How Enigma was broken: Warsaw, then Bletchley Park

Breaking Enigma began in Warsaw, not at Bletchley Park. In December 1932 a young Polish mathematician, Marian Rejewski, worked out the wiring of the German Army's Enigma machine, and for the next seven years he and his colleagues Jerzy Różycki and Henryk Zygalski read German traffic. In July 1939, weeks before the war, the Poles gave everything they had to the British and the French. Bletchley Park built on it with new methods and the bombe, and turned a Polish success that couldn't survive German changes into an industrial operation. We follow the sequence with dates from the record, and say what the popular story gets wrong. The machine itself, and a simulator you can type on, are on the Enigma page.

The machine, in a paragraph

Enigma scrambles each letter through three rotors (four in the naval M4), a reflector and an optional plugboard, and the rotors turn with every key press, so the substitution changes continually. The number of possible settings is astronomical, and the Germans believed nobody could break the machine. It had two structural weaknesses the codebreakers used. The reflector sends the current back through the rotors, so a letter is never enciphered as itself. And the operators were human, with habits that left patterns. Everything below is the exploitation of those two facts.

Warsaw, 1932

Poland had good reason to care, sitting between Germany and the Soviet Union. On September 1, 1932, the Cipher Bureau in Warsaw hired three young mathematicians: Marian Rejewski, Henryk Zygalski and Jerzy Różycki. In late October or early November the head of the German section, Captain Maksymilian Ciężki, gave Rejewski the German Army's Enigma to work on alone. Rejewski used something new in cryptanalysis, the theory of permutations. Each position of the machine is a permutation of the alphabet, and the Germans' procedure for sending the message key produced pairs of related permutations. The cycle structure of those (how the letters link into loops) depends on the rotor settings and not on the plugboard, and that reduced a vast problem to a solvable one.

He had help, which the Poles were careful to admit. In December 1931 French intelligence gave Gwido Langer, the Bureau's head, material about Enigma from a German spy, Hans-Thilo Schmidt, and the French supplied more in 1932 (one account gives the dates as May and September 1932). Rejewski received German operating manuals and monthly key lists around December 9 or 10, 1932 (the exact date is disputed), and by the end of the month he had reconstructed the wiring of all three rotors and the reflector. He later wrote that the intelligence material furnished to the Bureau "should be regarded as having been decisive to solution of the machine". The mathematics turned the documents into wiring, and the Poles did it with no machine in hand, only an analysis.

Reading the traffic, 1933 to 1939

Knowing the wiring was only the beginning. To read a message, the Poles had to find each day's key, and they built tools: a cyclometer (about 1934 or 1935) to catalog the cycle structures, a card catalog of them, and in autumn 1938 Rejewski's electromechanical bomba kryptologiczna, of which six were built in Warsaw. The Germans kept changing the procedure. On November 1, 1937, they changed the reflector. On September 15, 1938, operators began choosing their own starting positions, which ended the method that had worked on Army and Luftwaffe messages. On December 15, 1938, two extra rotors, IV and V, raised the number of rotor orders from 6 to 60, and on January 1, 1939, the number of plugboard connections rose to between seven and ten. The bomba worked only if three rotors were in use, the message key was repeated, and few plugboard leads were used. Each change made the Poles' task harder and hit their small team and limited machinery, and they fell back on hand methods, among them the perforated Zygalski sheets.

July 1939: the handover

By 1939 the Poles could see they couldn't keep up, and war was near. In late July 1939, at a conference near Warsaw (Rejewski gives July 25, at Pyry, and another account gives July 26 and 27), the Poles revealed their methods to French and British representatives, about five weeks before the war began. After Germany invaded on September 1, the Bureau's staff crossed into Romania on September 17 and reached Paris. On October 20, 1939, they resumed work at the station PC Bruno near Paris, and on January 17, 1940, they made the first break into wartime Enigma traffic, from messages of October 28, 1939. When France fell in June 1940, Rejewski and Zygalski moved to Vichy France, then escaped through the Pyrenees to Britain in 1943.

Bletchley Park

Alan Turing and Gordon Welchman reported to Bletchley Park on September 4, 1939. The British didn't simply copy the Poles. The Polish methods depended on features the Germans were removing (the repeated message key, few plugboard leads), so Turing designed a machine that needed none of them. The bombe (1939) takes a crib, a stretch of plaintext the analysts can guess, such as a weather report or a standard greeting, and tests thousands of rotor positions, looking for ones that contradict the assumed text. Because a letter is never enciphered as itself, the analysts could also rule out positions where the crib lined up wrongly. A bombe didn't decrypt a message. It narrowed the settings to a few candidates that people then finished by hand. Welchman added a refinement in 1940, the diagonal board, which used the symmetry of the plugboard to make the machine far more powerful, with the engineering done by Harold "Doc" Keen of the British Tabulating Machine Company at Letchworth.

The U-boat war was the sharpest test. Bulldog's boarding party under Sub-Lieutenant David Balme stripped U-110 of her short-signal code book and Enigma machine on May 9, 1941, and Bletchley's reading of naval traffic that summer coincided with a fall in merchant ship losses. When the Navy added a fourth rotor on February 1, 1942, Bletchley lost the U-boat traffic for most of a year. A boarding party from HMS Petard recovered the new weather codebooks from the sinking U-559 on October 30, 1942, at the cost of two lives (Tony Fasson and Colin Grazier, both awarded the George Cross; the young Tommy Brown survived and received the George Medal), and in December the Shark was broken again. The accounts differ in some details of the boarding, but nobody disputes the date and the significance.

Ultra, and what it was worth

The intelligence from Enigma and other broken ciphers, including the Lorenz teleprinter machine (the Lorenz page), was classified as Ultra, above "Most Secret". Britain kept the secret for decades. Wladyslaw Kozaczuk revealed in 1967 that Polish cryptologists had broken Enigma before the war, Gustave Bertrand's book discussed it publicly in 1973, and the ban was lifted in 1974, the year F. W. Winterbotham published The Ultra Secret, which he wrote from memory without access to the archives. How much it shortened the war is disputed, and honest historians say so. Harry Hinsley thought it was something like two to four years. John Keegan suggested it might have been as little as the three months needed for the atomic bomb. Guy Hartcup concluded that it's impossible to calculate in months or years.

Record and myth

• "Turing broke Enigma." The Poles solved the machine in 1932 and read it for seven years, and Britain's method was built on their handover. Turing designed the bombe and Welchman improved it, while Knox, others and thousands of staff, some 8,000 of them women, made the system work.
• "The bombe decrypted the messages." It searched for settings consistent with a guessed crib, and people finished the job.
• "Enigma couldn't be broken." The machine had a structural flaw, the reflector, and the Germans' procedures were full of habits. A large key space isn't the same as security.
• "Enigma was the only cipher." The British also broke the Lorenz machine ("Tunny"), which the High Command used, with no Polish head start. It was a harder task on a different machine, and it led to Colossus.

Rejewski after the war

Rejewski, born on August 16, 1905, in Bromberg (now Bydgoszcz), returned to Poland in November 1946 and for about two decades said nothing about his work, to avoid attracting the attention of Poland's Soviet-dominated government. He broke his silence in 1967, giving his memoirs to the Military Historical Institute. He died in Warsaw on February 13, 1980. Poland posthumously awarded him the Grand Cross of the Order of Polonia Restituta in 2000, and in 2014 the IEEE gave him a Milestone Award.

The lesson

The Enigma story is the practical form of Kerckhoffs's principle. The Germans' security leaned on keeping the machine secret and on procedures people followed badly, and a flaw in the machine's design guaranteed that once enough was known, it fell. A modern cipher is designed so a captured copy tells the enemy nothing, and so its security doesn't depend on operator discipline. The later machines show the other end of the scale. The American SIGABA (SIGABA) and the British Typex (Typex) fixed Enigma's weaknesses, and Allied traffic was never broken in the same way.

How cipher.ink uses this

cipher.ink doesn't use rotor machines, but the site has a working Enigma I, M3 and M4 you can type on, checked against a real wartime message: the Enigma simulator decrypts the Admiral Dönitz message of May 1, 1945, with its true settings. The story's central point applies to the site's own design. A cipher is only as strong as the way it's used, which is why a message here opens only with the key you chose, and why the code that makes it is public (the code).