Banburismus

[5] The aim of Banburismus was to reduce the time required of the electromechanical Bombe machines by identifying the most likely right-hand and middle wheels of the Enigma.

[11] In the first few months after arriving at Bletchley Park in September 1939, Alan Turing correctly deduced that the message-settings of Kriegsmarine Enigma signals were enciphered on a common Grundstellung (starting position of the rotors), and were then super-enciphered with a bigram and a trigram lookup table.

[13] The Germans did not have time to destroy all their cryptographic documents, and the captured material revealed the precise form of the indicating system, supplied the plugboard connections and Grundstellung for 23 and 24 April and the operators' log, which gave a long stretch of paired plaintext and enciphered message for the 25th and 26th.

[14] The bigram tables themselves were not part of the capture, but Hut 8 were able to use the settings-lists to read, retrospectively, all the Kriegsmarine traffic that had been intercepted from 22 to 27 April.

This allowed them do a partial reconstruction of the bigram tables and start the first attempt to use Banburismus to attack Kriegsmarine traffic, from 30 April onwards.

The First Lofoten pinch from the trawler Krebs on 3 March 1941 provided the complete keys for February – but no bigram tables or K book.

The consequent decrypts allowed the statistical scoring system to be refined so that Banburismus could become the standard procedure against Kriegsmarine Enigma until mid-1943.

This allows an attacker to take two messages whose indicators differ only in the third character, and slide them against each other looking for the giveaway repeat pattern that shows where they align in depth.

Turing's method of accumulating a score of a number of decibans allows the calculation of which of these situations is most likely to represent messages in depth.

Bletchley Park used the convention that the indicator plaintext of "VFX", being eight characters ahead of "VFG", or (in terms of just the third, differing, letter) that "X = G+8".

[22] They could then construct a "chain" as follows: If this is then compared at progressive offsets with the known letter-sequence of an Enigma rotor, quite a few possibilities are discounted due to violating either the "reciprocal" property or the "no-self-ciphering" property of the Enigma machine: The so-called "end-wheel alphabet" is already limited to just nine possibilities, merely by establishing a letter-chain of five letters derived from a mere four message-pairs.

Eventually they will hope to be left with just one candidate, maybe looking like this: Not only this, but such an end-wheel alphabet forces the conclusion that the end wheel is in fact "Rotor I".

[23] The workload of doing this is beyond manual labour, so BP punched the messages onto 80-column cards and used Hollerith machines to scan for tetragram repeats or better.

Taken together, the probable right hand and middle wheels would give a set of bombe runs for the day, that would be significantly reduced from the 336 possible.