## Example

We can use any value of *b* (apart from 1), but *a* should not share a factor with 26 (this is defined as being co-prime). Thus a can be 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 or 25.

The following is taken from Wikipedia:

plaintext | A | F | F | I | N | E | C | I | P | H | E | R |
---|---|---|---|---|---|---|---|---|---|---|---|---|

x | 0 | 5 | 5 | 8 | 13 | 4 | 2 | 8 | 15 | 7 | 4 | 17 |

Now, take each value of x, and solve the first part of the equation, (5*x* + 8). After finding the value of (5*x* + 8) for each character, take the remainder when dividing the result of (5*x* + 8) by 26. The following table shows the first four steps of the encrypting process.

plaintext | A | F | F | I | N | E | C | I | P | H | E | R |
---|---|---|---|---|---|---|---|---|---|---|---|---|

x | 0 | 5 | 5 | 8 | 13 | 4 | 2 | 8 | 15 | 7 | 4 | 17 |

(5x + 8) |
8 | 33 | 33 | 48 | 73 | 28 | 18 | 48 | 83 | 43 | 28 | 93 |

(5x + 8) mod 26 |
8 | 7 | 7 | 22 | 21 | 2 | 18 | 22 | 5 | 17 | 2 | 15 |

The final step in encrypting the message is to look up each numeric value in the table for the corresponding letters. In this example, the encrypted text would be IHHWVCSWFRCP. The table below shows the completed table for encrypting a message in the Affine cipher.

plaintext | A | F | F | I | N | E | C | I | P | H | E | R |
---|---|---|---|---|---|---|---|---|---|---|---|---|

x | 0 | 5 | 5 | 8 | 13 | 4 | 2 | 8 | 15 | 7 | 4 | 17 |

(5x + 8) |
8 | 33 | 33 | 48 | 73 | 28 | 18 | 48 | 83 | 43 | 28 | 93 |

(5x + 8) mod 26 |
8 | 7 | 7 | 22 | 21 | 2 | 18 | 22 | 5 | 17 | 2 | 15 |

ciphertext | I | H | H | W | V | C | S | W | F | R | C | P |

The cipher is generally weak as it is a monoalphabet and doesn't use a key. Overall there are 12 possible values of *a* (1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25), and 26 possible shifts (*b*). Thus there are 286 possible mappings (\(12 \times 26\))