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{{Infobox Person
| name        = Marian Rejewski
| image       = MR 1932 small.jpg
| image_size  = 150px
| caption     = Marian Rejewski (probably 1932, the year he first solved the [[Enigma machine]]). <br/>''Courtesy of Janina Sylwestrzak, Rejewski's daughter.''
| birth_name  = Marian Adam Rejewski
| birth_date  = {{birth date|1905|08|16}}
| birth_place = [[Bromberg]], [[German Empire]]
| death_date  = {{death date and age|1980|02|13|1905|08|16}}
| death_place = [[Warsaw]], [[Poland]]
| other_names = 
| known_for   = solving the [[Enigma Machine|Enigma machine-cipher]]
| occupation  = mathematician, cryptologist
}}
'''Marian Adam Rejewski''' ({{IPAudio|Rejewski.ogg|[ˈmarjan reˈjefski]}}; 16 August 1905 &ndash; 13 February 1980) was a [[Poland|Polish]] [[mathematician]] and [[cryptography|cryptologist]] who in 1932 solved the plugboard-equipped [[Enigma machine]], the main [[cipher]] device used by Germany. The success of Rejewski and his colleagues [[Jerzy Różycki]] and [[Henryk Zygalski]] jump-started [[United Kingdom|British]] reading of Enigma in [[World War II]]; the [[military espionage|intelligence]] so gained, code-named "[[ULTRA|Ultra]]", contributed, perhaps decisively, to the [[End of World War II in Europe|defeat of Nazi Germany]].<sup>[[#Notes|(Note 1)]]</sup>

While studying mathematics at [[Poznań University]], Rejewski had attended a secret [[cryptology]] course conducted by the [[Polish General Staff]]'s [[Biuro Szyfrów|Cipher Bureau]], which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he  deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular [[decryption]] of Enigma messages. Rejewski's contributions included devising the cryptologic "[[card catalog (cryptology)|card catalog]]," derived using his "[[cyclometer]]," and the "[[bomba (cryptography)|cryptologic bomb]]."

Five weeks before the [[Invasion of Poland (1939)|German invasion of Poland]] in 1939, Rejewski and his colleagues presented their results on Enigma decryption to [[France|French]] and [[Great Britain|British]] [[military espionage|intelligence]] representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to [[France]], where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the [[fall of France]] in June 1940, but within months returned to work undercover in [[Vichy France]]. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician [[Henryk Zygalski]] fled, via [[Spain]], [[Portugal]] and [[Gibraltar]], to [[UK|Britain]].  There  they worked at a Polish Army unit, solving low-level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967. 

==Education and early work==
[[File:Zamek Cesarski w Poznaniu całość.jpg|thumb|left|250px|[[Imperial Castle in Poznań|Poznań Castle]], site of [[Poznań University]]'s mathematics institute]]
Marian Rejewski was born 16 August 1905, in [[Bromberg]], now [[Bydgoszcz]].<sup>[[#Notes|(Note 2)]]</sup> His parents were Józef, a [[cigar]] merchant, and Matylda, ''née'' Thoms. He attended a German-speaking ''{{lang|de|Königliches Gymnasium zu Bromberg}}'' (Royal Grammar School in [[Bydgoszcz| Bromberg]]) and completed high school with his ''{{lang|pl|[[matura]]}}'' in 1923. Rejewski then studied [[mathematics]] at [[Adam Mickiewicz University in Poznań|Poznań University]], graduating on 1 March 1929.

In early 1929, shortly before he graduated, Rejewski began attending a secret cryptology course organized for selected German-speaking mathematics students by the [[Polish General Staff]]'s [[Biuro Szyfrów|Cipher Bureau]] (''{{lang|pl|Biuro Szyfrów}}'').<ref>The course began on 15 January 1929.  A letter dated "[[Warsaw]], 29 January 1929, To Professor [[Zdzisław Krygowski|Z. Krygowski]], in [[Poznań]], ul. Głogowska 74/75," and signed by the "[[Chief of the General Staff (Poland)|Chief of the General Staff]], ''Piskor'' [i.e., [[Tadeusz Piskor]]], ''[[Generał dywizji|Generał Dywizji]]''," reads:  "I hereby thank ''Pan Profesor'' for his efforts and assistance given to the General Staff in organizing the [[cipher]] [i.e., [[cryptology]]] course opened in Poznań on 15 January 1929."  The letter is reproduced in Stanisław Jakóbczyk and Janusz Stokłosa, ''Złamanie szyfru Enigma'' (The Breaking of the Enigma Cipher), 2007, p. 44.</ref>  The course was conducted off-campus at a military facility<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 230.</ref> and, as Rejewski would discover in France in 1939 during [[World War II]], "was entirely and literally based" on French General Marcel Givièrge's 1925 book, ''Cours de cryptographie'' (Course of Cryptography).<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 238.</ref>   Rejewski and fellow students [[Henryk Zygalski]] and [[Jerzy Różycki]] were among the few who could keep up with the course while balancing the demands of their normal studies.<ref>Kozaczuk, 1984, p. 4.</ref>  
[[Image:Dyplom Rejewskiego.jpg|thumb|right|Rejewski's ''Master of Philosophy'' diploma in [[mathematics]]]]
Rejewski graduated with a master's degree in mathematics on 1 March 1929; his thesis was titled, "Theory of double periodic functions of the second and third kind and its applications."  A few weeks later, without having completed the cryptology course, Rejewski began the first year of a two-year [[actuary|actuarial statistics]] course at [[Göttingen]], Germany.  He would not complete the actuarial-statistics course, for, while home for the summer in 1930, he accepted the offer of a mathematics teaching assistantship at [[Poznań University]]. 

He also began working part-time for the [[Biuro Szyfrów|Cipher Bureau]], which by then had concluded the cryptology course and set up an outpost at Poznań to decrypt intercepted German [[radio]] messages.<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 230–31.</ref> Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber".<ref>Kozaczuk, 1984, pp. 5&ndash;6</ref>

In the summer of 1932, the Poznań branch of the Cipher Bureau was disbanded. On 1 September 1932, as a civilian employee, Rejewski joined the [[Biuro Szyfrów|Cipher Bureau]] at the General Staff building ([[Pałac Saski|the Saxon Palace]]) in [[Warsaw]], as did Zygalski and Różycki.<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 231.</ref> 

Their first assignment was to solve a four-letter [[code (cryptography)|code]] used by the ''{{lang|de|[[Kriegsmarine]]}}'' (German Navy). Progress was initially slow, but sped up considerably after a test exchange was intercepted&mdash;a six-group signal, followed by a four-group response. The cryptologists guessed correctly that the first signal was the question, "When was [[Frederick the Great]] born?" followed by the response, "1712."<ref>Kozaczuk, 1984, pp. 10&ndash;11</ref>

==Enigma machine== 
[[Image:Palac Saski.jpg|thumb|left|250px|Warsaw's [[Saxon Palace]], where the [[Biuro Szyfrów|Cipher Bureau]] was housed in 1932. The palace was destroyed in [[World War II]] and is to be rebuilt.]]
In late October or early November 1932, while work on the Naval code was still underway, Rejewski was set to work, alone and in secret, on the output of the new standard German cipher machine, the [[Enigma machine|Enigma]] I, which was coming into widespread use.<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 232.</ref> 
While the Cipher Bureau had, by later report, succeeded in solving an earlier, plugboard-less Enigma,<sup>[[#Notes|(Note 3)]]</sup> it had had no success with the Enigma I.<ref>Kozaczuk, 1984, p. 12</ref>
[[Image:EnigmaMachineLabeled.jpg||150px|thumb|The [[Enigma machine]], solved by Rejewski in 1932]]
The Enigma machine was an [[electromechanical]] device, equipped with a 26-letter [[typewriter keyboard|keyboard]] and a set of 26 lamps, corresponding to the letters of the [[Latin alphabet|alphabet]]. Inside was a set of wired drums ("[[rotor machine|rotors]]" and a "[[reflector (cipher machine)|reflector]]") that scrambled the input. The machine also featured a [[plugboard]] to swap pairs of letters. To encipher a letter, the operator pushed the relevant key and noted down which of the lamps lit. Each key press caused one or more rotors to advance, and thus the encipherment varied from one key press to the next. 

In order for two operators to communicate, both Enigma machines had to be set up in exactly the same way. The large number of possibilities for setting the rotors and the plugboard combined to form an astronomical number of configurations, each of which would produce a different cipher. The settings were changed daily,<ref>One element of the key, the sequence of rotors in the machine, at first was changed quarterly; but from 1 January 1936 it was changed monthly; from 1 October 1936, daily; and later, during [[World War II]], as often as every eight hours. Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref> with the consequence that the machine had to be "broken" anew each day if the messages were to be read continually.

To decrypt Enigma messages, three pieces of information were needed: 
# A general understanding of how Enigma functioned
# The wiring of the rotors
# The daily settings:  the sequence and orientations of the rotors (of which there were three initially), and the plug connections on the plugboard
Rejewski had only the first at his disposal, based on information already acquired by the Cipher Bureau.<ref>Kozaczuk, 1984, pp. 12, 19&ndash;21</ref>

==Solving Enigma's wiring==
[[Image:AD-cycle.svg|thumb|200px|right|A [[cycle (mathematics)|cycle]] formed by the first and fourth letters of a set of indicators. Rejewski exploited these cycles to deduce the Enigma rotor wiring in 1932, and thereafter to solve the daily message settings.]]
First Rejewski tackled the problem of finding the wiring of the rotors. To do this, he pioneered the use of [[pure mathematics]] in [[cryptanalysis]]. Previous methods had largely exploited [[linguistics|linguistic pattern]]s and the [[statistics]] of [[natural language|natural-language]] texts &mdash; [[frequency analysis (cryptanalysis)|letter-frequency analysis]]. Rejewski, however, applied techniques from [[group theory]] &mdash; [[theorem]]s about [[permutation]]s &mdash; in his attack on Enigma. 

These mathematical techniques, combined with material supplied by Captain [[Gustave Bertrand]],<ref>Bertrand had obtained the material from a German ''Chiffrierdienst'' (Cryptographic Service) employee, [[Hans-Thilo Schmidt]]. Kozaczuk, 1984, pp. 16–17.</ref>  chief of French radio intelligence,<ref>In the 1920s, French radio intelligence had been decentralized. Decryption of foreign, chiefly German and Italian, ciphers and codes had been the responsibility of a General Staff cryptology department, while radio monitoring had been conducted by the intelligence service, ''Service de Renseignement'' or ''S.R.'' At the end of 1930, decryption was turned over to the ''S.R.'', which created a Section ''D'' (for ''Decryptement''), of which Bertrand became chief. He later took over all of French radio intelligence. Kozaczuk, 1984, p. 22.</ref> enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector. 

"The solution", writes historian [[David Kahn]], "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time".<ref>Kahn, 1996, p. 974</ref> Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem that won World War II".<ref>Good and Deavours, 1981, pp. 229, 232</ref>

Prior to receiving the French intelligence material, Rejewski had made a careful study of Enigma messages, particularly of the first six letters of  messages intercepted on a single day.<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 232.</ref> 

For security, each message was encrypted using different starting positions of the rotors, as selected by the operator. This ''message setting'' was three letters long. To convey it to the receiving operator, the sending operator began the message by sending the message setting in a disguised form &mdash; a six-letter ''indicator''. 

The indicator was formed using the Enigma with its rotors set to a common global setting for that day, termed the ''ground setting'', which was shared by all operators. 

The particular way that the indicator was constructed, introduced a  weakness into the cipher.

For example, suppose the operator chose the message setting <tt>KYG</tt> for a message. The operator would first set the Enigma's rotors to the ground setting, which might be <tt>GBL</tt> on that particular day, and then encrypt the message setting on the Enigma ''twice''; that is, the operator would enter <tt>KYGKYG</tt> (which might come out to something like <tt>QZKBLX</tt>). The operator would then reposition the rotors at <tt>KYG</tt>, and encrypt the actual message. A receiving operator could reverse the process to recover first the message setting, then the message itself. The repetition of the message setting was apparently meant as an error check to detect [[garble]]s, but it had the unforeseen effect of greatly weakening the cipher.  Due to the indicator's repetition of the message setting, Rejewski knew that, in the [[plaintext]] of the indicator, the first and fourth letters were the same, the second and fifth were the same, and the third and sixth were the same. These relations could be exploited to break into the cipher.

Rejewski studied these related pairs of letters. For example, if there were four messages that had the following indicators on the same day: <tt>BJGTDN</tt>, <tt>LIFBAB</tt>, <tt>ETULZR</tt>, <tt>TFREII</tt>, then by looking at the first and fourth letters of each set, he knew that certain pairs of letters were related. <tt>B</tt> was related to <tt>T</tt>, <tt>L</tt> was related to <tt>B</tt>, <tt>E</tt> was related to <tt>L</tt>, and <tt>T</tt> was related to <tt>E</tt>: (<tt>B</tt>,<tt>T</tt>), (<tt>L</tt>,<tt>B</tt>), (<tt>E</tt>,<tt>L</tt>), and (<tt>T</tt>,<tt>E</tt>).  If he had enough different messages to work with, he could build entire sequences of relationships: the letter <tt>B</tt> was related to <tt>T</tt>, which was related to <tt>E</tt>, which was related to <tt>L</tt>, which was related to <tt>B</tt> (see diagram).  This was a "cycle of 4", since it took four jumps until it got back to the start letter. Another cycle on the same day might be <tt>A</tt><math>\rightarrow</math><tt>F</tt><math>\rightarrow</math><tt>W</tt><math>\rightarrow</math><tt>A</tt>, or a "cycle of 3".  If there were enough messages on a given day, all the letters of the alphabet might be covered by a number of different cycles of various sizes. The cycles would be consistent for one day, and then would change to a different set of cycles the next day. Similar analysis could be done on the 2nd and 5th letters, and the 3rd and 6th, identifying the cycles in each case and the number of steps in each cycle.

Using the data thus gained, combined with Enigma operators' tendency to choose predictable letter combinations as indicators (such as girlfriends' initials or a pattern of keys that they saw on the Enigma keyboard), Rejewski was able to deduce six [[permutation]]s corresponding to the encipherment at six consecutive positions of the Enigma machine. These permutations could be described by six [[equation]]s with various unknowns, representing the wiring within the entry drum, rotors, reflector, and plugboard.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 254&ndash;55.</ref>

===Help from France===
At this point, Rejewski ran into difficulties due to the large number of unknowns in the set of equations that he had developed. He would later comment in 1980 that it was still not known whether such a set of six equations was soluble without further data.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref> But he was assisted by cryptographic documents that Section D of French [[military intelligence]] (the ''[[Deuxième Bureau]]''), under future General [[Gustave Bertrand]], had obtained and passed on to the [[Polish Cipher Bureau]]. The documents, procured from a [[spy]] in the German Cryptographic Service, [[Hans-Thilo Schmidt]], included the Enigma settings for the months of September and October 1932. About December 9 or 10,<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 233.</ref> <sup>[[#Notes|(Note 4)]]</sup> 1932, the documents were given to Rejewski. They enabled him to reduce the number of unknowns and solve the wirings of the rotors and reflector.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258–59.</ref>

There was another obstacle to be overcome, however. The military Enigma had been modified from the commercial Enigma, of which Rejewski had had an actual example to study. In the commercial machine, the keys were connected to the entry drum in German keyboard order ("QWERTZU…"). However, in the military Enigma, the connections had instead been wired in alphabetical order: "ABCDEF…" This new wiring sequence foiled British cryptologists working on Enigma, who dismissed the "ABCDEF…" wiring as too obvious. Rejewski, perhaps guided by an intuition about a German fondness for order, simply guessed that the wiring was the normal alphabetic ordering. He later recalled that, after he had made this assumption, "from my pencil, as by magic, began to issue numbers designating the connections in rotor ''N''. Thus the connections in one rotor, the right-hand rotor, were finally known."<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref>

The settings provided by French Intelligence covered two months which straddled a changeover period for the rotor ordering. A different rotor happened to be in the right-hand position for the second month, and so the wirings of two rotors could be recovered by the same method.<sup>[[#Notes|(Note 5)]]</sup>  Rejewski later recalled: "Finding the [wiring] in the third [rotor], and especially... in the [reflector], now presented no great difficulties. Likewise there were no difficulties with determining the correct torsion of the [rotors'] side walls with respect to each other, or the moments when the left and middle drums turned."  By year's end 1932, the wirings of all three rotors and the reflector had been recovered. A sample message in an Enigma instruction manual, providing a [[plaintext]] and its corresponding [[ciphertext]] produced using a stated daily key and message key, helped clarify some remaining details.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref>

There has been speculation as to whether the rotor wirings could have been solved without the documents supplied by French Intelligence. Rejewski recalled in 1980 that another way had been found that could have been used to achieve this, but that the method was "imperfect and tedious" and relied on chance. (In 2005, mathematician John Lawrence published a paper arguing that it would have taken four years for this method to have had a reasonable likelihood of success.<ref>Lawrence, 2005</ref>) Rejewski wrote that "the conclusion is that the intelligence material furnished to us should be regarded as having been decisive to solution of the machine."<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref>

==Solving daily settings==
After Rejewski had determined the wiring in the remaining rotors, he was joined in early 1933 by Różycki and Zygalski in devising methods and equipment to break Enigma ciphers routinely.<sup>[[#Notes|(Note 6)]]</sup> Rejewski later recalled:
<blockquote>Now we had the machine, but we didn't have the [[key (cryptography)|key]]s and we couldn't very well require Bertrand to keep on supplying us with the keys every month ... The situation had reversed itself: before, we'd had the keys but we hadn't had the machine &mdash; we solved the machine; now we had the machine but we didn't have the keys.  We had to work out methods to find the daily keys.<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 234&ndash;235</ref></blockquote>

===Early methods===
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 (cryptology)|grill]]", based on the fact that the plugboard's connections exchanged only six pairs of letters, leaving fourteen letters unchanged.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref> 

Next was Różycki's "[[clock (cryptology)|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.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984,  p. 262.</ref>

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.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref> 
[[Image:Cyclometer machine Drawing from M Rejewski’s papers.jpg|thumb|250px|[[Cyclometer]] (mid-1930s), devised by Rejewski to catalog the [[cycle (mathematics)|cycle]] structure of [[Enigma machine|Enigma]] [[permutation]]s. 1: Rotor lid closed, 2: Rotor lid open, 3: Rheostat, 4: Glowlamp, 5: Switches, 6: Letters.]] 
However, a method using a [[card catalog (cryptology)|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.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref>

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&ndash;20 minutes.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref><ref>Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp.  284&ndash;87.</ref> 

However, on November 1 or 2, 1937,<!-- some sources say 1 Nov, some 2 Nov; e.g. p290 vs p264 of Kozaczuk 1984--> the Germans replaced the [[reflector (cipher machine)|reflector]] in their Enigma machines, which meant that the entire catalog had to be recalculated from scratch.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref>

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%.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 265.</ref>

==="Bomb" and sheets===
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 put into effect new rules for enciphering message keys (a new "indicator procedure"), rendering the card-catalog method completely useless.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref> <sup>[[#Notes|(Note 7)]]</sup>  The Polish cryptologists rapidly responded with new techniques. 
[[Image:Cryptologic bomb machine - drawing from M.Rejewski's papers.jpg|thumb|left|150px|[[Cryptologic bomb]]. <br/>1: Rotors (for clarity, only one 3-rotor set is shown). <br/>2: Electric motor. <br/>3: Switches.]]

One was Rejewski's ''{{lang|pl|[[bomba (cryptography)|bomba]]}}'' ("bomb"), an electrically powered aggregate of six Enigmas, which made it possible to solve the daily keys in about two hours. Six [[bomba (cryptography)|bomb]]s were built and ready for use by mid-November 1938.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref><ref>Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 290.</ref> The [[bomba (cryptography)|bomb]] method, like the grill method, exploited the fact that the plug connections did not change all the letters. But while the grill method required unchanged ''pairs'' of letters, the bomb method required only unchanged letters.  Hence it could be applied even though the number of plug connections in this period was five to eight.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref>
[[Image:Płachta_Zygalskiego_-_decrypting_Enigma.jpg|thumb|right|A [[Zygalski sheets|Zygalski sheet]]]] 
But from 1 January 1939 the number of plug connections was increased to seven to ten, greatly decreasing the usefulness of the bombs. Moreover, two weeks earlier, on 15 December 1938, the Germans had increased the number of rotors from three to five, thereby increasing the bombs' workload tenfold.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 242.</ref> Building an additional 54 bombs, in order to increase the number tenfold to 60 from the original 6, would have utterly exceeded the [[Polish Cipher Bureau]]'s available funds.<ref>Kozaczuk, 1984, p. 63, note 6.</ref>

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 (cryptography)|bomb]], though according to [[Gordon Welchman]] the cryptanalytic methods embodied by the two machines were different.<ref>Welchman, 1986</ref>

Around the same time as the Polish [[bomba (cryptography)|bomb]], a manual method was invented by [[Henryk Zygalski|Zygalski]], that of "[[perforated sheets]]" ("Zygalski sheets"), which, like the card-catalog method, was independent of the number of plug connections. But production of these sheets was very time-consuming, so that by 15 December 1938 only one-third of the job had been done.<ref>Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 243.</ref>

===Allies informed===
[[Image:SekretEnigmyRejewski.jpg|thumb|right|280px|''The Enigma Secret'' (1979)—at 25 July 1939 [[Pyry]] meeting, Rejewski (''left'') explains Enigma to Poland's allies]] 
As it became clear that war was imminent and that Polish resources were insufficient to keep pace with the evolution of Enigma encryption (e.g., due to the prohibitive expense of an additional 54 bombs and due to the Poles' difficulty in producing in time the required 60 series of 26 "[[Zygalski sheets]]" each<ref>Marian Rejewski, "Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by [[Harry Hinsley|F.H. Hinsley]]," ''Cryptologia'', January 1982, p. 80. Cited in Kozaczuk, 1984, p. 63, note 7.</ref>), the Polish General Staff and government decided to let their Western allies in on the secret. 

The Polish methods were revealed to [[France|French]] and [[British Intelligence|British]] intelligence representatives in a meeting at [[Pyry]], south of [[Warsaw]], on 25 July 1939. France was represented by [[Gustave Bertrand]] and [[Henri Braquenié]]; Britain, by [[Alastair Denniston]], [[Alfred Dillwyn Knox]] and [[Royal Navy]] electronics expert Humphrey Sandwith. The Polish hosts included [[Stefan Mayer]], [[Gwido Langer]], [[Maksymilian Ciężki]] and the three cryptologists.<ref>Kozaczuk, 1984, p. 59.</ref><ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 236.</ref><ref>Ralph Erskine, "The Poles Reveal their Secrets: [[Alastair Denniston]]'s Account of the July 1939 Meeting at [[Pyry]]," ''Cryptologia'', vol. 30, no. 4 (December 2006), pp. 294–305.</ref>

The Poles' gift of Enigma decryption to their Western allies, five weeks before the outbreak of World War II, came not a moment too soon. Knowledge that the cipher was crackable was a morale boost to Allied cryptologists. The British were able to manufacture at least two complete sets of perforated sheets&mdash;they sent one to [[PC Bruno]], outside Paris,<ref>Kozaczuk, 1984, p. 84.</ref> in mid-December 1939&mdash;and began reading Enigma within months of the outbreak of war. 
[[Image:Warszawa - defilada.jpg|thumb|left|350px|[[Warsaw]], October 1939—[[Adolf Hitler|Hitler]] inspects his troops before [[Polish General Staff]] building, where [[Enigma machine|Enigma]] was broken 7 years earlier]]
Without the Polish assistance, British cryptologists would, at the very least, have been considerably delayed in reading Enigma. Author Hugh Sebag-Montefiore concludes that substantial breaks into German Army and Air Force Enigma ciphers by the British would have occurred only after November 1941 at the earliest, after an Enigma machine and key lists had been captured, and similarly into Naval Enigma only after late 1942.<ref>Sebag-Montefiore, 2000</ref> Former [[Bletchley Park]] cryptologist [[Gordon Welchman]] goes further, writing that the Army and Air Force Enigma section, [[Hut 6]], "would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military... Enigma machine, and of the operating procedures that were in use."<ref>Welchman, 1982, p. 289.</ref>

Intelligence gained from solving high-level German ciphers&mdash;intelligence codenamed "[[Ultra]]" by the British and Americans&mdash;came chiefly from Enigma decrypts. While the exact contribution of Ultra intelligence to Allied victory is disputed, Kozaczuk and Straszak note that "it is widely believed that Ultra saved the world at least two years of war and possibly prevented [[Hitler]] from winning."<ref>Kozaczuk and Straszak 2004, p. 74</ref>  The English historian Sir [[Harry Hinsley]], who worked at Bletchley Park, similarly assessed it as having "shortened the war by not less than two years and probably by four years".<ref>[http://www.cl.cam.ac.uk/Research/Security/Historical/hinsley.html The Influence of ULTRA in the Second World War<!-- Bot generated title -->]</ref>  The availability of Ultra was, at the least, due largely to the earlier Polish breaking of Enigma.

==In France and Britain==
===PC Bruno===
{{main|PC Bruno}}
[[Image:Gwido Langer Gustave Bertrand Kenneth McFarlan.jpg|thumb|left|200px|''[[PC Bruno]]''—from left, Polish Lt. Col. [[Gwido Langer]], French Major [[Gustave Bertrand]], British Capt. Kenneth McFarlan]]
In September 1939, after [[Polish September Campaign|the outbreak of World War II]], Rejewski and his fellow Cipher Bureau workers were evacuated from Poland to [[Romania]], crossing the border on September 17 (the day the [[Soviet Union]] invaded eastern Poland).<ref>Kozaczuk, 1984, p. 71.</ref>  
 
Rejewski, Zygalski and Różycki managed to avoid being interned in a refugee camp and made their way to [[Bucharest]], where they contacted the British embassy.  Having been told by the British to "come back in a few days," they next tried the French embassy, introducing themselves as "friends of ''Bolek''" (Bertrand's Polish code name) and asking to speak with a French military officer.  A French Army colonel telephoned Paris and immediately issued instructions for the three Poles to be assisted in evacuating to Paris.<ref>Kozaczuk, 1984, pp. 71–73, 79.</ref>  

On 20 October 1939 the three Polish cryptologists resumed work on German ciphers at a joint French-Polish-Spanish radio-intelligence unit stationed at Gretz-Armainvillers, forty kilometers northeast of Paris, and housed in the ''Château de Vignolles'' (code-named "''[[PC Bruno]]''").<ref>Kozaczuk, 1984, pp. 81–82.</ref> On January 17, 1940, the Poles found the first Enigma key to be solved in France, one for October 28, 1939.<ref>Kozaczuk, 1984, pp. 84; 94, note 8.</ref> 

The staff at PC Bruno collaborated by [[teletype]] with their opposite numbers at [[Bletchley Park]] in England. For communications security, the allied Polish, French and British cryptologic agencies used the Enigma machine itself—Bruno closing its Enigma-encrypted messages to Britain with an ironic "''[[Heil Hitler]]!''"<ref>Kozaczuk, 1984, p. 87</ref> 

On 24 June 1940, after Germany's victory in the [[Battle of France]], [[Gustave Bertrand]] flew Bruno's international personnel—fifteen Poles, and seven Spaniards who worked on [[Italy|Italian]] ciphers<ref>Kozaczuk, 1984, p. 82.</ref>—in three planes to [[Algeria]].<ref>Kozaczuk, 1984, p.  109.</ref>

===Cadix===
{{main|Cadix}}
[[Image:Zygalski-rozycki-rejewski.jpg|thumbnail|200px| [[Henryk Zygalski]] (''left''), [[Jerzy Różycki]] (''center''), Rejewski at ''[[Cadix]]'']]
During September 1940 they returned to work in secret in unoccupied southern (Vichy) France. Rejewski's cover was as Pierre Ranaud, a ''[[lycée]]'' professor from [[Nantes]]. A radio intelligence station was set up at the Château des Fouzes near [[Uzès]], code-named "''[[Cadix]]''".  Cadix began operations on 1 October. Rejewski and his colleagues solved German [[Telegraphy|telegraph]] ciphers, and also the Swiss version of the Enigma machine (which had no plugboard). Rejewski may have had little or no involvement in working on German Enigma at Cadix.<sup>[[#Notes|(Note 8)]]</sup>

In early July 1941, Rejewski and Zygalski were asked to try solving messages enciphered on the secret Polish [[Lacida]] cipher machine, which was used for secure communications between [[Cadix]] and the [[Polish General Staff]] in London. Lacida was a [[rotor machine]] based on the same cryptographic principle as Enigma, yet had never been subjected to rigorous security analysis. The two cryptologists created consternation by breaking the first message within a couple of hours; further messages were solved in a similar way.<ref>Kozaczuk, 1984, pp. 134&ndash;35</ref>
[[Image:Pol-Fra-radioint Cadix 40-42.jpg|thumb|left|200px|Polish-French-Spanish ''Cadix'' center. 11 individuals are identified at "''[[Cadix]]''."]]              
On 9 January 1942, [[Jerzy Różycki|Różycki]], the youngest of the three mathematicians, died in the sinking of a French [[passenger ship]] as he was returning from a stint in Algeria to Cadix in southern France.<ref>Kozaczuk, 1984, p. 128</ref><!--why did the ship sink? how did it affect Rejewski?-->

By summer 1942 work at [[Cadix]] was becoming dangerous, and plans for evacuation were drawn up. Vichy France itself was liable to be occupied by German troops, and Cadix's radio transmissions were increasingly at risk of detection by the ''Funkabwehr'', a German unit tasked with locating enemy radio transmitters. Indeed, on 6 November a [[pickup truck]] equipped with a circular [[antenna (radio)|antenna]] arrived at the gate of the chateau where the cryptologists were operating. The visitors, however, did not enter, and merely investigated &mdash; and terrorized &mdash; nearby farms. Nonetheless, the order to evacuate Cadix was given, and this was done by 9 November. The Germans occupied the chateau only three days later.<ref>[[Gustave Bertrand]], ''Enigma ou la plus grande énigme de la guerre 1939&ndash;1945'' (Enigma:  the Greatest Enigma of the War of 1939&ndash;1945), Paris, Librairie Plon, 1973, pp. 137–41.</ref>

===Escaping France===
The Poles were split into twos and threes. On 11 November Rejewski and Zygalski were sent to [[Nice]], which was in the Italian-occupied zone. They had to flee again after coming under suspicion, constantly moving or staying in hiding, to [[Cannes]], [[Antibes]], Nice again, [[Marseilles]], [[Toulouse]], [[Narbonne]], [[Perpignan]] and [[Ax-les-Thermes]], close to the Spanish border.<ref>Kozaczuk, 1984, pp. 148–50.</ref> 

The plan was to smuggle themselves over the [[Pyrenees]] into [[Spain]]. On 29 January 1943, accompanied by a local guide, Rejewski and Zygalski began their trek across the Pyrenees, avoiding German and Vichy patrols. Near midnight and near the Spanish border, the guide pulled out a [[pistol]] and demanded that they hand over the rest of their money. After being robbed they succeeded in reaching the Spanish side of the border, only to be arrested within hours by security police.<ref>Kozaczuk, 1984, pp. 150–51.</ref>  

The Poles were sent first to a prison in [[La Seu d'Urgell]] until 24 March, then moved to a prison at [[Lerida]]. The pair were eventually released on 4 May 1943, after the intervention of the [[Polish Red Cross]], and sent to [[Madrid]].<ref>Kozaczuk, 1984, pp. 151–54.</ref> Leaving Madrid on 21 July,<ref>Kozaczuk, 1984, pp. 155.</ref> they made it to [[Portugal]]; from there aboard ''HMS Scottish'' to [[Gibraltar]]; and thence aboard an old [[Douglas DC-3|Dakota]] to [[RAF Hendon]], in north [[London]], arriving on 3 August 1943.<ref>Kozaczuk, 1984, pp. 205–6.</ref>  

[[Image:Marian Rejewski.jpg|thumb|right|Marian Rejewski as second lieutenant (signals), Polish Army in Britain, in late 1943 or in 1944, some 11 or 12 years after he first broke [[Enigma machine|Enigma]].]]

===Britain===
Rejewski and Zygalski were inducted as [[private (rank)|private]]s into the [[Polish Army]] on 16 August 1943 and were posted to a Polish Army facility in [[Boxmoor]], cracking German ''[[Schutzstaffel|SS]]'' and ''[[Sicherheitsdienst|SD]]'' hand ciphers. The ciphers were usually based on the ''Doppelkassettenverfahren'' ("double [[Playfair cipher|Playfair]]") system, which the two cryptologists had already worked on in France.<ref>Kozaczuk, 1984, pp. 207–9.</ref> On 10 October 1943, Rejewski and Zygalski were commissioned [[second lieutenant]]s;<ref>Kozaczuk, 1984, p. 209.</ref> on 1 January 1945 Rejewski, and presumably also Zygalski, were promoted to [[lieutenant]].<ref>Kozaczuk, 1984, p. 220.</ref>  

Enigma decryption, however, had become an exclusively British and American domain; the two mathematicians who, with their late colleague, had laid the foundations for Allied Enigma decryption were now excluded from making further contributions to their métier.<ref>Kozaczuk, 1984, pp. 207–8.</ref>  British cryptologist [[Alan Stripp]] suggests that by that time, at [[Bletchley Park]], "very few even knew about the Polish contribution" because of the strict secrecy and the "[[need-to-know]]" principle. Stripp comments further that "Setting them to work on the ''Doppelkassetten'' system was like using racehorses to pull wagons."<ref>Stripp, 2004, p. 124.</ref>

==Back in Poland==
[[Image:Poland Bydgoszcz Rejewski monument.jpg|thumb|250px|Memorial to Rejewski in [[Bydgoszcz]], unveiled on 2005 [[centennial]] of his birth there. It resembles memorial to fellow-mathematician [[Alan Turing]] at [[Whitworth Gardens]], Manchester.]]
On 21 November 1946, Rejewski, having been on 15 November discharged from the [[Polish Army]] in Britain, returned to Poland to be reunited with his wife, Irena Maria Rejewska (née Lewandowska, whom Rejewski had married on 20 June 1934) and their son ''Andrzej'' (Andrew, born 1936) and daughter ''Janina'' (Jeanne, born 1939, who would later follow in her father's footsteps to become a mathematician).<ref>Kozaczuk, 1984, p. 226.</ref> 

{{blockquote|Rejewski [writes Kozaczuk] could after the war have worked academically and was urged to do so by Prof. [[Zdzisław Krygowski|[Zdzisław] Krygowski]], who proposed a [university] mathematics [position] at [[Poznań]] or [[Szczecin]]. [Rejewski]] was, however, exhausted psychically, in ill health (in the Spanish prisons he had contracted, among other things, rheumatism...). A grievous blow to him also was, not long after his return, in the summer of 1947, the almost sudden, after five days' illness ([[poliomyelitis]]), death of his 11-year-old son Andrzej. After that he did not want to part from his wife and daughter, as would have been necessary if he had accepted Krygowski's offer, which might... have promised him a rapid academic career in view of the postwar shortages in personnel, decimated by the enemy. In [[Bydgoszcz]] they lived with their fairly well-to-do in-laws (Mrs. Rejewska's father was a dentist).<ref>Kozaczuk, 1984, p. 226.</ref>|}}

Rejewski took a position in [[Bydgoszcz]] as director of the sales department at a cable manufacturing company, ''Kabel Polski'' (Polish Cable).<ref>Kozaczuk, 1984, p. 226.</ref> 

Between 1949 and 1958, Rejewski was repeatedly investigated by the Polish [[Służba Bezpieczeństwa|Security Service]] but never divulged that he had worked on Enigma; in 1950 they demanded that he be fired from his employment<!--why? please expand-->.<ref>Polak, 2005, p. 78.</ref> He then worked briefly as a director at the State Surveying Company, then at the Association of Polish Surveyors. From 1951 to 1954 he worked at the Association of Timber and Varied Manufactures Cooperatives. From 1954 until his retirement on a disability pension in February 1967, he was director of the inspectorate of costs and prices at a Provincial Association of Labor Cooperatives.

In 1969 Rejewski and his family moved back to [[Warsaw]], to the apartment that he had acquired in May 1939 with financial help from his father-in-law. (After the Germans suppressed the 1944 [[Warsaw Uprising (1944)|Warsaw Uprising]], they had sent Mrs. Rejewska and her children, along with other Warsaw survivors, west, where the family had eventually found refuge with her parents in Bydgoszcz.)<ref>Kozaczuk, 1984, p. 226.</ref>

Rejewski understandably took satisfaction from his accomplishments in breaking the German [[Enigma machine|Enigma cipher]] for nearly seven years (beginning in December 1932) prior to the outbreak of [[World War II]] and then into the war, in personal and teletype collaboration with [[Bletchley Park]], at least until the 1940 fall of France. In 1942, at [[Uzès]], [[Vichy France]], he wrote a "Report of Cryptologic Work on the German Enigma Machine Cipher."<ref>Kozaczuk, 1984, p. 326.</ref> Before his retirement in 1967 a quarter-century later, he began writing his "Memoirs of My Work in the Cipher Bureau of Section II of the [Polish] [[Polish General Staff|General Staff]]," which were purchased by the Military Historical Institute, located in Warsaw.<ref>Kozaczuk, 1984, p. 226.</ref>

Rejewski must often have wondered, after the 1940 French debacle, what use [[Alan Turing]] (who had visited the Polish cryptologists outside [[Paris]]) and [[Bletchley Park]] had ultimately made of the Polish discoveries and inventions.  For nearly three decades after the war, little was publicly known due to a ban that had been imposed on 25 May 1945 by British Prime Minister [[Winston Churchill]].<ref>[[F.W. Winterbotham]], ''The Ultra Secret'', p. 15.</ref> 
[[Image:2008-09 Kaiserschloss Kryptologen.JPG|thumb|left|250px|Bronze monument to the three cryptologists, erected in 2007 before the [[Imperial Castle in Poznań|Poznań Castle]]]]
What little was published attracted little attention. [[Ladislas Farago]]'s 1971 best-seller ''The Game of the Foxes'' presented a garbled account of [[Ultra]]'s origins: "Commander [[Alastair Denniston|Denniston]] went clandestinely to a secluded Polish castle [!] on the eve of the war [to pick up an Enigma, "the Wehrmacht's top system" during World War II]. [[Alfred Dillwyn Knox|Dilly Knox]] later solved its keying..."<ref>[[Ladislas Farago]], ''The Game of the Foxes'', p. 674.</ref> Still, this was closer to the truth than most of the British and American accounts that would follow after 1974. Their authors were at a disadvantage: they did not know that the founder of Enigma decryption, Marian Rejewski, was still alive and alert and that historical confabulation was therefore hazardous.

With [[Gustave Bertrand]]'s 1973 publication of his ''Enigma'', substantial information about the origins of [[Ultra]] began to seep out to the broader world public.  With [[F.W. Winterbotham]]'s 1974 best-seller ''The Ultra Secret'', the dam began to burst. Still, many authors likewise aspired to best-sellerdom and were not averse to filling gaps in their information with whole-cloth fabrications. Rejewski fought a gallant (if into the 21st century still not entirely successful) fight to get the truth before the public. He published a number of papers on his cryptologic work and contributed generously to articles, books and television programs. He was interviewed by scholars, journalists and television crews from Poland, East Germany, the United States, Britain, Sweden, Belgium, the Soviet Union, Yugoslavia and Brazil.<ref>Kozaczuk, 1984, p. 225.</ref>
 
He maintained a lively correspondence with his wartime French host, General [[Gustave Bertrand]], and at the General's bidding began translating Bertrand's ''Enigma'' into Polish.<ref>Kozaczuk, 1984, p. 225.</ref> A few years before his death, at the request of the Józef Piłsudski Institute of America, Rejewski broke [[encipher]]ed correspondence of [[Józef Piłsudski]] and his fellow [[Polish Socialist Party|Polish Socialist]] conspirators from 1904.<ref>Kozaczuk, 1990</ref> On 12 August 1978, a year and a half before his death, he received the Officer's Cross of the Order of [[Polonia Restituta]].<ref>Kozaczuk, 1984, p. 225.</ref> 

Rejewski, who had been suffering from [[heart disease]], died of a [[myocardial infarction|heart attack]] at his home on 13 February 1980, aged 74. He was buried with military honors at [[Warsaw]]'s [[Powązki Cemetery]].<ref>Kozaczuk, 1984, p. 226.</ref> 

In 2000, Rejewski and his colleagues Zygalski and Różycki were posthumously awarded the Grand Cross of the Order of [[Polonia Restituta]]. On 4 July 2005, Rejewski's daughter Janina Sylwestrzak received on his behalf, from the [[British Chief of the Defence Staff]], the [[War Medal 1939–1945]].<ref>[http://news.mod.uk/news/press/news_headline_story.asp?newsItem_id=3339 Untold Story of Enigma Code-Breaker], published 5 July 2005, retrieved 9 January 2006.</ref>

In 1979 Rejewski and his colleagues became heroes of ''Sekret Enigmy'' ("The Enigma Secret"), a Polish-cryptologists-and-German-spies movie [[Thriller (genre)|thriller]] about the Poles' solution of the German [[Enigma machine|Enigma cipher]]. Late 1980 also saw a Polish [[Serial (radio and television)|TV series]] with a similar theme, ''Tajemnice Enigmy'' ("The Secrets of Enigma").<ref>[[Christopher Kasparek]] and [[Richard Woytak]], "In Memoriam Marian Rejewski," p. 24.</ref> 

In 1983, a Polish [[postage stamp]] marked the 50th anniversary of the German military Enigma's first solution; the [[First Day Cover]] featured likenesses of the three mathematician-cryptologists.  Memorials to the trio have been unveiled at [[Bletchley Park]] and the Polish Embassy in the [[United Kingdom]], and at [[Uzès]] in France. In Rejewski's home city of Bydgoszcz, a street and school have been named for him, a plaque placed on the building where he had lived, and a sculpture commissioned (pictured above). In 2005 a postcard (below) was issued, commemorating the [[centennial]] of Rejewski's birth.

In 2007, a three-sided bronze monument was dedicated before [[Imperial Castle in Poznań|Poznań Castle]].  Each side bears the name of one of the three mathematics students who had attended the 1929 cryptology course and subsequently collaborated on breaking the Enigma cipher.<ref>Stanisław Jakóbczyk and Janusz Stokłosa, eds., ''Złamanie szyfru Enigma.  Poznański pomnik polskich kryptologów'' (The Breaking of the Enigma Cipher:  the Poznań Monument to the Polish Cryptologists), 2007.</ref>

{| style="margin:1em auto 0 auto"
|- style="vertical-align:top"
| [[Image:bp-polish-codebreakers-plaque.jpg|thumb|220px|<!-- Attempt give both boxes the same height.
--><div style="height:3.5em;float:right;clear:right;font-size:inherit;background:inherit;border:none;margin:0;"><!--
--></div>Plaque at [[Bletchley Park]], unveiled 2002. English side reads: "This plaque commemorates the work of Marian Rejewski, Jerzy Różycki and Henryk Zygalski, mathematicians of the Polish intelligence service, in first breaking the [[Enigma machine|Enigma]] [[code]] [''sic:'' it was a ''[[cipher]]'']. Their work greatly assisted the Bletchley Park code breakers and contributed to the Allied victory in World War II."]]
| [[Image:Rejewski-postcard.jpg|thumb|260px|<!-- Attempt give both boxes the same height.
--><div style="height:3.5em;float:right;clear:right;font-size:inherit;background:inherit;border:none;margin:0;"><!--
--></div>Polish prepaid postcard (2005) commemorating [[centennial]] of Rejewski's birth.]]
| [[Image:Rejewski-grave-100.JPG|thumb|220px|<!-- Attempt give both boxes the same height.
--><div style="height:3.5em;float:right;clear:right;font-size:inherit;background:inherit;border:none;margin:0;"><!--
--></div>[[Ceremony|Military ceremony]] (2005) at Rejewski's grave on centennial of his birth.]]
|}

==See also==
{{Cipher Bureau}}
*[[Biuro Szyfrów]] (Polish Cipher Bureau)
*[[Cryptanalysis of the Enigma]]
*[[List of cryptographers]]
*[[Polish contribution to World War II#Intelligence|Polish contribution to World War II]]
*[[Polish School of Mathematics]]
*[[Tadeusz Pełczyński#Enigma|Tadeusz Pełczyński]]
*[[Alan Turing]]

==Notes==
<div class="references-small">
# The exact extent of the contribution of Ultra to Allied victory is debated. The typical view is that Ultra shortened the war;  Supreme Allied Commander [[Dwight D. Eisenhower]] called Ultra "decisive" to Allied victory.<ref>Brzezinski, 2005, p. 18</ref> For a fuller discussion, see [[Ultra#Ultra's consequences|Ultra's consequences]].
# [[Bydgoszcz]] (called "Bromberg" in German) was then part of the [[Prussia]]n [[Province of Posen]]. Bydgoszcz &mdash; which had been seized by [[Prussia]] in the 1772 [[Partitions of Poland|First Partition of the Polish-Lithuanian Commonwealth]] &mdash; returned to Poland in 1919 after the [[Greater Poland Uprising (1918–1919)|Greater Poland Uprising]]. 
# An early Naval Enigma model (the "O Bar" machine) had been solved before 1931 by the Polish Cipher Bureau, but it did not have the plugboard of the later standard Enigma.<ref>Mahon, 1945, p. 12</ref> Mahon cites, as his source for "most of the information I have collected about prewar days", [[Alan Turing]], who had received it from the "Polish cryptographers", who Mahon says had done "nearly all the early work on German Naval Enigma [and] handed over the details of their very considerable achievements just before the outbreak of war." 
# Some writers, after Bloch (1987), argue that Rejewski is more likely to have received these documents in mid-November, rather than on 9 or 10 December, 1932. Rejewski, however, recalls: "I later... learned that... it was on December 8 [1932, that] Bertrand had come to Warsaw and delivered this material. [H]e describes it in his book [''Enigma''. T]here is a mistake [in the book] and he gives the year [as] 1931. But later I corresponded with him, and it turned out that it had been... the eighth of December, 1932." Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 233. 
# Lawrence (2004) shows how Rejewski could have adapted his method to solve for the second rotor, even if the settings lists had not straddled the quarterly changeover period.
# More Enigma settings were provided to the Polish Cipher Bureau by French Intelligence, but these were never passed on to Rejewski and his colleagues. A possible explanation for this is that the Poles wished to remain independent of French assistance for reading Enigma, and without outside help the cryptologists were forced to develop their own self-sufficient techniques.
# The Navy had already changed its Enigma indicator procedure on 1 May 1937. The SD net, which lagged behind the other services, changed procedure only on 1 July 1939.
# Rejewski later wrote that at Cadix they did not work on Enigma.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 270.</ref> Other sources indicate that they had, and Rejewski conceded that this was likely the case. Rejewski's correspondent concluded that "Rejewski either had forgotten or had not known that, e.g., Zygalski and Różycki had read Enigma after the fall of France".<ref>Kozaczuk, 1984, p. 117</ref>
</div>

==Footnote citations==
{{reflist|3}}

==Bibliography==
{{EnigmaSeries}}
:''The main source used for this article was Kozaczuk (1984).''
* [[Gustave Bertrand]], ''Enigma ou la plus grande énigme de la guerre 1939&ndash;1945'' (Enigma:  the Greatest Enigma of the War of 1939&ndash;1945), Paris, Librairie Plon, 1973. 
* Gilbert Bloch, "Enigma before Ultra: Polish Work and the French Contribution", translated by C.A. Deavours, ''Cryptologia'', July 1987, pp. 142&ndash;155.
* Zbigniew Brzezinski, "The Unknown Victors". pp.15&ndash;18, in Jan Stanislaw Ciechanowski, ed. ''Marian Rejewski 1905&ndash;1980, Living with the Enigma secret.'' 1st ed. Bydgoszcz: Bydgoszcz City Council, 2005, ISBN 83-7208-117-4.
* Stephen Budiansky, ''Battle of Wits: the Complete Story of Codebreaking in World War II'', New York, [[The Free Press]], 2000.
* Chris Christensen, "Polish Mathematicians Finding Patterns in Enigma Messages", ''Mathematics Magazine'', 80 (4), October 2007.
* Ralph Erskine, "The Poles Reveal their Secrets: [[Alastair Denniston]]'s Account of the July 1939 Meeting at [[Pyry]],"   ''Cryptologia'', vol. 30, no. 4 (December 2006), pp. 294–305.
* [[Ladislas Farago]], ''The Game of the Foxes: The Untold Story of German Espionage in the United States and Great Britain during World War II'', New York, Bantam Books, 1971.
* [[James Gannon]], ''Stealing Secrets, Telling Lies:  How Spies and Codebreakers Helped Shape the Twentieth Century'', Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4, pp. 27-58 and ''passim''.
* [[I. J. Good]] and Cipher A. Deavours, afterword to:  Marian Rejewski, "How Polish Mathematicians Deciphered the Enigma", ''Annals of the History of Computing'', 3 (3), July 1981. (This paper of Rejewski's appears as Appendix D in Kozaczuk, 1984.)
* [[Harry Hinsley|F.H. Hinsley]] and Alan Stripp, eds., ''Codebreakers:  The Inside Story of Bletchley Park'', [[Oxford University Press]], 1993, ISBN 0-19-820327-6.
* Stanisław Jakóbczyk and Janusz Stokłosa, editors, ''Złamanie szyfru Enigma.  Poznański pomnik polskich kryptologów'' (The Breaking of the Enigma Cipher:  the Poznań Monument to the Polish Cryptologists), [[Poznań]], Wydawnictwo Poznańskiego Towarzystwa Przyjaciół Nauk, 2007, ISBN 978-83-7063-527-5.  This 140-page book was published in connection with the 2007 dedication, before the [[Imperial Castle in Poznań|Poznań Castle]], of a three-sided bronze monument, each side bearing the name of one of the three Polish mathematician-cryptologists who attended the cryptology course there and subsequently collaborated on breaking the Enigma cipher.  The volume recounts the history of the cipher's breaking before and during [[World War II]] and the importance of this achievement in the prosecution of the war, provides brief biographies of a number of [[Interbellum]] Poznań mathematicians, and includes photographs of documents and of a growing number of [[Enigma machine|Enigma]]-[[decryption]]-related memorials to be found in various Polish locales.
* [[David Kahn]], ''The Codebreakers:  The Comprehensive History of Secret Communication from Ancient Times to the Internet'', 2nd edition, New York, Scribner, 1996, ISBN 0684831309.
* [[David Kahn]], ''Seizing the Enigma:  the Race to Break the German U-Boat Codes, 1939-1943'', Boston, Houghton Mifflin, 1991, ISBN 0-395-42739-8.
* [[Christopher Kasparek]] and [[Richard Woytak]], "In Memoriam Marian Rejewski," ''Cryptologia'', vol. 6, no. 1 (January 1982), pp. 19–25.
* [[Władysław Kozaczuk]], ''Enigma:  How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two'', edited and translated by [[Christopher Kasparek]], Frederick, MD, University Publications of America, 1984, ISBN 0-89093-547-5.  (The standard reference on the Polish part in the Enigma-decryption epic.  This English-language book is substantially revised from Kozaczuk's 1979 Polish-language ''{{lang|pl|W kręgu Enigmy}}'', and greatly augmented with documentation, including many additional substantive chapter notes and papers by, and interviews with, Marian Rejewski.) 
* Władysław Kozaczuk, "A New Challenge for an Old Enigma-Buster", ''Cryptologia'', 14 (3), July 1990.
* Jerzy Kubiatowski, "Rejewski, Marian Adam", ''{{lang|pl|Polski słownik biograficzny}}'' ([[Polish Biographical Dictionary]]), vol. XXXI/1, Wrocław, Wydawnictwo Polskiej Akademii Nauk ([[Polish Academy of Sciences]]), 1988, pp. 54&ndash;56.
* John Lawrence, "A Study of Rejewski's Equations", ''Cryptologia'', 29 (3), July 2005, pp. 233&ndash;247.
* John Lawrence, "The Versatility of Rejewski's Method: Solving for the Wiring of the Second Rotor", ''Cryptologia'', 28 (2), April 2004, pp. 149&ndash;152.
* John Lawrence, "Factoring for the Plugboard &mdash; Was Rejewski's Proposed Solution for Breaking the Enigma Feasible?", ''Cryptologia'', 29 (4), October 2005.
* A.P. Mahon, "The History of Hut Eight: 1939&ndash;1945", June 1945, 117 pp., PRO HW 25/2, [http://www.cs.usfca.edu/www.AlanTuring.net/turing_archive/archive/a/A09/A09-001.html].
* A. Ray Miller, "The Cryptographic Mathematics of Enigma", 2001, [http://www.nsa.gov/publications/publi00004.cfm].
* Wojciech Polak, "Marian Rejewski in the Sights of the Security Services," in Jan Stanisław Ciechanowski, ed., ''Marian Rejewski, 1905&ndash;1980: Living with the Enigma Secret'',  [[Bydgoszcz]]: Bydgoszcz City Council, 2005, ISBN 83-7208-117-4, pp. 75–88.
* Marian Rejewski, "Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by [[Harry Hinsley|F.H. Hinsley]]," translated by [[Christopher Kasparek]], ''Cryptologia:  a Quarterly Journal Devoted to All Aspects of [[Cryptology]]'', vol. 6, no. 1 (January 1982), pp. 75-83.
*Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 229–40.
*Marian Rejewski, "Summary of Our Methods for Reconstructing ENIGMA and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods," Appendix C to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 241–45.
* Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 246–71.
* Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 272–91. Covers much the same ground as the 1980 ''Applicationes Mathematicae'' paper referenced below.
* Marian Rejewski, "An Application of the Theory of Permutations in Breaking the Enigma Cipher," ''Applicationes Mathematicae'', 16 (4), 1980, pp. 543&ndash;559 [http://frode.home.cern.ch/frode/crypto/rew80.pdf (PDF)].
* Marian Rejewski, interview (transcribed by [[Christopher Kasparek]]) in: [[Richard Woytak]], ''Werble historii'' (History's Drumroll), edited by and with introduction by Stanisław Krasucki, illustrated with 36 photographs, [[Bydgoszcz]], Poland, Związek Powstańców Warszawskich w Bydgoszczy (Association of Warsaw Insurgents in Bydgoszcz), 1999, ISBN 83-902357-8-1, pp. 123–43. A more complete transcript of the interview, highlights of which earlier appeared in ''Cryptologia'', vol. 6, no. 1 (January 1982), pp. 50–60, and as Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 229–40. 
* Marian Rejewski, ''Sprawozdanie z prac kryptologicznych nad niemieckim szyfrem maszynowym Enigma'' (Report of Cryptologic Work on the German Enigma Machine Cipher). Manuscript written at [[Uzès]], France, 1942.
* Marian Rejewski, ''Wspomnienia z mej pracy w Biurze Szyfrów Oddziału II Sztabu Głównego 1932–1945'' (Memoirs of My Work in the Cipher Bureau of Section II of the [Polish] General Staff). Manuscript, 1967.
* Hugh Sebag-Montefiore, ''Enigma: the Battle for the Code'', London, Weidenfeld and Nicolson, 2000.
* [[Simon Singh]], ''[[The Code Book]]: the Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography'', Doubleday, 1999, pp. 149&ndash;160, ISBN 0-385-49531-5.
* Alan Stripp, "A British Cryptanalyst Salutes the Polish Cryptanalysts", Appendix E to [[Władysław Kozaczuk]] and Jerzy Straszak, ''Enigma: How the Poles Broke the Nazi Code'', New York, Hippocrene Books, 2004, ISBN 0-7818-0941-X, pp. 123-25.
* [[Gordon Welchman]], ''The Hut Six Story:  Breaking the Enigma Codes'', New York, McGraw-Hill, 1982.
* Gordon Welchman, "From Polish Bomba to British Bombe: the Birth of Ultra", ''Intelligence and National Security'', 1 (1), January 1986.
* [[F.W. Winterbotham]], ''The Ultra Secret'', New York, Dell, 1974.
* Fred B. Wrixon, ''Codes, Ciphers, & Other Cryptic & Clandestine Communication: Making and Breaking Secret Messages from Hieroglyphics to the Internet'', 1998, Black Dog & Leventhal Publishers, ISBN 1-57912-040-7, pp. 83&ndash;85.

==External links==
* [http://www.armyradio.com/publish/Articles/The_Enigma_Code_Breach/The_Enigma_Code_Breach.htm The Enigma Code Breach by Jan Bury:  an account of the Polish role]
* [http://www.codesandciphers.org.uk/virtualbp/poles/poles.htm The Breaking of Enigma by the Polish Mathematicians] by Tony Sale
* [http://news.mod.uk/news/press/news_headline_story.asp?newsItem_id=3339 Untold Story of Enigma Code-Breaker &mdash; The Ministry of Defence (U.K.) ]
* [http://www.nsa.gov/cch/cch00006.cfm How Mathematicians Helped Win WWII &mdash; National Security Agency]
* [http://www.spybooks.pl/en/enigma.html Enigma documents]
* [http://www-history.mcs.st-andrews.ac.uk/Biographies/Rejewski.html Rejewski biography, University of St Andrews]
* {{pl icon}} Photographs of Rejewski: [http://ww2.tvp.pl/2739,20050927249915.strona], [http://www.wiadomosci.tvp.com.pl/389,20050704221744.strona], [http://ww6.tvp.pl/389,20051013256196.strona]

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{{DEFAULTSORT:Rejewski, Marian}}
[[Category:1905 births]]
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{{Persondata
|NAME              = Rejewski, Marian Adam
|ALTERNATIVE NAMES = 
|SHORT DESCRIPTION = Polish mathematician and cryptologist
|DATE OF BIRTH     = 16 August 1905
|PLACE OF BIRTH    = [[Bydgoszcz]], [[Poland]]
|DATE OF DEATH     = 13 February 1980
|PLACE OF DEATH    = [[Warsaw]], [[Poland]]
}}
[[Category:Pre-computer cryptographers]]
[[Category:Polish cryptographers]]
[[Category:Polish inventors]]
[[Category:Polish Army officers]]
[[Category:Recipients of Polonia Restituta]]
[[Category:Biuro Szyfrów]]
[[Category:People from Bydgoszcz]]
[[Category:People from the Province of Posen]]

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