Marian Rejewski

Marian Rejewski (probably 1932, the year he "broke" Enigma).
Courtesy of Janina Sylwestrzak, Rejewski's daughter.

Marian Adam Rejewski (; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist, famous for his ground-breaking work in decrypting German Enigma ciphers from 1932 onwards. The success of Rejewski and his colleagues jump-started British reading of Enigma in World War II, and the intelligence so gained (codenamed "ULTRA") substantially altered the course of World War II, and may have considerably hastened the defeat of Germany.

While studying mathematics at Poznań University, Rejewski began attending a secret cryptology course conducted by the Polish General Staff's Cipher Bureau, which he joined full-time in 1932. In late 1932, Rejewski was set to work solving the main German cipher system, the Enigma machine, with which the Bureau had had no success. After only a few weeks he had completely solved the secret internal wiring of the Enigma. Rejewski and two mathematician colleagues then developed techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using the "cyclometer", and the cryptologic "bomb" (bomba, in Polish).

Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Armed with these results, the British were able to prepare to begin reading Enigma at Bletchley Park. Meanwhile, after the outbreak of war, Rejewski and his colleagues were evacuated to Romania, and from there made their way to France, where they carried on their work in collaboration with the British at Bletchley Park. After the fall of France in June 1940, following a hiatus the Polish team resumed work in southern, Vichy France until the "Free Zone" was occupied by Germany in November 1942.

Rejewski and fellow mathematician Henryk Zygalski then sought to reach Great Britain via Spain, where they were incarcerated for three months. On finally reaching Britain, they continued work on German ciphers, but only hand systems, Enigma having become the exclusive preserve of the British and Americans. In November 1946 Rejewski returned to his family in Poland and for the next two decades kept prudently quiet about his cryptologic work.

Education and joining the Cipher Bureau

Rejewski's Master of Philosophy diploma, Poznań University, March 1, 1929.

Marian Rejewski was born August 16 1905, in Bydgoszcz (then called Bromberg by the German governing authorities), Poland, in what was then the German-controlled Province of Posen. He parents were Józef, a cigar merchant, and Matylda, née Thoms. In 1917, Rejewski received his high school diploma from the German-speaking Königliches Gymnasium in Bydgoszcz, ranking fourth out of 48 students. He studied mathematics at Poznań University, graduating on 1 March 1929.

In early 1929, while still a student, Rejewski started attending a secret cryptology course organized for selected mathematics students by the Polish Cipher Bureau (Polish: Biuro Szyfrów). Rejewski and fellow students Henryk Zygalski and Jerzy Różycki were among the few that could keep up with the course while balancing the demands of their normal studies. After graduating, Rejewski studied actuarial statistics for a year at Göttingen, Germany.

Rejewski returned to Poland in the summer of 1930, and was employed teaching mathematics at Poznań University. He also began working part-time for the Cipher Bureau, which had by then concluded the cryptology course and had set up an outpost at Poznań to decrypt intercepted German radio messages. Rejewski worked some twelve hours a week in an underground vault, close to the Mathematics Institute, nicknamed the "Black Chamber."

In the summer of 1932, the Poznań branch of the Cipher Bureau was disbanded. On September 1 1932, as a civilian employee, Rejewski joined the Cipher Bureau at the General Staff building (the Saxon Palace) in Warsaw, as did Zygalski and Różycki. Their first assignment was to work out a four-letter code used by the Kriegsmarine, the German Navy. Progress on solving this system was initially slow, but sped up considerably after a coded message exchange was received — a short test signal in the form of a question and answer; the cryptologists guessed correctly that the question was, "When was Frederick the Great born?"

The Enigma machine

The Enigma machine, solved by Rejewski in 1932, was widely used by Germany's military services to secure their communications.

In October 1932, while work on the Naval code was still underway, Rejewski was set to work, alone and in secret, on the new German machine cipher, Enigma, which was coming into widespread use. While there had been attempts to solve Enigma earlier, the Bureau had had no success, and had even resorted to seeking the assistance of a clairvoyant (Kozaczuk, 1984, p.12).

The Enigma machine was an electromechanical device, equipped with a 26-letter keyboard and a set of 26 lamps, corresponding to the letters of the alphabet. Inside were a set of wired drums ("rotors" and a "reflector") which scrambled the input. The machine also featured a plugboard to swap pairs of letters. To encipher a letter, the operator pushed the relevant key, and noted down which of the lamps lit. Each key press caused one or more rotors to advance, and thus the encipherment varied from one key press to the next. In order for two operators to communicate, both Enigma machines had to be set exactly the same way. There were an astronomical number of possible configurations, changed daily.

To decrypt Enigma messages, one needed three pieces of information:

1. a general understanding of how Enigma functioned;
2. the wiring of the rotors; and
3. the daily settings: the sequence and letter-orientations of the (initially, 3) rotors, and the plug connections on the plugboard.

Rejewski had only the first at his disposal, based on information already acquired by the Cipher Bureau.

Solution of the Enigma wiring

A 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.

Rejewski first tackled the problem of finding the wiring of the rotors. To do this, Rejewski pioneered the use of pure mathematics in cryptanalysis. Previous methods had largely exploited linguistic patterns and the statistics of natural-language texts — letter-frequency analysis. Rejewski, however, applied techniques from group theory — theorems about permutations — in his attack on Enigma. These mathematical techniques, combined with material supplied by French military intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and non-rotating reflector. "The solution," historian David Kahn writes, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time" (Kahn, 1996, p. 974). Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem that won World War II" (Good and Deavours, 1981).

Rejewski first studied the set of "indicators" (also known as "message keys") received with the Enigma messages intercepted on a single day. Each indicator was a six-letter sequence, a disguised starting position for the three rotors when enciphering the actual message. An operator would construct the indicator by arbitrarily selecting three letters, representing the rotor start positions, and enciphering them twice on the Enigma, using a global setting shared amongst all operators. The double encipherment was meant as an error check to detect garbles, but it also had the unforeseen effect of greatly weakening the cipher.

Rejewski studied the cycles formed by the first and fourth letters of each indicator, and similarly the cycles formed by the second and fifth, and the third and sixth. Aided by Enigma operators' tendency to choose predictable letter combinations as indicators, Rejewski was able to deduce six permutations corresponding to the encipherment at six consecutive positions of the Enigma machine. These permutations could be described by six equations with various unknowns, representing the wiring within the entry drum, rotors, reflector, and plugboard.

Assistance from French Intelligence

At this point, Rejewski ran into difficulty; the large number of unknowns made the equations complex. He would later comment in 1980 that it was still not known whether such a set of six equations was soluble without further data. In the event, he was assisted by cryptographic documents that a French military intelligence agency, under future General Gustave Bertrand, had obtained and passed on to the Polish Cipher Bureau. The documents had been procured from a traitor in the German cipher office, Hans-Thilo Schmidt, and included the Enigma settings for the months of September and October 1932. On December 9 or 10^[1] 1932, the documents were given to Rejewski, who used them to eliminate the effect of the plugboard from the equations. With the reduced number of unknowns, solving the equations became a tractable problem.

But first another snag had to be overcome. The military Enigma had been modified from the commercial Enigma, of which Rejewski and 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 codebreakers 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 alphabet ordering. He would write in 1980 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" (Kozaczuk, 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. This simplified the analysis, and by year's end the wirings of all three rotors and the reflector had been solved. An example message in an Enigma instruction manual provided a sequence of plaintext and corresponding ciphertext enciphered at a given setting; this helped Rejewski eliminate remaining ambiguity from the wiring.

It has been speculated whether the rotor wirings could have been solved without the documents supplied by French Intelligence. Rejewski noted in 1980 that another way was found that could have been used to achieve this, but that the method was "imperfect and tedious" and relied on a chance favorable set of circumstances. Lawrence (2005) argues that it would have taken four years for this method to have had a reasonable likelihood of success. 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" (Kozaczuk, 1984, p. 258).

Methods for solving the daily Enigma 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 routinely break Enigma ciphers^[2]. Rejewski later recalled:

Now we had the machine, but we didn't have the keys 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. (Kozaczuk, 1984, pp. 234-35.)

Early methods

Cyclometer (mid-1930s), devised by Rejewski to catalogue the cycle structure of Enigma permutations.

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," based on the fact that the plugboard's connections exchanged only six pairs of letters, leaving fourteen letters unchanged. Next was Różycki's "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.

After 1 October 1936, German procedure changed, increasing the number of plugboard connections. As a result, the grill method became considerably less effective. However, a method using a card catalog had been devised around 1934/1935, and was independent of the number of plugboard 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.

The cyclometer comprised two sets of Enigma rotors, and was used to rapidly determine the length and number of cycles in the permutations 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. The 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 (Kozaczuk, 1984, pp. 242, 284–87). However, on November 1 or 2, 1937, the Germans replaced the reflector in their Enigma machines, which meant that the entire catalog had to be recalculated from scratch. Nonetheless, by January 1938, the Cipher Bureau's German section was reading a remarkable 75% of Enigma intercepts, and, according to Rejewski, with only a minimal increase in personnel, this could easily have been increased to 90%.

Rejewski's bomba and Zygalski's sheets

In 1937, Rejewski, along with the German section of the Cipher Bureau, transferred to a secret facility, near Pyry, in the Kabaty Woods south of Warsaw.

On September 15 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^[3]. The Polish cryptanalysts rapidly responded with new techniques. One was Rejewski's "bomba", an electrically-powered aggregate of six Enigmas, which enabled the daily keys to be solved in about two hours. Six bomba's were built, and were ready for use by mid-November 1938 (Kozaczuk, 1984, p. 242, 290). 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 method used in the two machines was completely different.

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 the 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.

Results given to the British and French

File:SekretEnigmyRejewski.jpg

The 1979 Polish film Sekret Enigmy documents the Polish Enigma story. Here, Rejewski (left, played by Tadeusz Borowski) explains the working of the Enigma machine to British and French specialists at the 1939 Pyry meeting.

As it became clear that war was imminent and Polish resources would not suffice to optimally keep pace with the evolution of Enigma encryption (e.g., due to the Poles' difficulty in producing, in timely fashion, the requisite 60 series of "Zygalski sheets"), the Polish General Staff and government decided to bring their Western allies into the secret. The Polish methods were revealed to British and French intelligence representatives in a meeting at Pyry on 25 July 1939.

The Poles' gift to their Western allies of Enigma decryption, a month before the outbreak of World War II, came not a moment too soon. The British were able to manufacture at least two complete sets of perforated sheets — they sent one to PC Bruno, outside Paris, in mid-December 1939 — and begin reading Enigma within months of the outbreak of war. Without the Polish assistance, British codebreakers would, at the very least, have been considerably delayed in reading Enigma. Sebag-Montefiore (2000) concludes that substantial breaks into German Army and Air Force Enigma 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 Naval Enigma only after late 1942. 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" (Welchman, 1982, p. 289).

Work in France and Britain

PC Bruno

In September 1939, after the outbreak of World War II, Rejewski and his fellow Cipher Bureau workers were evacuated from Poland to Romania. Rejewski, together with Zygalski and Różycki, managed to avoid being interned in a refugee camp, and made their way to Bucharest, where they contacted the French embassy. Having mentioned Betrand's codename to an embassy official, they were rapidly evacuated to France, arriving in Paris by the end of September.

On 20 October they resumed their work on German ciphers at a joint French-Polish-Spanish radio intelligence unit stationed at Château de Vignolles, forty kilometres northeast of Paris, codenamed "PC Bruno". Enigma keys were being broken again by December 1939 or January 1940. The staff at PC Bruno collaborated by teletype with their opposite numbers at Bletchley Park in England. For communications security the allied Polish, French and British cryptological agencies used the Enigma machine itself, with Braquenie closing "Bruno's" Enigma-encrypted messages to Britain with a "Heil Hitler!" (Kozaczuk, 1984, p. 87).

On 24 June 1940, Bruno was disbanded after Germany's victory in the Battle of France, and Rejewski and his colleagues were evacuated to Algeria.

Cadix

Rejewski (right) with colleagues Różycki (centre) and Zygalski (left) in the gardens at Cadix (taken at some point between September 1940 and June 1941).

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, codenamed "Cadix." Cadix began operations on 1 October. Rejewski and his colleagues solved German telegraph ciphers, and also the Swiss version of the Enigma machine (which had no plugboard). Rejewski may have had little or no involvement in working on German Enigma at Cadix ^[4].

In early July 1941, Rejewski and Zygalski were asked to try solving messages enciphered on the secret Polish Lacida cipher machine. Lacida — like Enigma, a rotor machine — had never been subjected to rigorous decryption attempts. The two cryptologists created consternation by breaking the first message within a couple of hours, and further messages in like manner.

On January 9, 1942, 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.

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 arrived at the gate of the chateau where the cryptologists were operating. The visitors, however, did not enter, and merely investigated — and terrorised — nearby farms. Nonetheless, the order to evacuate Cadix was given, and was completed by 9 November. The Germans occupied the chateau only three days later.

Escape from France

The Poles were split into twos and threes. Rejewski and Zygalski were sent to Nice on 11 November, which was in a zone occupied by the Italians. They had to flee again after coming under suspicion, constantly moving and in hiding, to Cannes, Antibes, Nice again, Marseilles, Toulouse, Narbonne, Perpignan and Aix-les-Thermes, close to the Spanish border.

The plan was to smuggle themselves over the Pyrenees across into Spain. Accompanied by a local guide, Rejewski and Zygalski began their trek through the Pyrenees on 29 January 1943. They avoided German and Vichy patrols, but, near midnight and near the border, their guide pulled out a pistol and demanded they hand over the rest of their money. Despite being robbed, they succeeded in reaching the Spanish side of the border, only to be arrested by Spanish security police within hours. The Poles were sent first to a prison in Séo de Urgel until 24 March, then moved to a prison at Lerida. The pair were eventually released on on 4 May, after the intervention of the Polish Red Cross, and sent to Madrid.

Leaving Madrid on 21 July, they made it to Portugal; from there, aboard the HMS Scottish, to Gibraltar; and thence, aboard an old Dakota, to Britain, arriving 3 August 1943.

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.

Despite their ordeal, Rejewski and Zygalksi had fared better than some of their colleagues. Cadix's Polish military chiefs, Langer and Ciężki, had also been captured — by the Germans, as they tried to cross from France into Spain, the night of March 10-11, 1943 — along with three of the other Poles, Antoni Palluth, Edward Fokczyński and Kazimierz Gaca. The first two became prisoners of war, and the other three were sent as slave labor to Germany, where Palluth and Fokczyński died. All five men protected the secret of Enigma decryption.

Britain

On 16 August, Rejewski and Zygalski were inducted as privates into the Polish Army and employed at cracking German SS and SD hand ciphers at Boxmoor. The SS and SD ciphers were largely based on the "Doppelkassetenverfahren" system (a double Playfair scheme).

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 the opportunity of making further contributions to their metier. British codebreaker 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 observance of the "need-to-know" principle. Stripp comments further that "setting them to work on the Doppelkassetten system was like using racehorses to pull wagons" (Stripp, 2004).

On October 10 1943, Rejewski was commissioned a second lieutenant, and on January 1 1945, he was promoted to lieutenant.

Post-war life and recognition

Sculptural memorial to Marian Rejewski in his home city, Bydgoszcz, Poland.

On November 21 1946, having been discharged from the Polish Army in Britain, Rejewski returned to Poland to reunite with his wife Irena, neé Lewandowska, and two children, Andrzej and Janina.

File:Enigma-stamp.jpg

1983 Polish 5-złoty postage stamp commemorating "the 50th anniversary of the breaking of the Enigma cipher" by Marian Rejewski. (The shaft of the spear "breaking" the "E," for "Enigma," is in the Polish national colors: white over red.)

He might have resumed teaching mathematics at a university in Poznań or Szczecin, as suggested by his old Poznań University professor, Zdzisław Krygowski. However, he did not pursue an academic career, for a number of possible reasons. After over seven years' harrowing wartime experiences and exile, Rejewski was exhausted and in ill health. Moreover, taking a university post would have entailed yet another separation from his family and elderly in-laws, with whom Rejewski and his family were now living in Bydgoszcz. A grievous blow to Rejewski, too, soon after his return, was the death in summer 1947 of his 11-year-old son Andrzej from poliomyelitis.

A plaque at Bletchley Park, unveiled in 2002. The English side reads: This plaque commemorates the work of Marian Rejewski, Jerzy Rozycki and Henryk Zygalski, mathematicians of the Polish intelligence service, in first breaking the Enigma code. Their work greatly assisted the Bletchley Park code breakers and contributed to the Allied victory in World War II.

Rejewski worked in Bydgoszcz as an accountant at a factory — bringing disfavor on himself when he discovered irregularities. The Polish Security Service repeatedly investigated him between 1949 and 1958 but never found out his real profession or history; in April 1950 they demanded that he be fired from his job (Polak, 2005, p. 78). He retired in February 1967, and in 1969 moved back with his family to Warsaw after he managed to get his prewar apartment there freed up.

Rejewski remained silent about his work before and during the war until he wrote military historian Władysław Kozaczuk soon after the 1967 publication of Kozaczuk's first book, Bitwa o tajemnice. Subsequently Rejewski published a number of papers on his cryptologic work and contributed generously to articles, books and television programs the world over on the subject. A few years before his death, at the request of Wacław Jędrzejewicz, president of the Józef Piłsudski Institute of America, Rejewski broke enciphered correspondence of Józef Piłsudski and his fellow Polish Socialist conspirators from 1904

Rejewski died at his home on February 13 1980, aged 74, and was buried at Warsaw's Powązki Cemetery.

In 1979, the cryptologic trio became heroes of Sekret Enigmy (The Enigma Secret), a Polish-cryptologists-and-German-spies movie thriller. Late 1980 also saw a Polish television serial based on the Enigma story.

For his military service, Rejewski was decorated with the Gold Cross of Merit, the Silver Cross of Merit with Swords, and the Army Medal. Later, on 12 August 1978, he received the Officer's Cross of the Order of Polonia Restituta. On July 4 2005, Rejewski was posthumously awarded a War Medal 1939-1945 by General Sir Michael Walker, the British Chief of the Defence Staff [5]. The Polish Mathematical Society, too, has honored Rejewski with a special medal. Rejewski turned down an honorary doctorate.

In 1983 a Polish postage stamp commemorated the achievements of Rejewski, Różycki and Zygalski. Polish streets and schools have been named for them; memorial tablets have been placed on buildings associated with their lives and careers, in Poland, France and the United Kingdom

Notes

1. ^ Some writers, after Bloch (1987), argue that Rejewski is more likely to have received these documents in mid-November 1932, rather than 9/10 December.
2. ^ More Enigma settings were provided to the Polish Cipher Bureau by French Intelligence, but these were never passed on to Rejewski and his colleagues. One explanation for this is that the Polish 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.
3. ^ The Navy Enigma had already changed their indicator procedure on 1 May 1937. The SD net, which lagged behind the other services, changed procedure only on 1 July 1939.
4. ^ Rejewski later wrote that at Cadix they did not work on Enigma (Kozaczuk, 1984, p. 270). 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" (Kozaczuk, 1984, p. 117).

See also

• Polish School of Mathematics
• Alan Turing
• List of cryptographers

References

• Gustave Bertrand, Enigma ou la plus grande énigme de la guerre 1939–1945 (Enigma: the Greatest Enigma of the War of 1939–1945), Paris, Librairie Plon, 1973.
• Gilbert Bloch, "Enigma before Ultra: Polish Work and the French Contribution", translated by C.A. Deavours, Cryptologia, July 1987, pp. 142–155.
• Stephen Budiansky, Battle of Wits: the Complete Story of Codebreaking in World War II, New York, The Free Press, 2000.
• 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.)
• David Kahn, The Codebreakers, 2nd edition, 1996, p. 974.
• Władysław Kozaczuk, Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, edited and translated by Christopher Kasparek, Frederick, MD, University Publications of America, 1984. (The standard reference on the Polish part in the Enigma-decryption epic.)
• Jerzy Kubiatowski, "Rejewski, Marian Adam," Polski słownik biograficzny (Polish Biographical Dictionary), vol. XXXI/1, Wrocław, Wydawnictwo Polskiej Akademii Nauk (Polish Academy of Sciences), 1988, pp. 54–56.
• John Lawrence, "A Study of Rejewski's Equations," Cryptologia, 29 (3), July 2005, pp. 233–247.
• John Lawrence, "The Versatility of Rejewksi's Method: Solving for the Wiring of the Second Rotor," Cryptologia, 28 (2), April 2004, pp. 149–152.
• John Lawrence, "Factoring for the Plugboard — Was Rejewski's Proposed Solution for Breaking the Enigma Feasible?", Cryptologia, 29 (4), October 2005.
• Wojciech Polak, "Marian Rejewski in the Sights of the Security Services", in Marian Rejewski: Living with the Enigma Secret, Bydgoszcz, 2005, ISBN 8372081174.
• Marian Rejewski, "An Application of the Theory of Permutations in Breaking the Enigma Cipher", Applicationes Mathematicae, 16 (4), 1980, pp. 543–559 (PDF).
• Marian Rejewski, interview 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 83-90-2357-8-1.
• Hugh Sebag-Montefiore, Enigma: the Battle for the Code, London, Weidenfeld and Nicolson, 2000.
• Alan Stripp, "A British Cryptanalyst Salutes the Polish Cryptanalysts", Appendix E in Władysław Kozaczuk and Jerzy Straszak, Enigma — How the Poles Broke the Nazi Code, 2004, ISBN 078180941X.
• Gordon Welchman, The Hut Six Story: Breaking the Enigma Codes, New York, McGraw-Hill, 1982.

External links

• The Enigma Code Breach by Jan Bury: an account of the Polish role
• The Breaking of Enigma by the Polish Mathematicians by Tony Sale
• Untold Story of Enigma Code-Breaker - The Ministry of Defence (U.K.)
• How Mathematicians Helped Win WWII - National Security Agency
• Enigma documents