Abstract
The bombe was an electromechanical machine devised by Alan Turing and Gordon Welchman for breaking the German Enigma cipher in World War II. Welchman's contribution was the ‘diagonal board’ and it was vital to its success. The device reduced the number of times that the bombe stopped for an apparent solution which was not valid. The ratio by which the false stops were reduced is calculated in this paper. The work showed that there remained a class of false stops which had not been eliminated and further investigation showed that an attachment called the ‘machine gun’ helped to reduce the time lost for this reason. While this work was in progress, numerical results derived by Turing became available, but he did not give the theory and these are consistent (apart from apparent numerical errors) with our results.
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