Cryptanalysis of the Lorenz cipher

Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II.

[3] These were intercepted non-Morse radio transmissions that had been enciphered by the Lorenz SZ teleprinter rotor stream cipher attachments.

[9] Unlike Enigma, no physical machine reached allied hands until the very end of the war in Europe, long after wholesale decryption had been established.

[14] Albert W. Small, a cryptanalyst from the US Army Signal Corps who was seconded to Bletchley Park and worked on Tunny, said in his December 1944 report back to Arlington Hall that: Daily solutions of Fish messages at GC&CS reflect a background of British mathematical genius, superb engineering ability, and solid common sense.

[20] The numbers of cams on the set of twelve wheels of the SZ42 machines totalled 501 and were co-prime with each other, giving an extremely long period before the key sequence repeated.

The fact that the psi wheels all moved together, but not with every input character, was a major weakness of the machines that contributed to British cryptanalytical success.

The system would typically send some ten characters per second, and so occupy the line or the radio channel for a shorter period of time than for online typing.

[45] The enciphering system was very good at ensuring that the ciphertext Z contained no statistical, periodic or linguistic characteristics to distinguish it from random.

So for a single character, the key K consisted of two components: The actual sequence of characters added by the psi wheels, including those when they do not advance, was referred to as the extended psi,[43] and symbolised by ψ′ Tutte's derivation of the ψ component was made possible by the fact that dots were more likely than not to be followed by dots, and crosses more likely than not to be followed by crosses.

Diagnosing the functioning of the Tunny machine in this way was a truly remarkable cryptanalytical achievement, and was described when Tutte was inducted as Officer of the Order of Canada in October 2001, as "one of the greatest intellectual feats of World War II".

Turing worked out that the XOR combination of the values of successive (adjacent) characters in a stream of ciphertext or key, emphasised any departures from a uniform distribution.

Turing's method of deriving the cam settings of the wheels from a length of key obtained from a depth, involved an iterative process.

The resulting putative bit pattern of x and • for each chi wheel, was recorded on a sheet of paper that contained as many columns as there were characters in the key, and five rows representing the five impulses of the Δχ.

Finally, in September, a depth was received that allowed Turing's method of wheel breaking, "Turingery", to be used, leading to the ability to start reading current traffic.

Once the Newmanry became operational in June 1943, the nature of the work performed in the Testery changed, with decrypts, and wheel breaking no longer relying on depths.

It was designed and built in Tommy Flowers' laboratory at the General Post Office Research Station at Dollis Hill by Gil Hayward, "Doc" Coombs, Bill Chandler and Sid Broadhurst.

[71] When Flowers was invited by Hayward to try the first British Tunny machine at Dollis Hill by typing in the standard test phrase: "Now is the time for all good men to come to the aid of the party", he much appreciated that the rotor functions had been set up to provide the following Wordsworthian output:[72] Additional features were added to the British Tunnies to simplify their operation.

[73][74] The Newmanry was a section set up under Max Newman in December 1942 to look into the possibility of assisting the work of the Testery by automating parts of the processes of decrypting Tunny messages.

Absolute accuracy of these tapes and their transcription was essential, as a single character in error could invalidate or corrupt a huge amount of work.

[77] W. T. Tutte developed a way of exploiting the non-uniformity of bigrams (adjacent letters) in the German plaintext using the differenced cyphertext and key components.

[78] The essence of this method was to find the initial settings of the chi component of the key by exhaustively trying all positions of its combination with the ciphertext, and looking for evidence of the non-uniformity that reflected the characteristics of the original plaintext.

[83] This technique could be applied to any pair of impulses and so provided the basis of an automated approach to obtaining the de-chi (D) of a ciphertext, from which the psi component could be removed by manual methods.

[88] Tommy Flowers' had reservations about Heath Robinson's two synchronised tape loops, and his previous, unique experience of thermionic valves (vacuum tubes) led him to realize that a better machine could be produced using electronics.

Flowers' suggestion that this could be achieved with a machine that was entirely electronic and would contain between one and two thousand valves, was treated with incredulity at both the Telecommunications Research Establishment and at Bletchley Park, as it was thought that it would be "too unreliable to do useful work".

He did, however, have the support of the Controller of Research at Dollis Hill, W Gordon Radley,[89] and he implemented these ideas producing Colossus, the world's first electronic, digital, computing machine that was at all programmable, in the remarkably short time of ten months.

[90] In this he was assisted by his colleagues at the Post Office Research Station Dollis Hill: Sidney Broadhurst, William Chandler, Allen Coombs and Harry Fensom.

The main parts of this machine were:[92] The five parallel processing units allowed Tutte's "1+2 break in" and other functions to be run at an effective speed of 25,000 characters per second by the use of circuitry invented by Flowers that would now be called a shift register.

[95] As well as the commercially produced teleprinters and re-perforators, a number of other machines were built to assist in the preparation and checking of tapes in the Newmanry and Testery.

Small describes the check of the frequency count of the ΔD characters as being the "acid test",[112] and that practically every cryptanalyst and Wren in the Newmanry and Testery knew the contents of the following table by heart.

Cryptanalyst Jerry Roberts made the point that this Testery work was a greater load on staff than the automated processes in the Newmanry.