# Cryptographic History of Work on the German Naval Enigma

K Book.

24. The K book contains almost all possible trigrams sorted in two different ways (1) in the Spaltenliste they are divided into 732 columns each of 24 trigrams chosen at random (2) In the Gruppenliste the trigrams are sorted into alphabetical order and cross-referenced each having two numbers after it one for the column and one for the position in the column at which the trigram occurs.

25. A Zuteilungsliste divides the 732 columns up amongst the various keys, allocating so many columns to each key. It is fairly frequently changed, whereas the K book itself has not been re-issued since 1941.

Bigram Tables.

26. These are reciprocal tables each giving equivalents for all 676 bigrams e.g. a table might read AA = PY, AB = ZR, AC = NV etc. (being reciprocal we shall also have PY = AA, ZR = AB etc.) 9 tables constitute a set and which of the set is in use on any given day is determined by a calendar. New sets of bigram tables were introduced in July 1940, June 1941, November 1941. March 1943, July 1944 and a set of 15 was to have been introduced in May 1945.

27. Now suppose a German operator wishes to send a message on a 3 wheel machine. (1) He looks up anywhere in the K book and chooses a trigram at random (the "Verfahrenkenngruppe" - usually called by us the trigram), say ARQ. He then sets his machine up at the Grund (a 3 letter group fixed for the day and part of the daily key - see Para. 14), say JNY, and at this position encodes ARQ giving, say, LVN. Then LVN is the message setting and is the position at which he will set up his machine to encode the message itself. (2) Now he proceeds to disguise ARQ (the "Verfahrenkenngruppe") and also to indicate which particular key (Home Waters, U Boat etc.) he happens to be using. To do this he chooses out of one of the columns of the Spaltenliste allotted to his key another trigram (the "Schluessel kenngruppe"). Suppose this is YVT. He then writes down

.YVT

ARQ.

and fills in the blanks with any letter he pleases, giving say

LYVT

ARQN

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