Hill Cipher

Hill Cipher is a polygraphic substitution cipher based on linear algebra. In this method, each letter of the alphabet is represented by a number modulo 26, commonly using the scheme A = 0, B = 1, …, Z = 25.

Example:

Input : Plaintext: ACT 
Key: GYBNQKURP
Output: Ciphertext: POH

Input: Plaintext: GFG
Key: HILLMAGIC
Output: Ciphertext: SWK

Encryption in Hill Cipher

For encryption ,

• Divide the plaintext into blocks of n letters.
• Treat each block as an n-dimensional vector.
• Multiply this vector by an invertible n × n key matrix.
• Take the result modulo 26.
• The final values form the ciphertext.

Illustration

We have to encrypt the message 'ACT' (n=3).The key is 'GYBNQKURP' which can be written as the nxn matrix ,

The message 'ACT' is written as vector, 

The enciphered vector is given as,

which corresponds to ciphertext of 'POH' 

Ciphertext: POH

Decryption in Hill Cipher

For decryption,

• Find the inverse of the key matrix (mod 26).
• Divide the ciphertext into blocks of n letters.
• Treat each block as an n-dimensional vector.
• Multiply each vector by the inverse key matrix.
• Take the result modulo 26.
• Convert the numbers back to letters to obtain the original plaintext.

Illustration

The inverse of the matrix the key "GYBNQKURP" will be ,

Now the Ciphertext is "POH",

So, the result is "ACT".

Decrypted Text: ACT