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Cryptanalysis of the Enigma

The story of the cryptanalysis of the Enigma is perhaps the only story of military cryptanalysis ever recounted where a detailed view was given of that cryptanalysis on an ongoing basis, over multiple revisions and modifications of the cipher system under attack.

The cryptanalytical methods used are sorted by type in the following sections, and thus a more chronological summary may help to make the story more understandable.

Initially, the Enigma was without a plugboard. The method of "cliques on the rods" was used against it at this stage; this was a version of the isomorph attack against a Hebern machine, modified as required for the Enigma.

Next, a plugboard was used, but only three cords were plugged into it, affecting only six of the twenty-six letters. A common ground setting was used to encipher the starting setting which operators were supposed to choose at random; this setting was enciphered twice. Here, the tables generated by the cyclometer were used: the doubly-enciphered indicator meant that if one message had A as its first letter and Q as its fourth, A as the first letter of the message always implied Q as the fourth. Thus, the relation between the first and fourth letters of a day's intercepts defined an alphabet, and the same was true of the second and fifth letters and the third and sixth. The characteristics of these alphabets allowed those tables to pinpoint the day's ground setting.

Then, instead of a ground setting, a setting picked also at random, and sent in the clear, was used. This nine-letter indicator was attacked on the basis of watching for cases where corresponding letters in the doubly-enciphered indicator, now the fourth and seventh, fifth and eighth, and sixth and ninth letters of the message, were the same. The original Polish Bombe, and also the perforated sheets, were used at this stage.

When the number of rotors in the rotor set was increased to five from three, the British took over from the Poles, and relied mainly on the perforated sheets.

When the rotor starting position for an individual message was enciphered only once, the Turing Bombe, soon augmented by the diagonal board, allowed decrypting Enigma messages to continue.

On the Naval Enigma, eight rotors as well as a split reflecting rotor were used. This was dealt with by aligning messages to find key overlaps; from this, and a study of the indicators, constraints on the possible rotor orders were found, allowing the Bombe to still be used.

Near the end of the war, the Uhr box and a rewirable reflecting rotor were used in some places. The Uhr box merely required giving up the diagonal board. The reflecting rotor required a major redesign of the Bombe, but decoding continued.

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