Editing Cryptanalysis of the Enigma (section)

===British ''bombe''===
{{Main|Bombe}}
The British bombe was an electromechanical device designed by Alan Turing soon after he arrived at Bletchley Park in September 1939. [[Harold Keen|Harold "Doc" Keen]] of the [[British Tabulating Machine Company]] (BTM) in [[Letchworth]] ({{convert|35|km|mi}} from Bletchley) was the engineer who turned Turing's ideas into a working machine—under the codename CANTAB.<ref>{{citation|contribution=BTM – British Tabulatuing Machine Company Ltd |contribution-url=http://www.jharper.demon.co.uk/btm1.htm |editor-last=Harper |editor-first=John |title=The British Bombe CANTAB |url=http://www.jharper.demon.co.uk/bombe1.htm |url-status=dead |archive-url=https://web.archive.org/web/20131204202741/http://www.jharper.demon.co.uk/bombe1.htm |archive-date=2013-12-04}}</ref> Turing's specification developed the ideas of the Poles' [[Bomba (cryptography)|''bomba kryptologiczna'']] but was designed for the much more general crib-based decryption.

The bombe helped to identify the ''wheel order'', the initial positions of the rotor cores, and the ''stecker partner'' of a specified letter. This was achieved by examining all 17,576 possible scrambler positions for a set of ''wheel orders'' on a comparison between a crib and the ciphertext, so as to eliminate possibilities that [[contradiction|contradicted]] the Enigma's known characteristics. In the words of Gordon Welchman "the task of the bombe was simply to reduce the assumptions of ''wheel order'' and scrambler positions that required 'further analysis' to a manageable number".<ref name="Welchman97p120"/>

[[File:RebuiltBombeFrontView.jpg|thumb|300px|right|The working rebuilt bombe now at [[The National Museum of Computing]] on Bletchley Park. Each of the rotating drums simulates the action of an Enigma rotor. There are 36 Enigma-equivalents and, on the right end of the middle row, three ''indicator'' drums.]]

The demountable drums on the front of the bombe were wired identically to the connections made by Enigma's different rotors. Unlike them, however, the input and output contacts for the left-hand and the right-hand sides were separate, making 104 contacts between each drum and the rest of the machine.<ref>{{citation |last=Sale |first=Tony |author-link=Anthony Sale |contribution=Alan Turing, the Enigma and the Bombe |contribution-url=https://www.codesandciphers.org.uk/virtualbp/tbombe/tbombe.htm |editor-last=Sale |editor-first=Tony |editor-link=Anthony Sale |title=The Enigma cipher machine |url=https://www.codesandciphers.org.uk/enigma/}}</ref> This allowed a set of scramblers to be connected [[series and parallel circuits#Series circuits|in series]] by means of 26-way cables. Electrical connections between the rotating drums' wiring and the rear plugboard were by means of metal brushes. When the bombe detected a scrambler position with no contradictions, it stopped and the operator would note the position before restarting it.

Although Welchman had been given the task of studying Enigma traffic [[call sign]]s and discriminants, he knew from Turing about the bombe design and early in 1940, before the first pre-production bombe was delivered, he showed him an idea to increase its effectiveness.<ref>{{Harvnb|Hodges|1983|p=183}}</ref> It exploited the reciprocity in plugboard connections, to reduce considerably the number of scrambler settings that needed to be considered further. This became known as the ''diagonal board'' and was subsequently incorporated to great effect in all the bombes.<ref name="Welchman97p245"/><ref>{{Harvnb|Ellsbury|1998b}}</ref>

A cryptanalyst would prepare a crib for comparison with the ciphertext. This was a complicated and sophisticated task, which later took the Americans some time to master. As well as the crib, a decision as to which of the many possible ''wheel orders'' could be omitted had to be made. Turing's [[Banburismus]] was used in making this major economy. The cryptanalyst would then compile a [[Bombe#Bombe menu|''menu'']] which specified the connections of the cables of the patch panels on the back of the machine, and a particular letter whose ''stecker partner'' was sought. The menu reflected the relationships between the letters of the crib and those of the ciphertext. Some of these formed loops (or ''closures'' as Turing called them) in a similar way to the ''cycles'' that the Poles had exploited.

The reciprocal nature of the plugboard meant that no letter could be connected to more than one other letter. When there was a contradiction of two different letters apparently being ''stecker partners'' with the letter in the menu, the bombe would detect this, and move on. If, however, this happened with a letter that was not part of the menu, a false stop could occur. In refining down the set of stops for further examination, the cryptanalyst would eliminate stops that contained such a contradiction. The other plugboard connections and the settings of the alphabet rings would then be worked out before the scrambler positions at the possible true stops were tried out on [[Typex]] machines that had been adapted to mimic Enigmas. All the remaining stops would correctly decrypt the crib, but only the true stop would produce the correct plaintext of the whole message.<ref name=CarterStopsKeys/>

To avoid wasting scarce bombe time on menus that were likely to yield an excessive number of false stops, Turing performed a lengthy probability analysis (without any electronic aids) of the estimated number of stops per rotor order. It was adopted as standard practice only to use menus that were estimated to produce no more than four stops per ''wheel order''. This allowed an 8-letter crib for a 3-closure menu, an 11-letter crib for a 2-closure menu, and a 14-letter crib for a menu with only one closure. If there was no closure, at least 16 letters were required in the crib.<ref name=CarterStopsKeys>{{citation |last=Carter |first=Frank |title=From Bombe 'stops' to Enigma keys |year=2004 |url=http://www.bletchleypark.org.uk/content/bombestops.pdf |access-date=1 March 2009 |url-status=dead |archive-url=https://web.archive.org/web/20100108030414/http://www.bletchleypark.org.uk/content/bombestops.pdf |archive-date=8 January 2010}}</ref> The longer the crib, however, the more likely it was that ''turn-over'' of the middle rotor would have occurred.

The production model 3-rotor bombes contained 36 scramblers arranged in three banks of twelve. Each bank was used for a different ''wheel order'' by fitting it with the drums that corresponded to the Enigma rotors being tested. The first bombe was named ''Victory'' and was delivered to Bletchley Park on 18 March 1940. The next one, which included the diagonal board, was delivered on 8 August 1940. It was referred to as a ''spider bombe'' and was named ''Agnus Dei'' which soon became ''Agnes'' and then ''Aggie''. The production of British bombes was relatively slow at first, with only five bombes being in use in June 1941, 15 by the year end,<ref>{{Harvnb|Copeland|2004|pp=253–256}}</ref> 30 by September 1942, 49 by January 1943<ref>{{Harvnb|Budiansky|2000|p=230}}</ref> but eventually 210 at the end of the war.

A refinement that was developed for use on messages from those networks that disallowed the plugboard (''Stecker'') connection of adjacent letters, was the ''Consecutive Stecker Knock Out''. This was fitted to 40 bombes and produced a useful reduction in false stops.<ref>{{Harvnb|Bauer|2002|p=482}}</ref>

Initially the bombes were operated by ex-BTM servicemen, but in March 1941 the first detachment of members of the [[Women's Royal Naval Service]] (known as ''Wrens'') arrived at Bletchley Park to become bombe operators. By 1945 there were some 2,000 Wrens operating the bombes.<ref>{{Harvnb|Smith|2007|p=75}}</ref> Because of the risk of bombing, relatively few of the bombes were located at Bletchley Park. The largest two outstations were at [[Eastcote]] (some 110 bombes and 800 Wrens) and Stanmore (some 50 bombes and 500 Wrens). There were also bombe outstations at Wavendon, Adstock, and Gayhurst. Communication with Bletchley Park was by [[teleprinter]] links.

When the German Navy started using 4-rotor Enigmas, about sixty 4-rotor bombes were produced at Letchworth, some with the assistance of the [[General Post Office]].<ref>{{citation|contribution=Bombe Types |contribution-url=http://www.jharper.demon.co.uk/types1.htm |editor-last=Harper |editor-first=John |title=The British Bombe CANTAB |url=http://www.jharper.demon.co.uk/bombe1.htm |url-status=dead |archive-url=https://web.archive.org/web/20131204202741/http://www.jharper.demon.co.uk/bombe1.htm |archive-date=2013-12-04}}</ref> The [[NCR Corporation|NCR]]-manufactured [[Bombe#US Navy Bombe|US Navy 4-rotor bombes]] were, however, very fast and the most successful. They were extensively used by Bletchley Park over teleprinter links (using the [[Combined Cipher Machine]]) to [[OP-20-G]]<ref>{{Harvnb|Mahon|1945|p=89}}
</ref> for both 3-rotor and 4-rotor jobs.<ref>{{Harvnb|Wenger|Engstrom|Meader|1998}}</ref>