Editing Cryptanalysis of the Enigma (section)

====German Navy 3-rotor Enigma====
The first break of wartime traffic was in December 1939, into signals that had been intercepted in November 1938, when only three rotors and six plugboard leads had been in use.<ref name=MahonP22>{{Harvnb|Mahon|1945|p=22}}</ref> It used "Forty Weepy Weepy" cribs.

A captured German ''Funkmaat'' ("radio operator") named Meyer had revealed that numerals were now spelt out as words. EINS, the German for "one", was present in about 90% of genuine German Navy messages. An EINS catalogue was compiled consisting of the encipherment of EINS at all 105,456 rotor settings.<ref>{{Harvnb|Alexander|c. 1945}} Ch. II Para. 21</ref> These were compared with the ciphertext, and when matches were found, about a quarter of them yielded the correct plaintext. Later this process was automated in Mr Freeborn's section using [[Unit record equipment|Hollerith equipment]]. When the ground key was known, this EINS-ing procedure could yield three bigrams for the tables that were then gradually assembled.<ref name=MahonP22/>

Further progress required more information from German Enigma users. This was achieved through a succession of ''pinches'', the capture of Enigma parts and codebooks. The first of these was on 12 February 1940, when rotors VI and VII, whose wiring was at that time unknown, were captured from the {{GS|U-33|1936|6}}, by minesweeper {{HMS|Gleaner|J83|6}}.

On 26 April 1940, the Narvik-bound German patrol boat ''VP2623'', disguised as a Dutch trawler named ''Polares'', was captured by {{HMS|Griffin|H31|6}}. This yielded an instruction manual, codebook sheets, and a record of some transmissions, which provided complete cribs. This confirmed that Turing's deductions about the trigram/bigram process were correct and allowed a total of six days' messages to be broken, the last of these using the first of the bombes.<ref name=MahonP22/> However, the numerous possible rotor sequences, together with a paucity of usable cribs, made the methods used against the Army and Air Force Enigma messages of very limited value with respect to the Navy messages.

At the end of 1939, Turing extended the [[Clock (cryptography)|clock method]] invented by the Polish cryptanalyst [[Jerzy Różycki]]. Turing's method became known as "[[Banburismus]]". Turing said that at that stage "I was not sure that it would work in practice, and was not in fact sure until some days had actually broken".<ref>{{Harvnb|Mahon|1945|p=14}}</ref> Banburismus used large cards printed in Banbury (hence the Banburismus name) to discover correlations and a statistical scoring system to determine likely rotor orders (''Walzenlage'') to be tried on the bombes. The practice conserved scarce bombe time and allowed more messages to be attacked. In practice, the 336 possible rotor orders could be reduced to perhaps 18 to be run on the bombes.<ref>{{Harvnb|Alexander|c. 1945}} "Background" Para. 42</ref> Knowledge of the bigrams was essential for Banburismus, and building up the tables took a long time. This lack of visible progress led to [[Francis Birch (cryptographer)|Frank Birch]], head of the Naval Section, to write on 21 August 1940 to [[Edward Travis]], Deputy Director of Bletchley Park: {{blockquote|"I'm worried about Naval Enigma. I've been worried for a long time, but haven't liked to say as much... Turing and Twinn are like people waiting for a miracle, without believing in miracles..."<ref>{{Harvnb|Mahon|1945|p=2}}</ref>}}

Schemes for capturing Enigma material were conceived including, in September 1940, [[Operation Ruthless]] by Lieutenant Commander [[Ian Fleming]] (author of the [[James Bond]] novels). When this was cancelled, Birch told Fleming that "Turing and Twinn came to me like undertakers cheated of a nice corpse..."<ref>{{Harvnb|Batey|2008|pp=4–6}}</ref>

A major advance came through [[Operation Claymore]], a [[British Commandos|commando]] raid on the [[Lofoten Islands]] on 4 March 1941. The German [[naval trawler|armed trawler]] ''Krebs'' was captured, including the complete Enigma keys for February, but no bigram tables or K-book. However, the material was sufficient to reconstruct the bigram tables by "EINS-ing", and by late March they were almost complete.<ref>{{Harvnb|Mahon|1945|p=26}}</ref>

Banburismus then started to become extremely useful. Hut 8 was expanded and moved to 24-hour working, and a crib room was established. The story of Banburismus for the next two years was one of improving methods, of struggling to get sufficient staff, and of a steady growth in the relative and absolute importance of cribbing as the increasing numbers of bombes made the running of cribs ever faster.<ref>{{Harvnb|Alexander|c. 1945}} Ch. III Para. 5</ref> Of value in this period were further "pinches" such as those from the [[German weather ship Lauenburg#The weather ships and Enigma|German weather ships]] ''München'' and ''Lauenburg'' and the submarines {{GS|U-110|1940|2}} and {{GS|U-559||2}}.

Despite the introduction of the 4-rotor Enigma for Atlantic U-boats, the analysis of traffic enciphered with the 3-rotor Enigma proved of immense value to the Allied navies. Banburismus was used until July 1943, when it became more efficient to use the many more bombes that had become available.