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Concept
Turingery
Summary
Turingery or Turing's method (playfully dubbed Turingismus by Peter Ericsson, Peter Hilton and Donald Michie) was a manual codebreaking method devised in July 1942 by the mathematician and cryptanalyst Alan Turing at the British Government Code and Cypher School at Bletchley Park during World War II. It was for use in cryptanalysis of the Lorenz cipher produced by the SZ40 and SZ42 teleprinter rotor stream cipher machines, one of the Germans' Geheimschreiber (secret writer) machines. The British codenamed non-Morse traffic "Fish", and that from this machine "Tunny" (another word for the tuna fish).
Reading a Tunny message required firstly that the logical structure of the system was known, secondly that the periodically changed pattern of active cams on the wheels was derived, and thirdly that the starting positions of the scrambler wheels for this message—the message key—was established. The logical structure of Tunny had been worked out by William Tutte and colleagues over several months ending in January 1942. Deriving the message key was called "setting" at Bletchley Park, but it was the derivation of the cam patterns—which was known as "wheel breaking"—that was the target of Turingery.
German operator errors in transmitting more than one message with the same key, producing a "depth", allowed the derivation of that key. Turingery was applied to such a key stream to derive the cam settings.
Lorenz cipher
The logical functioning of the Tunny system was worked out well before the Bletchley Park cryptanalysts saw one of the machines—which only happened in 1945, shortly before the allied victory in Europe.
The SZ machines were 12-wheel rotor cipher machines which implemented a Vernam stream cipher. They were attached in-line to standard Lorenz teleprinters. The message characters were encoded in the 5-bit International Telegraph Alphabet No. 2 (ITA2). The output ciphertext characters were generated by combining a pseudorandom character-by-character key stream with the input characters using the "exclusive or" (XOR) function, symbolised as "" in mathematical notation.
Official source
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