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 possibility, 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 themselves 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 .......
END OF EXHIBIT A
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DIGRESSION ON BANBURISMUS
Banburismus is not possible unless you have the bigram tables. The idea behind Banburismus is based on the fact that if two rows of letters of the alphabet, selected at random, are placed on top of each other the repeat rate between them will be 1 in 26 while if two stretches of German Naval plain language are compared in the same way the repeat rate will be 1 in 17. Cypher texts of enigma signals are in effect a selection of random letters and if compared in this way the repeat rate will be 1 in 26 but if, by any chance, both cypher texts were encyphered at the same position of the machine and then written level under each other, the repeat rate will be l in 17 because, wherever there was a plain language repeat, there will be a cypher repeat also. Two messages thus aligned are said to be set in depth, their correct relative position has been found. If by any chance