Caesar’s number

Julius Caesar shifted each letter of his alphabet by three positions. This is the oldest documented cipher, and the simplest to understand.

The principle

A shift is chosen — the key. With a key of 3:

clair    A B C D E ... W X Y Z
chiffré  D E F G H ... Z A B C

The end of the alphabet loops back to the beginning: after Z, we start again at A. The word MATHS therefore becomes PDWKV.

To decrypt, we shift in the opposite direction.

In mathematical notation

Let’s number the letters from 0 (A) to 25 (Z). Encrypting with the key k gives:

chiffré = (clair + k) mod 26

mod 26 means ‘the remainder when divided by 26’ — this is exactly what brings Z back to A. Decryption involves subtraction:

clair = (encrypted - k) mod 26

Why it’s broken

The key can only be between 0 and 25, giving 25 valid possibilities. An attacker can try them all in a matter of seconds and read the one that produces a French sentence: this is a brute-force attack.

clé 1 :  OZSGR   clé 2 :  NYRFQ   clé 3 :  MATHS  ← trouvé

Learn this lesson well; it applies to all modern cryptography: a key space that is too small dooms a system, no matter how elegant the method may be.