Affine Cipher

The Affine Cipher is a type of substitution cipher that uses mathematical functions for encryption and decryption. It involves two keys, a and b, to transform the plaintext.

Encryption Formula

The encryption function for the affine cipher is given by:

$C(x)=(a\cdot x+b)\mathrm{mod}(m)$

Where:

• E(x) is the encrypted character.
• x is the numerical representation of the plaintext character.
• a and b are the keys used for encryption.
• m is the size of the alphabet (for the English alphabet, $m=26$ ).

Decryption Formula

To decrypt, the following function is used:

$D(x)=a^{-1}\cdot (x-b)\mathrm{mod}(m)$

Where:

• $a^{-1}$ is the modular inverse of a modulo m.

Example

If we choose a = 5 and b = 8 for the English alphabet (where $m=26$):

• To encrypt the letter "C" (which corresponds to $x=2$): $E(2)=(5\cdot 2+8)\mathrm{mod}(26)=18$ The result, 18, corresponds to the letter "S", so "C" becomes "S".

Note

The keys a and m must be coprime (i.e., $gcd(a,m)=1$) to ensure that the encryption can be reversed during decryption.