Historical Ciphers
Ciphers have been used for thousands of years Usually based around either transportation or substitution
Everything about an algorithm is public
Caesar Cipher
- Early substitution cipher, replace each letter of plaintext with a shifted letter further down the alphabet.
- Caesar always used a key
Modular Arithmetic
- System of arithmetic for finite sets of integers (own rules)
- Common infinite sets include
- ... The congruence relation: can be written as
...
Integer Rings
Module arithmetic forms what in Mathematics we would call a Ring
Def
The integer ring consists of
- The set ...
- Two operations ...
...
Affine Cipher
Multiple the letters by a number, then shift them