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.

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.

Marian Rejewski was born 16 August 1905 in Bromberg in the Prussian Province of Posen (now Bydgoszcz, Poland)[8] to Józef and Matylda, née Thoms.

[15] 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.

[16] 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.

[16] Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber".

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).

These mathematical techniques, combined with material supplied by Gustave Bertrand,[Note 4] chief of French radio intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and nonrotating reflector.

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.

The documents, procured from a spy in the German Cryptographic Service, Hans-Thilo Schmidt, included the Enigma settings for the months of September and October 1932.

Likewise there were no difficulties with determining the correct torsion of the [rotors'] side walls with respect to each other, or the moments when the left and middle drums turned."

"[35] After Rejewski had determined the wiring in the remaining rotors, he was joined in early 1933 by Różycki and Zygalski in devising methods and equipment to break Enigma ciphers routinely.

On 15 September 1938, the Germans introduced new rules for enciphering message keys (a new "indicator procedure"), making the Poles' earlier techniques obsolete.

The British bombe, the main tool that would be used to break Enigma messages during World War II, would be named after, and likely inspired by, the Polish bomba, though the cryptologic methods embodied in the two machines were different.

[50] Two and a half weeks later, effective 1 January 1939, the Germans increased the number of plug connections to 7–10, which, writes Rejewski, "to a great degree, decreased the usefulness of the bombs."

"[51] As it became clear that war was imminent and that Polish financial resources were insufficient to keep pace with the evolution of Enigma encryption (e.g., due to the prohibitive expense of an additional 54 bombas and due to the Poles' difficulty in producing in timely fashion the full 60 series of 26 "Zygalski sheets"[52]), the Polish General Staff and government decided to initiate their Western allies into the secrets of Enigma decryption.

France was represented by Gustave Bertrand and Air Force cryptologist Captain Henri Braquenié; Britain, by Government Code and Cypher School chief Alastair Denniston, veteran cryptologist Alfred Dillwyn Knox, and Commander Humphrey Sandwith, head of the section that had developed and controlled the Royal Navy's intercept and direction-finding stations.

[Note 8] The British were able to manufacture at least two complete sets of perforated sheets—they sent one to PC Bruno, outside Paris,[57] in mid-December 1939—and began reading Enigma within months of the outbreak of war.

By the time the Cipher Bureau was ordered to cross the border into allied Romania on 17 September, they had destroyed all sensitive documents and equipment and were down to a single very crowded truck.

[64] On 20 October 1939 the three Polish cryptologists resumed work on German ciphers at a joint French–Polish–(anti-fascist) Spanish radio-intelligence unit stationed at Gretz-Armainvilliers, forty kilometers northeast of Paris, and housed in the Château de Vignolles (code-named PC Bruno).

[69] On 24 June 1940, after Germany's victory in the Battle of France, Gustave Bertrand flew Bruno's international personnel—including fifteen Poles, and seven Spaniards who worked on Italian ciphers[70]—in three planes to Algeria.

[75] The youngest of the three Polish mathematicians who had worked together since 1929—Jerzy Różycki—died in the sinking of a French passenger ship on 9 January 1942, as he was returning to Cadix from a stint in Algeria.

Indeed, on 6 November a pickup truck equipped with a circular antenna arrived at the gate of the Château des Fouzes where the cryptologists were operating.

[78] On 29 January 1943, accompanied by a local guide, Rejewski, and Zygalski, bound for Spain, began a climb over the Pyrenees, avoiding German and Vichy patrols.

[81] Leaving there on 21 July,[82] they made it to Portugal; from there, aboard HMS Scottish, to Gibraltar; and then by air to RAF Hendon in north London, arriving on 3 August 1943.

[87] When Gustave Bertrand fled to England in June 1944, he and his wife were provided with a house in Boxmoor, a short walk from the Polish radio station and cryptology office, where it seems likely that his collaboration with Rejewski and Zygalski continued.

He was interviewed by scholars, journalists, and television crews from Poland, East Germany, the United States, Britain, Sweden, Belgium, the Soviet Union, Yugoslavia, and Brazil.

[3] In 2009, the Polish Post issued a series of four commemorative stamps, one of which pictured Rejewski and fellow mathematician-cryptologists Jerzy Różycki and Henryk Zygalski.

[99] On 5 August 2014 the Institute of Electrical and Electronics Engineers (IEEE) honored Rejewski, Różycki, and Zygalski with its prestigious Milestone Award, which recognizes achievements that have changed the world.