Marian Adam Rejewski (Polish: [ˈmarjan rɛˈjɛfskʲi] ; 16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who in late 1932 reconstructed the sight-unseen German military Enigma cipher machine.
Over the next nearly seven years, Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski, working at the Polish General Staff's Cipher Bureau, developed techniques and equipment for decrypting the Enigma ciphers, even as the Germans introduced modifications to their Enigma machines and encryption procedures. Rejewski's contributions included the cryptologic card catalog and the cryptologic bomb.
Five weeks before the outbreak of World War II in Europe, the Poles shared their achievements with French and British counterparts who had made no progress, enabling Britain to begin reading German Enigma ciphers. The intelligence gained by the British from Enigma decrypts formed part of what they code-named Ultra and contributed—perhaps decisively—to the defeat of Nazi Germany.
Soon after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued breaking Enigma ciphers. After the fall of France in June 1940, they and their support staff were evacuated to Algeria in North Africa; a few months later, they resumed work clandestinely in southern Vichy France. After the Vichy "Free Zone" was occupied by Nazi Germany in November 1942, Rejewski and Zygalski escaped via Spain (and Spanish imprisonment), Portugal, and Gibraltar to Britain. There they enlisted in the Polish Armed Forces and were put to work solving low-grade German ciphers.
After the war, Rejewski returned to Poland and his family. For two decades, he remained silent about his prewar and wartime work so as to avoid the attention of Poland's Soviet-dominated government. In 1967, he broke his silence, providing Poland's Military Historical Institute his memoirs of work at the Cipher Bureau.
Marian Rejewski was born 16 August 1905 in Bromberg in the Prussian Province of Posen (now Bydgoszcz, Poland) to Józef and Matylda, née Thoms. After completing secondary school, he studied mathematics at Poznań University's Mathematics Institute, housed in Poznań Castle.
In 1929, shortly before graduating from university, Rejewski began attending a secret cryptology course which opened on 15 January, organized for select German-speaking mathematics students by the Polish General Staff's Cipher Bureau with the help of the Mathematics Institute's Professor Zdzisław Krygowski. The course was conducted off-campus at a military facility and, as Rejewski would discover in France in 1939, "was entirely and literally based" on a 1925 book by French colonel Marcel Givierge, Cours de cryptographie (Cryptography Course). 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.
On 1 March 1929, Rejewski graduated with a Master of Philosophy degree in mathematics. A few weeks after graduating, and without having completed the Cipher Bureau's cryptology course, he began the first year of a two-year actuarial statistics course at Göttingen, Germany. He did not complete the statistics course, because while home for the summer of 1930, he accepted an offer, from Professor Krygowski, of a mathematics teaching assistantship at Poznań University. He also began working part-time for the Cipher Bureau, which by then had set up an outpost at Poznań to decrypt intercepted German radio messages. Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber".
The Poznań branch of the Cipher Bureau was disbanded in the summer of 1932. In Warsaw, on 1 September 1932, Rejewski, Zygalski, and Różycki joined the Cipher Bureau as civilian employees working at the General Staff building (the Saxon Palace). Their first assignment was to solve a four-letter code used by the Kriegsmarine (German Navy). Progress was initially slow, but sped up after a test exchange—consisting of a six-group signal, followed by a four-group response—was intercepted. The cryptologists guessed correctly that the first signal was the question, "When was Frederick the Great born?" followed by the response, "1712."
On 20 June 1934 Rejewski married Irena Maria Lewandowska, daughter of a prosperous dentist. The couple eventually had two children: a son, Andrzej (Andrew), born in 1936; and a daughter, Janina (Joan), born in 1939. Janina would later become a mathematician like her father.
The Enigma machine was an electromechanical device, equipped with a 26-letter keyboard and 26 lamps, corresponding to the letters of the alphabet. Inside was a set of wired drums (rotors and a reflector) that scrambled the input. The machine used a plugboard to swap pairs of letters, and the encipherment varied from one key press to the next. For two operators to communicate, both Enigma machines had to be set up in the same way. The large number of possibilities for setting the rotors and the plugboard combined to form an astronomical number of configurations, and the settings were changed daily, so the machine code had to be "broken" anew each day.
Before 1932, the Cipher Bureau had succeeded in solving an earlier Enigma machine that functioned without a plugboard, but had been unsuccessful with the Enigma I, a new standard German cipher machine that was coming into widespread use. In late October or early November 1932, the head of the Cipher Bureau's German section, Captain Maksymilian Ciężki, tasked Rejewski to work alone on the German Enigma I machine for a couple of hours per day; Rejewski was not to tell his colleagues what he was doing.
To decrypt Enigma messages, three pieces of information were needed: (1) a general understanding of how Enigma functioned; (2) the wiring of the rotors; and (3) the daily settings (the sequence and orientations of the rotors, and the plug connections on the plugboard). Rejewski had only the first at his disposal, based on information already acquired by the Cipher Bureau.
First Rejewski tackled the problem of discovering the wiring of the rotors. To do this, according to historian David Kahn, he 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 applied techniques from group theory—theorems about permutations—in his attack on Enigma. These mathematical techniques, combined with material supplied by Gustave Bertrand, chief of French radio intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector. "The solution", writes Kahn, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time." Rejewski used a mathematical theorem—that two permutations are conjugate if and only if they have the same cycle structure—that mathematics professor and Cryptologia co-editor Cipher A. Deavours describes as "the theorem that won World War II".
Before receiving the French intelligence material, Rejewski had made a careful study of Enigma messages, particularly of the first six letters of messages intercepted on a single day. 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 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 KYG for a message. The operator would first set the Enigma's rotors to the ground setting, which might be GBL on that particular day, and then encrypt the message setting on the Enigma twice; that is, the operator would enter KYGKYG (which might come out to something like QZKBLX). The operator would then reposition the rotors at KYG, and encrypt the actual message. A receiving operator could reverse the process to recover first the message setting, then the message itself. The repetition of the message setting was apparently meant as an error check to detect garbles, but it had the unforeseen effect of greatly weakening the cipher. Due to the indicator's repetition of the message setting, Rejewski knew that, in the plaintext of the indicator, the first and fourth letters were the same, the second and fifth were the same, and the third and sixth were the same. These relations could be exploited to break into the cipher.