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{{Short description|Polish mathematician and cryptologist (1905–1980)}}
{{Featured article}}
{{Use dmy dates|date=August 2022}}
{{Infobox person
| name        = Marian Rejewski
| image       = Marian Rejewski 1932 small.jpg
| imagesize   = 150px
| caption     = Rejewski, {{C.|1932}}
| birth_name  = Marian Adam Rejewski
| birth_date  = {{Birth date|df=yes|1905|08|16}}
| birth_place = [[Bromberg]], [[German Empire]] (now [[Bydgoszcz]], [[Poland]])
| death_date  = {{Death date and age|df=yes|1980|02|13|1905|08|16}}
| death_place = [[Warsaw]], [[Polish People's Republic|Poland]]
| nationality = [[Polish people|Polish]]
| known_for   = Solving the [[Enigma machine|Enigma-machine]] cipher
| occupation  = [[Mathematician]] and [[Cryptography|cryptologist]]
| signature   = Rejewski (signature).jpg
| awards      = {{Plainlist|
* [[Order of Polonia Restituta#Grand Cross|Order of ''Polonia Restituta'', Grand Cross]]<ref name="Monitor Polski">{{Citation |title=Postanowienie Prezydenta Rzeczypospolitej Polskiej z dnia 14 lutego 2000 r. o nadaniu orderów |trans-title=Polish Order of the President of the Republic on 14 February 2000. On awarding orders. |language=pl |journal=[[Monitor Polski]] |url=http://isap.sejm.gov.pl/DetailsServlet?id=WMP20000130273 |date=14 February 2000 |volume=13 |issue=273 |access-date=27 February 2015 |archive-date=4 April 2015 |archive-url=https://web.archive.org/web/20150404203331/http://isap.sejm.gov.pl/DetailsServlet?id=WMP20000130273 |url-status=live }}</ref>
* [[War Medal 1939–1945]]<ref name="Untold Story">{{Citation |url=http://news.mod.uk/news/press/news_headline_story.asp?newsItem_id=3339|archive-url=https://web.archive.org/web/20051118083351/http://news.mod.uk/news/press/news_headline_story.asp?newsItem_id=3339 |archive-date= 18 November 2005 |title=Untold Story of Enigma Code-Breaker |date=5 July 2005 |access-date=9 January 2006}}</ref>
* [[Thomas Knowlton#Knowlton Award|Knowlton Award]]<ref name="PoleStar">{{Citation |title=Najwyższe odznaczenie amerykańskiego wywiadu za złamanie kodów Enigmy |trans-title=Highest American Intelligence Award for Breaking Enigma Ciphers |language=pl |journal=[[Gwiazda Polarna]] |volume=103 |issue=20 |date=22 September 2012 |page=6}}</ref>
* [[IEEE]] Milestone Award.<ref name="PAP">{{Citation |url=http://www.newsweek.pl/nauka/wyroznienie-milestone-dla-polskich-matematykow-za-zlamanie-enigmy,artykuly,345107,1.html |title=Wyróżnienie Milestone dla polskich matematyków za złamanie Enigmy |trans-title=Milestone Award for Polish mathematicians for breaking the Enigma |language=pl |date=5 August 2014 |author=Polska Agencja Prasowa |work=Newsweek |access-date=23 July 2016 |archive-date=25 August 2016 |archive-url=https://web.archive.org/web/20160825193008/http://www.newsweek.pl/nauka/wyroznienie-milestone-dla-polskich-matematykow-za-zlamanie-enigmy,artykuly,345107,1.html |url-status=live }}</ref><ref name="IEEE">{{Citation |first=Janina |last=Mazierska |author-link=Janina Mazierska |title=IEEE Milestone Dedication on the First Breaking of Enigma Code (Poland Section) |journal=The IEEE Region 10 Newsletter |url=http://www.ieeer10.org/wp-content/uploads/2015/01/IEEE-R10-Newsletter_Dec2014.pdf |date=December 2014 |pages=2–4 |access-date=1 February 2015 |archive-date=27 February 2015 |archive-url=https://web.archive.org/web/20150227211412/http://www.ieeer10.org/wp-content/uploads/2015/01/IEEE-R10-Newsletter_Dec2014.pdf |url-status=live }}</ref>
}}
}}
{{EnigmaSeries}}

'''Marian Adam Rejewski''' ({{IPA|pl|ˈmarjan rɛˈjɛfskʲi|lang|Pl-Marian_Rejewski-2.ogg}}; 16 August 1905 – 13 February 1980) was a [[Polish people|Polish]] [[mathematician]] and [[Cryptography|cryptologist]] who in late 1932 reconstructed the sight-unseen  German military [[Enigma machine|Enigma cipher machine]], aided by limited documents obtained by [[French secret service|French military intelligence]]. 

Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists [[Jerzy Różycki]] and [[Henryk Zygalski]], working at the [[Polish General Staff]]'s [[Cipher Bureau (Poland)|Cipher Bureau]], developed  techniques and equipment for decrypting the Enigma ciphers, even as the Germans introduced modifications to their Enigma machines and encryption procedures. Rejewski's contributions included the [[card catalog (cryptology)|cryptologic card catalog]] and the [[cryptologic bomb]].

Five weeks before the [[European theatre of World War II|outbreak of World War II in Europe]], the Poles shared their  achievements with French and British counterparts who had made no progress, enabling Britain to begin reading German Enigma ciphers. The intelligence gained by the British from Enigma decrypts formed part of what they code-named [[Ultra (cryptography)|Ultra]]<!--<ref>Much of Germany's cipher traffic was encrypted on the Enigma machine, and so the term ''Ultra'' has often been used almost synonymously with "[[Cryptanalysis of the Enigma|Enigma decrypts]]". However, Ultra also encompassed decrypts of the German [[Lorenz cipher|Lorenz SZ 40 and 42 machines]] that were used by the German High Command, and decrypts of [[C-36 (cipher machine)|Hagelin ciphers]] and other Italian ciphers and codes, as well as of Japanese ciphers such as [[Purple (cipher machine)|Purple]] and Japanese codes such as [[JN-25]].</ref>--> and contributed—perhaps decisively—to the [[End of World War II in Europe|defeat of Nazi Germany]].{{Refn|group=Note|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>{{Harvnb|Brzezinski|2005|p=18}}</ref> For a fuller discussion, see [[Ultra (cryptography)|Ultra]].}}

Soon after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued breaking Enigma ciphers. After the [[fall of France]] in June 1940, they and their support staff were evacuated to [[Algeria]] in North Africa; a few months later, they resumed work clandestinely in southern [[Vichy France]]. 

After the [[German military administration in occupied France during World War II|Vichy "Free Zone" was occupied by Nazi Germany]] in November 1942, Rejewski and Zygalski escaped via Spain (and Spanish imprisonment), Portugal, and Gibraltar to Britain. There they enlisted in the [[Polish Armed Forces]] and were put to work solving low-grade German [[cipher]]s.

After the war, Rejewski returned to Poland and his family. For two decades he remained silent about his prewar and wartime work so as to avoid the attention of [[Polish People's Republic|Poland's Soviet-dominated government]]. In 1967 he broke his silence, providing Poland's Military Historical Institute his memoirs of work at the Cipher Bureau. 

==Early life==
[[File:Bdg Wilenska6 4 01-2014.jpg|thumb|Rejewski's birthplace]]
[[File:Castillo Imperial, Poznan, Polonia, 2014-09-18, DD 47.jpg|thumb|Rejewski studied mathematics at [[Poznań University]].]]
[[File:Göttingen-Grave.of.Gauß.06.jpg|thumb|Rejewski laid flowers on [[Carl Friedrich Gauss|Gauss]]'s grave ([[Göttingen]]).<ref>{{Harvnb|Kozaczuk|1984|loc=p. 7, note 6}}</ref>]]

Marian Rejewski was born 16 August 1905 in Bromberg in the [[Prussia]]n [[Province of Posen]] (now [[Bydgoszcz]], Poland)<ref>{{Harvnb|Kasparek|Woytak|1982|p=19}}</ref> to Józef and Matylda, ''née'' Thoms.<ref>Information on Marian Rejewski's military service record, reproduced in {{Harvnb|Kozaczuk|1979|loc=opposite p. 257}}</ref> After completing secondary school, he studied mathematics at [[Adam Mickiewicz University in Poznań|Poznań University]]'s Mathematics Institute, housed in [[Imperial Castle in Poznań|Poznań Castle]].<ref>{{Harvnb|Kasparek|Woytak|1982|p=20}}</ref>

In 1929, shortly before graduating from university, Rejewski began attending a secret cryptology course which opened on 15 January,<ref>The exact opening date is pinpointed in a 29 January 1929 letter of appreciation to Professor Krygowski from the Chief of the Polish General Staff, Gen. [[Tadeusz Piskor]]. {{Harvnb|Jakóbczyk|Stokłosa|2007|p=44}}.</ref> organized for select German-speaking mathematics students by the Polish General Staff's [[Biuro Szyfrów|Cipher Bureau]] with the help of the Mathematics Institute's Professor [[Zdzisław Krygowski]].  The course was conducted off-campus at a military facility<ref>{{Harvnb|Woytak|1984|p=230}}</ref> and, as Rejewski would discover in France in 1939, "was entirely and literally based" on a 1925 book by French colonel {{ill|Marcel Givierge|fr}}, ''Cours de cryptographie'' (Cryptography Course).<ref>{{Harvnb|Woytak|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>{{Harvnb|Kozaczuk|1984|p=4}}</ref>

On 1 March 1929, Rejewski graduated with a Master of Philosophy degree in mathematics.<ref>Information on Marian Rejewski's Master of Philosophy diploma, 1 March 1929, reproduced in {{Harvnb|Kozaczuk|1979|loc=opposite p.&nbsp;128}}</ref> A few weeks after graduating, and without having completed the Cipher Bureau's cryptology course, he began the first year of a two-year [[actuary|actuarial statistics]] course at [[Göttingen]], Germany. He did not complete the statistics course, because while home for the summer of 1930, he accepted an offer, from Professor Krygowski, of a mathematics teaching assistantship at Poznań University.<ref name="harvnb|Woytak|1984|pp=230–231">{{Harvnb|Woytak|1984|pp=230–231}}</ref> He also began working part-time for the Cipher Bureau, which by then had set up an outpost at Poznań to decrypt intercepted German radio messages.<ref name="harvnb|Woytak|1984|pp=230–231"/> Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber".<ref>{{Harvnb|Kozaczuk|1984|pp=5–6}}</ref>

The Poznań branch of the Cipher Bureau was disbanded in the summer of 1932. In Warsaw, on 1 September 1932, Rejewski, Zygalski, and Różycki joined the Cipher Bureau as civilian employees working at the General Staff building (the [[Saxon Palace]]).<ref>{{Harvnb|Woytak|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 after a test exchange—consisting of a six-group signal, followed by a four-group response—was intercepted. The cryptologists guessed correctly that the first signal was the question, "When was [[Frederick the Great]] born?" followed by the response, "1712."<ref>{{Harvnb|Kozaczuk|1984|pp=10–11}}</ref>

On 20 June 1934 Rejewski married Irena Maria Lewandowska, daughter of a prosperous dentist.  The couple eventually had two children:  a son, Andrzej (Andrew), born in 1936; and a daughter, Janina (Joan), born in 1939.  Janina would later become a mathematician like her father.<ref name="Kozaczuk, 1984, p. 226">{{Harvnb|Kozaczuk|1984|p=226}}</ref>

==Enigma machine==
{{further|Cryptanalysis of the Enigma}}
[[File:EnigmaMachineLabeled.jpg|thumb|[[Enigma machine]], solved by Rejewski in 1932]]

The Enigma machine was an [[electromechanical]] device, equipped with a 26-letter keyboard and 26 lamps, corresponding to the letters of the alphabet. Inside was a set of wired drums ([[Enigma rotor details|rotors]] and a [[reflector (cipher machine)|reflector]]) that scrambled the input. The machine used a [[plugboard]] to swap pairs of letters, and the encipherment varied from one key press to the next.<ref>{{Harvnb|Rejewski|1984d|pp=247–251}}</ref> For two operators to communicate, both Enigma machines had to be set up in the same way. The large number of possibilities for setting the rotors and the plugboard combined to form an astronomical number of configurations, and the settings were changed daily,{{Refn|group=Note|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.<ref name="Marian Rejewski 1984, p. 242"/>}} so the machine code had to be "broken" anew each day.<ref name="kozaczuk8">{{Harvnb|Kozaczuk|1984|pp=12, 19–21}}</ref>

Before 1932, the Cipher Bureau had succeeded in solving an earlier Enigma machine that functioned without a plugboard,{{Refn|group=Note|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. {{Harvtxt|Mahon|1945}} 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."<ref>{{Harvnb|Mahon|1945|p=12}}</ref>}} but had been unsuccessful with the [[Enigma I]], a new standard German cipher machine that was coming into widespread use.<ref name="Marian Rejewski 1984, p. 232">{{Harvnb|Woytak|1984|p=232}}</ref><ref>{{Harvnb|Kozaczuk|1984|p=12}}</ref> In late October or early November 1932, the head of the Cipher Bureau's German section, Captain [[Maksymilian Ciężki]], tasked Rejewski to work alone on the [[Enigma machine|German Enigma I machine]] for a couple of hours per day; Rejewski was not to tell his colleagues what he was doing.<ref name="Marian Rejewski 1984, p. 232"/>

==Solving the wiring==
{{main|Cryptanalysis of the Enigma#Rejewski's characteristics method}}

To decrypt Enigma messages, three pieces of information were needed: (1) a general understanding of how Enigma functioned; (2) the wiring of the rotors; and (3) the daily settings (the sequence and orientations of the rotors, 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 name="kozaczuk8"/>

[[File:AD-cycle.svg|thumb|A [[cyclic permutation|cycle]] formed by the first and fourth letters of a set of [[Enigma machine#Indicator|indicators]]. Rejewski exploited these cycles to deduce the Enigma rotor wiring in 1932, and to solve the daily message settings.]]
First Rejewski tackled the problem of discovering the wiring of the rotors. To do this, according to historian [[David Kahn (writer)|David Kahn]], he pioneered the use of [[pure mathematics]] in [[cryptanalysis]].<ref>{{Harvnb|Kahn|1991|p=64}}</ref> Previous methods had largely exploited [[linguistics|linguistic pattern]]s and the statistics of [[natural language|natural-language]] texts—[[frequency analysis (cryptanalysis)|letter-frequency analysis]]. Rejewski applied techniques from [[group theory]]—theorems about [[permutation]]s—in his attack on Enigma. These mathematical techniques, combined with material supplied by [[Gustave Bertrand]],{{Refn|group=Note|Bertrand had obtained the material from a German ''Chiffrierdienst'' (Cryptographic Service) employee, [[Hans-Thilo Schmidt]].<ref>{{Harvnb|Kozaczuk|1984|pp=16–17}}</ref>}} chief of French radio intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector. "The solution", writes Kahn, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time."<ref>{{Harvnb|Kahn|1996|p=974}}</ref> Rejewski used a [[Symmetric group#Conjugacy classes|mathematical theorem]]—that two permutations are [[Conjugacy class|conjugate]] if and only if they have the same cycle structure—that mathematics professor and ''[[Cryptologia]]'' co-editor Cipher A. Deavours describes as "the theorem that won World War II".<ref>Cipher A. Deavours, in an afterword to {{Harvnb|Rejewski|1981|pp=229, 232}}.</ref>

Before 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 name="Marian Rejewski 1984, p. 232"/> 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—a six-letter [[Enigma machine#Indicator|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.<ref name="harvnb|Rejewski|1984e|p=274">{{Harvnb|Rejewski|1984e|p=274}}</ref> The particular way that the indicator was constructed introduced a weakness into the cipher.<ref>{{Harvnb|Rejewski|1984d|p=254}}</ref>

For example, suppose the operator chose the message setting {{mono|KYG}} for a message. The operator would first set the Enigma's rotors to the ground setting, which might be {{mono|GBL}} on that particular day, and then encrypt the message setting on the Enigma ''twice''; that is, the operator would enter {{mono|KYGKYG}} (which might come out to something like {{mono|QZKBLX}}). The operator would then reposition the rotors at {{mono|KYG}}, 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 garbles, 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.<ref name="harvnb|Rejewski|1984e|p=274"/>

Rejewski studied these related pairs of letters. For example, if there were four messages that had the following indicators on the same day: {{mono|BJGTDN}}, {{mono|LIFBAB}}, {{mono|ETULZR}}, {{mono|TFREII}}, then by looking at the first and fourth letters of each set, he knew that certain pairs of letters were related. {{mono|B}} was related to {{mono|T}}, {{mono|L}} was related to {{mono|B}}, {{mono|E}} was related to {{mono|L}}, and {{mono|T}} was related to {{mono|E}}: ({{mono|B}},{{mono|T}}), ({{mono|L}},{{mono|B}}), ({{mono|E}},{{mono|L}}), and ({{mono|T}},{{mono|E}}). If he had enough different messages to work with, he could build entire sequences of relationships: the letter {{mono|B}} was related to {{mono|T}}, which was related to {{mono|E}}, which was related to {{mono|L}}, which was related to {{mono|B}} (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 {{mono|A}}<math>\rightarrow</math>{{mono|F}}<math>\rightarrow</math>{{mono|W}}<math>\rightarrow</math>{{mono|A}}, 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.<ref>{{Harvnb|Rejewski|1984d|pp=251–254}}</ref>

Enigma operators also had a tendency to choose predictable letter combinations as indicators, such as girlfriends' initials or a pattern of keys that they saw on the Enigma keyboard. These became known to the allies as "Cillies" ("Sillies" misspelled). Using the data thus gained from the study of cycles and the use of predictable indicators, Rejewski was able to deduce six permutations corresponding to the encipherment at six consecutive positions of the Enigma machine. These permutations could be described by six equations with various unknowns, representing the wiring within the entry drum, rotors, reflector, and plugboard.<ref>{{Harvnb|Rejewski|1984d|pp=254–255}}</ref>

===French help===
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 solvable without further data.<ref name="Marian Rejewski 1984, p. 258">{{Harvnb|Rejewski|1984d|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 9 or 10 December 1932,<ref>{{Harvnb|Woytak|1984|p=233}}</ref>{{Refn|group=Note|Some writers, after {{Harvtxt|Bloch|Deavours|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 8 December, [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."<ref>Marian Rejewski, in {{Harvnb|Woytak|1984|p=233}}</ref>}} 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>{{Harvnb|Rejewski|1984d|pp=258–259}}</ref>

There was another obstacle to 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 name="Marian Rejewski 1984, p. 258"/>

The settings provided by French Intelligence covered two months that 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.{{Refn|group=Note|{{Harvtxt|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.}}  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 name="Marian Rejewski 1984, p. 258"/>

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 solve the wirings, but that the method was "imperfect and tedious" and relied on chance.  In 2005, mathematician John Lawrence claimed that it would have taken four years for this method to have had a reasonable likelihood of success.<ref>{{Harvnb|Lawrence|2005a}}; {{Harvnb|Lawrence|2005b}}</ref> Rejewski had earlier written that "the conclusion is that the intelligence material furnished to us should be regarded as having been decisive to solution of the machine."<ref name="Marian Rejewski 1984, p. 258"/>

==Solving daily settings==
{{main|Polish Cipher Bureau#Successes and setbacks}}
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. 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—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>{{Harvnb|Woytak|1984|pp=234–235}}</ref></blockquote>

===Early methods===
[[File:Cyclometer4.png|thumb|[[Cyclometer]], devised in the mid-1930s by Rejewski to catalog the [[cyclic permutation|cycle]] structure of Enigma [[permutation]]s.]]
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 name="Marian Rejewski 1984, p. 242">{{Harvnb|Rejewski|1984c|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>{{Harvnb|Rejewski|1984d|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 name="Marian Rejewski 1984, p. 242"/> 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 name="Marian Rejewski 1984, p. 242"/>

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.<ref name="Marian Rejewski 1984, p. 242"/><ref>{{Harvnb|Rejewski|1984e|pp=284–287}}</ref> However, on 1 or 2 November 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 name="Marian Rejewski 1984, p. 242"/> 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>{{Harvnb|Rejewski|1984d|p=265}}</ref>

===''Bomba'' and sheets===
[[File:Płachta Zygalskiego - decrypting Enigma.jpg|thumb|[[Zygalski sheets|Zygalski sheet]]]]
In 1937 Rejewski, along with the German section of the Cipher Bureau, transferred to a secret facility near [[Pyry (neighborhood)|Pyry]] in the [[Kabaty Woods]] south of Warsaw. On 15 September 1938, the Germans introduced new rules for enciphering message keys (a new "indicator procedure"), making the Poles' earlier techniques obsolete.{{Refn|group=Note|The Navy had already changed its Enigma indicator procedure on 1 May 1937. For most other branches, the message key procedure changed on 15 September 1938.<ref>{{Harvnb|Rejewski|1981|pp=225–226}}</ref> The SD net, which lagged behind the other services, changed procedure only on 1 July 1939.<ref>{{Harvnb|Rejewski|1981|p=227}}</ref>}} The Polish cryptanalysts rapidly responded with new techniques. One was Rejewski's ''{{Lang|pl|[[bomba (cryptography)|bomba]]}}'', an electrically powered aggregate of six Enigmas, which solved the daily keys within about two hours. Six ''bomba''s were built and were ready for use by mid-November 1938.<ref>{{Harvnb|Kozaczuk|1984|pp=242, 290}}</ref> The ''bomba'' exploited the fact that the plugboard connections did not affect all the letters; therefore, when another change to German operating procedure occurred on 1 January 1939, increasing the number of plugboard connections, the usefulness of the ''bomba''s was greatly reduced. The British [[bombe]], the main tool that would be used to break Enigma messages during World War II, would be named after, and likely inspired by, the Polish ''bomba'', though the cryptologic methods embodied in the two machines were different.<ref>{{Harvnb|Welchman|1986|pp=72–73, 80, 90, 94}}</ref>

Around the same time as Rejewski's ''bomba'', a manual method was invented by Henryk Zygalski, that of "[[perforated sheets]]" ("Zygalski sheets"), which was independent of the number of plugboard connections.  Rejewski describes the construction of the Zygalski mechanism and its manipulation:

{{blockquote|Fairly thick paper sheets, lettered "a" through "z", were prepared for all twenty-six possible positions of rotor L [the left-hand Enigma rotor] and a square was drawn on each sheet, divided into 51 by 51 smaller squares.  The sides, top, and bottom of each large square (it could as well be a rectangle) were lettered "a" through "z" and then again "a" through "y".  This was, as it were, a system of [[coordinate]]s in which the [[abscissa]]s and [[ordinate]]s marked successive possible positions of rotors M [the middle Enigma rotor] and N [the right-hand Enigma rotor], and each little square marked [[permutation]]s, with or without constant points, corresponding to those positions.  Cases with constant points were perforated.<ref>{{Harvnb|Rejewski|1984e|p=288}}</ref>

[E]ach constant point had to be perforated as many as four times.  [...]  When the sheets were superposed and moved in the proper sequence and the proper manner with respect to each other, in accordance with a [precisely] defined program, the number of visible apertures gradually decreased.  And, if a sufficient quantity of data was available, there finally remained a single aperture, probably corresponding to the right case, that is, to the solution.  From the position of the aperture one could calculate the order of the rotors, the setting of their rings, and, by comparing the letters of the cipher keys with the letters in the machine, likewise permutation S; in other words, the entire cipher key.<ref>{{Harvnb|Rejewski|1984e|p=289}}</ref>}}

However, application of both the ''bomba'' and Zygalski sheets was complicated by yet another change to the Enigma machine on 15 December 1938. The Germans had supplied Enigma operators with an additional two rotors to supplement the original three, and this increased the complexity of decryption tenfold.  Building ten times as many ''bomba''s (60 would now be needed) was beyond the Cipher Bureau's ability—that many ''bomba''s would have cost fifteen times its entire annual equipment budget.<ref>{{Harvnb|Kozaczuk|1984|loc=p. 63, note 6}}</ref>

Two and a half weeks later, effective 1 January 1939, the Germans increased the number of plug connections to 7–10, which, writes Rejewski, "to a great degree, decreased the usefulness of the bombs."   Zygalski's perforated ("Zygalski") sheets, writes Rejewski, "like the card-catalog method, was independent of the number of plug connections.  But the manufacture of these sheets, [...] in our [...] circumstances, was very time-consuming, so that by 15 December 1938, only one-third of the whole job had been done.  [T]he Germans' [introduction of rotors] IV and V [...] increased the labor of making the sheets tenfold [since 60, or ten times as many, sets of sheets were now needed], considerably exceeding our [...] capacities."<ref>{{Harvnb|Rejewski|1984c|pp=242–245}}</ref>

===Allies informed===
{{main|Polish Cipher Bureau#Gift to allies}}
[[File:bp-polish-codebreakers-plaque.jpg|thumb|2002 plaque, [[Bletchley Park]], "commemorat[ing] the work of Marian Rejewski, Jerzy Różycki, and Henryk Zygalski, mathematicians of the Polish intelligence service, in first breaking the 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."]]

As it became clear that war was imminent and that Polish financial resources were insufficient to keep pace with the evolution of Enigma encryption (e.g., due to the prohibitive expense of an additional 54 ''bomba''s and due to the Poles' difficulty in producing in timely fashion the full 60 series of 26 "[[Zygalski sheets]]"<ref>{{Harvnb|Rejewski|Kasparek|1982|p=80}}, cited in {{Harvnb|Kozaczuk|1984|loc=p. 63, note 7}}.</ref>), the Polish General Staff and government decided to initiate their Western allies into the secrets of Enigma decryption.<ref>{{Harvnb|Kozaczuk|1984|p=59}}</ref> The Polish methods were revealed to French and [[British Intelligence|British]] intelligence representatives in a meeting at [[Pyry (neighborhood)|Pyry]], south of Warsaw, on 25 July 1939. France was represented by Gustave Bertrand and Air Force cryptologist Captain [[Henri Braquenié]]; Britain, by [[Government Code and Cypher School]] chief [[Alastair Denniston]], veteran cryptologist [[Alfred Dillwyn Knox]], and Commander Humphrey Sandwith, head of the section that had developed and controlled the [[Royal Navy]]'s intercept and direction-finding stations. The Polish hosts included Cipher Bureau chief [[Gwido Langer]], the Bureau's German-Section chief [[Maksymilian Ciężki]], the Bureau's General-Staff-Intelligence supervisor [[Stefan Mayer]], and the three cryptologists Rejewski, Różycki and Zygalski.<ref>{{Harvnb|Kahn|1991|p=79}}; {{Harvnb|Kozaczuk|1984|p=59}}; {{Harvnb|Woytak|1984|p=236}}</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.{{Refn|group=Note|In a letter of 1 August 1939, a few days after the Warsaw conference, Alfred Dillwyn Knox wrote his Polish hosts, in Polish:  "My sincere thanks for your cooperation and patience.  A.D. Knox", and below that, in French:  "Enclosed:  (a) ''petits batons'', (b) a souvenir from England."  The souvenir was a scarf picturing a [[Derby (horse race)|Derby horse race]]—evidently emblematic of the cryptologic race that Knox had hoped to win using the little paper batons, and whose loss he was acknowledging.<ref>{{Harvnb|Kozaczuk|1984}}, illustration following p. 114</ref>  Knox may have used the paper batons to break the commercial Enigma during the [[Spanish Civil War]].<ref>{{Harvnb|Welchman|1986|p=97}}</ref>}}  The British were able to manufacture at least two complete sets of perforated sheets—they sent one to ''[[PC Bruno]]'', outside Paris,<ref>{{Harvnb|Kozaczuk|1984|p=84}}</ref> in mid-December 1939—and began reading Enigma within months of the outbreak of war.{{Refn|group=Note|[[Harry Hinsley|F. H. Hinsley]] writes:  "[D]ecrypts from the German Enigma were obtained regularly [by the British] from the spring of 1940 [though] they were confined for the next twelve months to an Enigma key used only in the [[Norwegian campaign]] and to two keys used by the German Air Force."<ref>{{Harvnb|Hinsley|1993b|p=2}}</ref>}}

Without the Polish assistance, British cryptologists would, at the very least, have been considerably delayed in reading Enigma. [[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>{{Harvnb|Sebag-Montefiore|2000}}</ref>

Intelligence gained from solving high-level German ciphers—intelligence codenamed [[Ultra (cryptography)|Ultra]] by the British and Americans—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>{{Harvnb|Kozaczuk|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>{{Harvnb|Hinsley|1993}}</ref>  The availability of Ultra was due to the earlier Polish breaking of Enigma; [[Gordon Welchman]], head of Bletchley Park's [[Hut 6]] (which solved German Army and Air Force Enigma ciphers), writes:  "Hut 6 Ultra 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 version of the commercial Enigma machine, and of the operating procedures that were in use."<ref>{{Harvnb|Welchman|1982|p=289}}</ref>{{Refn|group=Note|Welchman emphasizes that the Poles' demonstration of the German Enigma's breakability was extremely important to [[Bletchley Park]]'s subsequent "recruit[ment of] enough high-quality people to take advantage of the opportunities that came our way."  He writes of "the sheer piracy that we were able to employ in our recruiting until the spring of 1941, when [[C. P. Snow]] was put in charge of the allocation of all scientists and mathematicians.  Thanks to the Poles we got started quickly and recruited enough key people to see us through the crisis of May 1940.  The success of this first round of recruits made it possible to go on recruiting for the expansion [...] that lay ahead.  Without assistance from the Poles, our recruitment of high-quality people would have been too little and too late."  Welchman emphasizes that "Loss of continuity [in breaking Enigma] would, at all stages, have been very serious, if not disastrous."<ref>{{Harvnb|Welchman|1986|pp=98–99}}</ref>}}

==In France and Britain==

===''PC Bruno''===
{{Main|PC Bruno}}
On 5 September 1939 the Cipher Bureau began preparations to evacuate key personnel and equipment from Warsaw.  Soon a special evacuation train, the Echelon F, transported them eastward, then south.  By the time the Cipher Bureau was ordered to cross the border into allied Romania on 17 September, they had destroyed all sensitive documents and equipment and were down to a single very crowded truck. The vehicle was confiscated at the border by a Romanian officer, who separated the military from the civilian personnel. Taking advantage of the confusion, the three mathematicians ignored the Romanian's instructions. They anticipated that in an internment camp they might be identified by the [[Siguranța|Romanian security police]], in which the German ''[[Abwehr]]'' and [[Sicherheitsdienst|SD]] had informers.  The mathematicians went to the nearest railroad station, exchanged money, bought tickets, and boarded the first train headed south. After a dozen or so hours, they reached [[Bucharest]], at the other end of Romania. There they went to the [[List of diplomats of the United Kingdom to Romania|British embassy]]. Told by the British to "come back in a few days", they next tried the [[France–Romania relations|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 then issued instructions for the three Poles to be assisted in evacuating to Paris.<ref>{{Harvnb|Kozaczuk|1984|pp=70–73, 79}}</ref>

On 20 October 1939 the three Polish cryptologists resumed work on German ciphers at a joint French–Polish–[[Spanish Republican government in exile|(anti-fascist) Spanish]] radio-intelligence unit stationed at [[Gretz-Armainvilliers]], forty kilometers northeast of Paris, and housed in the Château de Vignolles (code-named ''PC Bruno'').<ref>{{Harvnb|Kozaczuk|1984|pp=81–82}}</ref>

As late as 3–7 December 1939, when Lt. Col. Langer and French Air Force Capt. [[Henri Braquenié]] visited [[London]] and [[Bletchley Park]], the British asked that the Polish cryptologists be made available to them in Britain. Langer, however, took the position that they must remain where the Polish Army in exile was forming—on French soil.<ref>{{Harvnb|Kozaczuk|1984|pp=84, 99}}</ref>

On 17 January 1940 the Poles found the first Enigma key to be solved in France, one for 28 October 1939.<ref>{{Harvnb|Kozaczuk|1984|pp=84; 94, note 8}}</ref> The ''PC Bruno'' staff collaborated by [[teleprinter]] with counterparts at Bletchley Park in England. For their mutual communications security, the Polish, French, and British cryptologic agencies used the Enigma machine itself.  ''Bruno'' closed its Enigma-encrypted messages to Britain with an ironic "''[[Heil Hitler]]!''"<ref>{{Harvnb|Kozaczuk|1984|p=87}}</ref>

In the first months of 1940, [[Alan Turing]]—principal designer of the British cryptological [[Bombe]], elaborated from the Polish ''[[bomba (cryptography)|bomba]]''—would visit ''Bruno'' to confer about Enigma decryption with the three Polish cryptologists.<ref name="Kozaczuk 1984 96–98">{{Harvnb|Kozaczuk|1984|pp=96–98}}</ref>

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

===Cadix===
{{Main|Cadix}}
Some three months later, in September 1940, they returned to work covertly 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, code-named ''[[Cadix]]'', near [[Uzès]].  ''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).<ref>{{Harvnb|Kozaczuk|1984|pp=113–114, 118–130}}</ref>  Rejewski may have had little or no involvement in working on German Enigma at ''Cadix''.{{Refn|group=Note|Rejewski later wrote that at ''Cadix'' they did not work on Enigma.<ref>{{Harvnb|Rejewski|1984d|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>{{Harvnb|Kozaczuk|1984|p=117}}</ref>}}

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>{{Harvnb|Kozaczuk|1984|pp=134–135}}</ref>

The youngest of the three Polish mathematicians who had worked together since 1929—[[Jerzy Różycki]]—died in the sinking of a French passenger ship on 9 January 1942, as he was returning  to ''Cadix'' from a stint in Algeria.<ref>{{Harvnb|Kozaczuk|1984|p=128}}</ref> By summer 1942 work at ''[[Cadix]]'' was becoming dangerous, and plans for evacuation were drawn up. Vichy France was liable to be occupied by German troops, and ''Cadix'''s radio transmissions were increasingly at risk of detection by the German ''[[Funkabwehr]]'', a unit tasked with locating enemy radio transmitters. Indeed, on 6 November a pickup truck equipped with a circular antenna arrived at the gate of the Château des Fouzes where the cryptologists were operating. The visitors, however, did not enter, and merely investigated nearby farms, badly frightening their occupants. Nonetheless, at Bertrand's suggestion French intelligence ordered the evacuation of ''Cadix''.  The order was carried out on 9 November, the day after the Allied "[[Operation Torch]]" landings in North Africa. Three days later, on 12 November, the Germans occupied the chateau.<ref name="librairie">{{Harvnb|Bertrand|1973|pp=137–141}}</ref>

===Escaping France===
The Poles were split into groups of two and three. On 11 November 1942 Rejewski and Zygalski were sent to [[Nice]], in the Italian-occupied zone.  After coming under suspicion there, they had to flee again, moving or hiding constantly.  Their trek took them to [[Cannes]], [[Antibes]], back to Nice, then on to [[Marseilles]], [[Toulouse]], [[Narbonne]], [[Perpignan]], and [[Ax-les-Thermes]], near the Spanish border.<ref>{{Harvnb|Kozaczuk|1984|pp=148–150}}</ref>  On 29 January 1943, accompanied by a local guide, Rejewski, and Zygalski, bound for Spain, began a climb over the [[Pyrenees]], avoiding German and Vichy patrols. Near midnight, close to the Spanish border, the guide pulled out a pistol and demanded that they hand over their remaining money.<ref>{{Harvnb|Kozaczuk|1984|pp=150}}</ref>

After being robbed, Rejewski and Zygalski succeeded in reaching the Spanish side of the border, only to be arrested within hours by security police.<ref>{{Harvnb|Kozaczuk|1984|pp=150–151}}</ref>  They were sent first to a prison in [[La Seu d'Urgell]], then on 24 March transferred to a prison at [[Lleida|Lerida]]. On 4 May 1943, after having spent over three months in Spanish prisons, on intervention by the [[Polish Red Cross]] the pair were released and sent to [[Madrid]].<ref>{{Harvnb|Kozaczuk|1984|pp=151–154}}</ref> Leaving there on 21 July,<ref>{{Harvnb|Kozaczuk|1984|p=155}}</ref> they made it to Portugal; from there, aboard HMS ''Scottish'', to Gibraltar; and then by air to [[RAF Hendon]] in north London, arriving on 3 August 1943.<ref>{{Harvnb|Kozaczuk|1984|pp=205–206}}</ref>

===Britain===
[[File:Marian Rejewski.jpg|thumb|Marian Rejewski, second lieutenant (signals), Polish Army in Britain, in late 1943 or in 1944, 11 or 12 years after he first broke Enigma]]
Rejewski and Zygalski were inducted as [[private (rank)|private]]s into the [[Polish Armed Forces]] 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>{{Harvnb|Kozaczuk|1984|pp=207–209}}</ref> British cryptologist [[Alan Stripp]] suggests that "Setting them to work on the ''Doppelkassetten'' system was like using racehorses to pull wagons."<ref name="Stripp 2004 124">{{Harvnb|Stripp|2004|p=124}}</ref> On 10 October 1943, Rejewski and Zygalski were commissioned second lieutenants;<ref>{{Harvnb|Kozaczuk|1984|p=209}}</ref> on 1 January 1945 Rejewski, and presumably also Zygalski, were promoted to lieutenant.<ref>{{Harvnb|Kozaczuk|1984|p=220}}</ref> When Gustave Bertrand fled to England in June 1944, he and his wife were provided with a house in Boxmoor, a short walk from the Polish radio station and cryptology office, where it seems likely that his collaboration with Rejewski and Zygalski continued.<ref name="librairie"/>

Enigma decryption, however, had become an exclusively British and American domain; the Polish mathematicians who had laid the foundations for Allied Enigma decryption were now excluded from making further contributions in this area.<ref>{{Harvnb|Kozaczuk|1984|pp=207–208}}</ref>  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.<ref name="Stripp 2004 124"/>

==Back in Poland==
After the Germans suppressed the 1944 [[Warsaw Uprising (1944)|Warsaw Uprising]], they sent Rejewski's wife and children west, along with other Warsaw survivors; the family eventually found refuge with her parents in Bydgoszcz.<ref name="Kozaczuk, 1984, p. 226"/>  Rejewski was discharged from the Polish Army in Britain on 15 November 1946. Six days later, he returned to Poland to be reunited with his wife and family.<ref name="Kozaczuk, 1984, p. 226"/> On his return, he was urged by his old Poznań University professor, [[Zdzisław Krygowski]], to take a university mathematics post at Poznań or [[Szczecin]], in western Poland. Rejewski could have looked forward to rapid advancement because of personnel shortages as a result of the war. However, he was still recovering from [[rheumatism]], which he had contracted in the Spanish prisons. Soon after his return to Poland, in the summer of 1947, his 11-year-old son Andrzej died of [[poliomyelitis|polio]] after only five days' illness.  After his son's death, Rejewski did not want to part, even briefly, with his wife and daughter, so they lived in Bydgoszcz with his in-laws.<ref name="Kozaczuk, 1984, p. 226"/> He took a position in Bydgoszcz as director of the sales department at a cable-manufacturing company, ''[[Bydgoszcz Cable Factory|Kabel Polski]]'' (Polish Cable).<ref>{{citation|first=G.|last=Łukomski|title=Poznańskie początki "Enigmy"|journal=Mars: Problematyka i Historia Wojskowości|volume=10|year=2001|pages=49–68|url=https://amu.edu.pl/__data/assets/pdf_file/0015/50532/Poznanskie-poczatki-Enigmy.pdf|access-date=2024-05-24|language=Polish}}</ref>
[[File:Poland Bydgoszcz Rejewski monument.jpg|thumb|2005 [[Bydgoszcz]] memorial unveiled on the centennial of Rejewski's birth. It resembles the [[Alan Turing Memorial]] in [[Manchester]].]]
[[File:Rejewski-postcard.jpg|thumb|2005 Polish prepaid postcard, on centennial of Rejewski's birth]]
Between 1949 and 1958 Rejewski was repeatedly investigated by the [[Ministry of Public Security (Poland)|Polish Office of Public Security]], who suspected he was a former member of the [[Polish Armed Forces in the West]].<ref>{{Harvnb|Polak|2005|p=78}}</ref> He retired in 1967, and moved with his family back to Warsaw in 1969, to an apartment he had acquired 30 years earlier with financial help from his father-in-law.<ref name="Kozaczuk, 1984, p. 226"/>

Rejewski had written a "Report of Cryptologic Work on the German Enigma Machine Cipher" in 1942.<ref>{{Harvnb|Kozaczuk|1984|p=326}}</ref>  Before his 1967 retirement, he began writing his "Memoirs of My Work in the Cipher Bureau of Section II of the [Polish] General Staff", which were purchased by the {{ill|Polish Military Historical Institute|pl|Wojskowy Instytut Historyczny}}, in Warsaw.<ref name="Kozaczuk, 1984, p. 226"/>  Rejewski had often wondered what use [[Alan Turing]] (who in early 1940 had visited the Polish cryptologists at ''[[PC Bruno]]'' outside Paris<ref name="Kozaczuk 1984 96–98"/>) and the British at 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 imposed in 1945 by British Prime Minister [[Winston Churchill]].<ref>{{Harvnb|Winterbotham|1974|p=15}}</ref>  In a 1967 book<ref>{{Harvnb|Kozaczuk|1967|pp=125 ff}}</ref> [[Władysław Kozaczuk]], associated with the Military Historical Institute, disclosed Poland's breaking of the German Enigma ciphers.

Until 1974, the scant information published concerning Enigma decryption 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 [''sic''] 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 [''sic'']..."<ref>{{Harvnb|Farago|1971|p=674}}</ref> Still, this was marginally closer to the truth than many British and American best-seller accounts that would follow after 1974. Their authors were at a disadvantage: they did not know that the founder of Enigma decryption, Rejewski, was still alive and alert, and that it was reckless to fabricate stories out of whole cloth.{{Refn|group=Note|In 1982, Polish-American historian [[Richard Woytak]] critiqued the stories that had been published in British and American best-seller books:  in [[F. W. Winterbotham]]'s ''The Ultra Secret'' (1974); in [[Anthony Cave Brown]]'s ''[[Bodyguard of Lies]]'' (1975); in [[William Stevenson (Canadian writer)|William Stevenson]]'s ''[[A Man Called Intrepid]]'' (1976); and in Appendix 1 of the official history of ''British Intelligence in the Second World War'', by [[Harry Hinsley|F. H. Hinsley]] et al., vol. 1, 1979.  (After Woytak published Rejewski's "Remarks on Appendix 1 to ''British Intelligence in the Second World War'', by F. H. Hinsley" in ''[[Cryptologia]]'', vol. 6, no. 1, January 1982, the spurious story about "a Pole who was working in an Enigma factory in Germany" was finally retracted in a subsequent volume of ''British Intelligence in the Second World War''.)<ref>[[Richard Woytak]], prefatory note (pp. 75–76) to {{Harvnb|Rejewski|Kasparek|1982}}</ref>}}

[[File:Marian Rejewski grób.jpg|thumb|left|Rejewski's grave in [[Powązki Military Cemetery]], Warsaw]]
With [[Gustave Bertrand]]'s 1973 publication of his ''Enigma'', substantial information about the origins of Ultra began to seep out; and with [[F. W. Winterbotham]]'s 1974 best-seller, ''[[F. W. Winterbotham#The Ultra Secret|The Ultra Secret]]'', the dam began to burst. Still, many aspiring authors were not averse to filling gaps in their information with whole-cloth fabrications. Rejewski fought a gallant (if, into the 21st century, 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 name="Kozaczuk, 1984, p. 225">{{Harvnb|Kozaczuk|1984|p=225}}</ref>

Rejewski maintained a lively correspondence with his wartime French host, General [[Gustave Bertrand]], and at the General's bidding he began translating Bertrand's ''Enigma'' into Polish.<ref name="Kozaczuk, 1984, p. 225"/> In 1976, 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>{{Harvnb|Kozaczuk|1990}}</ref> On 12 August 1978 he received from a grateful Polish people the Officer's Cross of the Order of ''[[Polonia Restituta]]''.<ref name="Kozaczuk, 1984, p. 225"/>

Rejewski, who had been suffering from [[heart disease]], died of a heart attack on 13 February 1980, aged 74, after returning home from a shopping trip. He was buried with military honors at [[Warsaw]]'s [[Powązki Military Cemetery]].<ref name="Kozaczuk, 1984, p. 226"/>

==Recognition==
[[File:Polish cryptologists breaking Enigma ciphers monument 01.JPG|thumb|2007 monument to cryptologists Rejewski, [[Jerzy Różycki|Różycki]], and [[Henryk Zygalski|Zygalski]] before [[Imperial Castle, Poznań|Imperial Castle]], [[Adam Mickiewicz University in Poznań|Poznań University]]]]
On 21 July 2000, Poland's President [[Aleksander Kwaśniewski]] posthumously awarded Poland's second-highest civilian decoration, the [[Order of Polonia Restitutaa#Grand Cross|Grand Cross of the Order of ''Polonia Restituta'']], to Marian Rejewski and Henryk Zygalski.<ref name="Monitor Polski"/>  In July 2005 Rejewski's daughter, Janina Sylwestrzak, received on his behalf the [[War Medal 1939–1945]] from the [[Chief of the Defence Staff (United Kingdom)|British Chief of the Defence Staff]].<ref name="Untold Story"/> On 1 August 2012 Marian Rejewski posthumously received the [[Thomas Knowlton#Knowlton Award|Knowlton Award]] of the U.S. [[Military Intelligence Corps Association]];<ref>{{Citation|url=http://www.micastore.com/AwardsAlphabeticallyR.html |title=Awards |work=MICAStore.com |publisher=Military Intelligence Corps Association |access-date=5 February 2015 |url-status=dead |archive-url=https://web.archive.org/web/20150113063737/http://www.micastore.com/AwardsAlphabeticallyR.html |archive-date=13 January 2015 }}</ref> his daughter Janina accepted the award at his home town, Bydgoszcz, on 4 September 2012. Rejewski had been nominated for the Award by [[NATO]] Allied Command Counterintelligence.<ref name="PoleStar"/>

In 2009, the [[Polish Post]] issued a series of four commemorative stamps, one of which pictured Rejewski and fellow mathematician-cryptologists [[Jerzy Różycki]] and [[Henryk Zygalski]].<ref>{{citation |url=https://www.kzp.pl/index.php?artykul=kat-zn-2009-index |title=Znaczki z 2009 roku |access-date=25 February 2019 |archive-date=1 May 2008 |archive-url=https://web.archive.org/web/20080501170221/https://www.kzp.pl/index.php?artykul=kat-zn-2009-index |url-status=live }}</ref>

On 5 August 2014 the [[Institute of Electrical and Electronics Engineers]] (IEEE) honored Rejewski, Różycki, and Zygalski with its prestigious Milestone Award, which recognizes achievements that have changed the world. The award was given for "the first breaking of Enigma ciphers by the Polish Cipher Bureau, in 1932-1939."  Their work was the foundation for British cipher-breaking efforts which helped end World War II.<!--  Only some 120 persons have been so honored.--><ref name="PAP"/><ref name="IEEE"/>

A three-sided bronze monument was dedicated in 2007 in front of the [[Imperial Castle, Poznań|Imperial Castle]] in [[Poznań]]. Each side bears the name of one of the three Polish mathematicians who broke the Enigma cipher.<ref>{{Harvnb|Jakóbczyk|Stokłosa|2007}}</ref>

Rejewski and colleagues were the heroes of ''Sekret Enigmy'' (''The Enigma Secret''), a [[Thriller (genre)|thriller movie]] about the Poles' solution of the German Enigma cipher. Late 1980 also saw a Polish TV series with a similar theme, ''Tajemnice Enigmy'' ("The Secrets of Enigma").<ref>{{Harvnb|Kasparek|Woytak|1982|p=24}}</ref>

In 2021 the [[Enigma Cipher Centre]], an educational and scientific institution dedicated to the Polish mathematicians who broke the Enigma cipher, including Marian Rejewski, opened in Poznań.<ref>{{citation | url = https://www.thefirstnews.com/article/new-centre-dedicated-to-polish-enigma-codebreakers-opens-in-poznan-24926 | title = New centre dedicated to Polish Enigma codebreakers opens in Poznań | access-date = 25 September 2021 | archive-date = 24 September 2021 | archive-url = https://web.archive.org/web/20210924195148/https://www.thefirstnews.com/article/new-centre-dedicated-to-polish-enigma-codebreakers-opens-in-poznan-24926 | url-status = live }}</ref>

==See also==
* [[List of cryptographers]]
* [[List of Poles#Mathematics|List of Poles]]
* [[Polish contribution to World War II#Intelligence|Polish contribution to World War II]]
* [[Timeline of Polish science and technology]]

==Notes==
{{Reflist|group=Note|30em}}

==References==
===Citations===
{{Reflist|30em}}

===Bibliography===
:''The main source used for this article was {{Harvtxt|Kozaczuk|1984}}.''
* {{Citation |last=Bertrand |first=Gustave |author1-link=Gustave Bertrand |title=Enigma ou la plus grande énigme de la guerre 1939–1945 |trans-title=Enigma: the Greatest Enigma of the War of 1939–1945 |language=fr |location=Paris |publisher=Librairie Plon |date=1973}}
* {{Citation |first1=Gilbert |last1=Bloch |title=Enigma before Ultra: Polish Work and the French Contribution <!--translated by -->|first2=C. A. |last2=Deavours |journal=Cryptologia |date=July 1987 |volume=11 |issue=3 |pages=142–155 |doi=10.1080/0161-118791861947}}
* {{Citation |last=Brzezinski |first=Zbigniew |author1-link=Zbigniew Brzezinski |contribution=The Unknown Victors |pages=15–18 |editor1-first=Jan Stanislaw |editor1-last=Ciechanowski |title=Marian Rejewski 1905–1980, Living with the Enigma secret |edition=1st |location=[[Bydgoszcz]] |publisher=Bydgoszcz City Council |date=2005 |isbn=978-83-7208-117-9}}
* {{Citation |last1=Farago |first1=Ladislas |author1-link=Ladislas Farago |title=The Game of the Foxes: The Untold Story of German Espionage in the United States and Great Britain during World War II |location=New York |publisher=Bantam Books |date=1971 |oclc=2371136}}
* {{Citation |last=Hinsley |first=Harry |author1-link=Harry Hinsley |chapter=The influence of Ultra in the Second World War |page=[https://archive.org/details/codebreakersinsi00hins/page/2 2] |editor1-last=Hinsley |editor1-first=F. H. |editor1-link=Harry Hinsley |editor2-first=Alan |editor2-last=Stripp |title=Codebreakers: The Inside Story of Bletchley Park |location=Oxford |publisher=Oxford University Press |date=1993b |isbn=978-0-19-820327-8 |chapter-url-access=registration |chapter-url=https://archive.org/details/codebreakersinsi00hins/page/2 }}
* {{Citation |first=Harry |last=Hinsley |date=19 October 1993 |url=http://www.cl.cam.ac.uk/research/security/Historical/hinsley.html |title=The Influence of Ultra in the Second World War |work=University of Cambridge History Research Group |access-date=5 February 2015|archive-url=https://web.archive.org/web/20110622015407/http://www.cl.cam.ac.uk/research/security/Historical/hinsley.html|archive-date=22 June 2011}}
* {{Citation |editor1-first=Stanisław |editor1-last=Jakóbczyk |editor2-first=Janusz |editor2-last=Stokłosa |title=Złamanie szyfru Enigma. Poznański pomnik polskich kryptologów |trans-title=The Breaking of the Enigma Cipher: the Poznań Monument to the Polish Cryptologists |language=pl |location=[[Poznań]] |publisher=Wydawnictwo Poznańskiego Towarzystwa Przyjaciół Nauk |date=2007 |isbn=978-83-7063-527-5}}
* {{Citation | last = Kahn | first = David | author-link = David Kahn (writer) | year = 1991 | title = Seizing the Enigma: The Race to Break the German U-boat Codes, 1939–1943 | publisher = Houghton Mifflin Co. | isbn = 978-0-395-42739-2 }}
* {{Citation |last=Kahn |first=David |author1-link=David Kahn (writer) |title=The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet |edition=2nd |location=New York |publisher=Scribner |date=1996 |isbn=978-0-684-83130-5}}
* {{Citation |last1=Kasparek |first1=Christopher |author1-link=Christopher Kasparek |last2=Woytak |first2=Richard |author2-link=Richard Woytak |title=In Memoriam Marian Rejewski |journal=Cryptologia |volume=6 |issue=1 |date=January 1982 |pages=19–25 |doi=10.1080/0161-118291856740}}
* {{Citation |last1=Kozaczuk |first=Władysław |author1-link=Władysław Kozaczuk |year=1967 |title=Bitwa o tajemnice: Służby wywiadowcze Polski i Rzeszy Niemieckiej 1922–1939 |trans-title=Secret Battle: The Intelligence Services of Poland and the German Reich, 1922–1939|language=pl |location=Warsaw |publisher=[[Książka i Wiedza]]}}
* {{Citation |first=Władysław |last=Kozaczuk |author1-link=Władysław Kozaczuk |title=W kręgu Enigmy |trans-title=In the Circle of Enigma |language=pl |location=Warsaw |publisher=[[Książka i Wiedza]] |date=1979}}  (Kozaczuk's Polish-language book that was later elaborated into the English-language {{Harvtxt|Kozaczuk|1984}}.)
* {{Citation |last1=Kozaczuk |first1=Władysław |author1-link=Władysław Kozaczuk |title=Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two |editor1-last=Kasparek |editor1-first=Christopher <!-- and translator--> |editor1-link=Christopher Kasparek |location=Frederick, MD |publisher=University Publications of America |date=1984 |url=https://archive.org/details/enigmahowgermanm0000koza |isbn=978-0-89093-547-7}}. (The standard reference on the Polish part in the Enigma-decryption epic. This English-language book is substantially revised from the Polish-language {{Harvtxt|Kozaczuk|1979}}, with additional documentation, including many substantive chapter notes and papers by, and interviews with, Marian Rejewski.)
* {{Citation |first=Władysław |last=Kozaczuk |author1-link=Władysław Kozaczuk |title=A New Challenge for an Old Enigma-Buster |journal=Cryptologia |volume=14 |issue=3 |pages=204–216 |date=July 1990 |doi=10.1080/0161-119091864913}}
* {{Citation |last1=Kozaczuk |first1=Władysław |author1-link=Władysław Kozaczuk |first2=Jerzy |last2=Straszak |title=Enigma: How the Poles Broke the Nazi Code |location=New York |publisher=Hippocrene Books |date=2004 |isbn=978-0-7818-0941-2}}
* {{Citation |first=John |last=Lawrence |title=The Versatility of Rejewski's Method: Solving for the Wiring of the Second Rotor |journal=Cryptologia |volume=28 |issue=2 |date=April 2004 |pages=149–152 |doi=10.1080/0161-110491892836|s2cid=205486319 }}
* {{Citation |first=John |last=Lawrence |title=A Study of Rejewski's Equations |journal=Cryptologia |volume=29 |issue=3 |date=July 2005a |pages=233–247 |doi=10.1080/01611190508951300|s2cid=205487467 }}
* {{Citation |first=John |last=Lawrence |title=Factoring for the Plugboard – Was Rejewski's Proposed Solution for Breaking the Enigma Feasible? |journal=Cryptologia |volume=29 |issue=4 |pages=343–366 |date=October 2005b |doi=10.1080/0161-110591893924 |s2cid=205486402 }}
* {{Citation |first=A. P. |last=Mahon |title=The History of Hut Eight: 1939–1945 |date=June 1945 |url=http://www.AlanTuring.net/turing_archive/archive/a/A09/A09-001.html |access-date=12 February 2019 |archive-url=https://web.archive.org/web/20160307134905/http://www.alanturing.net/turing_archive/archive/a/A09/A09-001.html |archive-date=7 March 2016 |url-status=dead  }}, 117 pp., PRO HW 25/2
* {{Citation |first=Wojciech |last=Polak |contribution=Marian Rejewski in the Sights of the Security Services |editor1-first=Jan Stanisław |editor1-last=Ciechanowski |title=Marian Rejewski, 1905–1980: Living with the Enigma Secret |location=[[Bydgoszcz]] |publisher=Bydgoszcz City Council |date=2005 |isbn=978-83-7208-117-9 |pages=75–88}}
* {{Citation|last=Rejewski |first=Marian |author1-link=Marian Rejewski |title=An Application of the Theory of Permutations in Breaking the Enigma Cipher |journal=Applicationes Mathematicae |volume=16 |issue=4 |date=1980 |pages=543–559 |doi=10.4064/am-16-4-543-559 |doi-access=free }}
* {{Citation |first=Marian |last=Rejewski |author-link=Marian Rejewski |title=How Polish Mathematicians Deciphered the Enigma |journal=[[IEEE Annals of the History of Computing|Annals of the History of Computing]] |volume=3 |issue=3 |pages=213–234 |date=July 1981 |url=http://chc60.fgcu.edu/images/articles/rejewski.pdf |doi=10.1109/MAHC.1981.10033 |s2cid=15748167 |access-date=7 February 2015 |archive-date=4 October 2011 |archive-url=https://web.archive.org/web/20111004194534/http://chc60.fgcu.edu/images/articles/rejewski.pdf |url-status=dead }}; has afterwords by [[I. J. Good]] and Cipher A. Deavours; also appears as {{Harvtxt|Rejewski|1984d}}
* {{Citation |first1=Marian |last1=Rejewski |author1-link=Marian Rejewski |title=Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by F. H. Hinsley <!--translator--> |first2=Christopher |last2=Kasparek |author2-link=Christopher Kasparek |journal=Cryptologia |volume=6 |issue=1 |date=January 1982 |pages=75–83 |doi=10.1080/0161-118291856867|title-link=Harry Hinsley }}
* {{Citation |last=Rejewski |first=Marian |author1-link=Marian Rejewski |chapter=Summary of Our Methods for Reconstructing Enigma and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods |id=Appendix C |editor1-last=Kozaczuk |editor1-first=Władysław |editor1-link=Władysław Kozaczuk |title=Enigma |date=1984c |pages=241–245 |isbn=978-0-89093-547-7}}
* {{Citation |last=Rejewski |first=Marian |author1-link=Marian Rejewski |chapter=How the Polish Mathematicians Broke Enigma |id=Appendix D |editor1-last=Kozaczuk |editor1-first=Władysław |editor1-link=Władysław Kozaczuk |title=Enigma |date=1984d |pages=246–271 |isbn=978-0-89093-547-7}}
* {{Citation |last=Rejewski |first=Marian |author1-link=Marian Rejewski |chapter=The Mathematical Solution of the Enigma Cipher |id=Appendix E |editor1-last=Kozaczuk |editor1-first=Władysław |editor1-link=Władysław Kozaczuk |title=Enigma |date=1984e |pages=272–291 |isbn=978-0-89093-547-7}}. Covers much the same ground as {{Harvnb|Rejewski|1980}}.
* Rejewski, Marian, interview (transcribed by [[Christopher Kasparek]]) in [[Richard Woytak|Woytak, Richard]] (1999), ''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], {{isbn|83-902357-8-1}}, pp.&nbsp;123–143. A more complete transcript of the interview, highlights of which earlier appeared in {{citation | doi = 10.1080/0161-118291856830 | volume=6 | title=A Conversation with Marian Rejewski | year=1982 | journal=Cryptologia | pages=50–60 | last1 = Woytak | first1 = Richard A.}}, and as Appendix B to Kozaczuk, Władysław, ''Enigma'', pp.&nbsp;229–240.
* {{Citation |last=Sebag-Montefiore |first=Hugh |title=Enigma: the Battle for the Code |location=London |publisher=Weidenfeld and Nicolson |date=2000 |isbn=978-0297842514 |url-access=registration |url=https://archive.org/details/enigmabattleforc0000seba }}
* {{Citation |first=Alan |last=Stripp |chapter=A British Cryptanalyst Salutes the Polish Cryptanalysts |id=Appendix E |editor1-last=Kozaczuk |editor1-first=Władysław  |editor1-link=Władysław Kozaczuk |editor2-first=Jerzy |editor2-last=Straszak |title=Enigma: How the Poles Broke the Nazi Code |location=New York |publisher=Hippocrene Books |date=2004 |isbn=978-0-7818-0941-2 |pages=123–125}}
* {{citation | last=Turing | first=Dermot |author1-link=Dermot Turing| title=[[X, Y & Z: The Real Story of How Enigma Was Broken]] | publisher=History Press | location=Gloustershire England | year=2018 | isbn=978-0-7509-8782-0 | oclc=1029570490 }}
* {{Citation |last=Welchman |first=Gordon |author1-link=Gordon Welchman |title=The Hut Six Story: Breaking the Enigma Codes |location=New York |publisher=McGraw-Hill |date=1982 |url=https://archive.org/details/hutsixstorybreak0000welc |isbn=978-0070691803}}
* {{Citation |last=Welchman |first=Gordon |author1-link=Gordon Welchman |title=From Polish Bomba to British Bombe: the Birth of Ultra |journal=Intelligence and National Security |volume=1 |issue=1 |pages=71–110 |date=January 1986 |doi=10.1080/02684528608431842}}
* {{Citation |last=Winterbotham |first=F. W. |author1-link=F. W. Winterbotham |title=The Ultra Secret |location=New York |publisher=Dell |date=1974}}
* {{Citation <!-- Marian Rejewski, in --> |last=Woytak |first=Richard |author1-link=Richard Woytak |chapter=A Conversation with Marian Rejewski |id=Appendix B |editor1-last=Kozaczuk |editor1-first=Władysław |editor1-link=Władysław Kozaczuk |title=Enigma |date=1984 |pages=229–240 |isbn=0-89093-547-5}}

==Further reading==
* {{citation |first=Jerzy |last=Kubiatowski |contribution=Rejewski, Marian Adam |title=Polski słownik biograficzny |trans-title=[[Polish Biographical Dictionary]] |language=pl |volume=XXXI/1 |location=Warsaw |publisher=Wydawnictwo Polskiej Akademii Nauk [[Polish Academy of Sciences]] |year=1988 |pages=54–56 }}

==External links==
* [http://www.codesandciphers.org.uk/virtualbp/poles/poles.htm The Breaking of Enigma by the Polish Mathematicians] by Tony Sale
* [https://www.nsa.gov/about/cryptologic_heritage/center_crypt_history/publications/how_math_helped_win.shtml How Mathematicians Helped Win WWII – National Security Agency]
* [http://www.spybooks.pl/en/enigma.html Enigma documents]
* [http://www.ams.org/samplings/feature-column/fcarc-enigma Marian Rejewski and the First Break into Enigma]
* [http://ethw.org/Milestones:First_Breaking_of_Enigma_Code_by_the_Team_of_Polish_Cipher_Bureau,_1932-1939 Plaque location]

{{Authority control}}

{{DEFAULTSORT:Rejewski, Marian}}
[[Category:1905 births]]
[[Category:1980 deaths]]
[[Category:20th-century Polish inventors]]
[[Category:20th-century Polish mathematicians]]
[[Category:Adam Mickiewicz University in Poznań alumni]]
[[Category:Cipher Bureau (Poland)]]
[[Category:Enigma machine]]
[[Category:Grand Crosses of the Order of Polonia Restituta]]
[[Category:People from Bydgoszcz]]
[[Category:People from the Province of Posen]]
[[Category:Polish cryptographers]]
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[[Category:Polish military personnel of World War II]]
[[Category:20th-century cryptographers]]