## Enigma, Turing, Welchman and the Bombes

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 ALAN TURING, working at Bletchley Park, had formed the opinion that the solution (to 'Enigma') would not be found by creating a machine that replicated sixty Enigmas. His idea was to use rotors and wires that would simulate a series of Enigma rotors and pass an electrical current from one rotor to the next. However, rather than looking for the one correct rotor setting based on the indicators, as the Polish Bomba did, Turing’s machine would look for all the settings and disregard those that were incorrect. For example, if the assumed letter was "B" and the corresponding cipher letter was "N," Turing’s test register ignored any results that did not allow the electrical current to pass from "B" to "N." By disproving several thousand rotor settings, those remaining were possibly correct settings. Gordon Welchman, a mathematician and Fellow of Sidney Sussex College, Cambridge, was meanwhile working on another facet of the Enigma, the plugboard. Because the plugboard uses a cable to connect one letter to another, it automatically connects the second letter back with the first. If A is plugged into E, E is also plugged into A. With this knowledge, Gordon Welchman, who had already redeveloped Zygalskis perforated sheets for five rotors, designed a diagonal board to reduce the complexities posed by the Enigma’s plugboard.    With Welchman's board combined with Turing’s machine, the number of possible rotor settings would decrease from thousands to just a few. Harold "Doc" Keen, an engineer at British Tabulating Machines (BTM) converted Turing and Welchman’s ideas into working machines, but It took until August 1940 for the first operational machine (called a ‘bombe’) to be installed at Bletchley Park. The construction of the first ‘Bombe’ by BTM took two months but eventually the firm was able to produce one machine each week. A total of around two hundred Bombes for use in England were produced during the war years. As well as at Bletchley Park, some were installed at units located in nearby Wavendon House, Whaddon Hall, Gayhurst House, Adstock Manor, a farm at Drayton Parslow and, reportedly, at Woburn Abbey, home of the Duke of Bedford.    A basic bombe weighed a ton and was over six feet high, seven feet long, and two feet wide. It had thirty-six sets of three rotors. Within each set, the top drum represented the left rotor on Enigma; the middle, the centre rotor, and the bottom, the right rotor. The Bombe produced settings which attempted to complete an electrical circuit through each of the test registers and through the diagonal board. Most of the settings could not complete the path correctly and these were discarded. Those that succeeded caused the machine to stop and a reading of the rotor settings was taken.    When a correct setting had been recorded, the operators (who were mainly members of the Women’s Royal Naval Service or ‘Wrens’) moved on to the next message. It took ten minutes for the Wrens to change the wheel order for the next run and further half-hour or more to set up the new connections. One of the excellent guides at Bletchley Park describing Alan Turing's 'Bombe'. (Right) The front view of the rotors. (Above, and right, to the left of the picture) The connecting looms at the rear of the bombe. (Right, on the right-hand side of the picture, and below, on a bombe under reconstruction) The front view of the rotors on a bombe presently under reconstruction (left).