Cryptanalysis of the Enigma

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Cryptanalysis of the Enigma enabled the western Allies in World War II to read substantial amounts of secret Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra. This was considered by western Supreme Allied Commander Dwight D. Eisenhower to have been "decisive" to the Allied victory.^[1]
The Enigma machines were a family of portable cipher machines with rotor scramblers.^[2] Good operating procedures, properly enforced, would have made the cipher unbreakable.^[3][4] However, most of the German armed and secret services and civilian agencies that used Enigma employed poor procedures and it was these that allowed the cipher to be broken.
The German plugboard-equipped Enigma became the Third Reich's principal crypto-system. It was reconstructed by the Polish General Staff's Cipher Bureau in December 1932—with the aid of French-supplied intelligence material that had been obtained from a German spy. Shortly before the outbreak of World War II, the Polish Cipher Bureau initiated the French and British into its Enigma-breaking techniques and technology at a conference held in Warsaw.
From this beginning, the British Government Code and Cypher School (GC&CS) at Bletchley Park built up an extensive cryptanalytic facility. Initially, the decryption was mainly of Luftwaffe and a few Army messages, as the German Navy employed much more secure procedures for using Enigma. Alan Turing, a Cambridge University mathematician and logician, provided much of the original thinking that led to the design of the cryptanalytical Bombe machines and the eventual breaking of naval Enigma. However, the German Navy introduced an Enigma version with a fourth rotor for its U-boats resulting in a prolonged period when these messages could not be decrypted. With the capture of relevant cipher keys and the use of much faster US Navy Bombes, regular, rapid reading of U-boat messages resumed.

The Enigma cipher machine
Enigma machine Enigma rotors Breaking Enigma Polish Cipher Bureau Doubles Grill Clock Cyclometer Bomba Zygalski sheets Bletchley Park Banburismus Herivel tip Crib Bombe Hut 6 Hut 8 PC Bruno Ultra
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Contents

• 1 General principles
• 2 The Enigma machines
  • 2.1 Structure
  • 2.2 Security properties
  • 2.3 Key setting
• 3 British efforts
• 4 Polish breakthrough
  • 4.1 Rejewski's characteristics method
  • 4.2 Perforated sheets
  • 4.3 Polish bomba
  • 4.4 Major setback
• 5 World War II
  • 5.1 Italian naval Enigma
  • 5.2 Polish disclosures
  • 5.3 PC Bruno
  • 5.4 Operating shortcomings
  • 5.5 Crib-based decryption
  • 5.6 British bombe
  • 5.7 Luftwaffe Enigma
  • 5.8 Abwehr Enigma
  • 5.9 German Army Enigma
  • 5.10 German naval Enigma
    • 5.10.1 German Navy 3-rotor Enigma
    • 5.10.2 German Navy 4-rotor Enigma
  • 5.11 American bombes
  • 5.12 German suspicions
• 6 Since World War II
• 7 See also
• 8 References and notes
• 9 Bibliography
• 10 External links

General principles

Main article: Cryptanalysis

The Enigma machines produced a polyalphabetic substitution cipher. During World War I, inventors in several countries realized that a purely random key sequence, containing no repetitive pattern, would, in principle, make a polyalphabetic substitution cipher unbreakable.^[5] This led to the development of rotor cipher machines which alter each character in the plaintext to produce the ciphertext, by means of a scrambler comprising a set of rotors that alter the electrical path from character to character, between the input device and the output device. This constant altering of the electrical pathway produces a very long period before the pattern—the key sequence or substitution alphabet—repeats.
Deciphering enciphered messages involves three stages, defined somewhat differently in that era than in modern cryptography.^[6] Firstly, there is the identification of the system in use, in this case Enigma; secondly, breaking the system by establishing exactly how encryption takes place, and thirdly, setting, which involves finding the way that the machine was set up for an individual message, i.e. the message key.^[7] Today, it's often assumed that an attacker knows how the encipherment process works and breaking specifically refers to finding a way to infer a particular key or message (see Kerckhoffs's principle). Enigma machines, however, had so many potential internal wiring states that reconstructing the machine, independent of particular settings, was a very difficult task.