CHAPTER 38

Banburismus revisited:

depths and Bayes

edward simpson

C

hapter 13 covered all aspects of Banburismus, but without much of the mathematical

and other detail. This chapter seeks to explain depth, Bayes’ theorem, logarithmic

scoring (and its application to the Banburies discovered in the roof of Hut 6), dec-

ibanning, chains and depth cribbing, comic strips, and twiddling. This seems to be the first

publication of much of this explanation.

Depth

In Chapter 13 I promised a simple illustrative example of depth and some of the terms associ-

ated with it.

In Table 38.1 QVAJX . . . and the others are three enciphered messages as transmitted. This

table does not relate to any particular real-life cipher, and its three enciphered messages are

unrealistically short. It illustrates an imaginary system which enciphers letter by letter (as

Enigma did), using an enciphering table which would provide hundreds, or more probably

thousands, of individual enciphering units, whatever the nature of the imaginary enciphering

system. The numbers 180, 181, . . . indicate the positions of the units in the table. The encipherer

could choose where in the table to begin enciphering (say, at position 183) and, once started,

continued to use the enciphering units in sequence (183, 184, 185, . . .). The legitimate receiver

of the message had to be told where to start in the table. This was done by an ‘indicator’, which

was itself enciphered, usually by a different system, and formed part of a preamble to the mes-

sage as transmitted.

The three enciphered messages in this example, which may have come from different sources,

start at different positions in the enciphering table. They have significant overlaps, and it is

where they overlap that they are said to be ‘in depth’. Here the depths are of two messages (as in

column 182) or of three (column 183). In real life they could be of ten or twenty. All the letters

in a particular column (as QDF in column 183) have been enciphered in exactly the same way.