Hill Cipher Encryption

Question

I'd have a quick question over hill cipher encrytion.

Say I have an input

[8 9]

I was to encrypt and an encryption matrix

[1 2]
[3 4]

I multiply the matrix by the input as:

[1 2][8] = [26 60]
[3 4][9]

I am now supposed to take mod 26 of both values of the output vector and convert them back to a corresponding letter using the table

1 = 'a', 2 = 'b', ... , 'z' = 26

However, considering 26 mod 26 is 0, how should I proceed?

Answer 1

Hill cipher associates with each letter, a number (generally from 0 to 25) and there's a logic behind modulo 26. We have 26 letters in English alphabet set, hence we do modulo 26.

Moreover, whenever, we do modulo n, the possible remainders are : 0, 1, 2, . . . , n-1.

Example: x mod 4, (x is any positive integer), we can get only 4 remainders: 0, 1,2,3 ....... never 4.

So, I suggest, one should number a=0, b=1, c=2, .. , z=25... you won't face this problem....

Hope this answered your question. :)