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. [1] 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 right 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. [2]
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. [3]
The Cipher Bureau's manual manufacture of the sheets, which for security reasons was done by the mathematician-cryptologists themselves, [4] using razor blades, was very time-consuming. By 15 December 1938 only a third of the job had been finished.
On that date, the Germans introduced rotors IV and V, thus increasing the labor of making the sheets tenfold, since ten times as many sheets were now needed (for the now 60 possible combinations of sequences, in an Enigma machine, of 3 rotors selected from among the now 5). [3]
On 25 July 1939, five weeks before the outbreak of World War II, the Polish General Staff's Cipher Bureau disclosed to their French and British allies, at Warsaw, their cryptologic achievements in breaking Enigma ciphers. [5] Part of the disclosures involved Zygalski's "perforated-sheet" method.
The British, at Bletchley Park, near London, England, undertook the production of two complete sets of perforated sheets. The work was done, with the aid of perforators, by a section headed by John R.F. Jeffreys. [6] [7] The sheets were known at Bletchley as Netz (from Netzverfahren, "net method"), though they were later remembered by Gordon Welchman as "Jeffreys sheets"; the latter term, however, referred to another catalog produced by Jeffreys' section. [6]
The first set was completed in late December 1939. On 28 December part of the second set was delivered to the Polish cryptologists, [7] who had by then escaped from German-overrun Poland to PC Bruno outside Paris, France. The remaining sheets were completed on 7 January 1940, [8] and were couriered by Alan Turing to France shortly thereafter. [7] "With their help," writes Rejewski, "we continued solving Enigma daily keys." [3] The sheets were used by the Poles to make the first wartime decryption of an Enigma message, on 17 January 1940. [7] [9]
In May 1940, the Germans once again completely changed the procedure for enciphering message keys (with the exception of a Norwegian network). As a result, Zygalski's sheets were of no use, though the Herivel tip could still be used. [10]
| The Enigma cipher machine |
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| Methods and technology |
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| Locations |
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Chief Gwido Langer German Section cryptologists Wiktor Michałowski Chief of Russian Section Jan Graliński Russian Section cryptologist Piotr Smoleński |
The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the German military. The Enigma machine was considered so secure that it was used to encipher the most top-secret messages.
Jerzy Witold Różycki was a Polish mathematician and cryptologist who worked at breaking German Enigma-machine ciphers before and during World War II.
Henryk Zygalski was a Polish mathematician and cryptologist who worked at breaking German Enigma ciphers before and during World War II.
The known-plaintext attack (KPA) is an attack model for cryptanalysis where the attacker has access to both the plaintext and its encrypted version (ciphertext). These can be used to reveal further secret information such as secret keys and code books. The term "crib" originated at Bletchley Park, the British World War II decryption operation, where it was defined as:
A plain language passage of any length, usually obtained by solving one or more cipher or code messages, and occurring or believed likely to occur in a different cipher or code message, which it may provide a means of solving.
The Cipher Bureau was the interwar Polish General Staff's Second Department's unit charged with SIGINT and both cryptography and cryptanalysis.
The bomba, or bomba kryptologiczna, was a special-purpose machine designed around October 1938 by Polish Cipher Bureau cryptologist Marian Rejewski to break German Enigma-machine ciphers.
Cryptanalysis of the Enigma ciphering system enabled the western Allies in World War II to read substantial amounts of Morse-coded radio communications of the Axis powers that had been enciphered using Enigma machines. This yielded military intelligence which, along with that from other decrypted Axis radio and teleprinter transmissions, was given the codename Ultra.
Antoni Palluth was a founder of the AVA Radio Company. The company built communications equipment for the Polish military; the work included not only radios but also cryptographic equipment. Palluth was involved with the German section (BS-4) of the Polish General Staff's interbellum Cipher Bureau. He helped teach courses on cryptanalysis, and he was involved with building equipment to break the German Enigma machine.
Cadix was a World War II clandestine intelligence center at Uzès, in southern France, from September 1940 to 9 November 1942. During this period southern France was under the control of Vichy France and not occupied by Nazi Germany. At Cadix, the predominantly Polish team of cryptanalysts who had previously worked at PC Bruno was reassembled, and worked against German and other Axis ciphers, including the German Enigma machine cipher. Cadix shut down when Germany occupied southern France.
The cyclometer was a cryptologic device designed, "probably in 1934 or 1935," by Marian Rejewski of the Polish Cipher Bureau's German section (BS-4) to facilitate decryption of German Enigma ciphertext. The original machines are believed to have been destroyed shortly before the German invasion of Poland that launched the Second World War, to prevent the Germans learning that their cipher had been broken.
The Lacida, also called LCD, was a Polish rotor cipher machine. It was designed and produced before World War II by Poland's Cipher Bureau for prospective wartime use by Polish military higher commands.
Władysław Kozaczuk was a Polish Army colonel and a military and intelligence historian.
The card catalog, or "catalog of characteristics," in cryptography, was a system designed by Polish Cipher Bureau mathematician-cryptologist Marian Rejewski, and first completed about 1935 or 1936, to facilitate decrypting German Enigma ciphers.
John William Jamieson Herivel was a British science historian and World War II codebreaker at Bletchley Park.
Marian Adam Rejewski was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen Nazi 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 in Europe, the Poles shared their technological achievements with the French and British at a conference in Warsaw, 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 Nazi Germany.
A Polish Enigma "double" was a machine produced by the Polish Cipher Bureau that replicated the German Enigma rotor cipher machine. The Enigma double was one result of Marian Rejewski's remarkable achievement of determining the wiring of the Enigma's rotors and reflectors.
Ludomir Danilewicz (1905–1960) was a Polish engineer and, for some ten years before the outbreak of World War II, one of the four directors of the AVA Radio Company in Warsaw, Poland. AVA designed and built radio equipment for the Polish General Staff's Cipher Bureau, which was responsible for the radio communications of the General Staff's Oddział II.
Leonard Stanisław Danilewicz was a Polish engineer and, for some ten years before the outbreak of World War II, one of the four directors of the AVA Radio Company in Warsaw, Poland.
The AVA Radio Company was a Polish electronics firm founded in 1929 in Warsaw, Poland. AVA designed and built radio equipment for the Polish General Staff's Cipher Bureau, which was responsible for the radio communications of the General Staff's Oddział II.
X, Y & Z: The Real Story of How Enigma Was Broken is a 2018 book by Dermot Turing about the Enigma machine, which was used by Nazi Germany in World War II, and about the French, British, and Polish teams that worked on decrypting messages transmitted using the Enigma cipher.