# Cryptographic History of Work on the German Naval Enigma

arise from a true distance or by chance - and how much more likely one way is than the other. It can be shown that it is about 12 times as likely that this particular score would arise in a true as in a false position; in the method of scoring and units used by us (logarithmic scoring) it would be a score of + 22 - and would be written

8. This is a first step although a small one towards finding "the alphabet" i.e. the clear values of which Q and B are encypherments. It tells us that if we can discover what letter encyphers as B then Q has a good chance of being the encypherment of the letter five further on in the alphabet. [Look back and note that the real answer is B encypherment of G, Q encypherment of G + 5 = L].

9. We now have to collect all information of this kind arising from comparisons of pairs of messages. We distinguish between two main groups of comparisons (1) between pairs of messages whose trigrams have the first two letters in common e.g. TYQ, TYB above (2) between pairs of messages whose trigrams have first letter only or no letters in common e.g. LJR, LXN or LJR, QYN.

10. In group (1) we know that the first two letters of the message set-ups are also identical (if TYQ is encypherment of xyz, then TYB must be the encypherment of xyw - w, x, y, z standing for unknown letters to be discovered) and therefore that the messages start within 25 spaces of each other. For, once in 26 times (ignoring the complication of double turnover wheels which leaves the general argument unaffected) the middle wheel moves over one; so, if the messages started more than 25 places apart their set-ups and hence the encyphered trigrams would be bound to be different. Therefore there are only 50 possible relative positions of messages such as TYQ, TYB and it is worth examining each of these positions. These comparisons are known as "End wheel comparisons" and were made by the Big Room on every pair of messages with the first two letters the same; the scores being turned into convenient scoring units and recorded as follows

-97-