Enigma

The Enigma machine was used extensively by Germany during World War II.

Components

  • Keyboard
  • Scrambler (rotor assembly)
  • Reflector
  • Plugboard
  • Lampboard

Operation

Each rotor implements a monoalphabetic substitution. After every keystroke:

  • The first rotor advances
  • After a full rotation, it steps the next rotor
  • This creates a polyalphabetic substitution cipher

With three rotors:

  • 26³ = 17,576 rotor positions
  • Rotor order increases combinations
  • Plugboard dramatically expands keyspace

Key Space Expansion

  • Rotor positions: 17,576
  • Rotor permutations: 3! = 6
  • Plugboard pairings ≈ 10¹⁴

Reflector

  • Sends signal back through rotors
  • Ensures encryption is reversible
  • Prevents any letter encrypting to itself

Key Definition

The key consists of:

  • Rotor selection
  • Rotor order
  • Initial rotor positions
  • Plugboard wiring

Note: The Enigma machine was bijective.

Bijection: a one-to-one correspondence between two sets.

Backward Polyalphabetic Substitution Cipher Asymmetric Cryptography Forward