Reading a text without its key: naming the cipher, peeling off encodings, counting letters, breaking nomenclators, replaying the Enigma breaks of the 1930s and 1940s, checking anagrams.
Banburismus
Replays Turing’s Banburismus, Hut 8’s attack on the naval Enigma in 1940–43: Hugh Alexander’s worked example step by step — two messages in depth, his fits, the chain scritched to his four alphabets, the turnover naming wheel III or V — and a simulated naval day broken the same way, scored by Turing’s weight of evidence in half-decibans.
Terms
About this tool
History
Alan Turing thought of Banburismus at Bletchley Park the day the naval indicating system was solved. Operators set each message by a trigram from the K book typed at the day’s ground setting, the trigram disguised by bigram tables; once Hut 8 had the tables, it knew every trigram, and two that share their first two letters mean messages starting within 25 letters of each other. Hugh Foss broke the first day by it, 8 May 1940, in November; the punched sheets came from Banbury. It was Hut 8’s daily work until mid-1943, given up that September when the bombes could take every wheel order.
How it works
Two messages set one over the other at their true distance repeat where their German does, about one letter in 17 against one in 26 at random. Turing’s weight of evidence turns a count into half-decibans, Hut 8’s unit; each distance’s prior is added, as long stretches without a turnover are less likely. Believed distances are chained and slid under A–Z, each pair reciprocal and none standing for itself — scritching — and the alphabets left are tested on all the comparisons. Stretches where the middle wheel stood still exclude the wheels with a notch in them.
How it was checked
Hugh Alexander’s worked example replays exactly: his two messages repeat seven times in 32 where their clear texts do, his fits make his chain, the chain scritches to his four alphabets, the weaker fits deny the three he rejects, and the turnover leaves wheel III or V. His listed sheet scores add to 89 for, against his printed 88. On 100 simulated days of 400 messages the alphabet and the wheel come out whole on 55 of the 58 with one of wheels I–V on the right, and 12 of the 42 with a naval wheel there.
Limits
No day of 1940–41 naval traffic is published with its key, so the days are simulated, their texts from a naval officer’s book of 1889, and repeat about one letter in 12 rather than the traffic’s 17. A naval wheel on the right turns the middle one every 13 letters: half the pairs are never in depth, such days often fail, and wheels VI–VIII cannot be told apart. The middle wheel’s Banburismus, from pairs sharing one letter, and the bombe run are left out.
- Hugh Alexander, Cryptographic History of Work on the German Naval Enigma (about 1945), chapter IX; The National Archives, HW 25/1
- Alan Turing, Treatise on the Enigma (about 1940), chapter VII; The National Archives, HW 25/3
- Patrick Mahon, The History of Hut Eight 1939–1945 (1945); The National Archives, HW 25/2
- I. J. Good, “Studies in the history of probability and statistics XXXVII: A. M. Turing’s statistical work in World War II”, Biometrika 66 (1979), pp. 393–396