Question

base on hill cipher is it possible to encrypt some given plain text that cannot be decrypted explore your answer with numeric example

Answer 1

In a Hill cipher encryption, the plaintext message is broken up into blocks of length  according to the  matrix chosen. Each block of plaintext letters is then converted into a vector of numbers and is dotted with the matrix. The results are then converted back to letters and the ciphertext message is produced. For decryption of the ciphertext message, the inverse of the encryption matrix must be found. Once found, the decryption matrix is then dotted with each -block of ciphertext, producing the plaintext message.

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

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

Encryption

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’

Decryption

To decrypt the message, we turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (IFKVIVVMI in letters).The inverse of the matrix used in the previous example is:

For the previous Ciphertext ‘POH’:

which gives us back ‘ACT’.