Bill Tutte
He deduced the complete wheel structure of the Lorenz SZ40 from two identical messages alone — the most remarkable feat of cryptanalysis in WWII.
Codebreaker Biography
Bill Tutte
William Thomas Tutte was a Cambridge chemistry graduate and research student when he was recruited to Bletchley Park in 1941. Assigned to the Research Section working on "Fish" — the German teleprinter cipher systems — he was given a 4,000-character depth: two messages that an operator had transmitted in the same Lorenz SZ40 settings, with a slightly altered start. John Tiltman first read the depth by hand: the XOR of the two ciphertexts is the XOR of the two plaintexts, which let him separate both messages and so recover the raw keystream. Tutte was then given that key to analyse. By analysing patterns in this recovered keystream, Tutte and colleagues in the Research Section inferred the machine’s structure by early 1942: the wheel groups, their lengths and their interaction. He did this entirely on paper, never having seen a Lorenz machine. His analysis was the foundation for the Tunny-breaking algorithms developed at Bletchley, which in turn drove the construction of the Robinson machines and ultimately Colossus. His work has been described by post-war analysts as "one of the greatest intellectual feats of World War II."
Why This Person Matters
Bill Tutte's Lorenz analysis is the purest example of what cryptanalysis at its highest level actually is: the reconstruction of an unknown physical system from its outputs alone. Unlike Enigma, where the machine's general design was known, the Lorenz SZ40 was entirely unknown to British intelligence when Tutte was given the key material Tiltman had recovered. The structure emerged through mathematical analysis. The practical consequence was Colossus — the machine designed by Tommy Flowers and programmed by a team to automate Tutte's statistical attacks — which became the world's first operational programmable digital electronic computer. The work connected cryptanalysis with an important early application of programmable electronics. Wartime secrecy long kept this contribution from wider public recognition. His postwar mathematical career was equally distinguished: he made major contributions to graph theory, matroid theory, and combinatorics. He holds the rare distinction of being a world-historical figure in two separate fields.
The Lorenz SZ40 (Schlüsselzusatz — "cipher attachment") was a teleprinter cipher machine used for Hitler's highest-level communications — the "Führer's telegraph." Unlike Enigma (a letter substitution device), Lorenz worked on the 5-bit Baudot teleprinter code and combined the plaintext with a pseudorandom keystream generated by twelve rotating pin wheels. The keystream was the XOR of contributions from two groups of wheels (the Chi wheels and the Psi wheels), further modified by a set of motor wheels that controlled irregular stepping. The complexity was far greater than Enigma: the number of possible wheel positions exceeded 10 to the 19th power. The cipher was used by German High Command, Army Group commanders, and directly by Hitler for strategic communications throughout the war.
On August 30, 1941, a German operator sent a 4,000-character message to another station. The receiving station asked for a repeat. The operator retransmitted — using the same Lorenz wheel settings, but with wording and abbreviations changed. This near-identical pair of ciphertexts was intercepted by the British "Y stations." When Tutte was given Tiltman’s recovered key, he performed a statistical attack called "wheel breaking": by XOR-differencing successive characters of the recovered keystream, he could identify statistical biases introduced by the Chi-wheel keystream. Working with the Research Section through early 1942, he inferred the wheel structure and sizes (41, 31, 29, 26, 23 in the Chi set; 43, 47, 51, 53, 59 for Psi; and 61, 37 for motor wheels) and their pin patterns. This was a tour de force of reverse engineering conducted entirely through mathematical inference.
Source: NSA Center for Cryptologic History, Brigadier John Tiltman: A Giant Among Cryptanalysts (2007), pp. 25–26, distinguishes Tiltman’s manual message/key recovery from the subsequent structural analysis.
Tutte's reconstruction of the Lorenz structure enabled the development of breaking procedures by Max Newman and others in the "Newmanry" section at Bletchley Park. The initial automation used Heath Robinson machines — relay-based systems that counted statistical correlations between ciphertext and trial keystreams by running two paper tape loops simultaneously. The Heath Robinsons were unreliable and slow. Tommy Flowers, a Post Office engineer, argued that vacuum tube logic could do the same work orders of magnitude faster and with far greater reliability. Flowers and his team at Dollis Hill built Colossus in eleven months. Colossus Mark 1 was operational at Bletchley in February 1944; Mark 2 (five times faster) arrived in June 1944, just before D-Day. Ten Colossi were eventually built. Most Colossi were dismantled after the war; two continued in secret service. The exact effect of secrecy and destruction on later computing cannot be reduced to a demonstrated ten-year delay.
| Born | May 14, 1917, Newmarket, Suffolk |
| Died | May 2, 2002, Waterloo, Ontario |
| Education | Trinity College Cambridge — Chemistry BA; Maths PhD |
| Key break | Lorenz SZ40 structure, by early 1942 |
| Enabled | Colossus — world's first programmable electronic computer |
| Postwar | Founder of modern graph theory; FRS |
| Classification | Work secret for decades |