Zygalski sheets

The method of Zygalski sheets was a cryptologic technique used by the Polish Cipher Bureau before and during World War II, and during the war also by British cryptologists at Bletchley Park, to decrypt messages enciphered on German Enigma machines.

The Zygalski-sheet apparatus takes its name from Polish Cipher Bureau mathematician–cryptologist Henryk Zygalski, who invented it about October 1938.

Zygalski's device comprised a set of 26 perforated sheets for each of the, initially, six possible sequences for inserting the three rotors into the Enigma machine's scrambler. Each sheet related to the starting position of the left (slowest-moving) rotor.

The 26 × 26 matrix represented the 676 possible starting positions of the middle and left rotors and was duplicated horizontally and vertically: a–z, a–y. The sheets were punched with holes in the positions that would allow a "female" to occur.

Polish mathematician–cryptologist Marian Rejewski writes about how the perforated-sheets device was operated:

When the sheets were superposed and moved in the proper sequence and the proper manner with respect to each other, in accordance with a strictly defined program, the number of visible apertures gradually decreased. And, if a sufficient quantity of data was available, there finally remained a single aperture, probably corresponding to the right case, that is, to the solution. From the position of the aperture one could calculate the order of the rotors, the setting of their rings, and, by comparing the letters of the cipher keys with the letters in the machine, likewise permutation S; in other words, the entire cipher key.

Like Rejewski's "card-catalog" method, developed using his "cyclometer," the Zygalski-sheet procedure was independent of the number of plugboard plug connections in the Enigma machine.

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