Mathematical Description of Affine Ciphers
Given a and b in Z 26  {0, 1, 2,  , 24, 25} where gcd( a, 26)  1 . We encipher a
plaintext letter x to obtain a ciphertext letter y by computing
y  (ax  b) MOD 26.
Here, the key is made up of a multiplicative parameter a and an additive parameter b .
The next example illustrates how a message is enciphered.
Example 13: Encipher “RADFORD” using the affine cipher y  (5 x  4) MOD 26.
Solution:
█
Note: Recall that for an affine cipher y  (ax  b) MOD 26 to be defined properly,
gcd( a, 26)  1 . Besides allowing a recipient to decipher a message, the next example
illustrates another reason why this requirement is essential.