Congruence is popular in cryptography applications. The oldest example is Caesar

Question

Congruence is popular in cryptography applications. The oldest example is Caesar Cipher used by Julius Caesar to communicate with his generals. In general, for Caesar Cipher, let p = plain text, c = cipher text, k = encryption key, the encryption algorithm is c = p + k mod 26, and decryption algorithm is p = c - k mod 26. Both parties must share a common secret key k. For example, LOVE rightarrow ORYH (circular shift by 3 places, k = 3). Suppose k is the sum of the eight digits of your EMPLID, what will be the cipher text for the plain text "cs"?

Explanation / Answer

Note: Some additional information needed.(What is your EMPLID?)

Let, the sum of the eight digits of your EMPLID be 12. (assuming)

then k = 13

given, p (plain text) = 'CS'

so c (cipher text) = p (plain text) + k (key) mod 26

First we translate all of our characters to numbers, 'a'=0, 'b'=1, 'c'=2, ... , 'z'=25.

So, 'CS' will be 'C' ->2, 'S' -> 18

'C' + k= 2+12 = 14(mod 26) -> 'O'

'S' + k = 18+12 = 30(mod 26) = 4 -> 'E'

so, c (cipher text) will be 'OE'

here I have taken k = 12, your k will be different according to your EMPLID(Student ID).

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