# Cryptographic History of Work on the German Naval Enigma

produced from our crib or alphabets which then tests every machine position in turn, its testing taking the form of attempting to produce a set of stecker which will make the letters from the crib with which it has been supplied decode correctly.

44. The 3 wheel bombe will test all the 17,576 possible positions in a wheel order on the 3 wheel Enigma in about 20 minutes (allowing time for setting the machine up). Thus to test all 336 W.O's would take about 112 bombe hours, or - to put it in a slightly different way - 5 bombes would take about 24 hours to test a job completely. If the number of W.O's can be reduced then the bombe time is reduced in almost exact proportion. So when very few bombes existed, the reduction in wheel orders obtained from Banburismus was very important.

45. The 3 wheel bombe was not adequate to deal with the 4 wheel Enigma. It would have taken 6 hours to run a W.O. and to get through 336 W.O's in 24 hours would have needed 80 to 90 machines. Moreover no W.O. reduction through Banburismus was available with the 4 wheel Enigma. A still faster machine, the 4 wheel bombe or "4 wheeler", was therefore devised capable of testing 264 - about 450,000 - positions in half an hour. This meant that cribs on the 4 wheel Enigma could be dealt with almost as quickly by the 4 wheel bombe as cribs on the 3 wheel Enigma by the 3 wheel bombe.

THROW-ON Systems.

46. With throw-on systems the indicators alone give sufficient information to find the key. The fact that if an encoded indicator is (ignoring dummy letters) QJVRTS, say, then Q and R must be the encodes of the same letter J and T of a second letter and V and S of third gives the equivalent (from the bombe's point of view) of three letters of crib; on traffic of as little as 20 messages a solution is theoretically possible - though it so happens that jobs of this type are very much slower on the bombe than other jobs and therefore to be avoided if possible. On traffic of 50 - 100 messages it is possible to determine the message set-ups themselves, thus putting us in the same position as after a successful Banburismus.

Summary.

47. There are two main methods of getting information to break a day's

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