The Affine cipher (gets it name from the definition of an affine function which is a combination of a translation and scaling) is another example of a substitution cipher where each letter is replaced by another based on some rule.

## Encryption

The affine cipher key consists of a pair of integers (a, b) which is used to are used to form the equation ax+b and subsequently used to generate the mapping of each plaintext character to ciphertext character.

Take (3, 5) as an example. Note a must be a co-prime (have no common factors other than 1) to 26 otherwise different characters may map to the same letter and thus wouldn’t be reversible. In group theory this is because a needs to be cyclic generator of the group Z/26Z

```
(a) 3*0+5=5 (F)
(d) 3*3+5=5 (O)
(x) 3*23+5=74=5 (mod 22) (W)
abcdefghijklmnopqrstuvwxyz
FILORUXADGJMPSVYBEHKNQTWZC
```

For each letter in your plaintext you replace it it with its corresponding ciphertext letter.

### Example

```
when the clock strikes twelve attack
TARS KAR LMVLJ HKEDJRH KTRMQR FKKFLJ
```

## Decryption

For each letter in your ciphertext you replace it it with its corresponding plaintext letter (the one above it in the mapping).

```
abcdefghijklmnopqrstuvwxyz - Key (9, 15)
PYHQZIRAJSBKTCLUDMVENWFOXG
FAZC EAZ HKLHB VEMJBZV EFZKWZ PEEPHB
when the clock strikes twelve attack
```