# The History of Hut Eight

these messages have identical content for 4 or 6 or 8 or more letters, their cypher texts will be the same for the number of letters concerned - such a coincidence between cypher texts is known as a 'fit'. Banburismus aims first of all at setting messages in depth with the help of fits and of a repeat rate much higher than the random expectation.

Long before the day is broken a certain amount can be done to the indicators of the messages. The bigram substitution can be performed and the trigrams obtained: these trigrams, when encyphered or 'transposed' at the Grundstellung will give us the starting positions of the messages. Once the day has been broken, the Grundstellung alphabets, i.e., the effect of encyphering each of the 26 letters of the alphabet at positions one, two and three of the trigrams, can he produced. The alphabets will look something like this:

 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. T V S M U I W N F L P J D H Y K Z S R A E B G C O Q 2. 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. 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

The aim of Banburismus is to obtain, with the help of the trigrams and fits between messages, alphabets 2 and 3, the middle and right hand wheel alphabets.

The chance a priori of 2 messages with completely different trigrams ZLE and OUX being correctly set in depth is 1 in 17,000, but if the trigrams are NPE and NLO the factor against them being in depth is only 1 in 676 as, although we do not know the transpose value of the trigrams, N will in each case transpose to the same letter and therefore both messages were encyphered with the left hand wheel in the same position. These messages are said to be 'at 676', messages with such trigrams as PDP and PDB are said to be 'at 26', they are known to have had starting positions close together on the machine. On our alphabets:

PDP = KWH

PDB = KWG

Therefore PDB started one place earlier than PDP. This is expressed as B + 1 = P: in the right hand wheel alphabet P will be seen one place ahead of B.

The first stage in attacking a day by Banburismus is to discover the fits. This was done largely by Freeborn who sorted all messages against all other messages and listed fits of 4 letters or more. At the same time messages were punched by hand onto Banburies, long strips of paper with alphabets printed

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