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forward by Hugh Alexander’s leadership and ingenuity in method—multiplied in manifold
ways the quantity of naval intelligence that those bombes could produce.
We are fortunate that Banburismus has been systematically described (although with some gaps)
in the two histories of Hut 8 written around 1945 by Hugh Alexander and Patrick Mahon, succes-
sive heads of the Hut after Alan Turing.^1 ,^2 This chapter makes continual reference to these histories,
and there are more opaque references to Banburismus in some of Alan Turing’s own writing.
what Banburismus did
A burglar facing a five-letter combination safe needs only the patience to try all the combina-
tions in turn, in the confident knowledge that one of them will open the door. The theory is
simple: the difficulty lies in the scale. The burglar has 26^5 , or some 12 million, combinations to
try. The cryptanalysts in Hut 8 faced a mind-boggling 890 million million million possible daily
keys, which is 75 million million times as many as the burglar. (The arithmetic of this is given in
Chapter 38.) Only one of the daily keys was right, and the next day it would be a different one.
The part that the bombe played in this was explained in Chapter 12. The speed at which the
bombe worked was mind-boggling: it could test the 26^3 (17,576) ring settings (see Chapter 10)
for one wheel order in 15 minutes. Allowing for time to set up, 60 such runs could be made in 24
hours—but to test all 336 possible wheel orders in turn, a total of nearly 6 million (17,576 × 336)
ring settings, would still take five and a half days. The war on the Atlantic U-boats could not
wait, and Hut 6 also needed its share of the limited number of available bombes for army and air
force work. The Banburismus procedure that Alan Turing devised came to the rescue.
To fill the three slots in the machine, the German naval encipherers had selected three out
of their eight wheels and placed them in a certain order. Half-a-dozen of the best minds in
Bletchley Park on duty at any one time used Banburismus to try to discover which of the eight
wheels were in the right-hand and middle slots, thus very significantly reducing the number of
tests that the bombes needed to run in order to produce a result.
Suppose, for example, that Banburismus had precisely identified the middle wheel and estab-
lished that the right-hand wheel was some one of the three special navy wheels (see Chapter 10).
Then for each of the three possibilities for the right-hand wheel there would be six out of the
eight wheels remaining from which to choose the left-hand wheel: 18 possible combinations.
Thus only 18 tests would now be required, instead of the original potential of 336. This chapter
and Chapter 38 explain how it was done.^3
Defining Banburismus
Bletchley Park’s 1944 cryptographic dictionary had these (far from self-explanatory) definitions:^4
BANBURISMUS
- The use of Banburies to set messages (especially Enigma messages) in depth with each
other. - Action or process of identifying right-hand and middle wheels of an Enigma machine by relating dis-
tances or intervals between message settings . . . to the possible intervals between the enciphered
settings . . . .