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w1zeman1p's solution

to Affine Cipher in the Ruby Track

Published at Mar 08 2019 · 0 comments
Instructions
Test suite
Solution

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 cypher is much stronger than the atbash cipher, because it has many more keys.

the encryption function is:

E(x) = (ax + b) mod m

  • where x is the letter's index from 0 - length of alphabet - 1
  • m is the length of the alphabet. For the roman alphabet m == 26.
  • and a and b make the key

the decryption function is:

D(y) = a^-1(y - b) mod m

  • where y is the numeric value of an encrypted letter, ie. y = E(x)
  • it is important to note that a^-1 is the modular multiplicative inverse of a mod m
  • the modular multiplicative inverse of a only exists if a and m are coprime.

To find the MMI of a:

an mod m = 1

  • where n is the modular multiplicative inverse of a mod m

More information regarding how to find a Modular Multiplicative Inverse and what it means can be found here.

Because automatic decryption fails if a is not coprime to m your program should return status 1 and "Error: a and m must be coprime." if they are not. Otherwise it should encode or decode with the provided key.

The Caesar (shift) cipher is a simple affine cipher where a is 1 and b as the magnitude results in a static displacement of the letters. This is much less secure than a full implementation of the affine cipher.

Ciphertext is written out in groups of fixed length, the traditional group size being 5 letters, and punctuation is excluded. This is to make it harder to guess things based on word boundaries.

Examples

  • Encoding test gives ybty with the key a=5 b=7
  • Decoding ybty gives test with the key a=5 b=7
  • Decoding ybty gives lqul with the wrong key a=11 b=7
  • Decoding kqlfd jzvgy tpaet icdhm rtwly kqlon ubstx
    • gives thequickbrownfoxjumpsoverthelazydog with the key a=19 b=13
  • Encoding test with the key a=18 b=13
    • gives Error: a and m must be coprime.
    • because a and m are not relatively prime

Examples of finding a Modular Multiplicative Inverse (MMI)

  • simple example:
    • 9 mod 26 = 9
    • 9 * 3 mod 26 = 27 mod 26 = 1
    • 3 is the MMI of 9 mod 26
  • a more complicated example:
    • 15 mod 26 = 15
    • 15 * 7 mod 26 = 105 mod 26 = 1
    • 7 is the MMI of 15 mod 26

For installation and learning resources, refer to the Ruby resources page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby affine_cipher_test.rb

To include color from the command line:

ruby -r minitest/pride affine_cipher_test.rb

Source

Wikipedia http://en.wikipedia.org/wiki/Affine_cipher

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

affine_cipher_test.rb

require 'minitest/autorun'
require_relative 'affine_cipher'

# Common test data version: 2.0.0 8026923
class AffineCipherTest < Minitest::Test
  def test_encode_yes
    # skip
    cipher = Affine.new(5, 7)
    plaintext = 'yes'
    ciphertext = 'xbt'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_no
    skip
    cipher = Affine.new(15, 18)
    plaintext = 'no'
    ciphertext = 'fu'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_omg
    skip
    cipher = Affine.new(21, 3)
    plaintext = 'OMG'
    ciphertext = 'lvz'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_o_m_g
    skip
    cipher = Affine.new(25, 47)
    plaintext = 'O M G'
    ciphertext = 'hjp'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_mindblowingly
    skip
    cipher = Affine.new(11, 15)
    plaintext = 'mindblowingly'
    ciphertext = 'rzcwa gnxzc dgt'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_numbers
    skip
    cipher = Affine.new(3, 4)
    plaintext = 'Testing,1 2 3, testing.'
    ciphertext = 'jqgjc rw123 jqgjc rw'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_deep_thought
    skip
    cipher = Affine.new(5, 17)
    plaintext = 'Truth is fiction.'
    ciphertext = 'iynia fdqfb ifje'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_all_the_letters
    skip
    cipher = Affine.new(17, 33)
    plaintext = 'The quick brown fox jumps over the lazy dog.'
    ciphertext = 'swxtj npvyk lruol iejdc blaxk swxmh qzglf'
    assert_equal ciphertext, cipher.encode(plaintext)
  end

  def test_encode_with_a_not_coprime_to_m
    skip
    assert_raises(ArgumentError) { Affine.new(6, 17) }
  end

  def test_decode_exercism
    skip
    cipher = Affine.new(3, 7)
    ciphertext = 'tytgn fjr'
    plaintext = 'exercism'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_a_sentence
    skip
    cipher = Affine.new(19, 16)
    ciphertext = 'qdwju nqcro muwhn odqun oppmd aunwd o'
    plaintext = 'anobstacleisoftenasteppingstone'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_numbers
    skip
    cipher = Affine.new(25, 7)
    ciphertext = 'odpoz ub123 odpoz ub'
    plaintext = 'testing123testing'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_all_the_letters
    skip
    cipher = Affine.new(17, 33)
    ciphertext = 'swxtj npvyk lruol iejdc blaxk swxmh qzglf'
    plaintext = 'thequickbrownfoxjumpsoverthelazydog'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_with_no_spaces_in_input
    skip
    cipher = Affine.new(17, 33)
    ciphertext = 'swxtjnpvyklruoliejdcblaxkswxmhqzglf'
    plaintext = 'thequickbrownfoxjumpsoverthelazydog'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_with_too_many_spaces
    skip
    cipher = Affine.new(15, 16)
    ciphertext = 'vszzm    cly   yd cg    qdp'
    plaintext = 'jollygreengiant'
    assert_equal plaintext, cipher.decode(ciphertext)
  end

  def test_decode_with_a_not_coprime_to_m
    skip
    assert_raises(ArgumentError) { Affine.new(13, 5) }
  end
end
require 'byebug'

class Affine
  ALPHA = ('a'..'z').to_a.freeze

  def initialize(a, b)
    raise ArgumentError.new if a.gcd(ALPHA.length) != 1

    @a, @b = a, b
  end

  def encode(pt)
    clean(pt)
      .chars
      .map {|c| encode_char(c)}
      .each_slice(5)
      .map(&:join)
      .join(" ")
  end

  def decode(ct)
    clean(ct).chars.map {|c| decode_char(c)}.join
  end

  private

  def clean(input)
    input.downcase.delete(" ,.")
  end

  def encode_char(c)
    return c if c =~ /[^a-z]/
    ALPHA[e_x(c)]
  end

  def e_x(c)
    x = ALPHA.index(c)
    ((@a * x) + @b) % ALPHA.length
  end

  def decode_char(c)
    return c if c =~ /[^a-z]/
    ALPHA[d_y(c)]
  end

  def d_y(c)
    y = ALPHA.index(c)
    (mmi(@a) * (y - @b)) % ALPHA.length
  end

  def mmi(a)
    (1..ALPHA.length).find {|x| (a * x) % ALPHA.length == 1}
  end
end

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w1zeman1p's Reflection

I had a tough time with all the math in this one :)