page_title: Marian Rejewski
section_title: Bomba and sheets
hierarchical_section_title: Marian Rejewski / Solving daily settings / Bomba and sheets
caption_attribution_description: English: Zygalski sheet diagramPolski: Płachta Zygalskiego- Zygalski sheets - element of decrypting German Enigma code
context_page_description: Marian Adam Rejewski was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine, aided by limited documents obtained by French military intelligence. Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski developed and used techniques and equipment to decrypt the German machine ciphers, even as the Germans introduced modifications to their equipment and encryption procedures. Five weeks before the outbreak of World War II the Poles, at a conference in Warsaw, shared their achievements with the French and British, thus enabling Britain to begin reading German Enigma-encrypted messages, seven years after Rejewski's original reconstruction of the machine. The intelligence that was gained by the British from Enigma decrypts formed part of what was code-named Ultra and contributed—perhaps decisively—to the defeat of Germany.
  In 1929, while studying mathematics at Poznań University, Rejewski attended a secret cryptology course conducted by the Polish General Staff's Cipher Bureau, which he joined in September 1932.
context_section_description: In 1937 Rejewski, along with the German section of the Cipher Bureau, transferred to a secret facility near Pyry in the Kabaty Woods south of Warsaw. On 15 September 1938, the Germans introduced new rules for enciphering message keys (a new "indicator procedure"), making the Poles' earlier techniques obsolete. The Polish cryptanalysts rapidly responded with new techniques. One was Rejewski's bomba, an electrically powered aggregate of six Enigmas, which solved the daily keys within about two hours. Six bombas were built and were ready for use by mid-November 1938. The bomba exploited the fact that the plugboard connections did not affect all the letters; therefore, when another change to German operating procedure occurred on 1 January 1939, increasing the number of plugboard connections, the usefulness of the bombas was greatly reduced. The British bombe, the main tool that would be used to break Enigma messages during World War II, would be named after, and likely inspired by, the Polish bomba, though the cryptologic methods embodied in the two machines were different.
  Around the same time as Rejewski's bomba, a manual method was invented by Henryk Zygalski, that of "perforated sheets" ("Zygalski sheets"), which was independent of the number of plugboard connections.  Rejewski describes the construction of the Zygalski mechanism and its manipulation:
  Fairly thick paper sheets, lettered "a" through "z", were prepared for all twenty-six possible positions of rotor L [the left-hand Enigma rotor] and a square was drawn on each sheet, divided into 51 by 51 smaller squares.  The sides, top, and bottom of each large square (it could as well be a rectangle) were lettered "a" through "z" and then again "a" through "y".  This was, as it were, a system of coordinates in which the abscissas and ordinates marked successive possible positions of rotors M [the middle Enigma rotor] and N [the right-hand Enigma rotor], and each little square marked permutations, with or without constant points, corresponding to those positions.  Cases with constant points were perforated.
  [E]ach constant point had to be perforated as many as four times.  [...]  When the sheets were superposed and moved in the proper sequence and the proper manner with respect to each other, in accordance with a [precisely] 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.
  However, application of both the bomba and Zygalski sheets was complicated by yet another change to the Enigma machine on 15 December 1938. The Germans had supplied Enigma operators with an additional two rotors to supplement the original three, and this increased the complexity of decryption tenfold.  Building ten times as many bombas (60 would now be needed) was beyond the Cipher Bureau's ability—that many bombas would have cost fifteen times its entire annual equipment budget.
  Two and a half weeks later, effective 1 January 1939, the Germans increased the number of plug connections to 7–10, which, writes Rejewski, "to a great degree, decreased the usefulness of the bombs."   Zygalski's perforated ("Zygalski") sheets, writes Rejewski, "like the card-catalog method, was independent of the number of plug connections.  But the manufacture of these sheets, [...] in our [...] circumstances, was very time-consuming, so that by 15 December 1938, only one-third of the whole job had been done.  [T]he Germans' [introduction of rotors] IV and V [...] increased the labor of making the sheets tenfold [since 60, or ten times as many, sets of sheets were now needed], considerably exceeding our [...] capacities."
caption: Zygalski sheet
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