page_title: Bombe
section_title: The Enigma machine
hierarchical_section_title: Bombe / The Enigma machine
caption_attribution_description: English: Enigma Machine at the Imperial War Museum, London.
context_page_description: The bombe is an electro-mechanical device used by the British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functional specification, albeit engineered differently both from each other and from Polish and British bombes.
  The British bombe was developed from a device known as the "bomba", which had been designed in Poland at the Biuro Szyfrów by cryptologist Marian Rejewski, who had been breaking German Enigma messages for the previous seven years, using it and earlier machines. The initial design of the British bombe was produced in 1939 at the UK Government Code and Cypher School at Bletchley Park by Alan Turing, with an important refinement devised in 1940 by Gordon Welchman. The engineering design and construction was the work of Harold Keen of the British Tabulating Machine Company. The first bombe, code-named Victory, was installed in March 1940 while the second version, Agnus Dei or Agnes, incorporating Welchman's new design, was working by August 1940.
context_section_description: The Enigma is an electro-mechanical rotor machine used for the encryption and decryption of secret messages. It was developed in Germany in the 1920s. The repeated changes of the electrical pathway from the keyboard to the lampboard implement a polyalphabetic substitution cipher, which turns plaintext into ciphertext and back again. The Enigma's scrambler contains rotors with 26 electrical contacts on each side, whose wiring diverts the current to a different position on the two sides. On depressing a key on the keyboard, an electric current flows through an entry drum at the right-hand end of the scrambler, then through the set of rotors to a reflecting drum (or reflector) which turns it back through the rotors and entry drum, and out to cause one lamp on the lampboard to be illuminated.
  At each key depression, the right-hand or "fast" rotor advances one position, which causes the encipherment to change. In addition, at a certain point, the right-hand rotor causes the middle rotor to advance; in a similar way, the middle rotor might cause the left-hand (or "slow") rotor to advance. Each rotor causes the "turnover" of the rotor to its left after a full rotation. The Enigma operator could rotate the wheels by hand to change the letter of the alphabet showing through a window, to set the start position of the rotors for enciphering a message. This three-letter sequence is the "message key". There are 26 × 26 × 26 = 17,576 possible positions of the set of three rotors, and hence different message keys. By opening the lid of the machine and releasing a compression bar, the set of three rotors on their spindle could be removed from the machine and their sequence (called the "wheel order" at Bletchley Park) could be altered. Multiplying 17,576 by the six possible wheel orders gives 105,456 different ways that the scrambler could be set up.
  Although 105,456 is a large number, it does not guarantee security. A brute-force attack is possible: one could imagine using 100 code clerks who each tried to decode a message using 1000 distinct rotor settings. The Poles developed card catalogs so they could easily find rotor positions; Britain built "EINS" (a common German word, meaning the number one) catalogs. Less intensive methods were also possible. If all message traffic for a day used the same rotor starting position, then frequency analysis for each position could recover the polyalphabetic substitutions. If different rotor starting positions were used, then overlapping portions of a message could be found using the index of coincidence. Many major powers (including the Germans) could break Enigma traffic if they knew the rotor wiring. The German military knew the Enigma was weak.
  In 1930, the German army introduced an additional security feature, a plugboard (Steckerbrett in German; each plug is a Stecker) that further scrambled the letters. The Enigma encryption is a self inverse, it swapped letters in pairs: if A is transformed into R then R is transformed into A. The plugboard maintained the self inverse, but the plugboard transformation, unlike the rotor transformation, does not change during the encryption. This regularity was exploited by Welchman's "diagonal board" enhancement to the bombe, which vastly increased its efficiency. With six plug leads in use (leaving 14 letters "unsteckered") this gives 100,391,791,500 possible ways of setting up the plugboard.
  An important feature of the machine from a cryptanalyst's point of view, and indeed Enigma's Achilles' heel, was that the reflector in the scrambler meant that a letter was never enciphered as itself. Any putative solution that gave, for any location, the same letter in the proposed plaintext and the ciphertext could therefore be eliminated.
  In the lead up to World War II, the Germans made successive improvements to their military Enigma machines. By January 1939, additional rotors had been introduced so that there was a choice of three from five (i.e. 60 wheel orders) for the army and airforce Enigmas, and three out of eight (336 wheel orders) for the navy machines. I
caption: A three-rotor Enigma with plugboard (Steckerbrett)
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