Marian Rejewski breaks Enigma
On a December afternoon in 1932, a 27-year-old mathematician at Warsaw’s Cipher Bureau received a slim packet of documents from French intelligence. Inside: German Enigma settings for September and October of that year, obtained at considerable risk by a spy inside the Reich’s cipher office. Marian Rejewski spread the papers on his desk, thought about permutation groups, and by Christmas had reconstructed — on paper alone — a cipher machine he had never touched or seen.
The German military had adopted the Enigma in the late 1920s, convinced that daily-changing rotor settings combined with a plugboard shuffling letter pairs made it unbreakable. To anyone armed with frequency tables, it was. The plugboard randomized the statistics that classical cryptanalysis depended on. But Rejewski was not using frequency tables. He was using the theory of permutations — a branch of abstract mathematics that German communications officers had apparently not consulted while writing procedure manuals.
The flaw he exploited was a bureaucratic shortcut. To guard against transmission errors, operators were required to encipher the three-letter message key twice, sending a six-letter indicator at the head of every transmission. This meant the letter in position 1 and the letter in position 4 were both encryptions of the same plaintext character, using rotor settings that differed by exactly three steps. Across thousands of intercepted messages, Rejewski tabulated these paired encryptions. They formed permutation cycles whose lengths depended entirely on the rotor wirings — and crucially, were independent of the plugboard. By solving the resulting equations, he deduced the rotor wirings from scratch, sight unseen (Wikipedia). The French documents did not give him the answer; they gave him enough known values to make the algebra tractable.
By 1934, the Bureau’s workshop had produced working Enigma replicas. By 1938, when the Germans added two new rotors and broke the existing attack, Rejewski had built the bomba kryptologiczna — an electromechanical assembly of six Enigma machines wired together, capable of grinding through daily keys in roughly two hours. Six machines were running by November of that year (Cryptanalysis of the Enigma — Wikipedia).
On July 25, 1939, five weeks before Germany invaded Poland, Rejewski and his colleagues met British and French counterparts in a forest clearing at Pyry, south of Warsaw. They handed over everything: Polish Enigma replicas, the mathematical methods, the bomba design. Alan Turing’s team at Bletchley Park rebuilt the bombe — scaled up, adapted, improved with Gordon Welchman’s diagonal board — and ran it against Wehrmacht, Luftwaffe, and Kriegsmarine traffic for the rest of the war. Welchman later wrote that “Hut 6 Ultra would never have gotten off the ground” without the Polish transfer (Britannica).
Rejewski survived the war in anonymity, working as an accountant in Bydgoszcz, his cryptographic role classified under British secrecy rules until 1973. He died in 1980. Historians who later studied the full record reckoned the Polish breakthrough, inherited and amplified at Bletchley, shortened the war by between two and four years.
The Enigma was a machine. Rejewski proved it was also a theorem — and theorems, once broken, stay broken.
Sources
- Marian Rejewski — Wikipedia — biographical timeline, the permutation-theory method, and the December 1932 breakthrough.
- Cryptanalysis of the Enigma — Wikipedia — the indicator-repeat flaw, the bomba kryptologiczna, and the July 1939 Pyry meeting.
- Marian Rejewski — Encyclopaedia Britannica — Bletchley Park inheritance, Welchman’s assessment, and postwar life.