Turing's Treatise on the Enigma

first two indicators that the bigrammes EX and XX have the same value, and this is confirmed from the second and third, where XX and EX occur in the second position instead of the first.

It so happened that the change of indicating system had not been very well made, and a certain torpedo boat, with the call AFA: had not been provided with the bigramme tables. This boat sent a message in another cipher explaining this on the 1st May, and it was arranged that traffic with AFA: was to take place according to the old system until May 4, when the bigramme tables would be supplied. Sufficient traffic passed on May 2, 3 to and from AFA: for the Grundstellung used to be found, the Stecker having already been found from the FORTYWEEPY messages. It was natural to assume that the Grundstellung used by AFA: was the Grundstellung to be used with the correct method of indication, and as soon as we noticed the two indicators mentioned above we tried this out and found it to be the case.

There actually turned out to be some more complications. There were two Grundstellungen at least instead of one. One of them was called the Allgemeine and the other the Offiziere Grundstellung. This made it extremely difficult to find either Grundstellung. The Poles pointed out another possiblity, viz that the trigrammes were still probably not chosen at random. They suggested that probably the window positions enciphered at the Grundstellung, rather than the window positions thenselves were taken off the restricted list.

In Nov. 1939 a prisoner told us that the German Navy had now given up writing numbers with Y...YY...Y and that the digits of the numbers were spelt out in full. When we heard this we examined the messages toward the end of 1937 which were expected to be continuations and wrote the expected beginnings under them. The proportion of 'crashes' i.e. of letters apparently left unaltered by encipherment, then shews how nearly correct our guesses were. Assuming that the change


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