enabling a system to be broken on quite a small number of messages and the enemy's use of it undoubtedly played a very large part in our success. From the user's point of view the system is a good one since every indicator is checked and corruptions are automatically shown up - for this reason no doubt, it was originally recommended by the makers and adopted by the Germans.
Weakness of the "Grundstellung" Method.
33. Both the foregoing systems suffer from the fault of having all the chosen trigrams encoded at a fixed machine position (the Grund). The whole of the method of Banburismus (see Chap.) depends entirely on this fact. Had the Germans had a variable Grund (e.g. used the Schluessel Kenngruppe for this purpose) our breaking would probably have been delayed a year. Apart from this fault the main system is a good one, particularly in that it does not allow the operator to choose anything out of his head but compels him to go to a book.
D. General Nature of the Problem and its Solution.
34. In a series of separate chapters an explanation will be given of the various methods used to solve the problem with which we were faced. Some readers may however not be interested in this but merely wish to read the general history of the development of the section and the kind of changes that took place in it as we were faced by new problems and as the equipment at our disposal increased. This section is written for their benefit and attempts to show the magnitude and general nature of the problem with which we were faced and the kind of methods available for attacking it. No technical account of the methods will be given here.
35. There were two main problems (1) the recovery of the trigram tables (2) the recovery of the daily keys. In order to be able to make a start at all a pinch either of some daily keys or of some bigram tables was necessary. Once one had got going (i.e. got to a state of breaking daily keys regularly) it was possible to work out a new set of bigram tables when these were introduced. I shall assume first that the bigram tables are known and that we have to recover the daily keys.
The Problem.
36. There are 336 W.O's and 263 or 264 ways (according to whether the machine is 3 or 4 wheel) in which the wheels can be set up. What we
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