Too large of message
+	msg := new(big.Int).Add(big.NewInt(1), group.n)
+	_, err = ek.Encrypt(domain, []*big.Int{msg})
+	require.Error(t, err)
+
+	// nil message
+	_, err = ek.Encrypt(domain, []*big.Int{nil})
+	require.Error(t, err)
+
+	// no messages
+	_, err = ek.Encrypt(domain, []*big.Int{})
+	require.Error(t, err)
+
+	// invalid domains
+	msg = new(big.Int).SetBytes([]byte("test message"))
+	cs, err := ek.Encrypt(domain, []*big.Int{msg})
+	require.NoError(t, err)
+	_, err = dk.Decrypt([]byte{}, cs)
+	require.Error(t, err)
+}
+
+func TestEncryptionKeyMarshaling(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+	ek, _, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	bin, err := ek.MarshalBinary()
+	require.NoError(t, err)
+
+	ekClone := new(EncryptionKey)
+	err = ekClone.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.Equal(t, 0, ek.y2.Cmp(ekClone.y2))
+	require.Equal(t, 0, ek.y3.Cmp(ekClone.y3))
+	require.Equal(t, 1, len(ekClone.y1))
+	require.Equal(t, 0, ek.y1[0].Cmp(ekClone.y1[0]))
+}
diff --git a/pkg/verenc/camshoup/paillier_group.go b/pkg/verenc/camshoup/paillier_group.go
new file mode 100644
index 00000000..59ea8f7e
--- /dev/null
+++ b/pkg/verenc/camshoup/paillier_group.go
@@ -0,0 +1,191 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+// Implements Camenisch-Shoup verifiable encryption based on the paper
+// Practical Verifiable Encryption and Decryption of Discrete Logarithms
+// see <https://www.shoup.net/papers/verenc.pdf> and
+// <https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf>
+
+import (
+	"math/big"
+
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/paillier"
+)
+
+// PaillierGroup holds public values for Verifiable Encryption
+// g and h correspond to the symbols with the same name in the paper.
+// n = p * q, where p = 2p' + 1, q = 2q' + 1, p, q, p', q' are all prime
+// See section 3.1 and 3.2 in verenc.pdf.
+// nd4 = n / 4 integer division
+// n2 = n^2
+// nd4 = n^2 / 4 integer division
+type PaillierGroup struct {
+	g, h, n, nd4, n2d2, n2d4, n2, twoInvTwo *big.Int
+}
+
+type paillierMarshal struct {
+	N []byte `bare:"n"`
+	G []byte `bare:"g"`
+}
+
+// NewPaillierGroup creates a new Paillier group for verifiable encryption
+// and generates safe primes for p and q.
+func NewPaillierGroup() (*PaillierGroup, error) {
+	return groupGenerator(crypto.GenerateSafePrime, paillier.PaillierPrimeBits)
+}
+
+// NewPaillierGroupWithPrimes create a new Paillier group for verifiable encryption
+// Order n^2 where n = p * q
+func NewPaillierGroupWithPrimes(p, q *big.Int) (*PaillierGroup, error) {
+	n := new(big.Int).Mul(p, q)
+	n2 := new(big.Int).Mul(n, n)
+	gTick, err := crypto.Rand(n2)
+	if err != nil {
+		return nil, err
+	}
+	twoInvTwo := new(big.Int).ModInverse(big.NewInt(2), n)
+	// 2n^2
+	twoN2 := new(big.Int).Lsh(n2, 1)
+	return &PaillierGroup{
+		g:         new(big.Int).Exp(gTick, twoN2, n2),
+		h:         new(big.Int).Add(n, big.NewInt(1)),
+		n:         n,
+		nd4:       new(big.Int).Rsh(n, 1),
+		n2:        n2,
+		n2d2:      new(big.Int).Rsh(n2, 1),
+		n2d4:      new(big.Int).Rsh(n2, 2),
+		twoInvTwo: new(big.Int).Lsh(twoInvTwo, 1),
+	}, nil
+}
+
+// create two safe primes and generate a new Paillier group
+func groupGenerator(genSafePrime func(uint) (*big.Int, error), bits uint) (*PaillierGroup, error) {
+	values := make(chan *big.Int, 2)
+	errors := make(chan error, 2)
+
+	var p, q *big.Int
+
+	for p == q {
+		for range []int{1, 2} {
+			go func() {
+				value, err := genSafePrime(bits)
+				values <- value
+				errors <- err
+			}()
+		}
+
+		for _, err := range []error{<-errors, <-errors} {
+			if err != nil {
+				return nil, err
+			}
+		}
+
+		p, q = <-values, <-values
+	}
+	return NewPaillierGroupWithPrimes(p, q)
+}
+
+// Abs computes a mod n^2 where 0 < a < n^2 or
+// (n^2 - a) mod n^2 if a > n^2/2
+// See section 3.2
+func (pg PaillierGroup) Abs(a *big.Int) *big.Int {
+	tv := new(big.Int).Mod(a, pg.n2)
+
+	// if a > n^2 / 2 then n^2 - a else a
+	if tv.Cmp(pg.n2d2) == 1 {
+		return new(big.Int).Sub(pg.n2, tv)
+	} else {
+		return tv
+	}
+}
+
+// Exp computes base^exp mod n^2
+func (pg PaillierGroup) Exp(base, exp *big.Int) *big.Int {
+	return new(big.Int).Exp(base, exp, pg.n2)
+}
+
+func (pg PaillierGroup) Mul(lhs, rhs *big.Int) *big.Int {
+	r := new(big.Int).Mul(lhs, rhs)
+	return r.Mod(r, pg.n2)
+}
+
+// Inv computes val^-1 mod n^2
+func (pg PaillierGroup) Inv(val *big.Int) *big.Int {
+	return new(big.Int).ModInverse(val, pg.n2)
+}
+
+// Gexp computes g^exp mod n^2
+func (pg PaillierGroup) Gexp(exp *big.Int) *big.Int {
+	return new(big.Int).Exp(pg.g, exp, pg.n2)
+}
+
+// Hexp computes h^exp mod n^2
+func (pg PaillierGroup) Hexp(exp *big.Int) *big.Int {
+	return new(big.Int).Exp(pg.h, exp, pg.n2)
+}
+
+// Rand returns a random v ∈ [1, n^2 / 4)
+func (pg PaillierGroup) Rand() (*big.Int, error) {
+	return crypto.Rand(pg.n2d4)
+}
+
+// RandForEncrypt returns a random v ∈ [1, n / 4)
+func (pg PaillierGroup) RandForEncrypt() (*big.Int, error) {
+	return crypto.Rand(pg.nd4)
+}
+
+// MarshalBinary serializes a paillier group to a byte sequence
+func (pg PaillierGroup) MarshalBinary() ([]byte, error) {
+	// Only serialize what's needed
+	// all values except g can be derived from n
+	// g is a random value
+	tv := new(paillierMarshal)
+	tv.N = pg.n.Bytes()
+	tv.G = pg.g.Bytes()
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary deserializes a paillier group from a byte sequence
+func (pg *PaillierGroup) UnmarshalBinary(data []byte) error {
+	tv := new(paillierMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	pg.n = new(big.Int).SetBytes(tv.N)
+	pg.g = new(big.Int).SetBytes(tv.G)
+	twoInvTwo := new(big.Int).ModInverse(big.NewInt(2), pg.n)
+	pg.h = new(big.Int).Add(pg.n, big.NewInt(1))
+	pg.n2 = new(big.Int).Mul(pg.n, pg.n)
+	pg.nd4 = new(big.Int).Rsh(pg.n, 1)
+	pg.n2d2 = new(big.Int).Rsh(pg.n2, 1)
+	pg.n2d4 = new(big.Int).Rsh(pg.n2, 2)
+	pg.twoInvTwo = new(big.Int).Lsh(twoInvTwo, 1)
+	return nil
+}
+
+// Hash computes h(u, e, L) for encryption/decryption
+func (pg PaillierGroup) Hash(u *big.Int, e []*big.Int, data []byte) (*big.Int, error) {
+	if u == nil || len(e) == 0 || crypto.AnyNil(e...) {
+		return nil, internal.ErrNilArguments
+	}
+	toHash := make([][]byte, len(e)+2)
+	toHash[0] = u.Bytes()
+	for i, ee := range e {
+		toHash[i+1] = ee.Bytes()
+	}
+	toHash[len(toHash)-1] = data
+	h, err := internal.Hash([]byte("Coinbase Hash 1.0"), toHash...)
+	if err != nil {
+		return nil, err
+	}
+	return new(big.Int).SetBytes(h), nil
+}
diff --git a/pkg/verenc/camshoup/paillier_group_test.go b/pkg/verenc/camshoup/paillier_group_test.go
new file mode 100644
index 00000000..a48b34a2
--- /dev/null
+++ b/pkg/verenc/camshoup/paillier_group_test.go
@@ -0,0 +1,184 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/coinbase/kryptology/internal"
+	crypto "github.com/coinbase/kryptology/pkg/core"
+	"github.com/stretchr/testify/require"
+)
+
+var (
+	// taken from https://github.com/mikelodder7/cunningham_chain/blob/master/findings.md
+	testP = internal.B10("37313426856874901938110133384605074194791927500210707276948918975046371522830901596065044944558427864187196889881993164303255749681644627614963632713725183364319410825898054225147061624559894980555489070322738683900143562848200257354774040241218537613789091499134051387344396560066242901217378861764936185029")
+	testQ = internal.B10("89884656743115795386465259539451236680898848947115328636715040578866337902750481566354238661203768010560056939935696678829394884407208311246423715319737062188883946712432742638151109800623047059726541476042502884419075341171231440736956555270413618581675255342293149119973622969239858152417678164815053566739")
+)
+
+func TestPaillierGroupAbs(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	var tests = []struct {
+		tst, expt *big.Int
+	}{
+		{new(big.Int).Sub(group.n2, big.NewInt(1)), big.NewInt(1)},
+		{new(big.Int).Add(group.n2, big.NewInt(1)), big.NewInt(1)},
+		{new(big.Int).Sub(group.n2d2, big.NewInt(1)), new(big.Int).Sub(group.n2d2, big.NewInt(1))},
+		{new(big.Int).Sub(group.n2d2, big.NewInt(2)), new(big.Int).Sub(group.n2d2, big.NewInt(2))},
+	}
+
+	// fixed tests
+	for _, test := range tests {
+		require.Equal(t, test.expt, group.Abs(test.tst))
+	}
+
+	// random tests
+	for i := 0; i < 10; i++ {
+		v, err := group.Rand()
+		require.NoError(t, err)
+		absV := group.Abs(v)
+		vSqr, err := crypto.Mul(v, v, group.n2)
+		require.NoError(t, err)
+		absVSqr, err := crypto.Mul(absV, absV, group.n2)
+		require.NoError(t, err)
+		// v^2 == abs(v)^2
+		require.Equal(t, vSqr, absVSqr)
+	}
+}
+
+func TestPaillierGroupGexp(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	group.g = big.NewInt(3)
+	tests := []struct {
+		tst, expt *big.Int
+	}{
+		{big.NewInt(2), big.NewInt(9)},
+		{big.NewInt(3), big.NewInt(27)},
+		{big.NewInt(-1), internal.B10("7499117220481606893649407997399583308623268248762862128736872698824860600842539649858603415089499373731123393918622048306032453674117198222428763400911316711446714484238108131853998795190806064022005540191591261850583540110613493142117711175554687907993186406437781941775859626227440416706732352534320731439315078729078870773717897878277521899968765343474198143801766637939617094139165566543814621094727209827280235001003967993120858315015118799915363205353758729304376784293822322166655094010593701655935398294477352938710477213434893715051831645405694928356029906438589615124561537156384355180319348277134506296769629916781958368753909584086440228342500729108626734803375134884502083805712504675865246881229463006603396559380854179010152629093144420272779479646825835945201621434552737270891411188707165574852172520548208219404678615150837351570584275400292453510652907722111673821881050068428228292352163743877772993566777118954034996545482953390011456036779111442131310187063702793015171803441885940720487623309201563428243215588648533078389653349518182776849735665081821416965810759310263601486813425303956567680549257436019232011620365483794625689049981027436030969508646999754826253132633834825366188937693881675421518323841")},
+	}
+	// fixed tests
+	for _, test := range tests {
+		require.Equal(t, test.expt, group.Gexp(test.tst))
+	}
+}
+
+func TestPaillierGroupInv(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	tests := []struct {
+		tst, expt *big.Int
+	}{
+		{big.NewInt(3), internal.B10("7499117220481606893649407997399583308623268248762862128736872698824860600842539649858603415089499373731123393918622048306032453674117198222428763400911316711446714484238108131853998795190806064022005540191591261850583540110613493142117711175554687907993186406437781941775859626227440416706732352534320731439315078729078870773717897878277521899968765343474198143801766637939617094139165566543814621094727209827280235001003967993120858315015118799915363205353758729304376784293822322166655094010593701655935398294477352938710477213434893715051831645405694928356029906438589615124561537156384355180319348277134506296769629916781958368753909584086440228342500729108626734803375134884502083805712504675865246881229463006603396559380854179010152629093144420272779479646825835945201621434552737270891411188707165574852172520548208219404678615150837351570584275400292453510652907722111673821881050068428228292352163743877772993566777118954034996545482953390011456036779111442131310187063702793015171803441885940720487623309201563428243215588648533078389653349518182776849735665081821416965810759310263601486813425303956567680549257436019232011620365483794625689049981027436030969508646999754826253132633834825366188937693881675421518323841")},
+		{big.NewInt(2), internal.B10("5624337915361205170237055998049687481467451186572146596552654524118645450631904737393952561317124530298342545438966536229524340255587898666821572550683487533585035863178581098890499096393104548016504155143693446387937655082960119856588283381666015930994889804828336456331894719670580312530049264400740548579486309046809153080288423408708141424976574007605648607851324978454712820604374174907860965821045407370460176250752975994840643736261339099936522404015319046978282588220366741624991320507945276241951548720858014704032857910076170286288873734054271196267022429828942211343421152867288266385239511207850879722577222437586468776565432188064830171256875546831470051102531351163376562854284378506898935160922097254952547419535640634257614471819858315204584609735119376958901216075914552953168558391530374181139129390411156164553508961363128013677938206550219340132989680791583755366410787551321171219264122807908329745175082839215526247409112215042508592027584333581598482640297777094761378852581414455540365717481901172571182411691486399808792240012138637082637301748811366062724358069482697701115110068977967425760411943077014424008715274112845969266787485770577023227131485249816119689849475376119024641703270411256566138742881")},
+		{big.NewInt(1), big.NewInt(1)},
+	}
+	for _, test := range tests {
+		tv := group.Inv(test.tst)
+		require.Equal(t, test.expt, tv)
+		tv1 := group.Inv(tv)
+		require.Equal(t, tv1, test.tst)
+	}
+}
+
+func TestPaillierGroupHexp(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	group.h = big.NewInt(3)
+	tests := []struct {
+		tst, expt *big.Int
+	}{
+		{big.NewInt(2), big.NewInt(9)},
+		{big.NewInt(3), big.NewInt(27)},
+		{big.NewInt(-1), internal.B10("7499117220481606893649407997399583308623268248762862128736872698824860600842539649858603415089499373731123393918622048306032453674117198222428763400911316711446714484238108131853998795190806064022005540191591261850583540110613493142117711175554687907993186406437781941775859626227440416706732352534320731439315078729078870773717897878277521899968765343474198143801766637939617094139165566543814621094727209827280235001003967993120858315015118799915363205353758729304376784293822322166655094010593701655935398294477352938710477213434893715051831645405694928356029906438589615124561537156384355180319348277134506296769629916781958368753909584086440228342500729108626734803375134884502083805712504675865246881229463006603396559380854179010152629093144420272779479646825835945201621434552737270891411188707165574852172520548208219404678615150837351570584275400292453510652907722111673821881050068428228292352163743877772993566777118954034996545482953390011456036779111442131310187063702793015171803441885940720487623309201563428243215588648533078389653349518182776849735665081821416965810759310263601486813425303956567680549257436019232011620365483794625689049981027436030969508646999754826253132633834825366188937693881675421518323841")},
+	}
+	// fixed tests
+	for _, test := range tests {
+		require.Equal(t, test.expt, group.Hexp(test.tst))
+	}
+}
+
+func TestPaillierGroupRand(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	for i := 0; i < 20; i++ {
+		v, err := group.Rand()
+		require.NoError(t, err)
+		require.Equal(t, v.Cmp(group.n2d4), -1)
+		require.Equal(t, v.Cmp(big.NewInt(0)), 1)
+	}
+}
+
+func TestPaillierGroupRandForEncrypt(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	for i := 0; i < 20; i++ {
+		v, err := group.RandForEncrypt()
+		require.NoError(t, err)
+		require.Equal(t, v.Cmp(group.nd4), -1)
+		require.Equal(t, v.Cmp(big.NewInt(0)), 1)
+	}
+}
+
+func TestPaillierGroupHashNilValues(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	_, err = group.Hash(nil, nil, nil)
+	require.Error(t, err)
+	_, err = group.Hash(big.NewInt(1), []*big.Int{}, []byte{})
+	require.Error(t, err)
+	_, err = group.Hash(big.NewInt(1), []*big.Int{nil, nil}, []byte{1, 1})
+	require.Error(t, err)
+}
+
+func TestPaillierGroupHash(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	tests := []struct {
+		u    *big.Int
+		e    []*big.Int
+		data []byte
+		expt *big.Int
+	}{
+		{u: big.NewInt(1), e: []*big.Int{big.NewInt(1), big.NewInt(1)}, data: []byte{1, 1}, expt: internal.B10("78460077383813730105521336387922347204000654707781568442686111557212361415874")},
+		{u: big.NewInt(2), e: []*big.Int{big.NewInt(2), big.NewInt(2)}, data: []byte{2, 2}, expt: internal.B10("25064057611008805877221384832284545038206881116061098969649782860410535162174")},
+	}
+
+	for _, tst := range tests {
+		hs, err := group.Hash(tst.u, tst.e, tst.data)
+		require.NoError(t, err)
+		require.Equal(t, hs, tst.expt)
+	}
+}
+
+func TestPaillierGroupMarshal(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	bin, err := group.MarshalBinary()
+	require.NoError(t, err)
+	group2 := new(PaillierGroup)
+	err = group2.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.Equal(t, group.n, group2.n)
+	require.Equal(t, group.n2, group2.n2)
+	require.Equal(t, group.n2d2, group2.n2d2)
+	require.Equal(t, group.n2d4, group2.n2d4)
+	require.Equal(t, group.g, group2.g)
+	require.Equal(t, group.h, group2.h)
+	require.Equal(t, group.twoInvTwo, group2.twoInvTwo)
+}
diff --git a/pkg/verenc/camshoup/proof_enc.go b/pkg/verenc/camshoup/proof_enc.go
new file mode 100644
index 00000000..c3d511d0
--- /dev/null
+++ b/pkg/verenc/camshoup/proof_enc.go
@@ -0,0 +1,266 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"fmt"
+	"math/big"
+
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	mod "github.com/coinbase/kryptology/pkg/core"
+)
+
+// ProofVerEnc is a proof of verifiable encryption for a discrete log
+type ProofVerEnc struct {
+	challenge, r *big.Int
+	m            []*big.Int
+}
+
+type proofMarshal struct {
+	M         [][]byte `bare:"m"`
+	R         []byte   `bare:"r"`
+	Challenge []byte   `bare:"challenge"`
+}
+
+func (pf ProofVerEnc) MarshalBinary() ([]byte, error) {
+	tv := new(proofMarshal)
+	tv.R = pf.r.Bytes()
+	tv.Challenge = pf.challenge.Bytes()
+	tv.M = make([][]byte, len(pf.m))
+	for i, m := range pf.m {
+		tv.M[i] = m.Bytes()
+	}
+
+	return bare.Marshal(tv)
+}
+
+func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error {
+	tv := new(proofMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	pf.r = new(big.Int).SetBytes(tv.R)
+	pf.challenge = new(big.Int).SetBytes(tv.Challenge)
+	pf.m = make([]*big.Int, len(tv.M))
+	for i, m := range tv.M {
+		pf.m[i] = new(big.Int).SetBytes(m)
+	}
+	return nil
+}
+
+// EncryptAndProve is a NIZK where the ciphertext and commitments are computed (t values).
+// The blindings are generated as part of calling this function
+// Return ciphertext and proof created during encryption.
+// "The protocol" from section 5.2 in <https://shoup.net/papers/verenc.pdf>
+// Not using t = g^m*h^s as the idemix protocol does not use it.
+// Guess is that since the knowledge of m is proved in the credential attribute proving protocol.
+// Use this function if the proof is by itself and not part of a bigger composite proof.
+func (ek EncryptionKey) EncryptAndProve(nonce []byte, msgs []*big.Int) (*CipherText, *ProofVerEnc, error) {
+	var err error
+	blindings := make([]*big.Int, len(msgs))
+	for i := 0; i < len(blindings); i++ {
+		blindings[i], err = ek.group.RandForEncrypt()
+		if err != nil {
+			return nil, nil, err
+		}
+	}
+	return ek.EncryptAndProveBlindings(nonce, msgs, blindings)
+}
+
+// EncryptAndProveBlindings is a NIZK where the ciphertext and commitments are computed (t values).
+// The blindings are generated prior to calling this function
+// Return ciphertext and proof created during encryption.
+// "The protocol" from section 5.2 in <https://shoup.net/papers/verenc.pdf>
+// Not using t = g^m*h^s as the idemix protocol does not use it.
+// Guess is that since the knowledge of m is proved in the credential attribute proving protocol.
+// Use this function if the proof will be part of more proofs.
+func (ek EncryptionKey) EncryptAndProveBlindings(nonce []byte, msgs []*big.Int, blindings []*big.Int) (*CipherText, *ProofVerEnc, error) {
+	if len(msgs) != len(blindings) {
+		return nil, nil, fmt.Errorf("number of messages %d != number of blindings %d", len(msgs), len(blindings))
+	}
+	if len(msgs) > len(ek.y1) {
+		return nil, nil, fmt.Errorf("number of messages %d is more than supported by this key %d", len(msgs), len(ek.y1))
+	}
+	for i, b := range blindings {
+		if b == nil {
+			return nil, nil, internal.ErrNilArguments
+		}
+		if msgs[i] == nil {
+			return nil, nil, internal.ErrNilArguments
+		}
+		if b.Cmp(mod.Zero) == 0 {
+			return nil, nil, internal.ErrZeroValue
+		}
+	}
+
+	r, err := ek.group.RandForEncrypt()
+	if err != nil {
+		return nil, nil, err
+	}
+
+	rBlinding, err := ek.group.RandForEncrypt()
+	if err != nil {
+		return nil, nil, err
+	}
+	ciphertext, err := ek.encryptWithR(nonce, msgs, r)
+	if err != nil {
+		return nil, nil, err
+	}
+	hs, err := ek.group.Hash(ciphertext.u, ciphertext.e, nonce)
+	if err != nil {
+		return nil, nil, err
+	}
+	ciphertextTValues, err := ek.ciphertextTestValues(rBlinding, hs, blindings)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	challenge, err := ek.fiatShamir(nonce, ciphertext, ciphertextTValues)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	// generate the schnorr proofs
+	rHat := ek.schnorr(rBlinding, challenge, r)
+	mHat := make([]*big.Int, len(msgs))
+	for i, m := range msgs {
+		mHat[i] = ek.schnorr(blindings[i], challenge, m)
+	}
+
+	return ciphertext, &ProofVerEnc{
+		challenge: challenge,
+		r:         rHat,
+		m:         mHat,
+	}, nil
+}
+
+// ciphertextTestValues computes commitments for the ciphertext when proving encryption is correct
+func (ek EncryptionKey) ciphertextTestValues(r, hash *big.Int, msgs []*big.Int) (*CipherText, error) {
+	twoR := new(big.Int).Lsh(r, 1)
+	twoMsgs := make([]*big.Int, len(msgs))
+	for i, m := range msgs {
+		twoMsgs[i] = new(big.Int).Lsh(m, 1)
+	}
+	u := ek.computeU(twoR)
+	e := ek.computeE(twoMsgs, twoR)
+	v := ek.computeV(twoR, hash, false)
+	return &CipherText{u, v, e}, nil
+}
+
+// fiatShamir computes h(n, g, Y2, Y3, Y1, C.U, C.V, C.E, CT.U, CT.V, CT.E)
+func (ek EncryptionKey) fiatShamir(nonce []byte, ciphertext *CipherText, ciphertextTValues *CipherText) (*big.Int, error) {
+	hValues := make([][]byte, len(ciphertext.e)+len(ciphertextTValues.e)+len(ek.y1)+9)
+	hValues[0] = ek.group.n.Bytes()
+	hValues[1] = ek.group.g.Bytes()
+	hValues[2] = ek.y2.Bytes()
+	hValues[3] = ek.y3.Bytes()
+	offset := 4
+	for _, y := range ek.y1 {
+		hValues[offset] = y.Bytes()
+		offset++
+	}
+	hValues[offset] = ciphertext.u.Bytes()
+	offset++
+	for _, n := range ciphertext.e {
+		hValues[offset] = n.Bytes()
+		offset++
+	}
+	hValues[offset] = ciphertext.v.Bytes()
+	offset++
+
+	hValues[offset] = ciphertextTValues.u.Bytes()
+	offset++
+	for _, n := range ciphertextTValues.e {
+		hValues[offset] = n.Bytes()
+		offset++
+	}
+	hValues[offset] = ciphertextTValues.v.Bytes()
+
+	hValues[len(hValues)-1] = nonce
+	h, err := internal.Hash([]byte("Coinbase Hash 1.0"), hValues...)
+	if err != nil {
+		return nil, err
+	}
+	return new(big.Int).SetBytes(h), nil
+}
+
+// schnorr computes tilde - challenge * value mod n^2
+func (ek EncryptionKey) schnorr(tilde, challenge, value *big.Int) *big.Int {
+	r := ek.group.Mul(challenge, value)
+	t := new(big.Int).Sub(tilde, r)
+	return t
+}
+
+// VerifyEncryptProof a Proof of Verifiable Encryption
+// See section 6.2.19 in <https://dominoweb.draco.res.ibm.com/reports/rz3730_revised.pdf>
+func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error {
+	if ciphertext == nil || proof == nil {
+		return internal.ErrNilArguments
+	}
+	if proof.r == nil || proof.challenge == nil || proof.m == nil {
+		return internal.ErrNilArguments
+	}
+	if ciphertext.u == nil || ciphertext.v == nil || ciphertext.e == nil {
+		return internal.ErrNilArguments
+	}
+	if len(proof.m) > len(ek.y1) {
+		return fmt.Errorf("number of messages %d is more than supported by this key %d", len(proof.m), len(ek.y1))
+	}
+
+	// Reconstruct u
+	// 2c
+	c2 := new(big.Int).Lsh(proof.challenge, 1)
+	// 2r
+	r2 := new(big.Int).Lsh(proof.r, 1)
+
+	// u^{2c} mod n^2
+	uc := ek.group.Exp(ciphertext.u, c2)
+
+	// Reconstruct e
+	// g^{2r} mod n^2
+	gr := ek.group.Gexp(r2)
+
+	// u^{2c} * g^{2r} mod n^2
+	u := ek.group.Mul(uc, gr)
+
+	e := make([]*big.Int, len(proof.m))
+	for i, mm := range proof.m {
+		// e^{2c}
+		ec := ek.group.Exp(ciphertext.e[i], c2)
+		// y1^{2r}
+		yr := ek.group.Exp(ek.y1[i], r2)
+		// h^{2m}
+		hm := ek.group.Hexp(new(big.Int).Lsh(mm, 1))
+		// e = ec * yr * hm mod n^2
+		e[i] = ek.group.Mul(ek.group.Mul(ec, yr), hm)
+	}
+
+	// Reconstruct v
+	// v^{2c}
+	hs, err := ek.group.Hash(ciphertext.u, ciphertext.e, nonce)
+	if err != nil {
+		return err
+	}
+	vc := ek.group.Exp(ciphertext.v, c2)
+	y3hs := ek.group.Exp(ek.y3, hs)
+	y2y3hs := ek.group.Mul(ek.y2, y3hs)
+	y2y3hsr := ek.group.Exp(y2y3hs, r2)
+	v := ek.group.Mul(vc, y2y3hsr)
+
+	ciphertextTestValues := &CipherText{u, v, e}
+	challenge, err := ek.fiatShamir(nonce, ciphertext, ciphertextTestValues)
+	if err != nil {
+		return err
+	}
+	if challenge.Cmp(proof.challenge) == 0 {
+		return nil
+	} else {
+		return fmt.Errorf("invalid ciphertext")
+	}
+}
diff --git a/pkg/verenc/camshoup/proof_enc_test.go b/pkg/verenc/camshoup/proof_enc_test.go
new file mode 100644
index 00000000..6f293f14
--- /dev/null
+++ b/pkg/verenc/camshoup/proof_enc_test.go
@@ -0,0 +1,111 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package camshoup
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestEncryptionKeyEncryptAndProve(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptAndProve")
+
+	ek, dk, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	testMsgs := []*big.Int{
+		big.NewInt(0),
+		big.NewInt(10),
+		big.NewInt(20),
+		big.NewInt(30),
+		big.NewInt(40),
+		big.NewInt(50),
+		big.NewInt(100),
+		big.NewInt(1000),
+		big.NewInt(10000),
+		big.NewInt(100000),
+		big.NewInt(1000000),
+	}
+	for _, msg := range testMsgs {
+		cs, proof, err := ek.EncryptAndProve(domain, []*big.Int{msg})
+		require.NoError(t, err)
+
+		err = ek.VerifyEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+
+		dmsg, err := dk.Decrypt(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, 0, msg.Cmp(dmsg[0]))
+	}
+}
+
+func TestEncryptionKeyEncryptAndProveBlindings(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptAndProveBlindings")
+
+	ek, dk, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	testMsgs := []*struct {
+		test, blinding *big.Int
+	}{
+		{big.NewInt(0), big.NewInt(1)},
+		{big.NewInt(10), big.NewInt(2)},
+		{big.NewInt(20), big.NewInt(3)},
+		{big.NewInt(30), big.NewInt(4)},
+		{big.NewInt(40), big.NewInt(5)},
+		{big.NewInt(50), big.NewInt(6)},
+		{big.NewInt(100), big.NewInt(7)},
+		{big.NewInt(1000), big.NewInt(8)},
+		{big.NewInt(10000), big.NewInt(9)},
+		{big.NewInt(100000), big.NewInt(10)},
+		{big.NewInt(1000000), big.NewInt(11)},
+	}
+	for _, msg := range testMsgs {
+		cs, proof, err := ek.EncryptAndProveBlindings(domain, []*big.Int{msg.test}, []*big.Int{msg.blinding})
+		require.NoError(t, err)
+
+		err = ek.VerifyEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+
+		dmsg, err := dk.Decrypt(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, 0, msg.test.Cmp(dmsg[0]))
+	}
+}
+
+func TestEncryptionKeyEncryptAndProveInvalidInputs(t *testing.T) {
+	group, err := NewPaillierGroupWithPrimes(testP, testQ)
+	require.NoError(t, err)
+
+	domain := []byte("TestEncryptionKeyEncryptAndProveInvalidInputs")
+
+	ek, _, err := NewKeys(1, group)
+	require.NoError(t, err)
+
+	_, _, err = ek.EncryptAndProve(domain, nil)
+	require.Error(t, err)
+
+	_, _, err = ek.EncryptAndProve(domain, []*big.Int{})
+	require.Error(t, err)
+
+	_, _, err = ek.EncryptAndProveBlindings(domain, []*big.Int{big.NewInt(1)}, nil)
+	require.Error(t, err)
+
+	_, _, err = ek.EncryptAndProveBlindings(domain, []*big.Int{big.NewInt(2)}, []*big.Int{})
+	require.Error(t, err)
+
+	_, _, err = ek.EncryptAndProveBlindings(domain, []*big.Int{big.NewInt(2)}, []*big.Int{big.NewInt(0)})
+	require.Error(t, err)
+}
diff --git a/pkg/verenc/elgamal/README.md b/pkg/verenc/elgamal/README.md
new file mode 100755
index 00000000..9b8d59c0
--- /dev/null
+++ b/pkg/verenc/elgamal/README.md
@@ -0,0 +1,269 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# elgamal
+
+```go
+import "github.com/coinbase/kryptology/pkg/verenc/elgamal"
+```
+
+## Index
+
+- [func NewKeys(curve *curves.Curve) (*EncryptionKey, *DecryptionKey, error)](<#func-newkeys>)
+- [type CipherText](<#type-ciphertext>)
+  - [func (c CipherText) MarshalBinary() ([]byte, error)](<#func-ciphertext-marshalbinary>)
+  - [func (c CipherText) ToHomomorphicCipherText() *HomomorphicCipherText](<#func-ciphertext-tohomomorphicciphertext>)
+  - [func (c *CipherText) UnmarshalBinary(data []byte) error](<#func-ciphertext-unmarshalbinary>)
+- [type DecryptionKey](<#type-decryptionkey>)
+  - [func (dk *DecryptionKey) Decrypt(cipherText *HomomorphicCipherText) curves.Point](<#func-decryptionkey-decrypt>)
+  - [func (dk DecryptionKey) EncryptionKey() *EncryptionKey](<#func-decryptionkey-encryptionkey>)
+  - [func (dk DecryptionKey) MarshalBinary() ([]byte, error)](<#func-decryptionkey-marshalbinary>)
+  - [func (dk *DecryptionKey) UnmarshalBinary(data []byte) error](<#func-decryptionkey-unmarshalbinary>)
+  - [func (dk DecryptionKey) VerifiableDecrypt(cipherText *CipherText) ([]byte, curves.Scalar, error)](<#func-decryptionkey-verifiabledecrypt>)
+  - [func (dk DecryptionKey) VerifiableDecryptWithDomain(domain []byte, cipherText *CipherText) ([]byte, curves.Scalar, error)](<#func-decryptionkey-verifiabledecryptwithdomain>)
+- [type EncryptParams](<#type-encryptparams>)
+- [type EncryptionKey](<#type-encryptionkey>)
+  - [func (ek EncryptionKey) HomomorphicEncrypt(msg curves.Scalar) (*HomomorphicCipherText, error)](<#func-encryptionkey-homomorphicencrypt>)
+  - [func (ek EncryptionKey) MarshalBinary() ([]byte, error)](<#func-encryptionkey-marshalbinary>)
+  - [func (ek *EncryptionKey) UnmarshalBinary(data []byte) error](<#func-encryptionkey-unmarshalbinary>)
+  - [func (ek EncryptionKey) VerifiableEncrypt(msg []byte, params *EncryptParams) (*CipherText, *ProofVerEnc, error)](<#func-encryptionkey-verifiableencrypt>)
+  - [func (ek EncryptionKey) VerifyDomainEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error](<#func-encryptionkey-verifydomainencryptproof>)
+  - [func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error](<#func-encryptionkey-verifyencryptproof>)
+- [type HomomorphicCipherText](<#type-homomorphicciphertext>)
+  - [func (c HomomorphicCipherText) Add(rhs *HomomorphicCipherText) *HomomorphicCipherText](<#func-homomorphicciphertext-add>)
+  - [func (c HomomorphicCipherText) Decrypt(dk *DecryptionKey) (curves.Point, error)](<#func-homomorphicciphertext-decrypt>)
+  - [func (c HomomorphicCipherText) MarshalBinary() ([]byte, error)](<#func-homomorphicciphertext-marshalbinary>)
+  - [func (c *HomomorphicCipherText) UnmarshalBinary(in []byte) error](<#func-homomorphicciphertext-unmarshalbinary>)
+- [type ProofVerEnc](<#type-proofverenc>)
+  - [func (pf ProofVerEnc) MarshalBinary() ([]byte, error)](<#func-proofverenc-marshalbinary>)
+  - [func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error](<#func-proofverenc-unmarshalbinary>)
+
+
+## func [NewKeys](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L52>)
+
+```go
+func NewKeys(curve *curves.Curve) (*EncryptionKey, *DecryptionKey, error)
+```
+
+NewKeys creates a new key pair for El\-Gamal encryption
+
+## type [CipherText](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L18-L23>)
+
+CipherText represents verifiably encrypted ciphertext using El\-Gamal encryption
+
+```go
+type CipherText struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(CipherText\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L49>)
+
+```go
+func (c CipherText) MarshalBinary() ([]byte, error)
+```
+
+### func \(CipherText\) [ToHomomorphicCipherText](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L91>)
+
+```go
+func (c CipherText) ToHomomorphicCipherText() *HomomorphicCipherText
+```
+
+ToHomomorphicCipherText returns the El\-Gamal points that can be homomorphically multiplied
+
+### func \(\*CipherText\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L62>)
+
+```go
+func (c *CipherText) UnmarshalBinary(data []byte) error
+```
+
+## type [DecryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L26-L28>)
+
+DecryptionKey decrypts verifiable ciphertext and verifies proofs
+
+```go
+type DecryptionKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(\*DecryptionKey\) [Decrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L67>)
+
+```go
+func (dk *DecryptionKey) Decrypt(cipherText *HomomorphicCipherText) curves.Point
+```
+
+Decrypt returns the resulting point from El\-Gamal decryption\. No checking is performed whether the ciphertext has been modified\. M = H \* m = C2 \- C1 \* x
+
+### func \(DecryptionKey\) [EncryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L31>)
+
+```go
+func (dk DecryptionKey) EncryptionKey() *EncryptionKey
+```
+
+EncryptionKey returns the corresponding encryption key for this decryption key
+
+### func \(DecryptionKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L38>)
+
+```go
+func (dk DecryptionKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary serializes a key to bytes
+
+### func \(\*DecryptionKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L46>)
+
+```go
+func (dk *DecryptionKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary deserializes a key from bytes
+
+### func \(DecryptionKey\) [VerifiableDecrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L78>)
+
+```go
+func (dk DecryptionKey) VerifiableDecrypt(cipherText *CipherText) ([]byte, curves.Scalar, error)
+```
+
+VerifiableDecrypt the ciphertext\. This performs verifiable decryption such that the decrypted data is checked against El\-Gamal C2 value\. If the plaintext does not match\, an error is returned been generated by Encrypt
+
+### func \(DecryptionKey\) [VerifiableDecryptWithDomain](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/decryption_key.go#L97>)
+
+```go
+func (dk DecryptionKey) VerifiableDecryptWithDomain(domain []byte, cipherText *CipherText) ([]byte, curves.Scalar, error)
+```
+
+VerifiableDecryptWithDomain the ciphertext\. This performs verifiable decryption such that the decrypted data is checked against El\-Gamal C2 value\. If the plaintext does not match\, an error is returned The Domain component is meant for scenarios where \`msg\` is used in more than just one setting and should be contextualized\. The ciphertext must have been generated by EncryptWithDomain
+
+## type [EncryptParams](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L37-L43>)
+
+EncryptParams is all the options for doing verifiable encryption\. Message must be supplied and is the value to be encrypted\. MessageIsHashed defines whether Message represents an unhashed arbitrary byte sequence or already represents a scalar in the elliptic curve\. Domain is an optional domain separation tag and used to generate a separate point for the pedersen commitment in El\-Gamal ciphertexts\. Blinding is blinding factor \(bf\) of the El\-Gamal ciphertext\. If nil a bf is generated at random\. GenProof indicates whether to return a proof of encryption correctness to the corresponding public key\. ProofNonce is the nonce used to generate the one time proof\. This value is required if GenProof is true\.
+
+```go
+type EncryptParams struct {
+    MessageIsHashed bool
+    Domain          []byte
+    Blinding        curves.Scalar
+    GenProof        bool
+    ProofNonce      []byte
+}
+```
+
+## type [EncryptionKey](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L47-L49>)
+
+EncryptionKey encrypts a message to a ciphertext from which zero\-knowledge proofs can be derived
+
+```go
+type EncryptionKey struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(EncryptionKey\) [HomomorphicEncrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L94>)
+
+```go
+func (ek EncryptionKey) HomomorphicEncrypt(msg curves.Scalar) (*HomomorphicCipherText, error)
+```
+
+### func \(EncryptionKey\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L68>)
+
+```go
+func (ek EncryptionKey) MarshalBinary() ([]byte, error)
+```
+
+MarshalBinary serializes a key to bytes
+
+### func \(\*EncryptionKey\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/encryption_key.go#L76>)
+
+```go
+func (ek *EncryptionKey) UnmarshalBinary(data []byte) error
+```
+
+UnmarshalBinary deserializes a key from bytes
+
+### func \(EncryptionKey\) [VerifiableEncrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L70>)
+
+```go
+func (ek EncryptionKey) VerifiableEncrypt(msg []byte, params *EncryptParams) (*CipherText, *ProofVerEnc, error)
+```
+
+VerifiableEncrypt a message using El\-Gamal\. This also functions as an ECIES encryption algorithm\. The advantage here is proofs can be made about the ciphertext versus plain ECIES if desired and/or linked to external proofs\.
+
+### func \(EncryptionKey\) [VerifyDomainEncryptProof](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L152>)
+
+```go
+func (ek EncryptionKey) VerifyDomainEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error
+```
+
+VerifyDomainEncryptProof a Proof of Verifiable Encryption that was generated with EncryptDomainAndProve or EncryptDomainAndProveBlinding\.
+
+### func \(EncryptionKey\) [VerifyEncryptProof](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L172>)
+
+```go
+func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error
+```
+
+VerifyEncryptProof a Proof of Verifiable Encryption that was generated with EncryptAndProve or EncryptAndProveBlinding
+
+## type [HomomorphicCipherText](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L30-L32>)
+
+HomomorphicCipherText represents encrypted ciphertexts that have been added together\. The result when decrypted does not include the AEAD encrypted ciphertexts since these are not homomorphic\. This is solely for checking results or ignoring the AEAD ciphertext\.
+
+```go
+type HomomorphicCipherText struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(HomomorphicCipherText\) [Add](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L99>)
+
+```go
+func (c HomomorphicCipherText) Add(rhs *HomomorphicCipherText) *HomomorphicCipherText
+```
+
+Add combines two ciphertexts multiplicatively homomorphic
+
+### func \(HomomorphicCipherText\) [Decrypt](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L107>)
+
+```go
+func (c HomomorphicCipherText) Decrypt(dk *DecryptionKey) (curves.Point, error)
+```
+
+Decrypt returns the C2 \- C1
+
+### func \(HomomorphicCipherText\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L114>)
+
+```go
+func (c HomomorphicCipherText) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*HomomorphicCipherText\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/ciphertext.go#L122>)
+
+```go
+func (c *HomomorphicCipherText) UnmarshalBinary(in []byte) error
+```
+
+## type [ProofVerEnc](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L18-L20>)
+
+ProofVerEnc is a proof of verifiable encryption for a discrete log
+
+```go
+type ProofVerEnc struct {
+    // contains filtered or unexported fields
+}
+```
+
+### func \(ProofVerEnc\) [MarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L29>)
+
+```go
+func (pf ProofVerEnc) MarshalBinary() ([]byte, error)
+```
+
+### func \(\*ProofVerEnc\) [UnmarshalBinary](<https://github.com/coinbase/kryptology/blob/master/pkg/verenc/elgamal/proof_enc.go#L39>)
+
+```go
+func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/pkg/verenc/elgamal/ciphertext.go b/pkg/verenc/elgamal/ciphertext.go
new file mode 100644
index 00000000..1f3c72b1
--- /dev/null
+++ b/pkg/verenc/elgamal/ciphertext.go
@@ -0,0 +1,143 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// CipherText represents verifiably encrypted ciphertext
+// using El-Gamal encryption
+type CipherText struct {
+	c1, c2      curves.Point
+	nonce       []byte
+	aead        []byte
+	msgIsHashed bool
+}
+
+// HomomorphicCipherText represents encrypted ciphertexts
+// that have been added together. The result when decrypted
+// does not include the AEAD encrypted ciphertexts since
+// these are not homomorphic. This is solely for checking
+// results or ignoring the AEAD ciphertext.
+type HomomorphicCipherText struct {
+	c1, c2 curves.Point
+}
+
+type cipherTextMarshal struct {
+	C1          []byte `bare:"c1"`
+	C2          []byte `bare:"c2"`
+	Nonce       []byte `bare:"nonce"`
+	Aead        []byte `bare:"aead"`
+	Curve       string `bare:"curve"`
+	MsgIsHashed bool   `bare:"msgIsHashed"`
+}
+
+type homomorphicCipherTextMarshal struct {
+	C1    []byte `bare:"c1"`
+	C2    []byte `bare:"c2"`
+	Curve string `bare:"curve"`
+}
+
+func (c CipherText) MarshalBinary() ([]byte, error) {
+	tv := new(cipherTextMarshal)
+	tv.C1 = c.c1.ToAffineCompressed()
+	tv.C2 = c.c2.ToAffineCompressed()
+	tv.Nonce = make([]byte, len(c.nonce))
+	copy(tv.Nonce, c.nonce)
+	tv.Aead = make([]byte, len(c.aead))
+	tv.Curve = c.c1.CurveName()
+	copy(tv.Aead, c.aead)
+	tv.MsgIsHashed = c.msgIsHashed
+	return bare.Marshal(tv)
+}
+
+func (c *CipherText) UnmarshalBinary(data []byte) error {
+	tv := new(cipherTextMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("unknown curve")
+	}
+	c1, err := curve.Point.FromAffineCompressed(tv.C1)
+	if err != nil {
+		return err
+	}
+	c2, err := curve.Point.FromAffineCompressed(tv.C2)
+	if err != nil {
+		return err
+	}
+	c.c1 = c1
+	c.c2 = c2
+	c.aead = tv.Aead
+	c.nonce = tv.Nonce
+	c.msgIsHashed = tv.MsgIsHashed
+
+	return nil
+}
+
+// ToHomomorphicCipherText returns the El-Gamal points that can be
+// homomorphically multiplied
+func (c CipherText) ToHomomorphicCipherText() *HomomorphicCipherText {
+	return &HomomorphicCipherText{
+		c1: c.c1,
+		c2: c.c2,
+	}
+}
+
+// Add combines two ciphertexts multiplicatively homomorphic
+func (c HomomorphicCipherText) Add(rhs *HomomorphicCipherText) *HomomorphicCipherText {
+	return &HomomorphicCipherText{
+		c1: c.c1.Add(rhs.c1),
+		c2: c.c2.Add(rhs.c2),
+	}
+}
+
+// Decrypt returns the C2 - C1
+func (c HomomorphicCipherText) Decrypt(dk *DecryptionKey) (curves.Point, error) {
+	if dk == nil {
+		return nil, internal.ErrNilArguments
+	}
+	return c.c2.Sub(c.c1.Mul(dk.x)), nil
+}
+
+func (c HomomorphicCipherText) MarshalBinary() ([]byte, error) {
+	tv := new(homomorphicCipherTextMarshal)
+	tv.C1 = c.c1.ToAffineCompressed()
+	tv.C2 = c.c2.ToAffineCompressed()
+	tv.Curve = c.c1.CurveName()
+	return bare.Marshal(tv)
+}
+
+func (c *HomomorphicCipherText) UnmarshalBinary(in []byte) error {
+	tv := new(homomorphicCipherTextMarshal)
+	err := bare.Unmarshal(in, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("unknown curve")
+	}
+	c1, err := curve.Point.FromAffineCompressed(tv.C1)
+	if err != nil {
+		return err
+	}
+	c2, err := curve.Point.FromAffineCompressed(tv.C2)
+	if err != nil {
+		return err
+	}
+	c.c1 = c1
+	c.c2 = c2
+	return nil
+}
diff --git a/pkg/verenc/elgamal/ciphertext_test.go b/pkg/verenc/elgamal/ciphertext_test.go
new file mode 100644
index 00000000..a4c5faef
--- /dev/null
+++ b/pkg/verenc/elgamal/ciphertext_test.go
@@ -0,0 +1,40 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestCipherTextMarshal(t *testing.T) {
+	domain := []byte("TestCipherTextMarshal")
+
+	k256 := curves.K256()
+	ek, _, err := NewKeys(k256)
+	require.NoError(t, err)
+
+	msg := k256.Scalar.New(1)
+	msgBytes := msg.Bytes()
+	require.NoError(t, err)
+	cs, _, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: true,
+	})
+	require.NoError(t, err)
+
+	bin, err := cs.MarshalBinary()
+	require.NoError(t, err)
+	dup := new(CipherText)
+	err = dup.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.True(t, cs.c1.Equal(dup.c1))
+	require.True(t, cs.c2.Equal(dup.c2))
+	require.Equal(t, cs.nonce, dup.nonce)
+	require.Equal(t, cs.aead, dup.aead)
+}
diff --git a/pkg/verenc/elgamal/decryption_key.go b/pkg/verenc/elgamal/decryption_key.go
new file mode 100644
index 00000000..7c3f1846
--- /dev/null
+++ b/pkg/verenc/elgamal/decryption_key.go
@@ -0,0 +1,163 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"crypto/aes"
+	"crypto/cipher"
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+)
+
+type decryptionKeyMarshal struct {
+	X     []byte `bare:"x"`
+	Curve string `bare:"curve"`
+}
+
+// DecryptionKey decrypts verifiable ciphertext and verifies proofs
+type DecryptionKey struct {
+	x curves.Scalar
+}
+
+// EncryptionKey returns the corresponding encryption key for this decryption key
+func (dk DecryptionKey) EncryptionKey() *EncryptionKey {
+	return &EncryptionKey{
+		value: dk.x.Point().Generator().Mul(dk.x),
+	}
+}
+
+// MarshalBinary serializes a key to bytes
+func (dk DecryptionKey) MarshalBinary() ([]byte, error) {
+	tv := new(decryptionKeyMarshal)
+	tv.X = dk.x.Bytes()
+	tv.Curve = dk.x.Point().CurveName()
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary deserializes a key from bytes
+func (dk *DecryptionKey) UnmarshalBinary(data []byte) error {
+	tv := new(decryptionKeyMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("unknown curve")
+	}
+	x, err := curve.Scalar.SetBytes(tv.X)
+	if err != nil {
+		return err
+	}
+	dk.x = x
+	return nil
+}
+
+// Decrypt returns the resulting point from El-Gamal decryption.
+// No checking is performed whether the ciphertext has been modified.
+// M = H * m = C2 - C1 * x
+func (dk *DecryptionKey) Decrypt(cipherText *HomomorphicCipherText) curves.Point {
+	if cipherText == nil {
+		return nil
+	}
+	return cipherText.c2.Sub(cipherText.c1.Mul(dk.x))
+}
+
+// VerifiableDecrypt the ciphertext. This performs verifiable decryption
+// such that the decrypted data is checked against El-Gamal C2 value.
+// If the plaintext does not match, an error is returned
+// been generated by Encrypt
+func (dk DecryptionKey) VerifiableDecrypt(cipherText *CipherText) ([]byte, curves.Scalar, error) {
+	msgBytes, msgScalar, rhs, err := dk.decryptData(cipherText)
+	if err != nil {
+		return nil, nil, err
+	}
+	h := dk.EncryptionKey().value.Generator()
+	lhs := h.Mul(msgScalar)
+	if !lhs.Equal(rhs) {
+		return nil, nil, fmt.Errorf("ciphertext mismatch")
+	}
+	return msgBytes, msgScalar, nil
+}
+
+// VerifiableDecryptWithDomain the ciphertext. This performs verifiable decryption
+// such that the decrypted data is checked against El-Gamal C2 value.
+// If the plaintext does not match, an error is returned
+// The Domain component is meant for scenarios where `msg` is used in more
+// than just one setting and should be contextualized. The ciphertext must have
+// been generated by EncryptWithDomain
+func (dk DecryptionKey) VerifiableDecryptWithDomain(domain []byte, cipherText *CipherText) ([]byte, curves.Scalar, error) {
+	msgBytes, msgScalar, rhs, err := dk.decryptData(cipherText)
+	if err != nil {
+		return nil, nil, err
+	}
+	ek := dk.EncryptionKey()
+	genBytes := append(domain, ek.value.ToAffineUncompressed()...)
+	genBytes = append(genBytes, cipherText.nonce...)
+
+	h := ek.value.Hash(genBytes)
+	lhs := h.Mul(msgScalar)
+	if !lhs.Equal(rhs) {
+		return nil, nil, fmt.Errorf("ciphertext mismatch")
+	}
+	return msgBytes, msgScalar, nil
+}
+
+func (dk DecryptionKey) decryptData(cipherText *CipherText) ([]byte, curves.Scalar, curves.Point, error) {
+	if cipherText == nil {
+		return nil, nil, nil, internal.ErrNilArguments
+	}
+	if cipherText.c1 == nil || cipherText.c2 == nil || cipherText.nonce == nil || cipherText.aead == nil {
+		return nil, nil, nil, internal.ErrNilArguments
+	}
+	// Have to check these because aesgcm will panic if not the correct length
+	if len(cipherText.nonce) < 12 || len(cipherText.aead) < 16 {
+		return nil, nil, nil, internal.ErrZeroValue
+	}
+	// r * Q
+	t := cipherText.c1.Mul(dk.x)
+
+	aeadKey, err := core.FiatShamir(new(big.Int).SetBytes(t.ToAffineCompressed()))
+	if err != nil {
+		return nil, nil, nil, err
+	}
+	block, err := aes.NewCipher(aeadKey)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+	aesGcm, err := cipher.NewGCM(block)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+
+	aad := cipherText.c1.ToAffineUncompressed()
+	aad = append(aad, cipherText.c2.ToAffineUncompressed()...)
+	// AAD = C1 || C2
+	msgBytes, err := aesGcm.Open(nil, cipherText.nonce, cipherText.aead, aad)
+	if err != nil {
+		return nil, nil, nil, err
+	}
+	msg := dk.x.New(0)
+	if cipherText.msgIsHashed {
+		msg, err = msg.SetBytes(msgBytes)
+		if err != nil {
+			return nil, nil, nil, err
+		}
+	} else {
+		msg = msg.Hash(msgBytes)
+	}
+	if err != nil {
+		return nil, nil, nil, err
+	}
+	rhs := cipherText.c2.Sub(t)
+
+	return msgBytes, msg, rhs, nil
+}
diff --git a/pkg/verenc/elgamal/decryption_key_test.go b/pkg/verenc/elgamal/decryption_key_test.go
new file mode 100644
index 00000000..0756447f
--- /dev/null
+++ b/pkg/verenc/elgamal/decryption_key_test.go
@@ -0,0 +1,57 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestDecryptionKeyMarshal(t *testing.T) {
+	k256 := curves.K256()
+	_, dk, err := NewKeys(k256)
+	require.NoError(t, err)
+	bin, err := dk.MarshalBinary()
+	require.NoError(t, err)
+	dup := new(DecryptionKey)
+	err = dup.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.Equal(t, 0, dk.x.Cmp(dup.x))
+}
+
+func TestDecryptionKeyDecryptBadCiphertext(t *testing.T) {
+	k256 := curves.K256()
+	_, dk, err := NewKeys(k256)
+	require.NoError(t, err)
+
+	// nil ciphertext
+	_, _, err = dk.VerifiableDecryptWithDomain([]byte{}, nil)
+	require.Error(t, err)
+
+	// empty ciphertext
+	_, _, err = dk.VerifiableDecryptWithDomain([]byte{}, new(CipherText))
+	require.Error(t, err)
+
+	cs := new(CipherText)
+	cs.c1 = k256.Point.Generator()
+	cs.c2 = k256.Point.Generator()
+	cs.nonce = make([]byte, 12)
+	cs.aead = make([]byte, 16)
+
+	// empty data in ciphertext
+	_, _, err = dk.VerifiableDecryptWithDomain([]byte{}, cs)
+	require.Error(t, err)
+
+	cs.c1 = k256.Point.Identity()
+	cs.c2 = k256.Point.Identity()
+	cs.nonce = []byte{}
+	cs.aead = []byte{}
+	// ensure no panic happens when nonce and aead are invalid lengths
+	_, _, err = dk.VerifiableDecryptWithDomain([]byte{}, cs)
+	require.Error(t, err)
+}
diff --git a/pkg/verenc/elgamal/encryption_key.go b/pkg/verenc/elgamal/encryption_key.go
new file mode 100644
index 00000000..61e139db
--- /dev/null
+++ b/pkg/verenc/elgamal/encryption_key.go
@@ -0,0 +1,154 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"crypto/aes"
+	"crypto/cipher"
+	crand "crypto/rand"
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/pkg/core"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"math/big"
+)
+
+type encryptionKeyMarshal struct {
+	Value []byte `bare:"value"`
+	Curve string `bare:"curve"`
+}
+
+// EncryptParams is all the options for doing verifiable encryption.
+// Message must be supplied and is the value to be encrypted.
+// MessageIsHashed defines whether Message represents an unhashed arbitrary
+// byte sequence or already represents a scalar in the elliptic curve.
+// Domain is an optional domain separation tag and used to generate a separate
+// point for the pedersen commitment in El-Gamal ciphertexts.
+// Blinding is blinding factor (bf) of the El-Gamal ciphertext. If nil
+// a bf is generated at random.
+// GenProof indicates whether to return a proof of encryption correctness to the
+// corresponding public key.
+// ProofNonce is the nonce used to generate the one time proof. This value
+// is required if GenProof is true.
+type EncryptParams struct {
+	MessageIsHashed bool
+	Domain          []byte
+	Blinding        curves.Scalar
+	GenProof        bool
+	ProofNonce      []byte
+}
+
+// EncryptionKey encrypts a message to a ciphertext from which
+// zero-knowledge proofs can be derived
+type EncryptionKey struct {
+	value curves.Point
+}
+
+// NewKeys creates a new key pair for El-Gamal encryption
+func NewKeys(curve *curves.Curve) (*EncryptionKey, *DecryptionKey, error) {
+	if curve == nil {
+		return nil, nil, fmt.Errorf("invalid curve")
+	}
+	x := curve.Scalar.Random(crand.Reader)
+	if x == nil {
+		return nil, nil, fmt.Errorf("cannot generate decryption key")
+	}
+	value := curve.Point.Generator().Mul(x)
+	if value == nil {
+		return nil, nil, fmt.Errorf("cannot generate encryption key")
+	}
+	return &EncryptionKey{value}, &DecryptionKey{x}, nil
+}
+
+// MarshalBinary serializes a key to bytes
+func (ek EncryptionKey) MarshalBinary() ([]byte, error) {
+	tv := new(encryptionKeyMarshal)
+	tv.Curve = ek.value.CurveName()
+	tv.Value = ek.value.ToAffineCompressed()
+	return bare.Marshal(tv)
+}
+
+// UnmarshalBinary deserializes a key from bytes
+func (ek *EncryptionKey) UnmarshalBinary(data []byte) error {
+	tv := new(encryptionKeyMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+	if curve == nil {
+		return fmt.Errorf("unknown curve")
+	}
+	value, err := curve.Point.FromAffineCompressed(tv.Value)
+	if err != nil {
+		return err
+	}
+	ek.value = value
+	return nil
+}
+
+func (ek EncryptionKey) HomomorphicEncrypt(msg curves.Scalar) (*HomomorphicCipherText, error) {
+	r := ek.value.Scalar().Random(crand.Reader)
+	return &HomomorphicCipherText{
+		c1: ek.value.Generator().Mul(r),
+		c2: ek.value.Mul(r).Add(ek.value.Generator().Mul(msg)),
+	}, nil
+}
+
+func (ek EncryptionKey) encryptWithRandNonce(msg []byte, msgIsHashed bool, r curves.Scalar, h curves.Point, nonce []byte) (*CipherText, error) {
+	// r * Q
+	t := ek.value.Mul(r)
+	// Derive AEAD encryption key
+	aeadKey, err := core.FiatShamir(new(big.Int).SetBytes(t.ToAffineCompressed()))
+	if err != nil {
+		return nil, err
+	}
+	block, err := aes.NewCipher(aeadKey)
+	if err != nil {
+		return nil, err
+	}
+	aesGcm, err := cipher.NewGCM(block)
+	if err != nil {
+		return nil, err
+	}
+
+	// C1 = r * G
+	c1 := ek.value.Generator().Mul(r)
+	// C2 = m * H + r * Q
+	msgScalar := r.New(0)
+	if msgIsHashed {
+		msgScalar, err = msgScalar.SetBytes(msg)
+		if err != nil {
+			return nil, err
+		}
+	} else {
+		msgScalar = msgScalar.Hash(msg)
+	}
+	c2 := h.Mul(msgScalar).Add(t)
+
+	aad := c1.ToAffineUncompressed()
+	aad = append(aad, c2.ToAffineUncompressed()...)
+	// AAD = C1 || C2
+	// this protects them from modifications
+	aead := aesGcm.Seal(nil, nonce, msg, aad)
+
+	return &CipherText{
+		c1, c2, nonce, aead, msgIsHashed,
+	}, nil
+}
+
+func (ek EncryptionKey) genNonce() []byte {
+	var nonce [12]byte
+	n, err := crand.Read(nonce[:])
+	if err != nil {
+		return nil
+	}
+	if n != 12 {
+		return nil
+	}
+	return nonce[:]
+}
diff --git a/pkg/verenc/elgamal/encryption_key_test.go b/pkg/verenc/elgamal/encryption_key_test.go
new file mode 100644
index 00000000..3ae7ed2f
--- /dev/null
+++ b/pkg/verenc/elgamal/encryption_key_test.go
@@ -0,0 +1,88 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestEncryptionKeyEncrypt(t *testing.T) {
+	k256 := curves.K256()
+	domain := []byte("TestEncryptionKeyEncrypt")
+
+	ek, dk, err := NewKeys(k256)
+	require.NoError(t, err)
+
+	testMsgs := []curves.Scalar{
+		k256.Scalar.New(0),
+		k256.Scalar.New(10),
+		k256.Scalar.New(20),
+		k256.Scalar.New(30),
+		k256.Scalar.New(40),
+		k256.Scalar.New(50),
+		k256.Scalar.New(100),
+		k256.Scalar.New(1000),
+		k256.Scalar.New(10000),
+		k256.Scalar.New(100000),
+		k256.Scalar.New(1000000),
+	}
+
+	for _, msg := range testMsgs {
+		msgBytes := msg.Bytes()
+		require.NoError(t, err)
+		cs, _, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+			Domain:          domain,
+			MessageIsHashed: true,
+		})
+		require.NoError(t, err)
+		_, m, err := dk.VerifiableDecryptWithDomain(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, m.Cmp(msg), 0)
+	}
+}
+
+func TestEncryptionKeyEncryptInvalidMessages(t *testing.T) {
+	k256 := curves.K256()
+	domain := []byte("TestEncryptionKeyEncryptInvalidMessages")
+
+	ek, dk, err := NewKeys(k256)
+	require.NoError(t, err)
+
+	// nil message
+	_, _, err = ek.VerifiableEncrypt(nil, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: true,
+	})
+	require.Error(t, err)
+
+	msg := k256.Scalar.New(1234567890)
+	msgBytes := msg.Bytes()
+	cs, _, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: true,
+	})
+	require.NoError(t, err)
+	// invalid domain i.e. not the same domain used to encrypt
+	_, _, err = dk.VerifiableDecryptWithDomain([]byte{}, cs)
+	require.Error(t, err)
+}
+
+func TestEncryptionKeyMarshaling(t *testing.T) {
+	k256 := curves.K256()
+	ek, _, err := NewKeys(k256)
+	require.NoError(t, err)
+
+	bin, err := ek.MarshalBinary()
+	require.NoError(t, err)
+
+	ekClone := new(EncryptionKey)
+	err = ekClone.UnmarshalBinary(bin)
+	require.NoError(t, err)
+	require.True(t, ek.value.Equal(ekClone.value))
+}
diff --git a/pkg/verenc/elgamal/proof_enc.go b/pkg/verenc/elgamal/proof_enc.go
new file mode 100644
index 00000000..179534b4
--- /dev/null
+++ b/pkg/verenc/elgamal/proof_enc.go
@@ -0,0 +1,210 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	crand "crypto/rand"
+	"fmt"
+	"git.sr.ht/~sircmpwn/go-bare"
+	"github.com/coinbase/kryptology/internal"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+)
+
+// ProofVerEnc is a proof of verifiable encryption for a discrete log
+type ProofVerEnc struct {
+	challenge, schnorr1, schnorr2 curves.Scalar
+}
+
+type proofMarshal struct {
+	Challenge []byte `bare:"challenge"`
+	Schnorr1  []byte `bare:"schnorr1"`
+	Schnorr2  []byte `bare:"schnorr2"`
+	Curve     string `bare:"curve"`
+}
+
+func (pf ProofVerEnc) MarshalBinary() ([]byte, error) {
+	tv := new(proofMarshal)
+	tv.Challenge = pf.challenge.Bytes()
+	tv.Schnorr1 = pf.schnorr1.Bytes()
+	tv.Schnorr2 = pf.schnorr2.Bytes()
+	tv.Curve = pf.challenge.Point().CurveName()
+
+	return bare.Marshal(tv)
+}
+
+func (pf *ProofVerEnc) UnmarshalBinary(data []byte) error {
+	tv := new(proofMarshal)
+	err := bare.Unmarshal(data, tv)
+	if err != nil {
+		return err
+	}
+	curve := curves.GetCurveByName(tv.Curve)
+
+	challenge, err := curve.Scalar.SetBytes(tv.Challenge)
+	if err != nil {
+		return err
+	}
+	schnorr1, err := curve.Scalar.SetBytes(tv.Schnorr1)
+	if err != nil {
+		return err
+	}
+	schnorr2, err := curve.Scalar.SetBytes(tv.Schnorr2)
+	if err != nil {
+		return err
+	}
+
+	pf.challenge = challenge
+	pf.schnorr1 = schnorr1
+	pf.schnorr2 = schnorr2
+
+	return nil
+}
+
+// VerifiableEncrypt a message using El-Gamal. This also functions as an ECIES
+// encryption algorithm. The advantage here is proofs can be made about the
+// ciphertext versus plain ECIES if desired and/or linked to external proofs.
+func (ek EncryptionKey) VerifiableEncrypt(msg []byte, params *EncryptParams) (*CipherText, *ProofVerEnc, error) {
+	var err error
+	var proof *ProofVerEnc
+	var cipherText *CipherText
+	var h curves.Point
+
+	if msg == nil {
+		return nil, nil, internal.ErrNilArguments
+	}
+	if params.Blinding == nil {
+		params.Blinding = ek.value.Scalar().Random(crand.Reader)
+		for params.Blinding.IsZero() {
+			params.Blinding = ek.value.Scalar().Random(crand.Reader)
+		}
+	} else if params.Blinding.IsZero() {
+		return nil, nil, internal.ErrZeroValue
+	}
+
+	cnonce := ek.genNonce()
+	if cnonce == nil {
+		return nil, nil, fmt.Errorf("unable to generate nonce")
+	}
+
+	if params.Domain == nil {
+		// With no domain, the generator is used as h
+		h = ek.value.Generator()
+	} else {
+		// If domain is provided, calculate h using domain as part of the input, then encrypt
+		genBytes := append(params.Domain, ek.value.ToAffineUncompressed()...)
+		genBytes = append(genBytes, cnonce...)
+		h = ek.value.Hash(genBytes)
+	}
+
+	cipherText, err = ek.encryptWithRandNonce(msg, params.MessageIsHashed, params.Blinding, h, cnonce)
+	if err != nil {
+		return nil, nil, err
+	}
+
+	if params.GenProof {
+		if params.ProofNonce == nil {
+			return nil, nil, internal.ErrNilArguments
+		}
+		proof, err = ek.genProof(params.ProofNonce, msg, params.MessageIsHashed, cipherText, params.Blinding, h)
+		if err != nil {
+			return nil, nil, err
+		}
+	}
+	return cipherText, proof, nil
+}
+
+func (ek EncryptionKey) genProof(nonce, msg []byte, msgIsHashed bool, cipherText *CipherText, blinding curves.Scalar, h curves.Point) (*ProofVerEnc, error) {
+	r := ek.value.Scalar().Random(crand.Reader)
+	// R1 = r * G
+	r1 := ek.value.Generator().Mul(r)
+	// R2 = r * Q + b * H
+	r2 := ek.value.Mul(r).Add(h.Mul(blinding))
+
+	challengeBytes := append(cipherText.c1.ToAffineCompressed(), cipherText.c2.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, r1.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, r2.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, nonce...)
+	challenge := ek.value.Scalar().Hash(challengeBytes)
+	// b - cm
+	var msgScalar curves.Scalar
+	var err error
+	msgScalar = r.New(0)
+	if msgIsHashed {
+		msgScalar, err = msgScalar.SetBytes(msg)
+		if err != nil {
+			return nil, err
+		}
+	} else {
+		msgScalar = msgScalar.Hash(msg)
+	}
+	schnorr1 := blinding.Sub(challenge.Mul(msgScalar))
+	// r - cb
+	schnorr2 := r.Sub(challenge.Mul(blinding))
+	return &ProofVerEnc{challenge, schnorr1, schnorr2}, nil
+}
+
+// VerifyDomainEncryptProof a Proof of Verifiable Encryption
+// that was generated with EncryptDomainAndProve or
+// EncryptDomainAndProveBlinding.
+func (ek EncryptionKey) VerifyDomainEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error {
+	if ciphertext == nil || proof == nil {
+		return internal.ErrNilArguments
+	}
+	if proof.challenge == nil || proof.schnorr1 == nil || proof.schnorr2 == nil {
+		return internal.ErrNilArguments
+	}
+	if ciphertext.c1 == nil || ciphertext.c2 == nil {
+		return internal.ErrNilArguments
+	}
+
+	genBytes := append(nonce, ek.value.ToAffineUncompressed()...)
+	genBytes = append(genBytes, ciphertext.nonce[:]...)
+	h := ek.value.Hash(genBytes)
+	return ek.verify(nonce, ciphertext, proof, h)
+}
+
+// VerifyEncryptProof a Proof of Verifiable Encryption
+// that was generated with EncryptAndProve or
+// EncryptAndProveBlinding
+func (ek EncryptionKey) VerifyEncryptProof(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc) error {
+	if ciphertext == nil || proof == nil {
+		return internal.ErrNilArguments
+	}
+	if proof.challenge == nil || proof.schnorr1 == nil || proof.schnorr2 == nil {
+		return internal.ErrNilArguments
+	}
+	if ciphertext.c1 == nil || ciphertext.c2 == nil {
+		return internal.ErrNilArguments
+	}
+
+	h := ek.value.Generator()
+	return ek.verify(nonce, ciphertext, proof, h)
+}
+
+func (ek EncryptionKey) verify(nonce []byte, ciphertext *CipherText, proof *ProofVerEnc, h curves.Point) error {
+	// Reconstruct R1
+	// R1 = c * C1 + schnorr2 * G = c * ( b * G ) + (r - cb) * G
+	// = (cb + r - cb) * G = r * G
+	r1 := ciphertext.c1.Mul(proof.challenge).Add(ek.value.Generator().Mul(proof.schnorr2))
+	// Reconstruct R2
+	// R2 = c * C2 + schnorr2 * Q + schnorr1 * H =
+	// c * (b * Q + m * H) + (r - cb) * Q + (b - cm) * H =
+	// (cb + r - cb) * Q + (cm + b - cm) * H =
+	// r * Q + b * H
+	r2 := ciphertext.c2.Mul(proof.challenge).Add(ek.value.Mul(proof.schnorr2)).Add(h.Mul(proof.schnorr1))
+
+	challengeBytes := append(ciphertext.c1.ToAffineCompressed(), ciphertext.c2.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, r1.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, r2.ToAffineCompressed()...)
+	challengeBytes = append(challengeBytes, nonce...)
+	challenge := proof.challenge.Hash(challengeBytes)
+
+	if challenge.Cmp(proof.challenge) == 0 {
+		return nil
+	}
+	return fmt.Errorf("invalid ciphertext")
+}
diff --git a/pkg/verenc/elgamal/proof_enc_test.go b/pkg/verenc/elgamal/proof_enc_test.go
new file mode 100644
index 00000000..4a8002df
--- /dev/null
+++ b/pkg/verenc/elgamal/proof_enc_test.go
@@ -0,0 +1,222 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package elgamal
+
+import (
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/stretchr/testify/require"
+	"testing"
+)
+
+func TestEncryptionKeyEncryptAndProve(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProve")
+
+	ek, dk, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	testMsgs := []curves.Scalar{
+		bls12381.Scalar.New(0),
+		bls12381.Scalar.New(10),
+		bls12381.Scalar.New(20),
+		bls12381.Scalar.New(30),
+		bls12381.Scalar.New(40),
+		bls12381.Scalar.New(50),
+		bls12381.Scalar.New(100),
+		bls12381.Scalar.New(1000),
+		bls12381.Scalar.New(10000),
+		bls12381.Scalar.New(100000),
+		bls12381.Scalar.New(1000000),
+	}
+	for _, msg := range testMsgs {
+		msgBytes := msg.Bytes()
+		require.NoError(t, err)
+		cs, proof, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+			Domain:          domain,
+			MessageIsHashed: true,
+			GenProof:        true,
+			ProofNonce:      domain,
+		})
+		require.NoError(t, err)
+
+		err = ek.VerifyDomainEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+
+		_, dmsg, err := dk.VerifiableDecryptWithDomain(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, 0, msg.Cmp(dmsg))
+	}
+}
+
+func TestEncryptionKeyEncryptAndProvePlaintextMsg(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProve")
+
+	ek, dk, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	msg := "testMessage"
+	msgBytes := []byte(msg)
+
+	cs, proof, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: false,
+		GenProof:        true,
+		ProofNonce:      domain,
+	})
+	require.NoError(t, err)
+
+	err = ek.VerifyDomainEncryptProof(domain, cs, proof)
+	require.NoError(t, err)
+
+	dmsgBytes, _, err := dk.VerifiableDecryptWithDomain(domain, cs)
+	require.NoError(t, err)
+	require.Equal(t, msgBytes, dmsgBytes)
+	require.Equal(t, msg, string(dmsgBytes))
+}
+
+func TestEncryptionKeyEncryptAndProveBlinding(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProveBlinding")
+
+	ek, dk, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	testMsgs := []*struct {
+		test, blinding curves.Scalar
+	}{
+		{bls12381.Scalar.New(0), bls12381.Scalar.New(1)},
+		{bls12381.Scalar.New(10), bls12381.Scalar.New(2)},
+		{bls12381.Scalar.New(20), bls12381.Scalar.New(3)},
+		{bls12381.Scalar.New(30), bls12381.Scalar.New(4)},
+		{bls12381.Scalar.New(40), bls12381.Scalar.New(5)},
+		{bls12381.Scalar.New(50), bls12381.Scalar.New(6)},
+		{bls12381.Scalar.New(100), bls12381.Scalar.New(7)},
+		{bls12381.Scalar.New(1000), bls12381.Scalar.New(8)},
+		{bls12381.Scalar.New(10000), bls12381.Scalar.New(9)},
+		{bls12381.Scalar.New(100000), bls12381.Scalar.New(10)},
+		{bls12381.Scalar.New(1000000), bls12381.Scalar.New(11)},
+	}
+	for _, msg := range testMsgs {
+		msgTestBytes := msg.test.Bytes()
+		cs, proof, err := ek.VerifiableEncrypt(msgTestBytes, &EncryptParams{
+			Domain:          domain,
+			MessageIsHashed: true,
+			Blinding:        msg.blinding,
+			GenProof:        true,
+			ProofNonce:      domain,
+		})
+		require.NoError(t, err)
+
+		err = ek.VerifyDomainEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+
+		_, dmsg, err := dk.VerifiableDecryptWithDomain(domain, cs)
+		require.NoError(t, err)
+		require.Equal(t, 0, msg.test.Cmp(dmsg))
+	}
+}
+
+func TestEncryptionKeyEncryptAndProveInvalidInputs(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProveInvalidInputs")
+
+	ek, _, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	_, _, err = ek.VerifiableEncrypt(nil, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: true,
+		GenProof:        true,
+		ProofNonce:      domain,
+	})
+	require.Error(t, err)
+
+	msg2 := bls12381.Scalar.New(2)
+	msg2Bytes := msg2.Bytes()
+	_, _, err = ek.VerifiableEncrypt(msg2Bytes, &EncryptParams{
+		Domain:          domain,
+		MessageIsHashed: true,
+		Blinding:        bls12381.Scalar.New(0),
+		GenProof:        true,
+		ProofNonce:      domain,
+	})
+	require.Error(t, err)
+}
+
+func TestMarshalUnmarshalWithDomain(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProve")
+
+	ek, _, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	testMsgs := []curves.Scalar{
+		bls12381.Scalar.New(0),
+		bls12381.Scalar.New(10),
+		bls12381.Scalar.New(100),
+		bls12381.Scalar.New(1000),
+		bls12381.Scalar.New(1000000),
+	}
+	for _, msg := range testMsgs {
+		msgBytes := msg.Bytes()
+		require.NoError(t, err)
+		cs, proof, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+			Domain:          domain,
+			MessageIsHashed: true,
+			GenProof:        true,
+			ProofNonce:      domain,
+		})
+		require.NoError(t, err)
+
+		proofBytes, err := proof.MarshalBinary()
+		require.NoError(t, err)
+
+		proofUnmarshaled := ProofVerEnc{}
+		err = proofUnmarshaled.UnmarshalBinary(proofBytes)
+		require.NoError(t, err)
+
+		err = ek.VerifyDomainEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+	}
+}
+
+func TestMarshalUnmarshal(t *testing.T) {
+	bls12381 := curves.BLS12381G1()
+	domain := []byte("TestEncryptionKeyEncryptAndProve")
+
+	ek, _, err := NewKeys(bls12381)
+	require.NoError(t, err)
+
+	testMsgs := []curves.Scalar{
+		bls12381.Scalar.New(0),
+		bls12381.Scalar.New(10),
+		bls12381.Scalar.New(100),
+		bls12381.Scalar.New(1000),
+		bls12381.Scalar.New(1000000),
+	}
+	for _, msg := range testMsgs {
+		msgBytes := msg.Bytes()
+		require.NoError(t, err)
+		cs, proof, err := ek.VerifiableEncrypt(msgBytes, &EncryptParams{
+			MessageIsHashed: true,
+			GenProof:        true,
+			ProofNonce:      domain,
+		})
+		require.NoError(t, err)
+
+		proofBytes, err := proof.MarshalBinary()
+		require.NoError(t, err)
+
+		proofUnmarshaled := ProofVerEnc{}
+		err = proofUnmarshaled.UnmarshalBinary(proofBytes)
+		require.NoError(t, err)
+
+		err = ek.VerifyEncryptProof(domain, cs, proof)
+		require.NoError(t, err)
+	}
+}
diff --git a/scripts/perf-comp-local b/scripts/perf-comp-local
new file mode 100755
index 00000000..fb77b79a
--- /dev/null
+++ b/scripts/perf-comp-local
@@ -0,0 +1,20 @@
+#! /usr/bin/env bash
+
+set -eo pipefail
+
+ROOT=$( cd $(dirname $0)/..;  pwd )
+
+TMP_DIR=$(mktemp -d)
+echo "tmp dir: $TMP_DIR"
+
+git clone --depth 1 -b master git@github.com:coinbase/kryptology.git "$TMP_DIR/kryptology"
+cd "$TMP_DIR/kryptology"
+go test -bench=. -short ./... > "$TMP_DIR/current-bench.log"
+
+cd "$ROOT"
+go test -bench=. -short ./... > "$TMP_DIR/new-bench.log"
+
+cd "$ROOT"
+go run cmd/benchcomp/main.go -current "$TMP_DIR/current-bench.log" -new "$TMP_DIR/new-bench.log"
+
+rm -rf "$TMP_DIR"
diff --git a/test/accumulator/ecc/README.md b/test/accumulator/ecc/README.md
new file mode 100755
index 00000000..435d69b8
--- /dev/null
+++ b/test/accumulator/ecc/README.md
@@ -0,0 +1,15 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# ecc
+
+```go
+import "github.com/coinbase/kryptology/test/accumulator/ecc"
+```
+
+## Index
+
+
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/accumulator/ecc/main.go b/test/accumulator/ecc/main.go
new file mode 100644
index 00000000..8bfa595e
--- /dev/null
+++ b/test/accumulator/ecc/main.go
@@ -0,0 +1,156 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"bufio"
+	"encoding/hex"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/accumulator"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"os"
+)
+
+func main() {
+	curve := curves.BLS12381(&curves.PointBls12381G1{})
+	sk, _ := new(accumulator.SecretKey).New(curve, []byte("1234567890"))
+	pk, _ := sk.GetPublicKey(curve)
+	skBytes, _ := sk.MarshalBinary()
+	pkBytes, _ := pk.MarshalBinary()
+	fmt.Println("Coinbase generates secret key and public key pair...")
+	fmt.Printf("Coinbase publishes public key %v\n", hex.EncodeToString(pkBytes))
+	fmt.Printf("Coinbase retains secret key %v\n", hex.EncodeToString(skBytes))
+
+	// Enter initial elements
+	fmt.Println("Coinbase starts initiating an accumulator")
+	var userInput []string
+	scanner := bufio.NewScanner(os.Stdin)
+	fmt.Println("Coinbase enters the elements accumulated in the initial accumulator, press enter to start")
+	for scanner.Scan() {
+		fmt.Println("Enter a string or stop")
+		line := scanner.Text()
+		if line == "stop" {
+			break
+		}
+		userInput = append(userInput, line+"\n")
+	}
+	elements := make([]accumulator.Element, len(userInput))
+	for i := 0; i < len(elements); i++ {
+		elements[i] = curve.Scalar.Hash([]byte(userInput[i]))
+	}
+
+	// Coinbase initiates a new accumulator with elements
+	acc, err := new(accumulator.Accumulator).WithElements(curve, sk, elements)
+	if err != nil || acc == nil {
+		panic(err)
+	}
+	accBytes, _ := acc.MarshalBinary()
+	fmt.Printf("Accumulator Initiated! Value is %v\n", hex.EncodeToString(accBytes))
+
+	// Initiate a new membership witness
+	fmt.Println("Coinbase issues a membership witness to a user")
+	fmt.Println("Coinbase enters the element that a membership witness is associated with")
+	reader := bufio.NewReader(os.Stdin)
+	witnessInput, _ := reader.ReadString('\n')
+	witElement := curve.Scalar.Hash([]byte(witnessInput))
+	wit, err := new(accumulator.MembershipWitness).New(witElement, acc, sk)
+	if err != nil {
+		panic(err)
+	}
+	fmt.Printf("Coinbase issued membership witness associated to element %v\n", witnessInput)
+
+	// User uses the witness to verify the membership
+	fmt.Println("The user can use the witness to verify the associated element is accumulated")
+	fmt.Println("verifying...")
+	err = wit.Verify(pk, acc)
+	if err != nil {
+		panic(err)
+	}
+	fmt.Println("membership verification succeeds!")
+
+	// Batch Update accumulator and membership witness
+	fmt.Println("Coinbase could batch update the accumulator")
+	fmt.Println("That is, Coinbase can add/delete multiple elements together")
+	var addInput []string
+	fmt.Println("Enter elements that you want to batch add, press enter the start")
+	for scanner.Scan() {
+		fmt.Println("Enter a string or stop")
+		line := scanner.Text()
+		if line == "stop" {
+			break
+		}
+		addInput = append(addInput, line+"\n")
+	}
+	additions := make([]accumulator.Element, len(addInput))
+	for i := 0; i < len(additions); i++ {
+		additions[i] = curve.Scalar.Hash([]byte(addInput[i]))
+	}
+
+	var deleteInput []string
+	fmt.Println("Enter elements that you want to batch delete, press enter to start")
+	for scanner.Scan() {
+		fmt.Println("Enter a string or stop")
+		line := scanner.Text()
+		if line == "stop" {
+			break
+		}
+		deleteInput = append(deleteInput, line+"\n")
+	}
+	deletions := make([]accumulator.Element, len(deleteInput))
+	for i := 0; i < len(deletions); i++ {
+		deletions[i] = curve.Scalar.Hash([]byte(deleteInput[i]))
+	}
+
+	// Batch update accumulator
+	_, coefficients, err := acc.Update(sk, additions, deletions)
+	if err != nil {
+		panic(err)
+	}
+	accBytes, _ = acc.MarshalBinary()
+	fmt.Println("Accumulator batch-update succeeds!")
+	fmt.Printf("The new accumulator value is %v\n", hex.EncodeToString(accBytes))
+
+	// Batch update witness accordingly
+	fmt.Println("User should batch-update his/her witness accordingly. This can be done by a trusted third party")
+	fmt.Println("so that the witness is still usable to verify the associated element is accumulated")
+	_, err = wit.BatchUpdate(additions, deletions, coefficients)
+	if err != nil {
+		panic(err)
+	}
+	err = wit.Verify(pk, acc)
+	if err != nil {
+		panic(err)
+	}
+	fmt.Println("Verification succeeds after batch-update")
+
+	// Proof ownership of witness
+	fmt.Println("The user can also generate a zero-knowledge proof proving the ownership of witness")
+	params, err := new(accumulator.ProofParams).New(curve, pk, []byte("entropy"))
+	if err != nil {
+		panic(err)
+	}
+	mpc, err := new(accumulator.MembershipProofCommitting).New(wit, acc, params, pk)
+	if err != nil {
+		panic(err)
+	}
+	challenge := curve.Scalar.Hash(mpc.GetChallengeBytes())
+	proof := mpc.GenProof(challenge)
+	finalProof := proof.Finalize(acc, params, pk, challenge)
+	proofBytes, err := proof.MarshalBinary()
+	if err != nil {
+		panic(err)
+	}
+	fmt.Println("ZK proof successfully generated!")
+	fmt.Printf("ZK proof value is %v\n", hex.EncodeToString(proofBytes))
+	fmt.Println("Verifying....")
+	challenge2 := finalProof.GetChallenge(curve)
+	if challenge.Cmp(challenge2) == 0 {
+		fmt.Println("proof verification succeeds!")
+	} else {
+		fmt.Println("proof verification fails!")
+	}
+}
diff --git a/test/data/sign.input.gz b/test/data/sign.input.gz
new file mode 100644
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zCUKiHDMb62+nWZ+bh{+RJw^UecDSinrUoINE_*>x`qI;qUnbRFa?!PUSbKJQm=j{_
zMd8a3BnGU6f|Wj|y5nsqA%vqQ{wTSWtUns7^GEgVjU)k(vnB?whE-9*nBMD!z5*iQ
z8%+fvO$T|-?N$k2&ZF5PK|v6KX#|I42*#wiX{g$Q>&&lAhWqj}#e_BdhTq@t`x}0L
T!|y*De*gRjX1oxufGGk1+|U8w

literal 0
HcmV?d00001

diff --git a/test/dkg/2p/README.md b/test/dkg/2p/README.md
new file mode 100755
index 00000000..35f6caef
--- /dev/null
+++ b/test/dkg/2p/README.md
@@ -0,0 +1,15 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# 2p
+
+```go
+import "github.com/coinbase/kryptology/test/dkg/2p"
+```
+
+## Index
+
+
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/dkg/2p/main.go b/test/dkg/2p/main.go
new file mode 100644
index 00000000..07004419
--- /dev/null
+++ b/test/dkg/2p/main.go
@@ -0,0 +1,139 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+//
+// Demonstrates 2-party (client-server) DKG and message serialization
+//
+
+package main
+
+import (
+	"encoding/json"
+	"fmt"
+	crypto "github.com/coinbase/kryptology/pkg/core/curves"
+	"log"
+	"os"
+
+	"github.com/coinbase/kryptology/pkg/dkg/gennaro2p"
+	"github.com/btcsuite/btcd/btcec"
+	"github.com/pkg/errors"
+)
+
+const (
+	clientSsid     = 1
+	serverSageSsid = 2
+	useJson        = true
+)
+
+// Scalar for the curve we're using
+var (
+	curveScalar = crypto.NewK256Scalar()
+	curve       = btcec.S256()
+)
+
+// Initiate and run a DKG with JSON-serialized messages
+func runClientJson(s *server) {
+	// Setup
+	lg := log.New(os.Stdout, "[client] ", log.Lshortfile|log.Lmsgprefix)
+
+	lg.Println("Creating client")
+	client, err := gennaro2p.NewParticipant(clientSsid, serverSageSsid, nil, curveScalar, curve)
+	dieOnError(err)
+
+	// DKG Round 1
+	lg.Println("Running DKG round 1")
+	clientR1, err := client.Round1(nil)
+	dieOnError(err)
+	lg.Printf("clientR1=%#v", clientR1)
+
+	// Marshal
+	clientR1Json, err := json.Marshal(clientR1)
+	dieOnError(errors.Wrap(err, "marhsaling clientR1Json"))
+
+	// Contact server
+	lg.Println("Calling server.Phase1")
+	phase1Json := s.phase1Json(clientR1Json)
+
+	// unmarshal
+	var p1 phase1Response
+	err = json.Unmarshal(phase1Json, &p1)
+	dieOnError(errors.Wrap(err, "unmarshaling phase 1 response"))
+
+	lg.Printf("phase 1 response=%v", p1)
+
+	// DKG Round 2
+	lg.Println("Running DKG round 2")
+	clientR2, err := client.Round2(&p1.R1)
+	dieOnError(err)
+	lg.Printf("clientR2=%#v", clientR2)
+
+	// DKG finalize
+	lg.Println("Finalize DKG")
+	result, err := client.Finalize(&p1.R2)
+	dieOnError(err)
+	lg.Printf("result=%#v", result)
+
+	// Marshal R2 output
+	clientR2Json, err := json.Marshal(clientR2)
+	dieOnError(err)
+
+	// Contact server
+	lg.Println("Calling server.Phase2")
+	s.phase2Json(clientR2Json)
+}
+
+// Initiate and run a DKG
+func runClient(s *server) {
+	// Setup
+	lg := log.New(os.Stdout, "[client] ", log.Lshortfile|log.Lmsgprefix)
+
+	lg.Println("Creating client")
+	client, err := gennaro2p.NewParticipant(clientSsid, serverSageSsid, nil, curveScalar, curve)
+	dieOnError(err)
+
+	// DKG Round 1
+	lg.Println("Running DKG round 1")
+	clientR1, err := client.Round1(nil)
+	dieOnError(err)
+	lg.Printf("clientR1=%#v", clientR1)
+
+	// Contact server
+	lg.Println("Calling server.Phase1")
+	serverR1, serverR2 := s.phase1(clientR1)
+
+	// DKG Round 2
+	lg.Println("Running DKG round 2")
+	clientR2, err := client.Round2(serverR1)
+	dieOnError(err)
+	lg.Printf("clientR2=%#v", clientR2)
+
+	// DKG finalize
+	lg.Println("Finalize DKG")
+	result, err := client.Finalize(serverR2)
+	dieOnError(err)
+	lg.Printf("result=%#v", result)
+
+	// Contact server
+	lg.Println("Calling server.Finalize")
+	s.phase2(clientR2)
+}
+
+// Run!
+func main() {
+	if useJson {
+		runClientJson(&server{})
+	} else {
+		runClient(&server{})
+	}
+}
+
+// If there's an error, print and exit(1)
+func dieOnError(err error) {
+	if err != nil {
+		fmt.Printf("Fatal: %v\n", err)
+		os.Exit(1)
+	}
+}
diff --git a/test/dkg/2p/server.go b/test/dkg/2p/server.go
new file mode 100644
index 00000000..e283abb0
--- /dev/null
+++ b/test/dkg/2p/server.go
@@ -0,0 +1,85 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"encoding/json"
+	"log"
+	"os"
+
+	dkg "github.com/coinbase/kryptology/pkg/dkg/gennaro2p"
+	"github.com/pkg/errors"
+)
+
+type server struct {
+	p *dkg.Participant
+	l *log.Logger
+}
+
+type phase1Response struct {
+	R1 dkg.Round1Message `json:"r1"`
+	R2 dkg.Round2Message `json:"r2"`
+}
+
+// Runs server's R1 and R2
+func (s *server) phase1(in *dkg.Round1Message) (*dkg.Round1Message, *dkg.Round2Message) {
+	// Setup logger
+	s.l = log.New(os.Stdout, "[server] ", log.Lshortfile|log.Lmsgprefix)
+
+	s.l.Println("Initializing server")
+	var err error
+	s.p, err = dkg.NewParticipant(serverSageSsid, clientSsid, in.Blind, curveScalar, curve)
+	dieOnError(err)
+
+	// DKG Round 1
+	s.l.Println("Running DKG round 1")
+	r1Out, err := s.p.Round1(nil)
+	dieOnError(err)
+
+	s.l.Printf("r1Out=%#v", r1Out)
+
+	// DKG Round 2
+	s.l.Println("Running DKG round 2")
+	r2out, err := s.p.Round2(in)
+	dieOnError(err)
+	s.l.Printf("r2out=%#v", r2out)
+	return r1Out, r2out
+}
+
+// Runs server's finalize
+func (s *server) phase2(in *dkg.Round2Message) {
+	// DKG finalize
+	s.l.Println("Finalize DKG")
+	result, err := s.p.Finalize(in)
+	dieOnError(err)
+	s.l.Printf("result=%#v", result)
+}
+
+// Runs server's R1 and R2 with in/out in JSON
+func (s *server) phase1Json(req []byte) []byte {
+	// Deserialize the Round1 input
+	in := &dkg.Round1Message{}
+	err := json.Unmarshal(req, &in)
+	dieOnError(errors.Wrapf(err, "unmarshaling Round1Message from req=%v", string(req)))
+
+	// Run phase 1 and marshal
+	r1, r2 := s.phase1(in)
+	out, err := json.Marshal(&phase1Response{*r1, *r2})
+	dieOnError(errors.Wrap(err, "marshaling phase1 response"))
+	return out
+}
+
+// Runs server's Finalize with in/out in JSON
+func (s *server) phase2Json(req []byte) {
+	// Deserialize the Round2 input
+	in := &dkg.Round2Message{}
+	err := json.Unmarshal(req, &in)
+	dieOnError(errors.Wrapf(err, "unmarshaling Round2Message from req=%v", string(req)))
+
+	// Run finalize
+	s.phase2(in)
+}
diff --git a/test/dkg/bls/README.md b/test/dkg/bls/README.md
new file mode 100755
index 00000000..21734141
--- /dev/null
+++ b/test/dkg/bls/README.md
@@ -0,0 +1,26 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# bls
+
+```go
+import "github.com/coinbase/kryptology/test/dkg/bls"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/dkg/bls/main.go b/test/dkg/bls/main.go
new file mode 100644
index 00000000..896378db
--- /dev/null
+++ b/test/dkg/bls/main.go
@@ -0,0 +1,205 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	sharing "github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	dkg "github.com/coinbase/kryptology/pkg/dkg/gennaro"
+	bls "github.com/coinbase/kryptology/pkg/signatures/bls/bls_sig"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing Gennaro DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	rnd2Bcast := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// DKG Round 3
+	verificationKey, signingShares := round3(participants, rnd2Bcast)
+
+	// Signing common setup for all participants
+	scheme := bls.NewSigEth2()
+	msg := []byte("All my bitcoin is stored here")
+
+	// Signing
+	partialSigs := make([]*bls.PartialSignature, 0, threshold)
+	cnt := 0
+	for id, sk := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		fmt.Printf("Signing for participant %d\n", id)
+		skShare := new(bls.SecretKeyShare)
+		// secret share expects 1 byte identifier at the end of the array
+		skBytes := make([]byte, bls.SecretKeyShareSize)
+		copy(skBytes, sk[4:])
+		skBytes[bls.SecretKeyShareSize-1] = sk[3]
+		err := skShare.UnmarshalBinary(skBytes)
+		if err != nil {
+			panic(err)
+		}
+
+		sig, err := scheme.PartialSign(skShare, msg)
+		if err != nil {
+			panic(err)
+		}
+		partialSigs = append(partialSigs, sig)
+	}
+	if verificationKey == nil {
+		panic("verification key was never complete")
+	}
+
+	sig, err := scheme.CombineSignatures(partialSigs...)
+	if err != nil {
+		panic(err)
+	}
+
+	curve := sharing.Bls12381G1()
+	pkBytes, err := curve.CompressedBytesFromBigInts(verificationKey.X, verificationKey.Y)
+	if err != nil {
+		panic(err)
+	}
+	pk := new(bls.PublicKey)
+	err = pk.UnmarshalBinary(pkBytes)
+	if err != nil {
+		panic(err)
+	}
+
+	ok, err := scheme.Verify(pk, msg, sig)
+	if err != nil {
+		panic(err)
+	}
+	fmt.Printf("Signature verification - %v\n", ok)
+}
+
+func round1(participants map[uint32]*dkg.Participant) (map[uint32]dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.Participant,
+	rnd1Bcast map[uint32]dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) map[uint32]dkg.Round2Bcast {
+	rnd2Bcast := make(map[uint32]dkg.Round2Bcast, len(participants))
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+
+		rnd1P2pForP := make(map[uint32]*dkg.Round1P2PSendPacket)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		bcast, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		rnd2Bcast[id] = bcast
+	}
+
+	return rnd2Bcast
+}
+
+func round3(participants map[uint32]*dkg.Participant, rnd2Bcast map[uint32]dkg.Round2Bcast) (*curves.EcPoint, map[uint32][]byte) {
+	signingShares := make(map[uint32][]byte, len(participants))
+	var verificationKey *curves.EcPoint
+	for id := range rnd2Bcast {
+		fmt.Printf("Computing DKG Round 3 for participant %d\n", id)
+		pk, sk, err := participants[id].Round3(rnd2Bcast)
+		verificationKey = pk
+		if err != nil {
+			panic(err)
+		}
+		fmt.Printf("DKG completed for participant %d\n", id)
+		signingShares[id] = sk.Bytes()
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.Participant {
+	curve := sharing.Bls12381G1()
+	gx, gy := curve.Hash([]byte("Fair is foul, and foul is fair: Hover through the fog and filthy air."))
+	generator := &curves.EcPoint{
+		Curve: curve,
+		X:     gx,
+		Y:     gy,
+	}
+	participants := make(map[uint32]*dkg.Participant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewParticipant(uint32(i), uint32(thresh), generator, curves.NewBls12381Scalar(), otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+bls INPUT
+Simulate a DKG using BLS keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/dkg/ed25519/README.md b/test/dkg/ed25519/README.md
new file mode 100755
index 00000000..c2b5709a
--- /dev/null
+++ b/test/dkg/ed25519/README.md
@@ -0,0 +1,26 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# ed25519
+
+```go
+import "github.com/coinbase/kryptology/test/dkg/ed25519"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/dkg/ed25519/main.go b/test/dkg/ed25519/main.go
new file mode 100644
index 00000000..7548fc90
--- /dev/null
+++ b/test/dkg/ed25519/main.go
@@ -0,0 +1,237 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"crypto/sha512"
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+
+	"filippo.io/edwards25519"
+	"github.com/coinbase/kryptology/internal"
+	dkg "github.com/coinbase/kryptology/pkg/dkg/gennaro"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing Gennaro DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	rnd2Bcast := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// DKG Round 3
+	verificationKey, signingShares := round3(participants, rnd2Bcast)
+
+	// Signing common setup for all participants
+	msg := []byte("All my bitcoin is stored here")
+	curve := v1.Ed25519()
+	scheme, _ := v1.NewShamir(threshold, limit, curves.NewField(curve.N))
+	shares := make([]*v1.ShamirShare, 0, threshold)
+	cnt := 0
+	for _, share := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		shares = append(shares, share)
+	}
+	sk, err := scheme.Combine(shares...)
+	if err != nil {
+		panic(err)
+	}
+
+	sk = internal.ReverseScalarBytes(sk)
+	var ska [32]byte
+	copy(ska[:], sk[:])
+
+	skC, err := edwards25519.NewScalar().SetCanonicalBytes(ska[:])
+	if err != nil {
+		panic(err)
+	}
+	vk := edwards25519.NewIdentityPoint().ScalarBaseMult(skC)
+	vk2, err := internal.BigInt2Ed25519Point(verificationKey.Y)
+	if err != nil {
+		panic(err)
+	}
+	if vk.Equal(vk2) == 0 {
+		panic("not equal")
+	}
+
+	r, s := sign(skC, vk2.Bytes(), []byte("no nonce"), msg)
+
+	ok := verify(vk2.Bytes(), msg, r, s)
+
+	fmt.Printf("Signature verification - %v\n", ok)
+}
+
+func sign(skC *edwards25519.Scalar, pubKey, nonce, msg []byte) (*edwards25519.Point, *edwards25519.Scalar) {
+	h := sha512.New()
+	_, _ = h.Write(nonce)
+	_, _ = h.Write(msg)
+	digest := h.Sum(nil)
+
+	digestReduced, err := edwards25519.NewScalar().SetUniformBytes(digest)
+	if err != nil {
+		panic(err)
+	}
+	r := edwards25519.NewGeneratorPoint().ScalarBaseMult(digestReduced)
+
+	encodedR := r.Bytes()
+	h.Reset()
+	_, _ = h.Write(encodedR)
+	_, _ = h.Write(pubKey)
+	_, _ = h.Write(msg)
+
+	k, err := edwards25519.NewScalar().SetUniformBytes(h.Sum(nil))
+	if err != nil {
+		panic(err)
+	}
+	s := edwards25519.NewScalar().MultiplyAdd(k, skC, digestReduced)
+	return r, s
+}
+
+func verify(pk, msg []byte, r *edwards25519.Point, s *edwards25519.Scalar) bool {
+	h := sha512.New()
+	_, _ = h.Write(r.Bytes())
+	_, _ = h.Write(pk)
+	_, _ = h.Write(msg)
+	k, err := edwards25519.NewScalar().SetUniformBytes(h.Sum(nil))
+	if err != nil {
+		panic(err)
+	}
+
+	minusA, _ := edwards25519.NewIdentityPoint().SetBytes(pk)
+	minusA.Negate(minusA)
+
+	lhs := edwards25519.NewIdentityPoint().VarTimeDoubleScalarBaseMult(k, minusA, s)
+
+	return lhs.Equal(r) == 1
+}
+
+func round1(participants map[uint32]*dkg.Participant) (map[uint32]dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.Participant,
+	rnd1Bcast map[uint32]dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) map[uint32]dkg.Round2Bcast {
+	rnd2Bcast := make(map[uint32]dkg.Round2Bcast, len(participants))
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+
+		rnd1P2pForP := make(map[uint32]*dkg.Round1P2PSendPacket)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		bcast, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		rnd2Bcast[id] = bcast
+	}
+
+	return rnd2Bcast
+}
+
+func round3(participants map[uint32]*dkg.Participant, rnd2Bcast map[uint32]dkg.Round2Bcast) (*curves.EcPoint, map[uint32]*v1.ShamirShare) {
+	signingShares := make(map[uint32]*v1.ShamirShare, len(participants))
+	var verificationKey *curves.EcPoint
+	for id := range rnd2Bcast {
+		fmt.Printf("Computing DKG Round 3 for participant %d\n", id)
+		pk, sk, err := participants[id].Round3(rnd2Bcast)
+		verificationKey = pk
+		if err != nil {
+			panic(err)
+		}
+		fmt.Printf("DKG completed for participant %d\n", id)
+		signingShares[id] = sk
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.Participant {
+	curve := v1.Ed25519()
+	gx, gy := curve.Hash([]byte("Fair is foul, and foul is fair: Hover through the fog and filthy air."))
+	generator := &curves.EcPoint{
+		Curve: curve,
+		X:     gx,
+		Y:     gy,
+	}
+	participants := make(map[uint32]*dkg.Participant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewParticipant(uint32(i), uint32(thresh), generator, curves.NewEd25519Scalar(), otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+bls INPUT
+Simulate a DKG using BLS keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/dkg/k256/README.md b/test/dkg/k256/README.md
new file mode 100755
index 00000000..14122567
--- /dev/null
+++ b/test/dkg/k256/README.md
@@ -0,0 +1,26 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# k256
+
+```go
+import "github.com/coinbase/kryptology/test/dkg/k256"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/dkg/k256/main.go b/test/dkg/k256/main.go
new file mode 100644
index 00000000..3d6ebd97
--- /dev/null
+++ b/test/dkg/k256/main.go
@@ -0,0 +1,197 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"crypto/ecdsa"
+	crand "crypto/rand"
+	"crypto/sha512"
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"math/big"
+
+	dkg "github.com/coinbase/kryptology/pkg/dkg/gennaro"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing Gennaro DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	rnd2Bcast := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// DKG Round 3
+	verificationKey, signingShares := round3(participants, rnd2Bcast)
+
+	// Signing common setup for all participants
+	msg := []byte("All my bitcoin is stored here")
+	scheme, _ := v1.NewShamir(threshold, limit, curves.NewField(btcec.S256().N))
+	shares := make([]*v1.ShamirShare, 0, threshold)
+	cnt := 0
+	for _, share := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		shares = append(shares, share)
+	}
+	sk, err := scheme.Combine(shares...)
+	if err != nil {
+		panic(err)
+	}
+
+	pk, err := curves.NewScalarBaseMult(btcec.S256(), new(big.Int).SetBytes(sk))
+	if err != nil {
+		panic(err)
+	}
+	if !pk.Equals(verificationKey) {
+		panic("verification keys are not equal")
+	}
+
+	privKey, pubKey := btcec.PrivKeyFromBytes(btcec.S256(), sk)
+
+	hBytes := sha512.Sum384(msg)
+	hMsg := new(big.Int).SetBytes(hBytes[:])
+	hMsg.Mod(hMsg, btcec.S256().N)
+
+	r, s, err := ecdsa.Sign(crand.Reader, privKey.ToECDSA(), hMsg.Bytes())
+	if err != nil {
+		panic(err)
+	}
+	ok := ecdsa.Verify(pubKey.ToECDSA(), hMsg.Bytes(), r, s)
+
+	fmt.Printf("Signature verification - %v\n", ok)
+}
+
+func round1(participants map[uint32]*dkg.Participant) (map[uint32]dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.Participant,
+	rnd1Bcast map[uint32]dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) map[uint32]dkg.Round2Bcast {
+	rnd2Bcast := make(map[uint32]dkg.Round2Bcast, len(participants))
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+
+		rnd1P2pForP := make(map[uint32]*dkg.Round1P2PSendPacket)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		bcast, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		rnd2Bcast[id] = bcast
+	}
+
+	return rnd2Bcast
+}
+
+func round3(participants map[uint32]*dkg.Participant, rnd2Bcast map[uint32]dkg.Round2Bcast) (*curves.EcPoint, map[uint32]*v1.ShamirShare) {
+	signingShares := make(map[uint32]*v1.ShamirShare, len(participants))
+	var verificationKey *curves.EcPoint
+	for id := range rnd2Bcast {
+		fmt.Printf("Computing DKG Round 3 for participant %d\n", id)
+
+		pk, sk, err := participants[id].Round3(rnd2Bcast)
+		verificationKey = pk
+		if err != nil {
+			panic(err)
+		}
+		fmt.Printf("DKG completed for participant %d\n", id)
+		signingShares[id] = sk
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.Participant {
+	curve := btcec.S256()
+	gx, gy, err := v1.K256GeneratorFromHashedBytes([]byte("Fair is foul, and foul is fair: Hover through the fog and filthy air."))
+	if err != nil {
+		panic(err)
+	}
+	generator := &curves.EcPoint{
+		Curve: curve,
+		X:     gx,
+		Y:     gy,
+	}
+	participants := make(map[uint32]*dkg.Participant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewParticipant(uint32(i), uint32(thresh), generator, curves.NewK256Scalar(), otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+k256 INPUT
+Simulate a DKG using secp256k1 keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/frost_dkg/bls/README.md b/test/frost_dkg/bls/README.md
new file mode 100755
index 00000000..f1d16d09
--- /dev/null
+++ b/test/frost_dkg/bls/README.md
@@ -0,0 +1,30 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# bls
+
+```go
+import "github.com/coinbase/kryptology/test/frost_dkg/bls"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const Ctx = "string to prevent replay attack"
+```
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/frost_dkg/bls/main.go b/test/frost_dkg/bls/main.go
new file mode 100644
index 00000000..cc6b7376
--- /dev/null
+++ b/test/frost_dkg/bls/main.go
@@ -0,0 +1,177 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	dkg "github.com/coinbase/kryptology/pkg/dkg/frost"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	bls "github.com/coinbase/kryptology/pkg/signatures/bls/bls_sig"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+const Ctx = "string to prevent replay attack"
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing FROST DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	verificationKey, signingShares := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// Signing common setup for all participants
+	scheme := bls.NewSigEth2()
+	msg := []byte("All my bitcoin is stored here")
+
+	// Signing
+	partialSigs := make([]*bls.PartialSignature, 0, threshold)
+	cnt := 0
+	for id, sk := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		fmt.Printf("Signing for participant %d\n", id)
+		skShare := new(bls.SecretKeyShare)
+		// secret share expects 1 byte identifier at the end of the array
+		skBytes := make([]byte, bls.SecretKeyShareSize)
+		copy(skBytes, sk[4:])
+		skBytes[bls.SecretKeyShareSize-1] = sk[3]
+		err := skShare.UnmarshalBinary(skBytes)
+		if err != nil {
+			panic(err)
+		}
+		sig, err := scheme.PartialSign(skShare, msg)
+		if err != nil {
+			panic(err)
+		}
+		partialSigs = append(partialSigs, sig)
+	}
+	if verificationKey == nil {
+		panic("verification key was never complete")
+	}
+
+	sig, err := scheme.CombineSignatures(partialSigs...)
+	if err != nil {
+		panic(err)
+	}
+
+	pk := new(bls.PublicKey)
+	err = pk.UnmarshalBinary(verificationKey.ToAffineCompressed())
+	if err != nil {
+		panic(err)
+	}
+
+	ok, err := scheme.Verify(pk, msg, sig)
+	if err != nil {
+		panic(err)
+	}
+	fmt.Printf("Signature verification - %v\n", ok)
+}
+
+func round1(participants map[uint32]*dkg.DkgParticipant) (map[uint32]*dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]*dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.DkgParticipant,
+	rnd1Bcast map[uint32]*dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) (curves.Point, map[uint32][]byte) {
+	signingShares := make(map[uint32][]byte, len(participants))
+	var verificationKey curves.Point
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+		rnd1P2pForP := make(map[uint32]*sharing.ShamirShare)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		rnd2Out, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		verificationKey = rnd2Out.VerificationKey
+		share := sharing.ShamirShare{
+			Id:    id,
+			Value: participants[id].SkShare.Bytes(),
+		}
+		signingShares[id] = share.Bytes()
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.DkgParticipant {
+	curve := curves.BLS12381G1()
+	participants := make(map[uint32]*dkg.DkgParticipant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewDkgParticipant(uint32(i), uint32(thresh), Ctx, curve, otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+bls INPUT
+Simulate a DKG using BLS keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/frost_dkg/ed25519/README.md b/test/frost_dkg/ed25519/README.md
new file mode 100755
index 00000000..0675ea8f
--- /dev/null
+++ b/test/frost_dkg/ed25519/README.md
@@ -0,0 +1,30 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# ed25519
+
+```go
+import "github.com/coinbase/kryptology/test/frost_dkg/ed25519"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const Ctx = "string to prevent replay attack"
+```
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/frost_dkg/ed25519/main.go b/test/frost_dkg/ed25519/main.go
new file mode 100644
index 00000000..41fd640d
--- /dev/null
+++ b/test/frost_dkg/ed25519/main.go
@@ -0,0 +1,246 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"crypto/sha512"
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"github.com/coinbase/kryptology/pkg/ted25519/frost"
+
+	"filippo.io/edwards25519"
+	dkg "github.com/coinbase/kryptology/pkg/dkg/frost"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+const Ctx = "string to prevent replay attack"
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing FROST DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	verificationKey, signingShares := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// Signing common setup for all participants
+	msg := []byte("All my bitcoin is stored here")
+	curve := curves.ED25519()
+	scheme, _ := sharing.NewShamir(uint32(threshold), uint32(limit), curve)
+	shares := make([]*sharing.ShamirShare, 0, threshold)
+	cnt := 0
+	for _, share := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		shares = append(shares, share)
+	}
+	sk, err := scheme.Combine(shares...)
+	if err != nil {
+		panic(err)
+	}
+	vk := curve.ScalarBaseMult(sk)
+	if !vk.Equal(verificationKey) {
+		panic("verification keys are not equal")
+	}
+
+	skC := sk.(*curves.ScalarEd25519).GetEdwardsScalar()
+
+	r, s := sign(skC, vk.ToAffineCompressed(), []byte("no nonce"), msg)
+	ok := verify(vk.ToAffineCompressed(), msg, r, s)
+	fmt.Printf("Signature verification - %v\n", ok)
+
+	// Test threshold signing
+	lCoeffs, err := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		signingShares[1].Id: signingShares[1],
+		signingShares[2].Id: signingShares[2],
+	})
+	if err != nil {
+		panic(err)
+	}
+	signers := make(map[uint32]*frost.Signer, 2)
+	signers[1], err = frost.NewSigner(participants[1], 1, uint32(threshold), lCoeffs, []uint32{1, 2}, &frost.Ed25519ChallengeDeriver{})
+	if err != nil {
+		panic(err)
+	}
+	signers[2], err = frost.NewSigner(participants[2], 2, uint32(threshold), lCoeffs, []uint32{1, 2}, &frost.Ed25519ChallengeDeriver{})
+	if err != nil {
+		panic(err)
+	}
+
+	sigRnd1Bcast := make(map[uint32]*frost.Round1Bcast, 2)
+	sigRnd1Bcast[1], err = signers[1].SignRound1()
+	if err != nil {
+		panic(err)
+	}
+	sigRnd1Bcast[2], err = signers[2].SignRound1()
+	if err != nil {
+		panic(err)
+	}
+	sigRng2BCast := make(map[uint32]*frost.Round2Bcast, 2)
+	sigRng2BCast[1], err = signers[1].SignRound2(msg, sigRnd1Bcast)
+	if err != nil {
+		panic(err)
+	}
+	sigRng2BCast[2], err = signers[2].SignRound2(msg, sigRnd1Bcast)
+	if err != nil {
+		panic(err)
+	}
+	sigRng3BCast, err := signers[1].SignRound3(sigRng2BCast)
+	if err != nil {
+		panic(err)
+	}
+
+	sigR := sigRng3BCast.R.(*curves.PointEd25519).GetEdwardsPoint()
+	sigS := sigRng3BCast.Z.(*curves.ScalarEd25519).GetEdwardsScalar()
+
+	ok = verify(vk.ToAffineCompressed(), msg, sigR, sigS)
+	fmt.Printf("Threshold Signature verification - %v\n", ok)
+}
+
+func sign(skC *edwards25519.Scalar, pubKey, nonce, msg []byte) (*edwards25519.Point, *edwards25519.Scalar) {
+	h := sha512.New()
+	_, _ = h.Write(nonce)
+	_, _ = h.Write(msg)
+	digest := h.Sum(nil)
+	digestReduced, err := edwards25519.NewScalar().SetUniformBytes(digest)
+	if err != nil {
+		panic(err)
+	}
+	r := edwards25519.NewGeneratorPoint().ScalarBaseMult(digestReduced)
+
+	encodedR := r.Bytes()
+	h.Reset()
+	_, _ = h.Write(encodedR)
+	_, _ = h.Write(pubKey)
+	_, _ = h.Write(msg)
+
+	k, err := edwards25519.NewScalar().SetUniformBytes(h.Sum(nil))
+	if err != nil {
+		panic(err)
+	}
+	s := edwards25519.NewScalar().MultiplyAdd(k, skC, digestReduced)
+	return r, s
+}
+
+func verify(pk, msg []byte, r *edwards25519.Point, s *edwards25519.Scalar) bool {
+	h := sha512.New()
+	_, _ = h.Write(r.Bytes())
+	_, _ = h.Write(pk)
+	_, _ = h.Write(msg)
+	k, err := edwards25519.NewScalar().SetUniformBytes(h.Sum(nil))
+	if err != nil {
+		panic(err)
+	}
+	minusA, _ := edwards25519.NewIdentityPoint().SetBytes(pk)
+	minusA.Negate(minusA)
+	lhs := edwards25519.NewIdentityPoint().VarTimeDoubleScalarBaseMult(k, minusA, s)
+	return lhs.Equal(r) == 1
+}
+
+func round1(participants map[uint32]*dkg.DkgParticipant) (map[uint32]*dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]*dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.DkgParticipant,
+	rnd1Bcast map[uint32]*dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) (curves.Point, map[uint32]*sharing.ShamirShare) {
+	signingShares := make(map[uint32]*sharing.ShamirShare, len(participants))
+	var verificationKey curves.Point
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+		rnd1P2pForP := make(map[uint32]*sharing.ShamirShare)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		rnd2Out, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		verificationKey = rnd2Out.VerificationKey
+		share := &sharing.ShamirShare{
+			Id:    id,
+			Value: participants[id].SkShare.Bytes(),
+		}
+		signingShares[id] = share
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.DkgParticipant {
+	curve := curves.ED25519()
+	participants := make(map[uint32]*dkg.DkgParticipant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewDkgParticipant(uint32(i), uint32(thresh), Ctx, curve, otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+ed25519 INPUT
+Simulate a DKG using Ed25519 keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/frost_dkg/frost/README.md b/test/frost_dkg/frost/README.md
new file mode 100755
index 00000000..cb2972ab
--- /dev/null
+++ b/test/frost_dkg/frost/README.md
@@ -0,0 +1,30 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# frost
+
+```go
+import "github.com/coinbase/kryptology/test/frost_dkg/frost"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const Ctx = "string to prevent replay attack"
+```
+
+```go
+const LIMIT = 5
+```
+
+```go
+const THRESHOLD = 3
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/frost_dkg/frost/main.go b/test/frost_dkg/frost/main.go
new file mode 100644
index 00000000..a7cb0645
--- /dev/null
+++ b/test/frost_dkg/frost/main.go
@@ -0,0 +1,217 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	dkg "github.com/coinbase/kryptology/pkg/dkg/frost"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"github.com/coinbase/kryptology/pkg/ted25519/frost"
+)
+
+const LIMIT = 5
+const THRESHOLD = 3
+const Ctx = "string to prevent replay attack"
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing FROST DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	fmt.Printf("**FROST DKG Round 1**\n")
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	fmt.Printf("**FROST DKG Round 2**\n")
+	verificationKey, _ := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// Prepare Lagrange coefficients
+	curve := curves.ED25519()
+	scheme, _ := sharing.NewShamir(uint32(threshold), uint32(limit), curve)
+	shares := make([]*sharing.ShamirShare, threshold)
+	for i := 0; i < threshold; i++ {
+		shares[i] = &sharing.ShamirShare{Id: uint32(i + 1), Value: participants[uint32(i+1)].SkShare.Bytes()}
+	}
+
+	lCoeffs, _ := scheme.LagrangeCoeffs(map[uint32]*sharing.ShamirShare{
+		shares[0].Id: shares[0],
+		shares[1].Id: shares[1],
+		shares[2].Id: shares[2],
+	})
+
+	// Using signer starting from 1 as cosigners
+	var err error
+	signerIds := make([]uint32, threshold)
+	for i := 0; i < threshold; i++ {
+		signerIds[i] = uint32(i + 1)
+	}
+	signers := make(map[uint32]*frost.Signer, threshold)
+	for i := 1; i <= threshold; i++ {
+		signers[uint32(i)], err = frost.NewSigner(participants[uint32(i)], uint32(i), uint32(threshold), lCoeffs, signerIds, &frost.Ed25519ChallengeDeriver{})
+		if err != nil {
+			panic(err)
+		}
+	}
+
+	// Running sign round 1
+	fmt.Printf("**FROST Sign Round 1**\n")
+	round2Input := make(map[uint32]*frost.Round1Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		fmt.Printf("Computing Sign Round 1 for cosigner %d\n", i)
+		round1Out, err := signers[uint32(i)].SignRound1()
+		if err != nil {
+			panic(err)
+		}
+		round2Input[uint32(i)] = round1Out
+	}
+
+	// Running sign round 2
+	fmt.Printf("**FROST Sign Round 2**\n")
+	msg := []byte("message")
+	round3Input := make(map[uint32]*frost.Round2Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		fmt.Printf("Computing Sign Round 2 for cosigner %d\n", i)
+		round2Out, err := signers[uint32(i)].SignRound2(msg, round2Input)
+		if err != nil {
+			panic(err)
+		}
+		round3Input[uint32(i)] = round2Out
+	}
+
+	// Running sign round 3
+	fmt.Printf("**FROST Sign Round 3**\n")
+	result := make(map[uint32]*frost.Round3Bcast, threshold)
+	for i := 1; i <= threshold; i++ {
+		fmt.Printf("Computing Sign Round 3 for cosigner %d\n", i)
+		round3Out, err := signers[uint32(i)].SignRound3(round3Input)
+		if err != nil {
+			panic(err)
+		}
+		result[uint32(i)] = round3Out
+	}
+
+	// Verify everybody's signature is valid
+	deriver := &frost.Ed25519ChallengeDeriver{}
+	for i := 1; i <= threshold; i++ {
+		Z := result[uint32(i)].Z
+		C := result[uint32(i)].C
+		// Compute R' = z*G + (-c)*vk
+		zG := curve.ScalarBaseMult(Z)
+		cvk := verificationKey.Mul(C.Neg())
+		tempR := zG.Add(cvk)
+		// Step 6 - c' = H(m, R')
+		tempC, err := deriver.DeriveChallenge(msg, verificationKey, tempR)
+		if err != nil {
+			panic(err)
+		}
+
+		// Step 7 - Check c = c'
+		if tempC.Cmp(C) != 0 {
+			fmt.Printf("invalid signature: c != c' for signer %d\n", i)
+		}
+	}
+	fmt.Printf("Signature is computed successfully!\n")
+}
+
+func round1(participants map[uint32]*dkg.DkgParticipant) (map[uint32]*dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]*dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.DkgParticipant,
+	rnd1Bcast map[uint32]*dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) (curves.Point, map[uint32]*sharing.ShamirShare) {
+	signingShares := make(map[uint32]*sharing.ShamirShare, len(participants))
+	var verificationKey curves.Point
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+		rnd1P2pForP := make(map[uint32]*sharing.ShamirShare)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		rnd2Out, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		verificationKey = rnd2Out.VerificationKey
+		share := &sharing.ShamirShare{
+			Id:    id,
+			Value: participants[id].SkShare.Bytes(),
+		}
+		signingShares[id] = share
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.DkgParticipant {
+	curve := curves.ED25519()
+	participants := make(map[uint32]*dkg.DkgParticipant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewDkgParticipant(uint32(i), uint32(thresh), Ctx, curve, otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+bls INPUT
+Simulate a DKG using K256 keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/frost_dkg/k256/README.md b/test/frost_dkg/k256/README.md
new file mode 100755
index 00000000..d0d0e0a0
--- /dev/null
+++ b/test/frost_dkg/k256/README.md
@@ -0,0 +1,30 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# k256
+
+```go
+import "github.com/coinbase/kryptology/test/frost_dkg/k256"
+```
+
+## Index
+
+- [Constants](<#constants>)
+
+
+## Constants
+
+```go
+const Ctx = "string to prevent replay attack"
+```
+
+```go
+const LIMIT = 4
+```
+
+```go
+const THRESHOLD = 2
+```
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/frost_dkg/k256/main.go b/test/frost_dkg/k256/main.go
new file mode 100644
index 00000000..e630eca3
--- /dev/null
+++ b/test/frost_dkg/k256/main.go
@@ -0,0 +1,168 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"crypto/ecdsa"
+	crand "crypto/rand"
+	"crypto/sha512"
+	"flag"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing"
+	"math/big"
+
+	dkg "github.com/coinbase/kryptology/pkg/dkg/frost"
+	"github.com/btcsuite/btcd/btcec"
+)
+
+const LIMIT = 4
+const THRESHOLD = 2
+const Ctx = "string to prevent replay attack"
+
+func main() {
+	var threshold int
+	var limit int
+	var help bool
+	flag.IntVar(&threshold, "t", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&threshold, "threshold", THRESHOLD, "the minimum number of participants to sign")
+	flag.IntVar(&limit, "n", LIMIT, "the total number of participants")
+	flag.IntVar(&limit, "limit", LIMIT, "the total number of participants")
+	flag.BoolVar(&help, "h", false, "Print this menu")
+	flag.BoolVar(&help, "help", false, "Print this menu")
+	flag.Parse()
+
+	if help {
+		printHelp()
+		return
+	}
+
+	fmt.Printf("Threshold is %d\n", threshold)
+	fmt.Printf("Total participants is %d\n", limit)
+
+	// DEMO doing FROST DKG and that signers can compute a signature
+	participants := createDkgParticipants(threshold, limit)
+
+	// DKG Round 1
+	rnd1Bcast, rnd1P2p := round1(participants)
+
+	// DKG Round 2
+	verificationKey, signingShares := round2(participants, rnd1Bcast, rnd1P2p)
+
+	// Signing common setup for all participants
+	curve := curves.K256()
+	msg := []byte("All my bitcoin is stored here")
+	scheme, _ := sharing.NewShamir(uint32(threshold), uint32(limit), curve)
+	shares := make([]*sharing.ShamirShare, 0, threshold)
+	cnt := 0
+	for _, share := range signingShares {
+		if cnt == threshold {
+			break
+		}
+		cnt++
+		shares = append(shares, share)
+	}
+	sk, err := scheme.Combine(shares...)
+	if err != nil {
+		panic(err)
+	}
+
+	pk := curve.ScalarBaseMult(sk)
+	if !pk.Equal(verificationKey) {
+		panic("verification keys are not equal")
+	}
+
+	privKey, pubKey := btcec.PrivKeyFromBytes(btcec.S256(), sk.Bytes())
+	hBytes := sha512.Sum384(msg)
+	hMsg := new(big.Int).SetBytes(hBytes[:])
+	hMsg.Mod(hMsg, btcec.S256().N)
+
+	r, s, err := ecdsa.Sign(crand.Reader, privKey.ToECDSA(), hMsg.Bytes())
+	if err != nil {
+		panic(err)
+	}
+	ok := ecdsa.Verify(pubKey.ToECDSA(), hMsg.Bytes(), r, s)
+	fmt.Printf("Signature verification - %v\n", ok)
+}
+
+func round1(participants map[uint32]*dkg.DkgParticipant) (map[uint32]*dkg.Round1Bcast, map[uint32]dkg.Round1P2PSend) {
+	// DKG Round 1
+	rnd1Bcast := make(map[uint32]*dkg.Round1Bcast, len(participants))
+	rnd1P2p := make(map[uint32]dkg.Round1P2PSend, len(participants))
+	for id, p := range participants {
+		fmt.Printf("Computing DKG Round 1 for participant %d\n", id)
+		bcast, p2psend, err := p.Round1(nil)
+		if err != nil {
+			panic(err)
+		}
+		rnd1Bcast[id] = bcast
+		rnd1P2p[id] = p2psend
+	}
+	return rnd1Bcast, rnd1P2p
+}
+
+func round2(participants map[uint32]*dkg.DkgParticipant,
+	rnd1Bcast map[uint32]*dkg.Round1Bcast,
+	rnd1P2p map[uint32]dkg.Round1P2PSend,
+) (curves.Point, map[uint32]*sharing.ShamirShare) {
+	signingShares := make(map[uint32]*sharing.ShamirShare, len(participants))
+	var verificationKey curves.Point
+	for id := range rnd1Bcast {
+		fmt.Printf("Computing DKG Round 2 for participant %d\n", id)
+		rnd1P2pForP := make(map[uint32]*sharing.ShamirShare)
+		for jid := range rnd1P2p {
+			if jid == id {
+				continue
+			}
+			rnd1P2pForP[jid] = rnd1P2p[jid][id]
+		}
+		rnd2Out, err := participants[id].Round2(rnd1Bcast, rnd1P2pForP)
+		if err != nil {
+			panic(err)
+		}
+		verificationKey = rnd2Out.VerificationKey
+		share := &sharing.ShamirShare{
+			Id:    id,
+			Value: participants[id].SkShare.Bytes(),
+		}
+		signingShares[id] = share
+	}
+	return verificationKey, signingShares
+}
+
+func createDkgParticipants(thresh, limit int) map[uint32]*dkg.DkgParticipant {
+	curve := curves.K256()
+	participants := make(map[uint32]*dkg.DkgParticipant, limit)
+	for i := 1; i <= limit; i++ {
+		otherIds := make([]uint32, limit-1)
+		idx := 0
+		for j := 1; j <= limit; j++ {
+			if i == j {
+				continue
+			}
+			otherIds[idx] = uint32(j)
+			idx++
+		}
+		p, err := dkg.NewDkgParticipant(uint32(i), uint32(thresh), Ctx, curve, otherIds...)
+		if err != nil {
+			panic(err)
+		}
+		participants[uint32(i)] = p
+	}
+	return participants
+}
+
+func printHelp() {
+	fmt.Printf(`
+bls INPUT
+Simulate a DKG using K256 keys
+FLAGS:
+  -h, --help						Show this help message and exit
+  -n, --limit						The total number of participants
+  -t, --treshold					The minimum number of participants needed to sign
+`)
+}
diff --git a/test/verenc/elgamal/README.md b/test/verenc/elgamal/README.md
new file mode 100755
index 00000000..0691f7fa
--- /dev/null
+++ b/test/verenc/elgamal/README.md
@@ -0,0 +1,15 @@
+<!-- Code generated by gomarkdoc. DO NOT EDIT -->
+
+# elgamal
+
+```go
+import "github.com/coinbase/kryptology/test/verenc/elgamal"
+```
+
+## Index
+
+
+
+
+
+Generated by [gomarkdoc](<https://github.com/princjef/gomarkdoc>)
diff --git a/test/verenc/elgamal/main.go b/test/verenc/elgamal/main.go
new file mode 100644
index 00000000..d69051ff
--- /dev/null
+++ b/test/verenc/elgamal/main.go
@@ -0,0 +1,106 @@
+//
+// Copyright Coinbase, Inc. All Rights Reserved.
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+
+package main
+
+import (
+	"crypto/elliptic"
+	crand "crypto/rand"
+	"encoding/hex"
+	"fmt"
+	"github.com/coinbase/kryptology/pkg/core/curves"
+	"github.com/coinbase/kryptology/pkg/sharing/v1"
+	"github.com/coinbase/kryptology/pkg/verenc/elgamal"
+)
+
+func main() {
+	curve := curves.P256()
+	fmt.Printf("Coinbase generates verifiable encryption keys\n")
+	ek, dk, _ := elgamal.NewKeys(curve)
+	ekBytes, _ := ek.MarshalBinary()
+	dkBytes, _ := dk.MarshalBinary()
+	fmt.Printf("Coinbase publishes encryption key %v\n", hex.EncodeToString(ekBytes))
+	fmt.Printf("Coinbase retains decryption key %v\n", hex.EncodeToString(dkBytes))
+	fmt.Printf("Coinbase stores encrypted key shares on behalf\n")
+	fmt.Printf("of users. Users refresh their keys after signing.\n")
+	fmt.Printf("Coinbase wants to ensure the refreshed shares are correct\n")
+	fmt.Printf("so users submit verifiable encryptions which prove\n")
+	fmt.Printf("the sum of the encrypted shares is equal to the expected public key.\n")
+
+	// Normally users use DKG, but for demo simplicity we skip that
+	shamir, _ := v1.NewShamir(2, 2, curves.NewField(elliptic.P256().Params().N))
+	// signing key
+	sk := curve.Scalar.Random(crand.Reader)
+	// public verification key
+	vk := curve.Point.Generator().Mul(sk)
+	// user's shares
+	shares, _ := shamir.Split(sk.Bytes())
+
+	user1Pk, user1Sk, _ := elgamal.NewKeys(curve)
+	s1, _ := curve.Scalar.SetBytes(shares[0].Value.Bytes())
+	ctxt1, proof1, _ := ek.VerifiableEncrypt(shares[0].Value.Bytes(), &elgamal.EncryptParams{
+		Domain:          []byte("initial upload user 1"),
+		MessageIsHashed: true,
+		GenProof:        true,
+		ProofNonce:      []byte("initial upload user 1"),
+	})
+	user1Ctxt, _, _ := user1Pk.VerifiableEncrypt(shares[0].Value.Bytes(), &elgamal.EncryptParams{
+		MessageIsHashed: true,
+	})
+	ctxt1Bytes, _ := ctxt1.MarshalBinary()
+	fmt.Printf("User 1 submits ciphertext %v\n", hex.EncodeToString(ctxt1Bytes))
+
+	ctxt2, proof2, _ := ek.VerifiableEncrypt(shares[1].Value.Bytes(), &elgamal.EncryptParams{
+		Domain:          []byte("initial upload user 2"),
+		MessageIsHashed: true,
+		GenProof:        true,
+		ProofNonce:      []byte("initial upload user 2"),
+	})
+	ctxt2Bytes, _ := ctxt2.MarshalBinary()
+	fmt.Printf("User 2 submits ciphertext %v\n", hex.EncodeToString(ctxt2Bytes))
+
+	fmt.Printf("Coinbase verifies each user's ciphertext\n")
+	fmt.Printf("User 1 ciphertext is valid = %v\n", ek.VerifyEncryptProof([]byte("initial upload user 1"), ctxt1, proof1) == nil)
+	fmt.Printf("User 2 ciphertext is valid = %v\n", ek.VerifyEncryptProof([]byte("initial upload user 2"), ctxt2, proof2) == nil)
+
+	m1 := dk.Decrypt(ctxt1.ToHomomorphicCipherText())
+	m2 := dk.Decrypt(ctxt2.ToHomomorphicCipherText())
+	avk := shamirCombinePoint(curve, []curves.Point{m1, m2})
+	fmt.Printf("users ciphertexts should sum to vk %v\n", hex.EncodeToString(vk.ToAffineCompressed()))
+	fmt.Printf("sum of ciphertexts is %v\n", hex.EncodeToString(avk.ToAffineCompressed()))
+	fmt.Printf("Values are equal, allowing shares to be uploaded.\n")
+
+	fmt.Printf("User 1 wants check that Coinbase has the correct ciphertext\n")
+	fmt.Printf("and wants to decrypt it to see if its what she expects.\n")
+	fmt.Printf("User 1 verifiably decrypts share from sent from Coinbase\n")
+	_, share, err := user1Sk.VerifiableDecrypt(user1Ctxt)
+	fmt.Printf("User 1 share decrypts properly = %v\n", err == nil && share.Cmp(s1) == 0)
+}
+
+func shamirCombinePoint(curve *curves.Curve, points []curves.Point) curves.Point {
+	result := curve.Point.Identity()
+
+	for i, p := range points {
+		basis := curve.Scalar.One()
+		for j := range points {
+			if i == j {
+				continue
+			}
+
+			// x_m - x_j
+			denom := curve.Scalar.New(j + 1).Sub(curve.Scalar.New(i + 1))
+			if denom.IsZero() {
+				return nil
+			}
+			// x_m / x_m - x_j
+			basis = basis.Mul(curve.Scalar.New(j + 1).Div(denom))
+		}
+
+		result = result.Add(p.Mul(basis))
+	}
+
+	return result
+}