diff --git a/config.json b/config.json index fb44e2f..747f661 100644 --- a/config.json +++ b/config.json @@ -1367,6 +1367,14 @@ "practices": [], "prerequisites": [], "difficulty": 3 + }, + { + "slug": "affine-cipher", + "name": "Affine Cipher", + "uuid": "e3a84895-fb1b-4d03-b56a-84cb00b3cf93", + "practices": [], + "prerequisites": [], + "difficulty": 5 } ] }, diff --git a/exercises/practice/affine-cipher/.busted b/exercises/practice/affine-cipher/.busted new file mode 100644 index 0000000..86b84e7 --- /dev/null +++ b/exercises/practice/affine-cipher/.busted @@ -0,0 +1,5 @@ +return { + default = { + ROOT = { '.' } + } +} diff --git a/exercises/practice/affine-cipher/.docs/instructions.md b/exercises/practice/affine-cipher/.docs/instructions.md new file mode 100644 index 0000000..4eff918 --- /dev/null +++ b/exercises/practice/affine-cipher/.docs/instructions.md @@ -0,0 +1,74 @@ +# Instructions + +Create an implementation of the affine cipher, an ancient encryption system created in the Middle East. + +The affine cipher is a type of monoalphabetic substitution cipher. +Each character is mapped to its numeric equivalent, encrypted with a mathematical function and then converted to the letter relating to its new numeric value. +Although all monoalphabetic ciphers are weak, the affine cipher is much stronger than the atbash cipher, because it has many more keys. + +[//]: # " monoalphabetic as spelled by Merriam-Webster, compare to polyalphabetic " + +## Encryption + +The encryption function is: + +```text +E(x) = (ai + b) mod m +``` + +Where: + +- `i` is the letter's index from `0` to the length of the alphabet - 1. +- `m` is the length of the alphabet. + For the Roman alphabet `m` is `26`. +- `a` and `b` are integers which make up the encryption key. + +Values `a` and `m` must be _coprime_ (or, _relatively prime_) for automatic decryption to succeed, i.e., they have number `1` as their only common factor (more information can be found in the [Wikipedia article about coprime integers][coprime-integers]). +In case `a` is not coprime to `m`, your program should indicate that this is an error. +Otherwise it should encrypt or decrypt with the provided key. + +For the purpose of this exercise, digits are valid input but they are not encrypted. +Spaces and punctuation characters are excluded. +Ciphertext is written out in groups of fixed length separated by space, the traditional group size being `5` letters. +This is to make it harder to guess encrypted text based on word boundaries. + +## Decryption + +The decryption function is: + +```text +D(y) = (a^-1)(y - b) mod m +``` + +Where: + +- `y` is the numeric value of an encrypted letter, i.e., `y = E(x)` +- it is important to note that `a^-1` is the modular multiplicative inverse (MMI) of `a mod m` +- the modular multiplicative inverse only exists if `a` and `m` are coprime. + +The MMI of `a` is `x` such that the remainder after dividing `ax` by `m` is `1`: + +```text +ax mod m = 1 +``` + +More information regarding how to find a Modular Multiplicative Inverse and what it means can be found in the [related Wikipedia article][mmi]. + +## General Examples + +- Encrypting `"test"` gives `"ybty"` with the key `a = 5`, `b = 7` +- Decrypting `"ybty"` gives `"test"` with the key `a = 5`, `b = 7` +- Decrypting `"ybty"` gives `"lqul"` with the wrong key `a = 11`, `b = 7` +- Decrypting `"kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx"` gives `"thequickbrownfoxjumpsoverthelazydog"` with the key `a = 19`, `b = 13` +- Encrypting `"test"` with the key `a = 18`, `b = 13` is an error because `18` and `26` are not coprime + +## Example of finding a Modular Multiplicative Inverse (MMI) + +Finding MMI for `a = 15`: + +- `(15 * x) mod 26 = 1` +- `(15 * 7) mod 26 = 1`, ie. `105 mod 26 = 1` +- `7` is the MMI of `15 mod 26` + +[mmi]: https://en.wikipedia.org/wiki/Modular_multiplicative_inverse +[coprime-integers]: https://en.wikipedia.org/wiki/Coprime_integers diff --git a/exercises/practice/affine-cipher/.meta/config.json b/exercises/practice/affine-cipher/.meta/config.json new file mode 100644 index 0000000..5c9b540 --- /dev/null +++ b/exercises/practice/affine-cipher/.meta/config.json @@ -0,0 +1,19 @@ +{ + "authors": [ + "ryanplusplus" + ], + "files": { + "solution": [ + "affine-cipher.lua" + ], + "test": [ + "affine-cipher_spec.lua" + ], + "example": [ + ".meta/example.lua" + ] + }, + "blurb": "Create an implementation of the Affine cipher, an ancient encryption algorithm from the Middle East.", + "source": "Wikipedia", + "source_url": "https://en.wikipedia.org/wiki/Affine_cipher" +} diff --git a/exercises/practice/affine-cipher/.meta/example.lua b/exercises/practice/affine-cipher/.meta/example.lua new file mode 100644 index 0000000..fbcbb98 --- /dev/null +++ b/exercises/practice/affine-cipher/.meta/example.lua @@ -0,0 +1,48 @@ +local M = 26 + +local function coprime(x, y) + while y ~= 0 do + x, y = y, x % y + end + return x == 1 +end + +local function partition(s) + return s:gsub('.....', '%0 '):gsub(' $', '') +end + +local function mmi(x, mod) + local mmi = 1 + while (x * mmi) % mod ~= 1 do + mmi = mmi + 1 + end + return mmi +end + +local function encode_char(char, key) + local x = char:byte() - ('a'):byte() + return string.char((key.a * x + key.b) % M + ('a'):byte()) +end + +local function decode_char(char, key) + local x = char:byte() - ('a'):byte() + return string.char((mmi(key.a, M) * (x - key.b)) % M + ('a'):byte()) +end + +local function encode(phrase, key) + assert(coprime(key.a, M), 'a and m must be coprime.') + + return partition(phrase:gsub('%W', ''):gsub('%a', function(char) + return encode_char(char:lower(), key) + end)) +end + +local function decode(phrase, key) + assert(coprime(key.a, M), 'a and m must be coprime.') + + return phrase:gsub('%s', ''):gsub('%a', function(char) + return decode_char(char:lower(), key) + end) +end + +return { encode = encode, decode = decode } diff --git a/exercises/practice/affine-cipher/.meta/spec_generator.lua b/exercises/practice/affine-cipher/.meta/spec_generator.lua new file mode 100644 index 0000000..2825e80 --- /dev/null +++ b/exercises/practice/affine-cipher/.meta/spec_generator.lua @@ -0,0 +1,20 @@ +return { + module_name = 'affine_cipher', + + generate_test = function(case) + if type(case.expected) == 'string' then + local template = [[ + local phrase = '%s' + local expected = '%s' + assert.are.same(expected, affine_cipher.%s(phrase, { a = %d, b = %d }))]] + return template:format(case.input.phrase, case.expected, case.property, case.input.key.a, case.input.key.b) + else + local template = [[ + local phrase = '%s' + assert.has.error(function() + affine_cipher.%s(phrase, { a = %d, b = %d }) + end, '%s')]] + return template:format(case.input.phrase, case.property, case.input.key.a, case.input.key.b, case.expected.error) + end + end +} diff --git a/exercises/practice/affine-cipher/.meta/tests.toml b/exercises/practice/affine-cipher/.meta/tests.toml new file mode 100644 index 0000000..07cce7c --- /dev/null +++ b/exercises/practice/affine-cipher/.meta/tests.toml @@ -0,0 +1,58 @@ +# This is an auto-generated file. +# +# Regenerating this file via `configlet sync` will: +# - Recreate every `description` key/value pair +# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications +# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion) +# - Preserve any other key/value pair +# +# As user-added comments (using the # character) will be removed when this file +# is regenerated, comments can be added via a `comment` key. + +[2ee1d9af-1c43-416c-b41b-cefd7d4d2b2a] +description = "encode -> encode yes" + +[785bade9-e98b-4d4f-a5b0-087ba3d7de4b] +description = "encode -> encode no" + +[2854851c-48fb-40d8-9bf6-8f192ed25054] +description = "encode -> encode OMG" + +[bc0c1244-b544-49dd-9777-13a770be1bad] +description = "encode -> encode O M G" + +[381a1a20-b74a-46ce-9277-3778625c9e27] +description = "encode -> encode mindblowingly" + +[6686f4e2-753b-47d4-9715-876fdc59029d] +description = "encode -> encode numbers" + +[ae23d5bd-30a8-44b6-afbe-23c8c0c7faa3] +description = "encode -> encode deep thought" + +[c93a8a4d-426c-42ef-9610-76ded6f7ef57] +description = "encode -> encode all the letters" + +[0673638a-4375-40bd-871c-fb6a2c28effb] +description = "encode -> encode with a not coprime to m" + +[3f0ac7e2-ec0e-4a79-949e-95e414953438] +description = "decode -> decode exercism" + +[241ee64d-5a47-4092-a5d7-7939d259e077] +description = "decode -> decode a sentence" + +[33fb16a1-765a-496f-907f-12e644837f5e] +description = "decode -> decode numbers" + +[20bc9dce-c5ec-4db6-a3f1-845c776bcbf7] +description = "decode -> decode all the letters" + +[623e78c0-922d-49c5-8702-227a3e8eaf81] +description = "decode -> decode with no spaces in input" + +[58fd5c2a-1fd9-4563-a80a-71cff200f26f] +description = "decode -> decode with too many spaces" + +[b004626f-c186-4af9-a3f4-58f74cdb86d5] +description = "decode -> decode with a not coprime to m" diff --git a/exercises/practice/affine-cipher/affine-cipher.lua b/exercises/practice/affine-cipher/affine-cipher.lua new file mode 100644 index 0000000..1ba99bb --- /dev/null +++ b/exercises/practice/affine-cipher/affine-cipher.lua @@ -0,0 +1,9 @@ +local function encode(phrase, key) + +end + +local function decode(phrase, key) + +end + +return { encode = encode, decode = decode } diff --git a/exercises/practice/affine-cipher/affine-cipher_spec.lua b/exercises/practice/affine-cipher/affine-cipher_spec.lua new file mode 100644 index 0000000..b46dbf6 --- /dev/null +++ b/exercises/practice/affine-cipher/affine-cipher_spec.lua @@ -0,0 +1,105 @@ +local affine_cipher = require('affine-cipher') + +describe('affine-cipher', function() + describe('encode', function() + it('encode yes', function() + local phrase = 'yes' + local expected = 'xbt' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 5, b = 7 })) + end) + + it('encode no', function() + local phrase = 'no' + local expected = 'fu' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 15, b = 18 })) + end) + + it('encode omg', function() + local phrase = 'OMG' + local expected = 'lvz' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 21, b = 3 })) + end) + + it('encode o m g', function() + local phrase = 'O M G' + local expected = 'hjp' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 25, b = 47 })) + end) + + it('encode mindblowingly', function() + local phrase = 'mindblowingly' + local expected = 'rzcwa gnxzc dgt' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 11, b = 15 })) + end) + + it('encode numbers', function() + local phrase = 'Testing,1 2 3, testing.' + local expected = 'jqgjc rw123 jqgjc rw' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 3, b = 4 })) + end) + + it('encode deep thought', function() + local phrase = 'Truth is fiction.' + local expected = 'iynia fdqfb ifje' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 5, b = 17 })) + end) + + it('encode all the letters', function() + local phrase = 'The quick brown fox jumps over the lazy dog.' + local expected = 'swxtj npvyk lruol iejdc blaxk swxmh qzglf' + assert.are.same(expected, affine_cipher.encode(phrase, { a = 17, b = 33 })) + end) + + it('encode with a not coprime to m', function() + local phrase = 'This is a test.' + assert.has.error(function() + affine_cipher.encode(phrase, { a = 6, b = 17 }) + end, 'a and m must be coprime.') + end) + end) + + describe('decode', function() + it('decode exercism', function() + local phrase = 'tytgn fjr' + local expected = 'exercism' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 3, b = 7 })) + end) + + it('decode a sentence', function() + local phrase = 'qdwju nqcro muwhn odqun oppmd aunwd o' + local expected = 'anobstacleisoftenasteppingstone' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 19, b = 16 })) + end) + + it('decode numbers', function() + local phrase = 'odpoz ub123 odpoz ub' + local expected = 'testing123testing' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 25, b = 7 })) + end) + + it('decode all the letters', function() + local phrase = 'swxtj npvyk lruol iejdc blaxk swxmh qzglf' + local expected = 'thequickbrownfoxjumpsoverthelazydog' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 17, b = 33 })) + end) + + it('decode with no spaces in input', function() + local phrase = 'swxtjnpvyklruoliejdcblaxkswxmhqzglf' + local expected = 'thequickbrownfoxjumpsoverthelazydog' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 17, b = 33 })) + end) + + it('decode with too many spaces', function() + local phrase = 'vszzm cly yd cg qdp' + local expected = 'jollygreengiant' + assert.are.same(expected, affine_cipher.decode(phrase, { a = 15, b = 16 })) + end) + + it('decode with a not coprime to m', function() + local phrase = 'Test' + assert.has.error(function() + affine_cipher.decode(phrase, { a = 13, b = 5 }) + end, 'a and m must be coprime.') + end) + end) +end)