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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 k=3k = 3

Modular Arithmetic​

  • System of arithmetic for finite sets of integers (own rules)
  • Common infinite sets include
  • N={1,2,3,...}\N = \{1,2,3,...\}
  • Z={...,−3,−2,−1,0,1,2,3,...}\Z = \{...,-3,-2,-1,0,1,2,3,...\}
  • Q,R,CQ,R,C ... The congruence relation: a≡r(modm)a \equiv r (mod m) can be written as a=q×m+ra=q \times m + r

...

Integer Rings​

Module arithmetic forms what in Mathematics we would call a Ring

Def​

The integer ring zz consists of

  1. The set ...
  2. Two operations ...

...

Affine Cipher​

Multiple the letters by a number, then shift them