AFFINE $($LINEAR$)$ CIPHER:

Affine cipher, also known as linear cipher, is a geometric encryption method.

$y=ax+b$

Here, x is the text to be encrypted and $($a$,$b$)$ are the key values.

Encryption:

Step $1$: All characters of the text to be encrypted are converted to their corresponding values in the alphabet. For example, if we use the English alphabet, we should use values from $0$ to $25.A0,B1,C2,D3,E4,$ etc.

Step $2$: For each value, apply the operation $E(x)=(ax+b)modn.$ Here, $n$ is the number of characters in the alphabet. For instance, for the English alphabet, $n$ is chosen as $26.$

Step $3$: The result of each value produced by the function is written as a character corresponding to that value in the alphabet.

Decryption:

Step $1$: The encrypted text is broken down into individual characters, and the position of each character in the alphabet is determined.

Step $2$: Find the appropriate value of $z$ for which $a.$zmodn$=1.$ Here, the value of $"$a$"$ was initially provided as a key.

Step $3$: After finding the appropriate z value, apply the operation $D(x)=z(y-b)modn$ to each value.

Step $4$: Find the corresponding character in the alphabet for each value, and the encrypted message is decrypted.

NOTE: For this method to work correctly, $"$a$"$ and $"n"$ must be coprime. For this reason, for an alphabet with $29$ characters, there are $29**28=812$ possible keys.