132 | 13 INTRODUCING BANBURISmUS
But it could not be used in all circumstances. Work on Army and Air Force Enigma could not
use it because those German encipherers were free to choose their own ground setting when
enciphering a message’s starting position, instead of having one imposed on all from the centre.
In Naval Enigma it could be used only against the three-wheel (and not the four-wheel) version,
only when the bigram tables were known, either by reconstruction or thanks to a ‘pinch’, and
even then only if at least some 300 messages on the same version of the cipher were available. A
‘pinch’ was the capture of actual German enciphering documents (or other Enigma material)
from a vessel or a fighting unit in the field. Banburismus was mainly employed against Dolphin,
the German Navy’s ‘home waters’ cipher.
Setting ‘in depth’
Let us consider the first part of the definition. Depth was the cryptanalyst’s staple diet—not
just for Enigma but for a wide variety of ciphers. Where two or more messages (whether in
the form of letters or numbers or encoded phrases) had been enciphered in exactly the same
way (whether by manual or electrical substitution or by other methods, like the addition of
additives or whatever) they were said to be ‘in depth’. Because their encipherments had been
identical, certain features of the structure of the underlying language or code (such as the fre-
quencies of its commonest elements) would reappear in the enciphered texts. Very often it
was this opportunity to study two or more messages enciphered in exactly the same way that
enabled the cryptanalyst to begin to penetrate the cipher. A simple illustrative example of depth
is given in Chapter 38.
In Enigma, a depth occurred when two messages were enciphered with the same plugboard
settings, the same wheels in the machine (in the same order), and starting positions for the
wheels that caused some parts of two messages to overlap and be identically enciphered. Depths
in connection with a different cipher, ‘Tunny’, are described in Chapters 14 and 16.
Mahon’s history offers a detailed source of information on how depths were used in breaking
Enigma. Mahon joined Hut 8 in October 1941: his history prior to that date relies on conversa-
tions he had with Turing. Mahon tells us that Turing devised the Banburismus approach before
the end of 1939, on the same night that he worked out the naval indicator system. Turing com-
mented at the time that:^5
I was not sure that it would work in practice, and was not in fact sure until some days had actually
broken.
Enigma’s enciphering system, with its several components and many details, changed daily.
Turing’s shorthand ‘days had actually broken’ stood for the solving of a day’s details which
made it possible to decipher all that day’s messages. In fact, it was not until November 1940 that
Hugh Foss, an old hand from the 1930s who had temporarily joined Hut 8, successfully broke
a day using Banburismus. Thanks to several pinches in the months that followed, Banburismus
passed from the research stage into operational use.
Turing’s invention stemmed from combining two observations. First: when two Enigma
messages were in depth, a pair of letters that matched when the two clear texts were written
one above the other, properly aligned, would match again in the enciphered texts, because they
had been enciphered in exactly the same way. Secondly: letters in language occur unevenly.
Writers and students of writing have often turned the spiky distribution of language to their