# Cryptographic History of Work on the German Naval Enigma

Chapter IX

Banburismus

Introduction.

1. Banburismus is a method of determining the right hand wheel and middle wheel Grundstellung alphabets i.e. given the message bigram (Verfahren kenngruppen) [and as explained earlier Banburismus is only possible when bigram tables - and hence the message trigrams - are known] it enables us to decypher the second and third letters. The next paragraphs will explain how information is obtained connecting the encypherments of the set ups of two different messages; an example will then be given to show how such information is put together to give the alphabets themselves. The section on "Depth Cribbing" should be read in connection with this chapter.

2. It may help the reader if the actual Grund alphabets for the examples discussed later on are written out

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1. [left hand wheel] T V X M U I W N F L P J D H Y K Z S R A E B G C O Q 2. [middle wheel] E Y K W A Q X R T U C N S L V Z F H M I J O D G B P 3. [right hand wheel] J G D C F E B P Z A V Q W O N H L T U R S K M Y X I

This means that if the trigram for a message is FRJ say the actual set up is IHA (letters underlined to show how the result is obtained). Notice that the alphabets are reciprocal [See Chap. I, Para. 5] i.e. FRJ encyphers as IHA and IHA encyphers as FRJ. When we say that for instance H is 4 ahead of Q [or H = Q + 4] in the right hand (or end) wheel alphabet we mean that its encypherment (P) is 4 letters ahead of the encypherment of Q (L) in the ordinary alphabet. Another way of looking at it is that H is 4 places ahead of Q in line 3 above. If we like instead of saying H is 4 ahead of Q we may say Q is 22 ahead of H, since the alphabet goes on cyclically from Z to A. Which way we take it depends normally on the turnover of the end wheel; if there was no turn-over in going from Q to H we should say H = Q + 4 - if no turn-over in going from H to Q we say Q = H + 22.

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