Old page wikitext, before the edit (old_wikitext ) | '{{Use dmy dates|date=November 2013}}
{{Infobox person
| name = Marian Rejewski
| image = MR 1932 small.jpg
| imagesize = 155px
| caption = Rejewski, c. 1932
| birth_name = Marian Adam Rejewski
| birth_date = {{birth date|df=yes|1905|08|16}}
| birth_place = [[Bydgoszcz|Bromberg]], [[German Empire]]
| death_date = {{death date and age|df=yes|1980|02|13|1905|08|16}}
| death_place = [[Warsaw]], [[People's Republic of Poland]]
| known_for = Solving the [[Enigma machine|Enigma-machine]] cipher
| occupation = Mathematician, cryptologist
| awards = [[Thomas Knowlton#The Knowlton Award|Knowlton Award]]<ref>{{cite web|url=http://article.wn.com/view/2012/09/04/odznaczenie_knowltona_dla_mariana_rejewskiego_dzi_uroczysto/|title=Odznaczenie Knowltona dla Mariana Rejewskiego. Dziś uroczystość|work=World News}}</ref><br> [[File:POL Polonia Restituta Wielki BAR.svg|40px| Order of Polonia Restituta- Grand Cross]] [[File:POL Polonia Restituta Oficerski BAR.svg|40px| Order of Polonia Restituta – Officer's Cross]] [[File:War Medal 39-45 BAR.svg|40px|War Medal 1939–1945]] <ref>[[:pl:Marian Rejewski]]</ref>
}}
'''Marian Adam Rejewski''' {{IPA-pl|ˈmarjan reˈjefski||Pl-Marian_Rejewski-2.ogg}} (16 August 1905 – 13 February 1980) was a Polish mathematician and [[cryptography|cryptologist]] who in 1932 solved the plugboard-equipped [[Enigma machine]], the main [[cipher]] device used by [[Nazi Germany]]. The success of Rejewski and his colleagues [[Jerzy Różycki]] and [[Henryk Zygalski]] jump-started British reading of Enigma in the Second World War; the intelligence so gained, code-named ''[[Ultra (cryptography)|Ultra]]'', contributed, perhaps decisively, to the [[End of World War II in Europe|defeat of 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 French and British 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 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|180px|[[Imperial Castle in Poznań|Poznań Castle]], then site of [[Poznań University]]'s mathematics institute]]
[[File:Göttingen-Grave.of.Gauß.06.jpg|thumb|180px|At Prof. [[Zdzisław Krygowski|Krygowski]]'s request, Rejewski at [[Göttingen]] laid flowers on [[Carl Friedrich Gauss|Gauss]]'s grave.<ref>{{harvnb|Kozaczuk|1984|loc=p. 7, note 6}}</ref>]]
Marian Rejewski was born 16 August 1905 in [[Bromberg]], now [[Bydgoszcz]],<ref>{{harvnb|Kasparek|Woytak|1982|p=19}}</ref><sup>[[#Notes|(Note 2)]]</sup> to Józef and Matylda, ''née'' Thoms.<ref>Information on Marian Rejewski's military service record, reproduced in {{harvtxt|Kozaczuk|1979|loc=opposite p. 257}}.</ref> After completing secondary school, he studied mathematics at [[Adam Mickiewicz University in Poznań|Poznań University]].<ref>{{harvnb|Kasparek|Woytak|1982|p=20}}</ref>
In early 1929, shortly before he graduated from university, 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 name="assistance"/> The course was conducted off-campus at a military facility<ref name="conversation"/> 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 name="conversation1"/> 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>
Rejewski graduated with a Master of Philosophy 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."<ref>Information on Marian Rejewski's Master of Philosophy diploma, 1 March 1929, reproduced opposite p. 128 in [[Władysław Kozaczuk]], ''W kręgu Enigmy'' (Enigma), 1979.</ref> 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]].<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 230–31.</ref> 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 name="conversation3"/> 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>
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 name="conversation5"/> 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—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>{{harvnb|Kozaczuk|1984|pp=10–11}}</ref>
==Enigma machine==
[[Image:EnigmaMachineLabeled.jpg|thumb|150px|The [[Enigma machine]], solved by Rejewski in 1932]]
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 I]], which was coming into widespread use.<ref name="Marian Rejewski 1984, p. 232"/>
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>{{harvnb|Kozaczuk|1984|p=12}}</ref>
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 ("[[Enigma rotor details|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.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 247–51.</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, each of which would produce a different cipher. The settings were changed daily,<ref name="reconstructing"/> and consequently the machine had to be "broken" anew each day if the messages were to be read continually.<ref name="kozaczuk8">{{harvnb|Kozaczuk|1984|pp=12, 19–21}}</ref>
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 name="kozaczuk8"/>
==Solving Enigma's wiring==
[[Image:AD-cycle.svg|thumb|A [[cyclic permutation|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—[[frequency analysis (cryptanalysis)|letter-frequency analysis]]. Rejewski, however, applied techniques from [[group theory]]—[[theorem]]s about [[permutation]]s—in his attack on Enigma. These mathematical techniques, combined with material supplied by Captain [[Gustave Bertrand]],<ref name="chiffrierdienst"/> chief of French radio intelligence,<ref name="responsibility"/> enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector. "The solution", writes historian [[David Kahn (writer)|David 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 one mathematics professor has since described as "the theorem that won World War II."<ref name="deavours"/>
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 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. 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 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.
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 name="mathematicians"/>
===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 name="Marian Rejewski 1984, p. 258"/> 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 name="conversation9"/> <sup>[[#Notes|(Note 4)]]</sup> 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 name="mathematicians10"/>
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 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 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 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 name="lawrence"/>) 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 name="Marian Rejewski 1984, p. 258"/>
==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 — 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 name="conversation11"/></blockquote>
===Early methods===
[[File:Cyclometer4.png|thumb|175px|[[Cyclometer]], devised in the mid-1930s by Rejewski to catalog the [[cyclic permutation|cycle]] structure of [[Enigma machine|Enigma]] [[permutation]]s. 1: Rotor lid closed, 2: Rotor lid open, 3: Rheostat, 4: Glowlamps, 5: Switches, 6: Letters.]]
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"/> 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 name="mathematicians12"/>
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 name="mathematical"/> 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 name="mathematicians13"/>
===Rejewski's ''{{lang|pl|bomba}}'' and Zygalski's sheets===
[[Image:Płachta Zygalskiego - decrypting Enigma.jpg|thumb|upright|A [[Zygalski sheets|Zygalski sheet]]]]
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, new rules for enciphering message keys (a new "indicator procedure") were put into effect by the Germans, making the techniques then in use obsolete.<sup>[[#Notes|(Note 7)]]</sup> 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 enabled the daily keys to be solved in about two hours. Six bombas were built and 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 machines 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, although the cryptanalytic methods embodied by the two machines were very different.<ref>{{harvnb|Welchman|1986}}</ref>
A manual method was invented around the same time by Zygalski, that of "[[perforated sheets]]" ("Zygalski sheets"), which was independent of the number of plugboard connections. However, application of both the bomba and Zygalski's 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 bombes was beyond the Biuro's ability—that many bombes would have cost fifteen times their entire annual equipment budget. The following month, things became even worse when the number of plugboard cables increased from six to ten. Instead of twelve letters being swapped before entering the rotor scrambler, there were now twenty swapped letters, reducing the effectiveness of the bomba and increasing the number of possible plugboard settings by more than a thousandfold.<ref><nowiki>{{harvnb|Miller|2001}}</nowiki> Nonexistent citation</ref>
===Allies informed===
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 name="intelligence"/>), the Polish General Staff and government decided to let their Western allies in on the secret.<ref name="cryptologia">{{harvnb|Erskine|2006}}<!-- not a pinpoint--></ref> The Polish methods were revealed to 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>{{harvnb|Kozaczuk|1984|p=59}}</ref><ref name="conversation18"/><ref name="cryptologia"/>
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—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.{{cn|date=February 2015}}
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>{{harvnb|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>{{harvnb|Welchman|1982|p=289}}</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><nowiki>{{harvnb|Kozaczuk|Straszak|2004|p=74}} Awkward citation</nowiki></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 name="cam"/> 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|''[[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 17 September (the day the [[Soviet Union]] invaded eastern Poland).<ref>{{harvnb|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>{{harvnb|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>{{harvnb|Kozaczuk|1984|pp=81–82}}</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 staff at PC Bruno collaborated by [[teleprinter]] 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>{{harvnb|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 Italian ciphers<ref>{{harvnb|Kozaczuk|1984|p=82}}</ref>—in three planes to [[Algeria]].<ref>{{harvnb|Kozaczuk|1984|p=109}}</ref>
===Cadix===
{{Main|Cadix}}
[[Image:Zygalski-rozycki-rejewski.jpg|thumb|left|upright|[[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).<ref>{{harvnb|Kozaczuk|1984|pp=113-14, 118-30}}</ref> Rejewski may have had little or no involvement in working on German Enigma at Cadix.<sup>[[#Notes|(Note 8)]]</sup>
[[Image:Pol-Fra-radioint Cadix 40-42.jpg|thumb|Polish-French-Spanish ''Cadix'' center. 11 individuals are identified at "''[[Cadix]]''."]]
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=134–35}}</ref>
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>{{harvnb|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 — and terrorized — 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 name="librairie">{{harvnb|Bertrand|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>{{harvnb|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>{{harvnb|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>{{harvnb|Kozaczuk|1984|pp=151–54}}</ref> Leaving Madrid on 21 July,<ref>{{harvnb|Kozaczuk|1984|p=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>{{harvnb|Kozaczuk|1984|pp=205–6}}</ref>
[[Image:Marian Rejewski.jpg|thumb|upright|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>{{harvnb|Kozaczuk|1984|pp=207–9}}</ref> On 10 October 1943, Rejewski and Zygalski were commissioned [[second lieutenant]]s;<ref>{{harvnb|Kozaczuk|1984|pp=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 cypher 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 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>{{harvnb|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>{{harvnb|Stripp|2004|p=124}}</ref>
==Back in Poland==
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 name="Kozaczuk, 1984, p. 226">{{harvnb|Kozaczuk|1984|p=226}}</ref>
{{blockquote|Rejewski [writes Kozaczuk] could after the war have worked in academia 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 name="Kozaczuk, 1984, p. 226"/>|}}
[[Image:Poland Bydgoszcz Rejewski monument.jpg|thumb|Memorial to Rejewski in [[Bydgoszcz]], unveiled on 2005 centennial of his birth there. It resembles the memorial to fellow-mathematician [[Alan Turing]] at [[Whitworth Gardens]], Manchester.]]
Rejewski took a position in [[Bydgoszcz]] as director of the sales department at a cable manufacturing company, ''Kabel Polski'' (Polish Cable).<ref name="Kozaczuk, 1984, p. 226"/>
Between 1949 and 1958, Rejewski was repeatedly investigated by the Polish [[Ministry of Public Security (Poland)|Office of Public Security]] but never divulged that he had worked on Enigma; in 1950 they demanded that he be fired from his employment<!--why? please expand-->.<ref>{{harvnb|Polak|2005|p=78}}</ref> 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 to the west, along with other Warsaw survivors. The family had eventually found refuge with her parents in Bydgoszcz.)<ref name="Kozaczuk, 1984, p. 226"/>
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 [[teleprinter]] 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>{{harvnb|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 name="Kozaczuk, 1984, p. 226"/>
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>{{harvnb|Winterbotham|1974|p=15}}</ref>
What little was published attracted little attention. [[Ladislas Farago]]'s 1971 best-seller ''The Game of the Foxes'' presented a garbled account of [[Ultra (cryptography)|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>{{harvnb|Farago|1971|p=674}}</ref> Still, this was closer to the truth than many 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.<ref>Historian [[Richard Woytak]] wrote in 1982: "[[F. W. Winterbotham|[F.W.] Winterbotham]]'s [''The Ultra Secret'' (1974)] spoke of 'a Polish mechanic... employed in [an Enigma] factory in Eastern Germany' who 'was sacked and sent back to Poland' and 'got in touch with our man in Warsaw.' By 1975... [[Anthony Cave Brown]] in his ''[[Bodyguard of Lies]]'' had promoted the nameless Polish mechanic to a 'Richard Lewinski (not his real name)' who had worked as a mathematician and engineer at the [Enigma] factory in Berlin'... [T]o be on the safe side, though, Brown... mention[ed] 'Polish cryptanalysts, led by M. Rejewski and H. Zygalski', as well as a German 'officer of the ''Forschungsamt''...' In 1976, another... best-seller, ''[[A Man Called Intrepid]]'' by... [[William Stevenson (Canadian writer)|William Stevenson]]... g[o]t wrong... Rejewski's sex and marital status. Then [Stevenson] went on to a... story about [Elizabeth Thorpe, a Minneapolis-born] spy codenamed CYNTHIA, who was 'married to a British diplomat, Arthur Pack, who had been transferred to Warsaw... [She] formed a series of liaisons with top-ranking members of Poland's Foreign Service' [and from an aide of Foreign Minister [[Józef Beck]] obtained documents and information about Polish Enigma decryption that Stevenson suggests were somehow important to subsequent British efforts]. In conversations with me, Rejewski, in Warsaw, and Colonel [[Stefan Mayer]]... prewar chief of Polish military counter-intelligence, in London, have denied that there is any truth in... these... accounts.... The official history of ''British Intelligence in the Second World War'', by [[Harry Hinsley|F.H. Hinsley]] et al...., vol. 1... 1979, repeats, in Appendix 1, the story about 'a Pole who was working in an Enigma factory in Germany'..." [[Richard Woytak]], prefatory note (pp. 75–76) to Marian Rejewski, "Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by F.H. Hinsley", ''[[Cryptologia]]'', vol. 6, no. 1 (January 1982), pp. 75–83.</ref>
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 name="Kozaczuk, 1984, p. 225">{{harvnb|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 name="Kozaczuk, 1984, p. 225"/> 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>{{harvnb|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 name="Kozaczuk, 1984, p. 225"/>
Rejewski, who had been suffering from [[heart disease]], died of a heart attack at his home on 13 February 1980, aged 74. He was buried with military honors at [[Warsaw]]'s [[Powązki Military Cemetery]].<ref name="Kozaczuk, 1984, p. 226"/>
==Recognition==
[[Image:Polish cryptologists breaking Enigma ciphers monument 01.JPG|thumb|upright|Bronze monument to the three cryptologists, erected in 2007 before the [[Imperial Castle in Poznań|Poznań Castle]]]]
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 TV series with a similar theme, ''Tajemnice Enigmy'' ("The Secrets of Enigma").<ref>{{harvnb|Kasparek|Woytak|1982|p=24}}</ref>
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 name="news"/>
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 name="cryptologists"/>
On 1 August 2012 Marian Rejewski posthumously received the [[Thomas Knowlton#The Knowlton Award|Knowlton Award]] of the U.S. [[Military Intelligence Corps Association]].<ref>{{cite web|url=http://www.micastore.com/AwardsAlphabeticallyR.html|title=Awards|work=MICAStore.com|publisher=Military Intelligence Corps Association|accessdate=5 February 2015}}</ref> Rejewski's mathematician daughter Janina accepted the award on behalf of her late father at his home town, [[Bydgoszcz]], on 4 September 2012. Rejewski had been nominated for the award by [[NATO]] Allied Command Counterintelligence. The Knowlton Award, named for an [[American War of Independence]] military intelligence chief, was established in 1995.<ref>"''Najwyższe odznaczenie amerykańskiego wywiadu za złamanie kodów Enigmy''" ("Highest American Intelligence Award for Breaking Enigma Ciphers"), ''[[Gwiazda Polarna]]'' (The Pole Star), vol. 103, no. 20 (22 September 2012), p. 6.</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}}
*[[Cryptanalysis of the Enigma]]
*[[List of cryptographers]]
*[[Polish contribution to World War II#Intelligence]]
*[[Polish School of Mathematics]]
*[[Tadeusz Pełczyński#Enigma]]
*[[List of Poles#Mathematics|List of Poles]]
==Notes==
{{refbegin}}
# 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 name="brzezinski">{{harvnb|Brzezinski|2005|p=18}}</ref> For a fuller discussion, see "[[Ultra]]".
# [[Bydgoszcz]] (called "Bromberg" in German) was then part of the [[Prussia]]n [[Province of Posen]]. Bydgoszcz—which had been seized by [[Prussia]] in the 1772 [[First Partition of Poland]]—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 name="mahon"/> 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 name="mathematicians42"/> 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>
{{refend}}
==Footnote citations==
{{reflist|3|refs=
<ref name="Marian Rejewski 1984, p. 232">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 232.</ref>
<ref name="Marian Rejewski 1984, p. 242">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 name="Marian Rejewski 1984, p. 258">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref>
<ref name="assistance">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>
<ref name="cam">{{cite web|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|accessdate=5 February 2015|archiveurl=http://web.archive.org/web/20110622015407/http://www.cl.cam.ac.uk/research/security/Historical/hinsley.html|archivedate=22 June 2011}}</ref>
<ref name="chiffrierdienst">Bertrand had obtained the material from a German ''Chiffrierdienst'' (Cryptographic Service) employee, [[Hans-Thilo Schmidt]]. {{harvnb|Kozaczuk|1984|pp=16–17}}</ref>
<ref name="conversation">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 230.</ref>
<ref name="conversation1">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 238.</ref>
<ref name="conversation11">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 234–235</ref>
<ref name="conversation18">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 236.</ref>
<ref name="conversation3">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 230–31.</ref>
<ref name="conversation5">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 231.</ref>
<ref name="conversation9">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 233.</ref>
<ref name="cryptologists">{{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=Polish |date=2007 |isbn=9788370635275}}</ref>
<ref name="deavours">Good and Deavours, 1981, pp. 229, 232</ref>
<ref name="intelligence">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 {{harvtxt|Kozaczuk|1984|loc=p. 63, note 7}}.</ref>
<ref name="lawrence">Lawrence, 2005</ref>
<ref name="mahon">Mahon, 1945, p. 12</ref>
<ref name="mathematical">Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 284–87.</ref>
<ref name="mathematicians">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 254–55.</ref>
<ref name="mathematicians10">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258–59.</ref>
<ref name="mathematicians12">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 262.</ref>
<ref name="mathematicians13">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 265.</ref>
<ref name="mathematicians42">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 270.</ref>
<ref name="news">[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>
<ref name="reconstructing">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>
<ref name="responsibility">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>
}}
==Bibliography==
{{EnigmaSeries}}
:''The main source used for this article was 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=French |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=83-7208-117-4}}
* {{citation |first=Ralph |last=Erskine |title=The Poles Reveal their Secrets: [[Alastair Denniston]]'s Account of the July 1939 Meeting at [[Pyry]] |journal=Cryptologia |volume=30 |issue=4 |date=December 2006 |pages=294–305}}
* {{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}}
* [[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.)
* {{citation |editor1-last=Hinsley |editor1-first=F. Harry |editor1-link=Harry Hinsley |editor2-first=Alan |editor2-last=Stripp |title=Codebreakers: The Inside Story of Bletchley Park |publisher=[[Oxford University Press]] |date=1993 |isbn=0-19-820327-6}}
* {{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=Polish |location=[[Poznań]] |publisher=Wydawnictwo Poznańskiego Towarzystwa Przyjaciół Nauk |date=2007 |isbn=978-83-7063-527-5}}
* {{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=0-684-83130-9}}
* {{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}}
* {{citation |first=Władysław |last=Kozaczuk |author1-link=Władysław Kozaczuk |title=W kręgu Enigmy |trans_title=In the Circle of Enigma |language=Polish |location=Warsaw |publisher=[[Książka i Wiedza]] |date=1979}} (Kozaczuk's Polish-language book that was later elaborated into his English-language 1984 book, ''Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two''.)
* {{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 |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 augmented with documentation, including many additional 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}}
* 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. 54–56.
* {{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}}
* {{citation |first=John |last=Lawrence |title=A Study of Rejewski's Equations |journal=Cryptologia |volume=29 |issue=3 |date=July 2005 |pages=233–247}}
* {{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= |date=October 2005}}
* A.P. Mahon, "The History of Hut Eight: 1939–1945", June 1945, 117 pp., PRO HW 25/2, [http://www.cs.usfca.edu/www.AlanTuring.net/turing_archive/archive/a/A09/A09-001.html].
* {{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=83-7208-117-4 |pages=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.
* {{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 |url=https://cryptocellar.web.cern.ch/cryptocellar/Enigma/rew80.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.
* {{citation |last=Sebag-Montefiore |first=Hugh |title=Enigma: the Battle for the Code |location=London |publisher=Weidenfeld and Nicolson |date=2000 |isbn= 9780297842514}}
* {{citation |last=Singh |first=Simon |author1-link=Simon Singh |title=[[The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography]] |publisher=Doubleday |date=1999 |pages=149–160 |isbn=0-385-49531-5}}
* {{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=0-7818-0941-X |pages=123–25}}
* {{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}}
* {{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 |date=January 1986}}
* {{citation |last=Winterbotham |first=F. W. |author1-link=F. W. Winterbotham |title=The Ultra Secret |location=New York |publisher=Dell |date=1974}}
==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://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/featurecolumn/archive/enigma.html Marian Rejewski and the First Break into Enigma]
{{featured article}}
{{Authority control|VIAF=20828187}}
{{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
}}
{{DEFAULTSORT:Rejewski, Marian}}
[[Category:1905 births]]
[[Category:1980 deaths]]
[[Category:Biuro Szyfrów]]
[[Category:People from Bydgoszcz]]
[[Category:People from the Province of Posen]]
[[Category:Polish cryptographers]]
[[Category:Polish inventors]]
[[Category:Polish Army officers]]
[[Category:Pre-computer cryptographers]]
[[Category:Grand Crosses of the Order of Polonia Restituta]]
[[Category:Adam Mickiewicz University in Poznań alumni]]
[[Category:20th-century Polish mathematicians]]' |
New page wikitext, after the edit (new_wikitext ) | '{{Use dmy dates|date=November 2013}}
{{Infobox person
| name = Marian Rejewski
| image = MR 1932 small.jpg
| imagesize = 155px
| caption = Rejewski, c. 1932
| birth_name = Marian Adam Rejewski
| birth_date = {{birth date|df=yes|1905|08|16}}
| birth_place = [[Bydgoszcz|Bromberg]], [[German Empire]]
| death_date = {{death date and age|df=yes|1980|02|13|1905|08|16}}
| death_place = [[Warsaw]], [[People's Republic of Poland]]
| known_for = Solving the [[Enigma machine|Enigma-machine]] cipher
| occupation = Mathematician, cryptologist
| awards = [[Thomas Knowlton#The Knowlton Award|Knowlton Award]]<ref>{{cite web|url=http://article.wn.com/view/2012/09/04/odznaczenie_knowltona_dla_mariana_rejewskiego_dzi_uroczysto/|title=Odznaczenie Knowltona dla Mariana Rejewskiego. Dziś uroczystość|work=World News}}</ref><br> [[File:POL Polonia Restituta Wielki BAR.svg|40px| Order of Polonia Restituta- Grand Cross]] [[File:POL Polonia Restituta Oficerski BAR.svg|40px| Order of Polonia Restituta – Officer's Cross]] [[File:War Medal 39-45 BAR.svg|40px|War Medal 1939–1945]] <ref>[[:pl:Marian Rejewski]]</ref>
}}
'''Marian Adam Rejewski''' {{IPA-pl|ˈmarjan reˈjefski||Pl-Marian_Rejewski-2.ogg}} (16 August 1905 – 13 February 1980) was a Polish mathematician and [[cryptography|cryptologist]] who in 1932 solved the plugboard-equipped [[Enigma machine]], the main [[cipher]] device used by [[Nazi Germany]]. The success of Rejewski and his colleagues [[Jerzy Różycki]] and [[Henryk Zygalski]] jump-started British reading of Enigma in the Second World War; the intelligence so gained, code-named ''[[Ultra (cryptography)|Ultra]]'', contributed, perhaps decisively, to the [[End of World War II in Europe|defeat of 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 French and British 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 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|180px|[[Imperial Castle in Poznań|Poznań Castle]], then site of [[Poznań University]]'s mathematics institute]]
[[File:Göttingen-Grave.of.Gauß.06.jpg|thumb|180px|At Prof. [[Zdzisław Krygowski|Krygowski]]'s request, Rejewski at [[Göttingen]] laid flowers on [[Carl Friedrich Gauss|Gauss]]'s grave.<ref>{{harvnb|Kozaczuk|1984|loc=p. 7, note 6}}</ref>]]
Marian Rejewski was born 16 August 1905 in [[Bromberg]], now [[Bydgoszcz]],<ref>{{harvnb|Kasparek|Woytak|1982|p=19}}</ref><sup>[[#Notes|(Note 2)]]</sup> to Józef and Matylda, ''née'' Thoms.<ref>Information on Marian Rejewski's military service record, reproduced in {{harvtxt|Kozaczuk|1979|loc=opposite p. 257}}.</ref> After completing secondary school, he studied mathematics at [[Adam Mickiewicz University in Poznań|Poznań University]].<ref>{{harvnb|Kasparek|Woytak|1982|p=20}}</ref>
In early 1929, shortly before he graduated from university, 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 name="assistance"/> The course was conducted off-campus at a military facility<ref name="conversation"/> 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 name="conversation1"/> 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>
Rejewski graduated with a Master of Philosophy 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."<ref>Information on Marian Rejewski's Master of Philosophy diploma, 1 March 1929, reproduced opposite p. 128 in [[Władysław Kozaczuk]], ''W kręgu Enigmy'' (Enigma), 1979.</ref> 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]].<ref>Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 230–31.</ref> 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 name="conversation3"/> 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>
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 name="conversation5"/> 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—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>{{harvnb|Kozaczuk|1984|pp=10–11}}</ref>
==Enigma machine==
[[Image:EnigmaMachineLabeled.jpg|thumb|150px|The [[Enigma machine]], solved by Rejewski in 1932]]
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 I]], which was coming into widespread use.<ref name="Marian Rejewski 1984, p. 232"/>
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>{{harvnb|Kozaczuk|1984|p=12}}</ref>
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 ("[[Enigma rotor details|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.<ref>Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 247–51.</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, each of which would produce a different cipher. The settings were changed daily,<ref name="reconstructing"/> and consequently the machine had to be "broken" anew each day if the messages were to be read continually.<ref name="kozaczuk8">{{harvnb|Kozaczuk|1984|pp=12, 19–21}}</ref>
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 name="kozaczuk8"/>
==Solving Enigma's wiring==
[[Image:AD-cycle.svg|thumb|A [[cyclic permutation|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—[[frequency analysis (cryptanalysis)|letter-frequency analysis]]. Rejewski, however, applied techniques from [[group theory]]—[[theorem]]s about [[permutation]]s—in his attack on Enigma. These mathematical techniques, combined with material supplied by Captain [[Gustave Bertrand]],<ref name="chiffrierdienst"/> chief of French radio intelligence,<ref name="responsibility"/> enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector. "The solution", writes historian [[David Kahn (writer)|David 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 one mathematics professor has since described as "the theorem that won World War II."<ref name="deavours"/>
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 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. 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 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.
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 name="mathematicians"/>
===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 name="Marian Rejewski 1984, p. 258"/> 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 name="conversation9"/> <sup>[[#Notes|(Note 4)]]</sup> 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 name="mathematicians10"/>
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 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 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 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 name="lawrence"/>) 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 name="Marian Rejewski 1984, p. 258"/>
==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 — 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 name="conversation11"/></blockquote>
===Early methods===
[[File:Cyclometer4.png|thumb|175px|[[Cyclometer]], devised in the mid-1930s by Rejewski to catalog the [[cyclic permutation|cycle]] structure of [[Enigma machine|Enigma]] [[permutation]]s. 1: Rotor lid closed, 2: Rotor lid open, 3: Rheostat, 4: Glowlamps, 5: Switches, 6: Letters.]]
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"/> 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 name="mathematicians12"/>
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 name="mathematical"/> 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 name="mathematicians13"/>
===Rejewski's ''{{lang|pl|bomba}}'' and Zygalski's sheets===
[[Image:Płachta Zygalskiego - decrypting Enigma.jpg|thumb|upright|A [[Zygalski sheets|Zygalski sheet]]]]
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, new rules for enciphering message keys (a new "indicator procedure") were put into effect by the Germans, making the techniques then in use obsolete.<sup>[[#Notes|(Note 7)]]</sup> 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 enabled the daily keys to be solved in about two hours. Six bombas were built and 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 machines 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, although the cryptanalytic methods embodied by the two machines were very different.<ref>{{harvnb|Welchman|1986}}</ref>
A manual method was invented around the same time by Zygalski, that of "[[perforated sheets]]" ("Zygalski sheets"), which was independent of the number of plugboard connections. However, application of both the bomba and Zygalski's 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 bombes was beyond the Biuro's ability—that many bombes would have cost fifteen times their entire annual equipment budget. The following month, things became even worse when the number of plugboard cables increased from six to ten. Instead of twelve letters being swapped before entering the rotor scrambler, there were now twenty swapped letters, reducing the effectiveness of the bomba and increasing the number of possible plugboard settings by more than a thousandfold.<ref><nowiki>{{harvnb|Miller|2001}}</nowiki> Nonexistent citation</ref>
===Allies informed===
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 name="intelligence"/>), the Polish General Staff and government decided to let their Western allies in on the secret.<ref name="cryptologia">{{harvnb|Erskine|2006}}<!-- not a pinpoint--></ref> The Polish methods were revealed to 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>{{harvnb|Kozaczuk|1984|p=59}}</ref><ref name="conversation18"/><ref name="cryptologia"/>
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—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.{{cn|date=February 2015}}
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>{{harvnb|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>{{harvnb|Welchman|1982|p=289}}</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><nowiki>{{harvnb|Kozaczuk|Straszak|2004|p=74}} Awkward citation</nowiki></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 name="cam"/> 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|''[[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 17 September (the day the [[Soviet Union]] invaded eastern Poland).<ref>{{harvnb|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>{{harvnb|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>{{harvnb|Kozaczuk|1984|pp=81–82}}</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 staff at PC Bruno collaborated by [[teleprinter]] 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>{{harvnb|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 Italian ciphers<ref>{{harvnb|Kozaczuk|1984|p=82}}</ref>—in three planes to [[Algeria]].<ref>{{harvnb|Kozaczuk|1984|p=109}}</ref>
===Cadix===
{{Main|Cadix}}
[[Image:Zygalski-rozycki-rejewski.jpg|thumb|left|upright|[[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).<ref>{{harvnb|Kozaczuk|1984|pp=113-14, 118-30}}</ref> Rejewski may have had little or no involvement in working on German Enigma at Cadix.<sup>[[#Notes|(Note 8)]]</sup>
[[Image:Pol-Fra-radioint Cadix 40-42.jpg|thumb|Polish-French-Spanish ''Cadix'' center. 11 individuals are identified at "''[[Cadix]]''."]]
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=134–35}}</ref>
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>{{harvnb|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 — and terrorized — 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 name="librairie">{{harvnb|Bertrand|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>{{harvnb|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>{{harvnb|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>{{harvnb|Kozaczuk|1984|pp=151–54}}</ref> Leaving Madrid on 21 July,<ref>{{harvnb|Kozaczuk|1984|p=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>{{harvnb|Kozaczuk|1984|pp=205–6}}</ref>
[[Image:Marian Rejewski.jpg|thumb|upright|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>{{harvnb|Kozaczuk|1984|pp=207–9}}</ref> On 10 October 1943, Rejewski and Zygalski were commissioned [[second lieutenant]]s;<ref>{{harvnb|Kozaczuk|1984|pp=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 cypher 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 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>{{harvnb|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>{{harvnb|Stripp|2004|p=124}}</ref>
==Back in Poland==
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 name="Kozaczuk, 1984, p. 226">{{harvnb|Kozaczuk|1984|p=226}}</ref>
{{blockquote|Rejewski [writes Kozaczuk] could after the war have worked in academia 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 name="Kozaczuk, 1984, p. 226"/>|}}
[[Image:Poland Bydgoszcz Rejewski monument.jpg|thumb|Memorial to Rejewski in [[Bydgoszcz]], unveiled on 2005 centennial of his birth there. It resembles the memorial to fellow-mathematician [[Alan Turing]] at [[Whitworth Gardens]], Manchester.]]
Rejewski took a position in [[Bydgoszcz]] as director of the sales department at a cable manufacturing company, ''Kabel Polski'' (Polish Cable).<ref name="Kozaczuk, 1984, p. 226"/>
Between 1949 and 1958, Rejewski was repeatedly investigated by the Polish [[Ministry of Public Security (Poland)|Office of Public Security]] but never divulged that he had worked on Enigma; in 1950 they demanded that he be fired from his employment<!--why? please expand-->.<ref>{{harvnb|Polak|2005|p=78}}</ref> 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 to the west, along with other Warsaw survivors. The family had eventually found refuge with her parents in Bydgoszcz.)<ref name="Kozaczuk, 1984, p. 226"/>
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 [[teleprinter]] 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>{{harvnb|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 name="Kozaczuk, 1984, p. 226"/>
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>{{harvnb|Winterbotham|1974|p=15}}</ref>
What little was published attracted little attention. [[Ladislas Farago]]'s 1971 best-seller ''The Game of the Foxes'' presented a garbled account of [[Ultra (cryptography)|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>{{harvnb|Farago|1971|p=674}}</ref> Still, this was closer to the truth than many 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.<ref>Historian [[Richard Woytak]] wrote in 1982: "[[F. W. Winterbotham|[F.W.] Winterbotham]]'s [''The Ultra Secret'' (1974)] spoke of 'a Polish mechanic... employed in [an Enigma] factory in Eastern Germany' who 'was sacked and sent back to Poland' and 'got in touch with our man in Warsaw.' By 1975... [[Anthony Cave Brown]] in his ''[[Bodyguard of Lies]]'' had promoted the nameless Polish mechanic to a 'Richard Lewinski (not his real name)' who had worked as a mathematician and engineer at the [Enigma] factory in Berlin'... [T]o be on the safe side, though, Brown... mention[ed] 'Polish cryptanalysts, led by M. Rejewski and H. Zygalski', as well as a German 'officer of the ''Forschungsamt''...' In 1976, another... best-seller, ''[[A Man Called Intrepid]]'' by... [[William Stevenson (Canadian writer)|William Stevenson]]... g[o]t wrong... Rejewski's sex and marital status. Then [Stevenson] went on to a... story about [Elizabeth Thorpe, a Minneapolis-born] spy codenamed CYNTHIA, who was 'married to a British diplomat, Arthur Pack, who had been transferred to Warsaw... [She] formed a series of liaisons with top-ranking members of Poland's Foreign Service' [and from an aide of Foreign Minister [[Józef Beck]] obtained documents and information about Polish Enigma decryption that Stevenson suggests were somehow important to subsequent British efforts]. In conversations with me, Rejewski, in Warsaw, and Colonel [[Stefan Mayer]]... prewar chief of Polish military counter-intelligence, in London, have denied that there is any truth in... these... accounts.... The official history of ''British Intelligence in the Second World War'', by [[Harry Hinsley|F.H. Hinsley]] et al...., vol. 1... 1979, repeats, in Appendix 1, the story about 'a Pole who was working in an Enigma factory in Germany'..." [[Richard Woytak]], prefatory note (pp. 75–76) to Marian Rejewski, "Remarks on Appendix 1 to ''British Intelligence in the Second World War'' by F.H. Hinsley", ''[[Cryptologia]]'', vol. 6, no. 1 (January 1982), pp. 75–83.</ref>
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 name="Kozaczuk, 1984, p. 225">{{harvnb|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 name="Kozaczuk, 1984, p. 225"/> 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>{{harvnb|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 name="Kozaczuk, 1984, p. 225"/>
Rejewski, who had been suffering from [[heart disease]], died of a heart attack at his home on 13 February 1980, aged 74. He was buried with military honors at [[Warsaw]]'s [[Powązki Military Cemetery]].<ref name="Kozaczuk, 1984, p. 226"/>
==Recognition==
[[Image:Polish cryptologists breaking Enigma ciphers monument 01.JPG|thumb|upright|Bronze monument to the three cryptologists, erected in 2007 before the [[Imperial Castle in Poznań|Poznań Castle]]]]
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 TV series with a similar theme, ''Tajemnice Enigmy'' ("The Secrets of Enigma").<ref>{{harvnb|Kasparek|Woytak|1982|p=24}}</ref>
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 name="news"/>
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 name="cryptologists"/>
On 1 August 2012 Marian Rejewski posthumously received the [[Thomas Knowlton#The Knowlton Award|Knowlton Award]] of the U.S. [[Military Intelligence Corps Association]].<ref>{{cite web|url=http://www.micastore.com/AwardsAlphabeticallyR.html|title=Awards|work=MICAStore.com|publisher=Military Intelligence Corps Association|accessdate=5 February 2015}}</ref> Rejewski's mathematician daughter Janina accepted the award on behalf of her late father at his home town, [[Bydgoszcz]], on 4 September 2012. Rejewski had been nominated for the award by [[NATO]] Allied Command Counterintelligence. The Knowlton Award, named for an [[American War of Independence]] military intelligence chief, was established in 1995.<ref>"''Najwyższe odznaczenie amerykańskiego wywiadu za złamanie kodów Enigmy''" ("Highest American Intelligence Award for Breaking Enigma Ciphers"), ''[[Gwiazda Polarna]]'' (The Pole Star), vol. 103, no. 20 (22 September 2012), p. 6.</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}}
*[[Cryptanalysis of the Enigma]]
*[[List of cryptographers]]
*[[Polish contribution to World War II#Intelligence]]
*[[Polish School of Mathematics]]
*[[Tadeusz Pełczyński#Enigma]]
*[[List of Poles#Mathematics|List of Poles]]
==Notes==
{{refbegin}}
# 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 name="brzezinski">{{harvnb|Brzezinski|2005|p=18}}</ref> For a fuller discussion, see "[[Ultra]]".
# [[Bydgoszcz]] (called "Bromberg" in German) was then part of the [[Prussia]]n [[Province of Posen]]. Bydgoszcz—which had been seized by [[Prussia]] in the 1772 [[First Partition of Poland]]—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 name="mahon"/> 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 name="mathematicians42"/> 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>
{{refend}}
==Footnote citations==
{{reflist|3|refs=
<ref name="Marian Rejewski 1984, p. 232">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 232.</ref>
<ref name="Marian Rejewski 1984, p. 242">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 name="Marian Rejewski 1984, p. 258">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258.</ref>
<ref name="assistance">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>
<ref name="cam">{{cite web|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|accessdate=5 February 2015|archiveurl=http://web.archive.org/web/20110622015407/http://www.cl.cam.ac.uk/research/security/Historical/hinsley.html|archivedate=22 June 2011}}</ref>
<ref name="chiffrierdienst">Bertrand had obtained the material from a German ''Chiffrierdienst'' (Cryptographic Service) employee, [[Hans-Thilo Schmidt]]. {{harvnb|Kozaczuk|1984|pp=16–17}}</ref>
<ref name="conversation">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 230.</ref>
<ref name="conversation1">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 238.</ref>
<ref name="conversation11">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 234–235</ref>
<ref name="conversation18">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 236.</ref>
<ref name="conversation3">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 230–31.</ref>
<ref name="conversation5">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 231.</ref>
<ref name="conversation9">Marian Rejewski, in [[Richard Woytak]], "A Conversation with Marian Rejewski," Appendix B to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 233.</ref>
<ref name="cryptologists">{{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=Polish |date=2007 |isbn=9788370635275}}</ref>
<ref name="deavours">Good and Deavours, 1981, pp. 229, 232</ref>
<ref name="intelligence">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 {{harvtxt|Kozaczuk|1984|loc=p. 63, note 7}}.</ref>
<ref name="lawrence"><nowiki>{{harvnb|Lawrence|2005}}</nowiki> Unclear reference</ref>
<ref name="mahon">Mahon, 1945, p. 12</ref>
<ref name="mathematical">Marian Rejewski, "The Mathematical Solution of the Enigma Cipher," Appendix E to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 284–87.</ref>
<ref name="mathematicians">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, pp. 254–55.</ref>
<ref name="mathematicians10">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 258–59.</ref>
<ref name="mathematicians12">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 262.</ref>
<ref name="mathematicians13">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 265.</ref>
<ref name="mathematicians42">Marian Rejewski, "How the Polish Mathematicians Broke Enigma," Appendix D to [[Władysław Kozaczuk]], ''Enigma'', 1984, p. 270.</ref>
<ref name="news">[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>
<ref name="reconstructing">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>
<ref name="responsibility">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>
}}
==Bibliography==
{{EnigmaSeries}}
:''The main source used for this article was 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=French |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=83-7208-117-4}}
* {{citation |first=Ralph |last=Erskine |title=The Poles Reveal their Secrets: [[Alastair Denniston]]'s Account of the July 1939 Meeting at [[Pyry]] |journal=Cryptologia |volume=30 |issue=4 |date=December 2006 |pages=294–305}}
* {{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}}
* [[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.)
* {{citation |editor1-last=Hinsley |editor1-first=F. Harry |editor1-link=Harry Hinsley |editor2-first=Alan |editor2-last=Stripp |title=Codebreakers: The Inside Story of Bletchley Park |publisher=[[Oxford University Press]] |date=1993 |isbn=0-19-820327-6}}
* {{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=Polish |location=[[Poznań]] |publisher=Wydawnictwo Poznańskiego Towarzystwa Przyjaciół Nauk |date=2007 |isbn=978-83-7063-527-5}}
* {{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=0-684-83130-9}}
* {{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}}
* {{citation |first=Władysław |last=Kozaczuk |author1-link=Władysław Kozaczuk |title=W kręgu Enigmy |trans_title=In the Circle of Enigma |language=Polish |location=Warsaw |publisher=[[Książka i Wiedza]] |date=1979}} (Kozaczuk's Polish-language book that was later elaborated into his English-language 1984 book, ''Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two''.)
* {{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 |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 augmented with documentation, including many additional 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}}
* 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. 54–56.
* {{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}}
* {{citation |first=John |last=Lawrence |title=A Study of Rejewski's Equations |journal=Cryptologia |volume=29 |issue=3 |date=July 2005 |pages=233–247}}
* {{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= |date=October 2005}}
* A.P. Mahon, "The History of Hut Eight: 1939–1945", June 1945, 117 pp., PRO HW 25/2, [http://www.cs.usfca.edu/www.AlanTuring.net/turing_archive/archive/a/A09/A09-001.html].
* {{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=83-7208-117-4 |pages=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.
* {{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 |url=https://cryptocellar.web.cern.ch/cryptocellar/Enigma/rew80.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.
* {{citation |last=Sebag-Montefiore |first=Hugh |title=Enigma: the Battle for the Code |location=London |publisher=Weidenfeld and Nicolson |date=2000 |isbn= 9780297842514}}
* {{citation |last=Singh |first=Simon |author1-link=Simon Singh |title=[[The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography]] |publisher=Doubleday |date=1999 |pages=149–160 |isbn=0-385-49531-5}}
* {{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=0-7818-0941-X |pages=123–25}}
* {{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}}
* {{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 |date=January 1986}}
* {{citation |last=Winterbotham |first=F. W. |author1-link=F. W. Winterbotham |title=The Ultra Secret |location=New York |publisher=Dell |date=1974}}
==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://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/featurecolumn/archive/enigma.html Marian Rejewski and the First Break into Enigma]
{{featured article}}
{{Authority control|VIAF=20828187}}
{{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
}}
{{DEFAULTSORT:Rejewski, Marian}}
[[Category:1905 births]]
[[Category:1980 deaths]]
[[Category:Biuro Szyfrów]]
[[Category:People from Bydgoszcz]]
[[Category:People from the Province of Posen]]
[[Category:Polish cryptographers]]
[[Category:Polish inventors]]
[[Category:Polish Army officers]]
[[Category:Pre-computer cryptographers]]
[[Category:Grand Crosses of the Order of Polonia Restituta]]
[[Category:Adam Mickiewicz University in Poznań alumni]]
[[Category:20th-century Polish mathematicians]]' |