hill_cipher.md

Hill Cipher

The Hill cipher was invented by Lester S. Hill.

Hill cipher is a polygraphic substitution cipher based on linear algebra. Each letter is represented by a number modulo 26. Often the simple scheme A = 0, B = 1, …, Z = 25 is used, but this is not an essential feature of the cipher. To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.

Example

Suppose we take an example as: Plain Text (PT):ACT key:GYBNQKURP

Steps

Encryption

1. We have to write key as an n × n matrix as

   [6 24   1]
   [13 16 10]
   [20 17 15]

2. Same way convert PT into a vector as

    [0]
    [2]
    [19]

3. Now, we need to encipher the vector by just multiplying these two matrices

    [6 24   1]      [0]         [67]        [15]
    [13 16 10]  *   [2]     =   [222]   ≈   [4]   (mod 26)
    [20 17 15]      [19]        [319]       [7]

So we will get the encrypted text as POH.

Decryption

1. We need to first inverse our key matrix

           -1 
   [6 24   1]      [8 5  10]
   [13 16 10]   ≈  [21 8 21]  (mod 26) 
   [20 17 15]      [21 12 8]

2. For the previous Cipher Text POH

    [8 5  10]     [15]      [260]     [0]
    [21 8 21]  *  [14]  ≈   [574]  ≈  [2]    (mod 26)  ≈ ACT
    [21 12 8]     [7]       [539]     [19]

Video Explanation

Video explanation of the Hill Cipher