Cryptology Cryptanalysis of Enigma

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The number of variants of Enigma and of the corresponding appropriate approaches to cryptanalysis is hardly manageable. For this reason we only treat three selected topics:

1. Cryptanalysis of the Enigma without plugboard [PDF], Example
2. Message key analysis after Rejewski [PDF]
3. Wehrmacht-Enigma and known plaintext [PDF]

Special Features of Enigma

• Control logic: Because the middle rotor moves only after 26 steps, and the slow rotor moves almost never, the ciphertext essentially consists of sections of length 26 where only the fast rotor moves by one position with each step.
• The decomposition of a rotor permutation into cycles is not affected by the plugboard. The substitution by the set of rotors is simply conjugated by the plugboard substitution.
  • If the attacker has enough known plaintext she finds cycles.
  • The diverse rotor orders differ by their cycle types [REJEWSKI's catalogue, TURING's »classes«].
  • In this way the attacker gets information on the rotor order.
• Negative pattern search allows to narrow down the position of known plaintext.

In World War II this last effect allowed for the detection of test messages by the Italians that consisted only of LLL...LLL. This was a stroke of genius by the british cryptanalyst Mavis LEVER who noticed that several cipher messages didn't contain any L, and turned out to be an essential step in uncovering the wiring of newly introduced rotors.