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Marian Rejewski, the Polish Mathematician who solved the Enigma Cipher Machine
The earliest Polish work on the intercepted German machine ciphers had
begun already in 1928, right after the system's introduction by the German
Army. However, no progress was made during the next four years. Then the
Polish Cipher Bureau - which was part of 2nd Section (Military Intelligence)
of the General Staff - decided to recruit three young mathematicians, all
of them graduates of the Mathematical Institute at the University in Poznan.
To be sure they were first all given, along with twenty-odd their fellow-students,
a rudimentary training in codebreaking during a special course, organized
by the military. Their real aim was to find cryptological talents, the
most promising of which was considered Marian Rejewski. After his graduation,
he went for a one-year period of advanced study in actuarial mathematics
to Goettingen and following his return, had thought at the Mathematical
Institute in Poznan.
On September 1, 1932, Rejewski and his two somewhat younger colleagues, Jerzy Rozycki, and Henryk Zygalski began work as regular employees at the Cipher Bureau in Warsaw. During the first few weeks, the young mathematicians worked on relatively simpler German Navy codes. By that time the Kriegsmarine was particularly active in Polish shore, while the German government tried to curtail the Polish rights in then-Free City of Danzig against the Versailles Treaty stipulations, in early-October, 1932, Rejewski was given a separate room and told to take a closer look at a pile of the Enigma-researchers. He was also supplied with an obsolete commercial Enigma machine, initial type, which had been bought in Germany. This, however, lacking many essential parts of the military-type machine, especially the commutator ("plug board"), was quite useless. Polish penetration into the secrets of the Enigma - remarks an American cipher expert and historian - began in ernest when Rejewski realized the applicability of some properties of permutations to his analysis of the German machine cipher.
The French puzzled over this information, then consulted with the British, who agreed that it was insufficient to be of any practical use. Bertrand then offered it to Marian Rejewski in Poland who was overjoyed upon receiving even this small crumb. Rejewski asked Bertrand if he could obtain some outdated Enigma keys. The Frenchman relayed this request to Schmidt who readily obliged, and the keys were passed back to Poland.
The order in which the rotors were placed in the machine was changed every three months, after which the order was repeated. As each of the different rotors was dropped into the right-hand position, the same analysis was performed, until the wiring of each of the three rotors was known.
The Poles had a replica Enigma machine made, based on the commercial model with the rotors rewired, in great secrecy. They set up the machine according to the code, fed in the encoded message and - out came gibberish! Rejewski checked and re-checked his equations, and was almost ready to give up in despair when he wondered if the wiring from the keyboard to the scrambler was A to A, B to B, etc., unlike the commercial model, which was Q to A, W to B, ... (keyboard order). The machine was re-wired and out came plaintext! The year was 1933, and they now had a functional Enigma replica.
(There are various accounts of how the Poles reconstructed the Enigma. Kahn states that the Poles built a machine by mathematical analysis based on stolen keys and intercepted messages. Winterbotham claims that a Polish factory worker memorized the rotor wiring. Lewin relates that the Poles intercepted an Enigma machine being shipped to the German embassy in Warsaw. Welchman repeats Stevenson's story of an ambushed German truck, its Enigma replaced by a dummy, then set on fire. The evidence, particularly that from the codebreakers themselves, overwhelmingly supports the view that the Enigma replica was reconstructed from mathematical models.)
The German operators helped the codebreakers no end by selecting message keys like AAA, ZZZ, or QAY (the leftmost diagonal of the keyboard).
Rejewski collected a list of the first six letters from all messages transmitted each day. It was known that the first and fourth (1,4), second and fifth (2,5), and third and sixth (3,6) letters of the message key were identical. He was able to construct chains of how the identical letters changed as the scrambler moved each time a letter was entered. He discovered a characteristic cycle that was different for each scrambler position. In 1934 the "cyclometre" was invented, a device consisting of two sets of rotors and reversing drums three letters out of phase, interconnected by switches and lamps, and operated by hand. It took them a year, but the Poles were able to construct a card catalog of the characteristic cycles at each of the 6 x 17576 possible positions (the 6 possible combinations of the 3 rotor placements multiplied by the number of scrambler positions). After that, it took only 20 minutes to look through the card file and discover the daily setting. On November 1, 1937, the Germans changed the umkherwalze wiring, and the card catalog was useless. The cataloging process had to be done all over again.
10 sets of "Zygalski sheets" (one set for each of the ten possible rotor positions) were prepared. Each set consisted of 26 large squares of paper (one for each position of the slow rotor), marked at the top and side with letters of the alphabet. Rows represented the position of the of the middle rotor; columns positions of the slow rotor. If a female was possible at some position of the rotors (for example, the "A" sheet of the slow rotor, with center rotor at "M" and the fast rotor at "R"), a hole was laboriously cut at the intersection using a razor blade.
The sheets were placed one by one on top of each other, positioned according to 12 females found in the messages. If, after 12 sheets had been stacked, light shone through all the sheets in one place, a possible key had been found. If not, a different sheet (or set) was selected, and another stacking performed. These settings were tried, one by one, on an Enigma replica.
The Enigma scrambler was single-ended; one set of terminals served both as input and output. What was needed was a device where certain input terminals could be energized, and as it went through all the possible positions, a second set of terminals monitored to detect a desired output. For example, if it was assumed that the first three letters of a coded message HJQ represented the plaintext anx, input terminals H, J, and Q are energized and output terminals a, n, and x monitored. The machine steps through all cycles until a match is found, and then stops.
Three sets of double-ended scramblers, one machine cycle apart, were driven by a motor. In our example, input terminals H, J, X were energized, and the machine stopped at any occurence of a, n, x. For each test run, 6 bomby were required, one for each of the 6 possible rotor positions.
The machines made a ticking noise as they worked, and stopped when they arrived a solution. The Poles called them bomby (plural, "bomba" singular), perhaps from the ticking of the clockwork in a bomb fuse which stopped just before it exploded. Another possibility is that the name came from an ice cream dish they were eating at the time.
With keys given them by the French, and using replica machines they had built, the Polish team of Marian Rejewski, Jerzy R?zycki and Henryk Zygalski were able to decode most German messages. They were particularly interested in radio traffic between German troops training in Russia, a ploy which allowed them to circumvent terms of the Versailles Treaty. However, they never related their results to the French, probably because they feared the Germans would find out that their codes had been compromised and institute new procedures which would nullify their success. The French, puzzled at receiving no intelligence, continued to pass on the keys nevertheless.
The Poles began their efforts when the Germans used only three rotors. Although the keys were out of date, they were able to apply them to a backlog of messages.
Dec. 15, 1938 the Germans added two new rotors, making five available, although only three were used in the machine at any one time. The Polish resources were severely strained, as now 60 sets of Zygalski sheets and 60 bomby (at a cost of 1.5 million zlotych, about $350,000) would have been required. This, and knowing from intercepts that their country was about to be invaded, persuaded the Poles to share their information with the French and British. The British had decided to take a crack at Enigma codes, but it was too late; the Germans had added complications that made a break impossible. The Poles, having a ten year head start, were able to take advantage of the days when coding methods were simpler, and operators, becoming used to the new system, made some serious mistakes.
July 25, 1939, at a secret meeting in the Kabackie Woods near the town of Pyry, the Poles handed over their complete solution to the German codes, their Enigma replicas and bomby to the dumbfounded British.
Many accounts of the meeting mention a mysterious "Mr. Sandwich", speculating that he was Stewart Menzies, head of British Intelligence. In an interview with Patrick Beesly ("Who was the Third Man at Pyry", Cryptologia, II, #2, 324-330) Admiral John Godfrey Director of O.N.I. (Office of Naval Intelligence) disclosed that he had sent Commander Humphrey Sandwith to the meeting. In later interview with Beesly, Gustav Bertrand confirmed that he was indeed Sandwith.
On September 1, Hitler invaded Poland. On the 5th, the codebreakers packed up their Enigma replicas, Zygalski sheets and bomby, and made a run for France. After a mad flight in the company of thousands of others trying desperately to flee the Germans, they made it through Austria to France, but had to destroy all their equipment along the way. The Poles continued their work in France, sharing their work with the British. In fact, the British furnished them with sixty sets of 26 Zygalski sheets, since theirs had been destroyed in the evacuation.
Since it was their brilliant work, turned over to the British, which allowed the Allies to read the German messages, it is hard to believe that the English never allowed them to work as codebreakers on the vital Kriegsmarine (Navy) Schl?ssel-M traffic, which was not broken until naval rotors VI and VII were captured. Might not Rejewski have been able to employ the same methods in solving the wiring of those rotors that he had so successfully used before?
Was it British arrogance that denied the Poles their due in so many publications once "Ultra" was no longer under wraps? Perhaps not. The secrecy was so tight that most of the British codebreakers could not have known that their work was based on Polish success.
And what of the three men who did so much to shorten World War II? Jerzy R?zycki was lost at sea Jan. 9, 1942, enroute from Algeria to France. Henryk Zygalski decided to remain in England after the War, where he died in 1978. Marian Rejewski returned to Poland, where he died in 1980 at the age of 74.
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