Affine Cipher in Haskell

The affine cipher is a substitution cipher, similar to the Caesar cipher. Each letter is encrypted with the function (a * x + b) mod 26, where b is the magnitude of the shift.

Variables

Private key pair: (a,b)
Numeric value of the plaintext char: x
Numeric value of the encrypted char: y
Alphabet size / modulo: m

Input constraints

• a < b
• a must be co-prime to m
• a and b must be within [0 ... (m-1)]

Number ranges

• a: [1,3,5,7,9,11,15,17,19,21,23,25] = 12 elements
• b: [0 - 25] = 26 elements
• possible key value pairs using the latin lowercase alphabet: 12 * 26 - 1 = 311

Encrypt

• ((a * x) + b) mod m
• decode a b "text"

Decrypt

• ((a^-1) * (y - b)) mod m
• encode a b "text"

How to crack

This code uses quadgram statistics to crack an encrypted text.

1. First a reference text is used to determine the quadgram distribution in english text.
2. Then the ciphertext is deciphered with all possible key combinations => 311 possible combinations
3. The likelihood of each deciphered quadgram is looked up in the reference text.
4. To determine the fitness of a deciphered text, all log likelihoods are sumed up.
5. The higher the fitness number the more likely the particular keys are correct. Therefore both texts have a similar distribution of characters.

Usage

• generate blind text with BLINDTEXTGENERATOR
• crack "text_to_crack" "blind_text"