page_title: Marian Rejewski
section_title: Early methods
hierarchical_section_title: Marian Rejewski / Solving daily settings / Early methods
caption_attribution_description: Français&#160;: Diagramme du cyclomètre de Marian Rejewski, conçu en 1934 ou 1935. English: Diagram of Marian Rejewski's cyclometer (Inkscape)..
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: A number of methods and devices had to be invented in response to continual improvements in German operating procedure and to the Enigma machine itself. The earliest method for reconstructing daily keys was the "grill", based on the fact that the plugboard's connections exchanged only six pairs of letters, leaving fourteen letters unchanged. Next was Różycki's "clock" method, which sometimes made it possible to determine which rotor was at the right-hand side of the Enigma machine on a given day.
  After 1 October 1936, German procedure changed, and the number of plugboard connections became variable, ranging between five and eight. As a result, the grill method became considerably less effective. However, a method using a card catalog had been devised around 1934 or 1935, and was independent of the number of plug connections. The catalog was constructed using Rejewski's "cyclometer", a special-purpose device for creating a catalog of permutations. Once the catalog was complete, the permutation could be looked up in the catalog, yielding the Enigma rotor settings for that day.
  The cyclometer comprised two sets of Enigma rotors, and was used to determine the length and number of cycles of the permutations that could be generated by the Enigma machine. Even with the cyclometer, preparing the catalog was a long and difficult task. Each position of the Enigma machine (there were 17,576 positions) had to be examined for each possible sequence of rotors (there were 6 possible sequences); therefore, the catalog comprised 105,456 entries. Preparation of the catalog took over a year, but when it was ready about 1935, it made obtaining daily keys a matter of 12–20 minutes. However, on 1 or 2 November 1937, the Germans replaced the reflector in their Enigma machines, which meant that the entire catalog had to be recalculated from scratch. Nonetheless, by January 1938 the Cipher Bureau's German section was reading a remarkable 75% of Enigma intercepts, and according to Rejewski, with a minimal increase in personnel this could have been increased to 90%.
caption: Cyclometer, devised in the mid-1930s by Rejewski to catalog the cycle structure of Enigma permutations.
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