Zygalski sheets
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The method of Zygalski sheets was a
cryptologic Cryptologic Limited was a Dublin, Ireland-based software application service provider (formerly Toronto, Ontario, Canada), one of the oldest established in the online gambling industry. It was acquired by the Amaya Gaming Group in 2012 and has si ...
technique used by the
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, w ...
Cipher Bureau before and during
World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, and during the war also by British cryptologists at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
, to
decrypt In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can deci ...
messages enciphered on German Enigma machines. The Zygalski-sheet apparatus takes its name from Polish Cipher Bureau
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
–
cryptologist This is a list of cryptographers. Cryptography is the practice and study of techniques for secure communication in the presence of third parties called adversaries. Pre twentieth century * Al-Khalil ibn Ahmad al-Farahidi: wrote a (now lost) bo ...
Henryk Zygalski Henryk Zygalski (; 15 July 1908 – 30 August 1978) was a Polish mathematician and cryptologist who worked at breaking German Enigma ciphers before and during World War II. Life Zygalski was born on 15 July 1908 in Posen, German Empire (now Pozn ...
, who invented it about October 1938.


Method

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 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 Female (Venus symbol, symbol: ♀) is the sex of an organism that produces the large non-motile ovum, ova (egg cells), the type of gamete (sex cell) that fuses with the Sperm, male gamete during sexual reproduction. A female has larger gamet ...
" to occur. Polish mathematician–cryptologist
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) 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 mili ...
writes about how the perforated-sheets device was operated: Like Rejewski's " card-catalog" method, developed using his "
cyclometer 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 ...
," the Zygalski-sheet procedure was independent of the number of
plugboard A plugboard or control panel (the term used depends on the application area) is an array of jacks or sockets (often called hubs) into which patch cords can be inserted to complete an electrical circuit. Control panels are sometimes used to di ...
plug connections in the Enigma machine.
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) 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 mili ...
, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys...", Appendix C to
WÅ‚adysÅ‚aw Kozaczuk WÅ‚adysÅ‚aw Kozaczuk (23 December 1923 – 26 September 2003) was a Polish Army colonel and a military and intelligence historian. Life Born in the village of Babiki near Sokółka, Kozaczuk joined the army in 1944, during World War II, at BiaÅ ...
, ''Enigma'', 1984, p. 243.


Manufacture

The Cipher Bureau's manual manufacture of the sheets, which for security reasons was done by the mathematician-cryptologists themselves, using
razor blade A razor is a bladed tool primarily used in the removal of body hair through the act of shaving. Kinds of razors include straight razors, safety razors, disposable razors, and electric razors. While the razor has been in existence since before ...
s, 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). On 25 July 1939, five weeks before the outbreak of World War II, the
Polish General Staff Polish General Staff, formally known as the General Staff of the Polish Armed Forces ( Polish: ''Sztab Generalny Wojska Polskiego'') is the highest professional body within the Polish Armed Forces. Organizationally, it is an integral part of the M ...
's Cipher Bureau disclosed to their French and
British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the British identity and common culture * British English, ...
allies, at
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...
, their cryptologic achievements in breaking Enigma ciphers. Part of the disclosures involved Zygalski's "perforated-sheet" method. The British, at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
, near
London London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a majo ...
,
England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...
, 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 John Robert Fisher Jeffreys (25 January 1916 – 13 January 1944) was a British mathematician and World War II Cryptanalysis, codebreaker. A research fellow at Downing College, Cambridge, Jeffreys joined the codebreaking efforts at Bletchley ...
.Ralph Erskine, "The Poles Reveal their Secrets: Alastair Denniston's Account of the July 1939 Meeting at Pyry," ''Cryptologia'' 30 (4), December 2006, pp. 294–305.Ralph Erskine, "Breaking Air Force and Army Enigma," in ''Action this Day'', edited by Ralph Erskine and Michael Smith, 2001, p. 53. The sheets were known at Bletchley as Netz (from ''Netzverfahren'', "net method"), though they were later remembered by
Gordon Welchman William Gordon Welchman (15 June 1906 – 8 October 1985) was a British mathematician. During World War II, he worked at Britain's secret codebreaking centre, "Station X" at Bletchley Park, where he was one of the most important contributors. ...
as "Jeffreys sheets"; the latter term, however, referred to another catalog produced by Jeffreys' section. The first set was completed in late December 1939. On 28 December part of the second set was delivered to the Polish cryptologists, who had by then escaped from German-overrun Poland to ''
PC Bruno ''PC Bruno'' was a Polish–French–Spanish signals–intelligence station near Paris during World War II, from October 1939 until June 1940. Its function was decryption of cipher messages, most notably German messages enciphered on the Enigma ...
'' outside Paris, France. The remaining sheets were completed on 7 January 1940, and were couriered by
Alan Turing Alan Mathison Turing (; 23 June 1912 â€“ 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical com ...
to France shortly thereafter. "With their help," writes Rejewski, "we continued solving Enigma daily keys." The sheets were used by the Poles to make the first wartime decryption of an Enigma message, on 17 January 1940. 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.
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) 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 mili ...
, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys...", Appendix C to
WÅ‚adysÅ‚aw Kozaczuk WÅ‚adysÅ‚aw Kozaczuk (23 December 1923 – 26 September 2003) was a Polish Army colonel and a military and intelligence historian. Life Born in the village of Babiki near Sokółka, Kozaczuk joined the army in 1944, during World War II, at BiaÅ ...
, ''Enigma'', 1984, pp. 243, 245.


See also

*
Cryptanalysis of the Enigma 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 in ...
* ''Bomba'' ("cryptologic bomb"): machine designed about October 1938 by
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) 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 mili ...
to facilitate the retrieval of Enigma keys *
Bombe The bombe () was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functiona ...
: a machine, inspired by Rejewski's "cryptologic bomb," that was used by British and American cryptologists during World War II * Grille (cryptography) *
Punched card A punched card (also punch card or punched-card) is a piece of stiff paper that holds digital data represented by the presence or absence of holes in predefined positions. Punched cards were once common in data processing applications or to di ...
*
Jacquard loom The Jacquard machine () is a device fitted to a loom that simplifies the process of manufacturing textiles with such complex patterns as brocade, damask and matelassé. The resulting ensemble of the loom and Jacquard machine is then called a Ja ...


Notes


References

* * A revised and augmented translation of ''W kręgu enigmy'',
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...
, Książka i Wiedza, 1979, supplemented with appendices by
Marian Rejewski Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) 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 mili ...
and others. * * Appendix C of * Appendix E of


External links


Javascript demonstration of Zygalski sheets

"Polish Enigma Double"

About the Enigma (National Security Agency)


by Jan Bury
The "Enigma" and the Intelligence


* ttps://web.archive.org/web/20060418205857/http://www.smithsrisca.demon.co.uk/STMsubtypes-pt3.html A Brief History of Computing Technology, 1930 to 1939* * {{citation , first=Bill , last=Casselman , title=The Polish Attack on Enigma II: Zygalski sheets , series=Feature Column , publisher=American Mathematical Society , url=http://www.ams.org/samplings/feature-column/fcarc-enigma , access-date=2014-11-15 * The Daily Telegraph obituary of Mavis Batey https://www.telegraph.co.uk/news/obituaries/military-obituaries/special-forces-obituaries/10447712/Mavis-Batey-obituary.html Cryptographic attacks Science and technology in Poland Cipher Bureau (Poland) Polish inventions Perforation-based computational tools