The Polish Cryptologists Who Broke Enigma

Abstract

Before Bletchley Park, there was Poznań. In December 1932, the 27-year-old Polish mathematician Marian Rejewski reconstructed the internal wiring of the German Enigma machine using permutation group theory, without ever seeing the machine. With Jerzy Różycki and Henryk Zygalski, he then built the machinery of industrial-scale decryption: the cyclometer, the perforated Zygalski sheets, and in 1938 the bomba (the electromechanical ancestor of Turing’s Bombe. Five weeks before the Second World War began, Poland gave everything) machines, methods, mathematics, to Britain and France. The three men spent the war breaking ciphers in exile and were never told that their work had grown into the largest intelligence operation in history; the Anglo-American telling of the Enigma story overlooked them for decades. Theirs is the founding story of mathematical cryptanalysis, and of how credit follows the flag.

Mathematics Enters the Cipher War

Enigma (the rotor cipher machine the German military adopted in the late 1920s) defeated the linguistic codebreaking tradition of the First World War. The French and British bureaus made little sustained progress against it. Poland, squeezed between Germany and the USSR, could not afford to fail, and its Cipher Bureau tried something structurally new: in 1929 it ran a secret cryptology course for mathematics students at Poznań University, selected for fluency in German. Three of them, Marian Rejewski (1905–1980), Jerzy Różycki (1909–1942), and Henryk Zygalski (1908–1978), were hired into the Bureau in Warsaw in 1932.

That autumn, Rejewski was given the problem alone, in secrecy even from his colleagues. His weapon was the theory of permutations, the theorem that permutations conjugate by a permutation have the same cycle structure, later half-jokingly called “the theorem that won World War II.” The Germans’ procedure of enciphering each message key twice at the start of a message leaked exactly the algebraic structure his equations needed. In December 1932, aided by French intelligence material from the spy Hans-Thilo Schmidt (“Asché”), passed on by Gustave Bertrand, which fixed enough unknowns to make the equations tractable: Rejewski solved the wiring of the rotors and reflector. Poland then built working Enigma replicas. It was the first time in history that a cipher of this class fell to pure mathematics; the historian David Kahn ranked it among the greatest cryptanalytic achievements of all time.

Industrializing the Break

Recovering the machine was half the war; the daily keys still had to be found, every day. Through the 1930s the trio invented a production line of methods and machines (see also Cryptography: The Secret Science):

The grill, clock (Różycki’s statistical method), and characteristic tables for recovering settings by hand.
The cyclometer (mid-1930s), a device that mechanized the cataloguing of Enigma’s permutation cycle structures, a card catalog of 105,456 entries that took a year to build and cut daily key recovery to 12–20 minutes.
The Zygalski sheets (1938), perforated sheets that found keys by stacking and backlighting, an optical set-intersection computation on paper.
The bomba kryptologiczna (autumn 1938): six linked Enigma replicas driven by a motor, exhaustively testing rotor positions, an electromechanical special-purpose search machine, operational years before comparable Allied hardware, and the direct namesake of the Anglo-American Bombes.

In December 1938 Germany added two additional rotors, multiplying the search space tenfold. Poland (its cryptologic budget a rounding error of Germany’s) could no longer manufacture enough bomby and sheets. The mathematics still worked; the economics did not.

Pyry, July 1939: The Gift

With invasion visibly imminent, Polish intelligence made a decision of extraordinary strategic generosity. On July 25–26, 1939, at the Cipher Bureau’s facility in the Kabaty Woods near Pyry, south of Warsaw, the Poles revealed everything to stunned British and French delegations (the reconstructed machines, the mathematics, the bomba concept, the sheets) and gave each ally an Enigma replica. Britain’s codebreakers had assumed the machine unbroken. Five weeks later Germany invaded Poland; Bletchley Park began its work not from zero but from a running start handed to it by three Polish mathematicians.

Exile, Prison, and Silence

The three escaped through Romania to France, resuming work at the secret station PC Bruno near Paris (from October 1939, breaking wartime Enigma keys jointly with Bletchley by January 1940), then (after France fell) at station Cadix in the unoccupied south, under false identities. In January 1942, Jerzy Różycki drowned when the passenger ship Lamoricière sank in the Mediterranean, returning from Cadix’s Algiers outpost. He was 32.

After Germany occupied Vichy France in November 1942, Rejewski and Zygalski fled over the Pyrenees, robbed at gunpoint by their guide on the crossing in January 1943, then imprisoned for months in Spain. They reached Britain in August 1943 and were assigned to a Polish signals unit at Boxmoor, breaking SS and SD hand ciphers. The two men who had made Bletchley possible were never brought to Bletchley, never cleared for Ultra, and never told what their prewar work had become.

Zygalski stayed in Britain, teaching mathematics, and died in 1978. Rejewski returned to Poland in 1946 to find his family, worked for two decades as a clerk and accountant in Bydgoszcz (occasionally harassed by security police who never learned what he had actually done) and lived to see the secret begin to surface in the 1970s, writing his own precise accounts before his death in February 1980.

Misconception: Enigma was broken at Bletchley Park

Bletchley industrialized and sustained the break against wartime Enigma (an immense achievement) but the machine was first broken in Warsaw in 1932, and Britain started from the Polish machines, methods, and replicas handed over at Pyry in July 1939. Decades of Anglo-American books and films omitted this, partly because Ultra remained classified until 1974 and the first public accounts were written from British sources. Poland’s role is now formally acknowledged, including by memorials at Bletchley Park itself and an IEEE Milestone in Warsaw (2014). See Myths and Misconceptions.

Dead End: Brilliance Without Resources

The Polish operation is also a case study in a recurring pattern: a small actor invents the paradigm and cannot afford to scale it. Poland pioneered mathematical cryptanalysis and machine-assisted search, then hit the wall of December 1938, ten times the rotor orders meant ten times the bomby and sheets, money and industrial capacity Poland did not have. Britain and America had both, plus time and safety. The lesson generalizes far beyond cryptology: in computing history, the fate of an idea is decided as often by the resources behind it as by its correctness. What distinguishes the Polish case is the handover, rather than let the idea die with the state, they gave it away, and it won the war in other hands.