# Cryptographic History of Work on the German Naval Enigma

whole wheel order question. Wheel orders disobeying this rule were regarded as "bogs" by the keymaker and we called the whole thing the "Bog Wheel Order Rule".

(2) "Left hand preferences". The keymaker apparently had this W.O's written out in eight blocks determined by the left hand wheel i.e. all the W.O.'s with wheel 1 on the left formed one block, those with wheel 2 another and so on. When making up his list he would dodge about as much as possible which produced the result that if for example wheel 2 was used on the left one day, 1 and 3 on the left were very unlikely the next day and 6, 7 or 8 was the best bet. Analysing 175 W.O's on different keys, the immediately preceding key having had wheel 2 on the left in every case, we get the following remarkable distribution of left hand wheels

 L. H. W. 1 2 3 4 5 6 7 8 No. of cases 1 0 4 13 16 42 41 58

Thus if the key for the 1st and 2nd of the month had been say 284 by running only W.O's with 6, 7 or 8 on the left for the 3rd/4th keys one would get an 80% chance of success.

(3) "Threes". Each month had 15 keys and there were 8 possible left hand wheels; 15 being almost exactly twice 8 proved irresistible for the keymaker who made it a rule to use 7 of the 8 wheels twice and the 8th one once in the left hand position. No wheel therefore was used 3 times on the left and late in the month this rule was very powerful.

26. These and other similar rules greatly reduced the number of W.O's that normally had to be run and there was a correspondingly great saving in bombe time. Our policy was to run first class cribs on all except really bad W.O's (running the best W.O's first of course) while second class cribs were only run on really good W.O's. An illustration will make this clear; referring back to the example at the end of Para. 25(2). With W.O. 284 on the 1st/2nd of the month we would only try 6, 7 and 8 on the left for the 3rd/4th on a mediocre crib whereas on a good crib we would try 4 and 5 as well. 1 and 3 on the left would not be tried until at least two first class cribs had gone down on other wheel orders and 2 on the left not until

-69-