Marian Rejewski

Marian Rejewski as second lieutenant (signals), Polish Army in Britain, in late 1943 or in 1944.

Marian Rejewski (pronounced "MAHR-yahn Rey-EFF-ski"; August 26, 1905—February 13, 1980) was a Polish mathematician and cryptologist, famous for his ground-breaking, long-running work in decrypting German Enigma ciphers. His remarkable achievements doubtless altered substantially the ultimate outcome of World War II.

Education and codebreaking in Poland

Born in Bydgoszcz, Poland, Rejewski was a graduate of Poznań University and a civilian employee of Polish military intelligence. As a postgraduate student he studied actuarial statistics at Göttingen, Germany. Two years after his return, on September 1, 1932, he joined the Biuro Szyfrów (Cipher Bureau) of Polish Military Intelligence 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, applied permutation theory from pure mathematics for the first time in his attack on the Enigma cipher. From his equations he was able to deduce the wirings of the drums in the German military Enigma, a feat about which David Kahn says: "The solution was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time." Rejewski devised a mathematical theorem that wartime Bletchley Park luminary, Professor I.J. Good, has described, without hyperbole, as "the mathematical theorem that won World War II."

Part of Rejewski's success 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. "It turned out later," Rejewski writes, "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." The proverbially orderly Germans had, to their detriment, surpassed even themselves!

After Rejewski had determined the wiring in the remaining drums, he and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski devised practical ways to routinely break Enigma ciphers. The trio designed machinery to help with the cryptanalytic work. Rejewski's cyclometer was the first, a device used for compiling a catalog of Enigma settings. Another device was his bomba — Polish for "bomb": an account by Cipher Bureau technician Czesław Betlewski relates that the device was called by this curious name (also "washing machine" and "mangle") after the characteristic muffled noise it produced. A bomba could find the Enigma machine's wheel order and starting position by searching through a vast number of possibilities.

Details of the Polish achievements were revealed to British and French intelligence at a meeting in 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 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 came not a moment too soon. As another Bletchley Park luminary, mathematician 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."

Work in France and Britain

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

In September 1939, after the outbreak of World War II, Rejewski and his fellow Cipher Bureau workers were evacuated from Poland via Rumania to France, where at "PC Bruno," outside Paris, they continued their work at breaking Enigma ciphers (collaborating by teletype with their opposite numbers at Bletchley Park). 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 1960's, he contacted the military historian Władysław Kozaczuk. He published a number of papers on his cryptological work and contributed generously to a number of 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."

References

• Marian Rejewski, An Application of the Theory of Permutations in Breaking the Enigma Cipher
• 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.)
• Marian Rejewski, "How the Polish Mathematicians Decrypted Enigma" (in Polish), Annales Societatis Mathematicae Poloniae, Warsaw, Państwowe Wydawnictwo Naukowe, 1981.