Bombe and Spider (1940)

This material forms chapter 6 of Turing’s Treatise on the Enigma (known at Bletchley Park as ‘Prof ’s Book’). The text has been prepared by Ralph Erskine, Philip Marks and Frode weierud from the two known surviving copies of Turing’s original typescript. The pagination of Turing’s typescript indicates that the chapter may possibly have continued for a further four pages; however, these pages are not to be found in either of the archived copies. When one has asteckered Enigma to deal with one’s problems naturally divide themselves into what is to be done to find the Stecker, and what is to be done afterwards. Unless the indicating system is very well designed there will be no problem at all when the Stecker have been found, and evenwith a good indicating system we shall be able to apply the methods of the last two chapters [of Turing’s Treatise] to the individual messages. The obvious example of a good indicating system is the German Naval Enigma cipher, which is dealt with in Chapter VII [of the Treatise]. This chapter is devoted to methods of finding the Stecker. Naturally enough we never find the Stecker without at the same time finding much other information. The most obvious kind of data for finding the keys is a ‘crib’, i.e. a message of which a part of the decode is known. fie shall mostly assume that our data is a crib, although actually it may be a number of constatations arising from another source, e.g. a number of CILLIs or a Naval Banburismus. It is sometimes possible to find the keys by pencil and paper methods when the number of Stecker is not very great, e.g. 5 to 7. One would have to hope that several of the constatations of the crib were ‘unsteckered’. The best chance would be if the same pair of letters occurred twice in the crib (a ‘half-bombe’). In this case, assuming 6 or 7 Stecker there would be a 25% chance of both constatations being unsteckered. The positions at which these constatations occurred could be found by means of the Turing sheets (if there were three wheels) or the Jeffreys sheets.

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