Marian Rejewski

Marian Rejewski as second lieutenant (signals), Polish Army in Britain, in late 1943 or in 1944, some 11 or 12 years after his first break into Enigma.

Marian Adam Rejewski (pronounced "MAHR-yahn AH-dahm Rey-EFF-ski"; Bydgoszcz, Poland, August 16, 1905 – February 13, 1980 in Warsaw, Poland) was a Polish mathematician and cryptologist, famous for his ground-breaking, long-running work in decrypting German Enigma ciphers. His achievements jump-started British reading of Enigma in World War II ("Ultra"), and the intelligence so gained may have substantially altered the course of the war.

Education and codebreaking in Poland

Born in Bydgoszcz, Poland, Rejewski was a mathematics graduate of Poznań University who, as a student, had attended a cryptology course organized there for selected mathematics students by the Polish General Staff's Cipher Bureau. As a postgraduate student he studied actuarial statistics for a year at Göttingen, Germany. Returning to Poland, he taught mathematics for two years at Poznań University. On September 1, 1932, as a civilian employee, he joined the Biuro Szyfrów (Cipher Bureau) of Polish Military Intelligence at the General Staff building in Warsaw. Shortly thereafter, he was asked to study ways of attacking the German Army's Enigma cipher machine, which had come into service in 1930.

In doing so, he fundamentally advanced cryptanalysis. Previous methods had exploited patterns and statistics in natural language texts: for example, letter-frequency analysis. Rejewski, however, for the first time applied techniques from pure mathematics — permutation theory — in his attack on the Enigma cipher. These mathematical techniques, combined with material supplied by French military intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and reflector and, equally important, to develop methods of breaking the periodic as well as individual keys used in encrypting messages on the Enigma machine. "The solution," David Kahn writes, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time." (David Kahn, The Codebreakers, revised ed., p. 974). Rejewski devised a mathematical theorem that wartime Bletchley Park luminary, Professor I. J. Good, has described as "the mathematical theorem that won World War II."Template:Ref

A good deal of confusion persists regarding the sequence and relative contribution of mathematics and intelligence in Rejewski's break into the German machine cipher. It may therefore be well to consider Rejewski's own description of the process, as recorded in a 1978 interview:

The first six letters of any message held a special meaning. You could see that by inspection. This was a doubly enciphered key... I very quickly... [solved] these first six letters which constituted the key (every message had its own individual key which was doubly enciphered). If the Germans... hadn't enciphered these keys but had given them plain at the head [of the message] they would have come out better in the end. Because I managed to solve the keys anyway, and in addition [I got] this material on which I was able to work and solve the Enigma [machine] itself.

One day Major [Maksymilian] Ciężki [head of the Cipher Bureau's German section, Biuro Szyfrów-4] brought me a commercial [Enigma] machine, when I already had the first results, so that I could get a better feel for the thing.

Subsequent work consisted in manipulating certain equations in order to solve them. [I] hadn't expected [the work] to go quickly, but in any event there was a snag here. Then... one fine day, it may have been the ninth or tenth of December 1932, Major Ciężki brought some intelligence material. I didn't know it came from the French. It included... tables of keys for two months. September and October 1932. This was a great help to me, because thanks to my having these keys... the number of unknowns in the equations was reduced, and I was able to solve these equations, and one fine day, as I was sitting there writing, the internal connections [or "wirings"] just came out in the form... of letters or numbers. [These were the wirings] for the first [rotor] on the far right, which always... revolved at every depression of a key...

I later... learned that [on December 8, 1932, Captain — later, General — Gustave] Bertrand [chief of French radio intelligence and decryption] had come to Warsaw and delivered this material [obtained from Hans-Thilo Schmidt, codename "Asche"].

I think that by the end of that year, 1932, the machine was solved... in the sense that the [wirings] in the three [rotors] and the [stationary] fourth drum [the "reflector"] were known. Now an ordinary commercial machine was altered [by rewiring the drums, thus making it possible] to read... messages to which Bertrand had supplied the keys, for those two months, September and October 1932. It was very important that the months happened to be September and October, in other words, periods that belonged to two different quarters. [That is] because... the key consisted of several elements [and] one element of the key was changed only once a quarter. Namely, the order of the [rotors]. The [rotors] were numbered I, II, III. One could insert them [into the machine] in any order he pleased. At that time they were changed once a quarter. Since September and October belonged to two different quarters, in September and October the orders of the [rotors] were different. [With] the method that I had been using to find the [wirings] in a [rotor], I could only solve the [far] right-hand [rotor], the one that revolved one place every time [a key was depressed]. Thanks to the keys for September, I could solve the [rotor] that was in the far right-hand position in September. And since I also had the keys for October, using the same method I was later able to find the [wirings] in the [rotor] that was at the [far] right in October... So... I already had two [rotors]. The third [rotor] and... the [reflector] now weren't so difficult... I managed to find them by other methods.

[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. Supposely he did supply [further keys] but I never got any more. 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... Within a short time we had found... several methods [particularly] the grill [and] the cyclometer... The cyclometer method especially was very important; ...it required a lot of preparation but, after that, finding the keys would take ten to twenty minutes...Template:Ref

It has been speculated whether the Enigma-drum wirings could have been solved without Hans-Thilo Schmidt's documents supplied to the Polish Cipher Bureau by French intelligence. It may be illuminating to consider Rejewski's last word on this:

To this day, it is not known whether equation set (3) is soluble. [Its solution would yield the wirings.] To be sure, another way was found, at least in theory, to reconstruct the [wirings] in the drums. Still, this approach is imperfect and tedious. It requires possession of messages from two days with the same or close settings of the drums, and hence it conditions the discovery of the drum connections on chance, and then it also requires many trials, so that it is not clear that the Cipher Bureau's directors would have had the patience to employ several personnel for a long period without certainty of getting results... Hence the conclusion is that the intelligence material furnished to us should be regarded as having been decisive to solution of the machine.Template:Ref

Part of Rejewski's success in reconstructing the German Enigma machine stemmed from an intimate knowledge of the German mind, gleaned as a child in German-occupied western Poland. A factor that had helped frustrate British cryptologist Alfred Dillwyn Knox's attempts to reconstruct the German Enigma was his inability to determine the wiring connections in the entry drum. Rejewski writes,

It turned out later, that they can be found by deduction, but in December 1932, or perhaps in the first days of 1933, I obtained [them] by guessing. I assumed that, since the keyboard keys were not connected with the successive contacts in the entry drum in the order of the letters on the keyboard, then maybe they were connected up in alphabetical order; that is, that the permutation caused by the entry drum was an identity and need not be taken into account at all. This time, luck smiled upon me. The hypothesis proved correct, and the very first trial yielded a positive result. From my pencil, as by magic, began to issue numbers designating the connections in drum N. Thus the connections in one drum, the right-hand drum, were finally known.Template:Ref

After Rejewski had determined the wiring in the remaining drums, he and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski devised methods and equipment to routinely break Enigma ciphers. The earliest method for reconstructing daily keys was the "grill" method, based on the fact that the commutator's ("plugboard's") plug connections exchanged only six pairs of letters, leaving fourteen letters unchanged.Template:Ref Next was Różycki's "clock" method, which sometimes made it possible to determine which rotor was in the N rotor's position, that is, at the right-hand side of the Enigma machine, on a given day.Template:Ref That was followed by Rejewski's "cyclometer," basically comprising two sets of Enigma rotors, which permitted the determination of the length and number of cycles in the "characteristics" for all 17,576 positions of the rotors for a given sequence of rotors (there being 6 such possible sequences, the resultant card catalog of characteristics encompassed 105,456 entries). This method's utility was independent of the number of plug connections in the commutator (and of the reconstruction of message keys). The catalog's preparation took over a year, but when it was ready, it made obtaining daily keys a matter of 10-20 minutes.Template:Ref The cyclometer and card catalog were followed, at that stage in the evolution of German Enigma cryptography, by Rejewski's "bomb" (Polish: bomba), essentially an electrically powered aggregate of six Enigmas, which shortened the time needed to reconstruct daily keys to about two hours.Template:Ref At about that same time, Zygalski invented a manual method, that of "perforated sheets" ("Zygalski sheets"), which, like the "card-catalog" method, was independent of the number of plug connections in the commutator; when the sheets were superposed and moved in the proper manner with respect to each other, the number of visible apertures gradually decreased, and if enough data were available there finally remained a single aperture, probably corresponding to the solution.Template:Ref

Details of the Polish achievements were revealed to British and French intelligence representatives in a meeting at a secret Polish Cipher Bureau facility at Pyry, in the Kabaty Woods south of Warsaw, on July 25, 1939. The Germans had made changes to Enigma equipment and procedures in 1938 and 1939 that increased the difficulty of breaking messages; and as it became clear that war was imminent and Polish resources would not suffice to optimally keep pace with the evolution of Enigma encryption, the Polish General Staff and government had decided to bring their western allies into the secret. With the crucial Polish contribution of reconstructed sight-unseen German Enigma machines and the Poles' cryptological techniques and equipment, the British at Bletchley Park, and later the Americans, were able to continue the work of breaking German Army, Air Force, Nazi Party SD, and (though with substantially greater difficulty) Naval Enigma traffic.

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. Former Bletchley Park cryptologist Gordon Welchman has written: "Ultra [the British Enigma-decryption operation] 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."Template:Ref

Work in France and Britain

In September 1939, after the outbreak of World War II, Rejewski and his fellow Cipher Bureau workers were evacuated from Poland via Romania to France. At "PC Bruno," outside Paris, they continued their work at breaking Enigma ciphers, collaborating by teletype with their opposite numbers at Bletchley Park, 50 miles (80 km.) north of London. According to French Air Force Captain Henri Braquenie — who had, with Bertrand, attended the historic July 25, 1939, Warsaw conference — for maximum communications security the allied Polish, French and British cryptological agencies used Enigma itself, with Braquenie closing "Bruno's" Enigma-encrypted messages to Britain with a "Heil Hitler!"Template:Ref

When "Bruno" was evacuated upon Germany's invasion of France, the Polish cryptologists and their ancillary staff worked for two years in unoccupied southern (Vichy) France and outside of Algiers in French North Africa. Following the German takeover of the "Free Zone" in November 1942, the secret French-Polish "Cadix" center in southern France was evacuated. Its Polish military chiefs were captured and imprisoned by the Germans but protected the secret of Enigma decryption. Różycki, the youngest of the three mathematicians, had died in the January 1942 sinking of a French passenger ship as he was returning from a stint in Algeria to "Cadix" in southern France.

Rejewski and Zygalski fled France for Spain, where they were arrested and imprisoned for three months. Released upon the intervention of the Polish Red Cross, almost three months later, in July 1943, they made it to Portugal; from there, aboard the HMS Scottish, to Gibraltar; and thence, aboard an old Dakota, to Britain. Here Rejewski and Zygalski were inducted as privates into the Polish Army (they would eventually be promoted to lieutenant) and employed at cracking German SS and SD hand ciphers. Enigma decryption had become a British and American monopoly; the two mathematicians who, with their late colleague, had laid the foundations for Allied Enigma decryption and had conferred at "PC Bruno" with Alan Turing, were now excluded from the opportunity of making further contributions to their metier. No doubt they must have wondered what use Poland's allies had made of their achievements.

Post-war life

After the war, Zygalski remained in Britain while Rejewski took a big chance and returned to Poland in 1946 to reunite with his wife and two children. He worked as a bookkeeper at a factory—bringing disfavor on himself when he discovered irregularities—until his retirement, and was silent about his work before and during the war until, in the 1970's, he contacted the military historian Władysław Kozaczuk. He published a number of papers on his cryptological work and contributed generously to books on the subject.

Rejewski died in 1980 in Warsaw and was buried at the Powązki Cemetery, one of Poland's pantheons of the great and valiant.

The Polish Mathematical Society has honored him with a special medal.

An odd footnote to the story of Rejewski's cryptologic contributions is that his role in World War II had been so obscure that one best-selling book (William Stevenson's A Man Called Intrepid, 1976) not only did not credit him with the work he had done (repeating, instead, a variant of the cock-and-bull story about a "machine stolen from a transport truck") but identified him as "Mademoiselle Marian Rewjeski."

Notes

1. Template:Note I.J. Good, prefatory remarks to: Marian Rejewski...
2. Template:Note Marian Rejewski, in Richard Woytak's 1978 interview, first published in Cryptologia, vol. 6, no. 1 [January 1982], reprinted in Władysław Kozaczuk's Enigma 1984, pp. 232-35.
3. Template:Note Marian Rejewski, in Władysław Kozaczuk's Enigma 1984, p. 258.
4. Template:Note ibid
5. Template:Note ibid, p. 242.
6. Template:Note ibid, p. 290.
7. Template:Note ibid, pp. 242, 285-87.
8. Template:Note ibid, pp. 242, 290.
9. Template:Note ibid, pp. 243, 287-89.
10. Template:Note Gordon Welchman, The Hut Six Story, p. 289.
11. Template:Note Kozaczuk, Enigma, p. 87.

References

• Marian Rejewski, An Application of the Theory of Permutations in Breaking the Enigma Cipher (http://frode.home.cern.ch/frode/crypto/rew80.pdf). (Appears to be the same paper as appendix E in Kozaczuk 1984.
• 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.)
• Gustave Bertrand, Enigma ou la plus grande énigme de la guerre 1939–1945, Paris, Librairie Plon, 1973.
• Gordon Welchman, The Hut Six Story: Breaking the Enigma Codes, New York, McGraw-Hill, 1982.
• Stephen Budiansky, Battle of Wits: the Complete Story of Codebreaking in World War II, New York, The Free Press, 2000.
• Hugh Sebag-Montefiore, Enigma: the Battle for the Code, London, Weidenfeld and Nicolson, 2000. (Includes information on Asche's fate, obtained from his daughter.)
• I.J. Good, afterword to: Marian Rejewski, "How Polish Mathematicians Deciphered the Enigma," Annals of the History of Computing, vol. 3, no. 3 (July 1981). This paper of Rejewski's appears as appendix D in Kozaczuk 1984.
• Marian Rejewski, "How the Polish Mathematicians Decrypted Enigma" (in Polish), Annales Societatis Mathematicae Poloniae, Warsaw, Państwowe Wydawnictwo Naukowe, 1981. (Same paper as the preceding.)
• "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.

External links

• The Enigma Code Breach (http://www.armyradio.com/publish/Articles/The_Enigma_Code_Breach/The_Enigma_Code_Breach.htm) by Jan Bury: an account of the Polish role.de:Marian Rejewski

nl:Marian Rejewski pl:Marian Rejewski sl:Marian Rejewski zh:马里安·雷耶夫斯基