Marian Rejewski

At this point, Rejewski ran into difficulties due to the large number of unknowns in the set of equations that he had developed. He would later comment in 1980 that it was still not known whether such a set of six equations was solvable without further data.[35] But he was assisted by cryptographic documents that Section D of French military intelligence (the Deuxième Bureau), under future General Gustave Bertrand, had obtained and passed on to the Polish Cipher Bureau. 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. About 9 or 10 December 1932,[36][Note 5] the documents were given to Rejewski. They enabled him to reduce the number of unknowns and solve the wirings of the rotors and reflector.[38]

There was another obstacle to overcome, however. The military Enigma had been modified from the commercial Enigma, of which Rejewski had had an actual example to study. In the commercial machine, the keys were connected to the entry drum in German keyboard order ("QWERTZU..."). However, in the military Enigma, the connections had instead been wired in alphabetical order: "ABCDEF..." This new wiring sequence foiled British cryptologists working on Enigma, who dismissed the "ABCDEF..." wiring as too obvious. Rejewski, perhaps guided by an intuition about a German fondness for order, simply guessed that the wiring was the normal alphabetic ordering. He later recalled that, after he had made this assumption, "from my pencil, as by magic, began to issue numbers designating the connections in rotor N. Thus the connections in one rotor, the right-hand rotor, were finally known."[35]

The settings provided by French Intelligence covered two months that straddled a changeover period for the rotor ordering. A different rotor happened to be in the right-hand position for the second month, and so the wirings of two rotors could be recovered by the same method.[Note 6] Rejewski later recalled: "Finding the [wiring] in the third [rotor], and especially... in the [reflector], now presented no great difficulties. 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." By year's end 1932, the wirings of all three rotors and the reflector had been recovered. A sample message in an Enigma instruction manual, providing a plaintext and its corresponding ciphertext produced using a stated daily key and message key, helped clarify some remaining details.[35]

There has been speculation as to whether the rotor wirings could have been solved without the documents supplied by French Intelligence. Rejewski recalled in 1980 that another way had been found that could have been used to solve the wirings, but that the method was "imperfect and tedious" and relied on chance. In 2005, mathematician John Lawrence claimed that it would have taken four years for this method to have had a reasonable likelihood of success.[39] Rejewski had earlier written that "the conclusion is that the intelligence material furnished to us should be regarded as having been decisive to solution of the machine."[35]

Cyclometer, devised in the mid-1930s by Rejewski to catalog the cycle structure of Enigma permutations.

A number of methods and devices had to be invented in response to continual improvements in German operating procedure and to the Enigma machine itself. The earliest method for reconstructing daily keys was the "grill", based on the fact that the plugboard's connections exchanged only six pairs of letters, leaving fourteen letters unchanged.[22] Next was Różycki's "clock" method, which sometimes made it possible to determine which rotor was at the right-hand side of the Enigma machine on a given day.[41]

After 1 October 1936, German procedure changed, and the number of plugboard connections became variable, ranging between five and eight. As a result, the grill method became considerably less effective.[22] However, a method using a card catalog had been devised around 1934 or 1935, and was independent of the number of plug connections. The catalog was constructed using Rejewski's "cyclometer", a special-purpose device for creating a catalog of permutations. Once the catalog was complete, the permutation could be looked up in the catalog, yielding the Enigma rotor settings for that day.[22]

The cyclometer comprised two sets of Enigma rotors, and was used to determine the length and number of cycles of the permutations that could be generated by the Enigma machine. Even with the cyclometer, preparing the catalog was a long and difficult task. Each position of the Enigma machine (there were 17,576 positions) had to be examined for each possible sequence of rotors (there were 6 possible sequences); therefore, the catalog comprised 105,456 entries. Preparation of the catalog took over a year, but when it was ready about 1935, it made obtaining daily keys a matter of 12–20 minutes.[22][42] However, on 1 or 2 November 1937, the Germans replaced the reflector in their Enigma machines, which meant that the entire catalog had to be recalculated from scratch.[22] Nonetheless, by January 1938 the Cipher Bureau's German section was reading a remarkable 75% of Enigma intercepts, and according to Rejewski, with a minimal increase in personnel this could have been increased to 90%.[43]

Zygalski sheet

In 1937 Rejewski, along with the German section of the Cipher Bureau, transferred to a secret facility near Pyry in the Kabaty Woods south of Warsaw. On 15 September 1938, the Germans introduced new rules for enciphering message keys (a new "indicator procedure"), making the Poles' earlier techniques obsolete.[Note 7] The Polish cryptanalysts rapidly responded with new techniques. One was Rejewski's bomba, an electrically powered aggregate of six Enigmas, which solved the daily keys within about two hours. Six bombas were built and were ready for use by mid-November 1938.[46] The bomba exploited the fact that the plugboard connections did not affect all the letters; therefore, when another change to German operating procedure occurred on 1 January 1939, increasing the number of plugboard connections, the usefulness of the bombas was greatly reduced. 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.[47]

Around the same time as Rejewski's bomba, a manual method was invented by Henryk Zygalski, that of "perforated sheets" ("Zygalski sheets"), which was independent of the number of plugboard connections. Rejewski describes the construction of the Zygalski mechanism and its manipulation:

Fairly thick paper sheets, lettered "a" through "z", were prepared for all twenty-six possible positions of rotor L [the left-hand Enigma rotor] and a square was drawn on each sheet, divided into 51 by 51 smaller squares. The sides, top, and bottom of each large square (it could as well be a rectangle) were lettered "a" through "z" and then again "a" through "y". This was, as it were, a system of coordinates in which the abscissas and ordinates marked successive possible positions of rotors M [the middle Enigma rotor] and N [the right-hand Enigma rotor], and each little square marked permutations, with or without constant points, corresponding to those positions. Cases with constant points were perforated.[48] [E]ach constant point had to be perforated as many as four times. [...] When the sheets were superposed and moved in the proper sequence and the proper manner with respect to each other, in accordance with a [precisely] defined program, the number of visible apertures gradually decreased. And, if a sufficient quantity of data was available, there finally remained a single aperture, probably corresponding to the right case, that is, to the solution. From the position of the aperture one could calculate the order of the rotors, the setting of their rings, and, by comparing the letters of the cipher keys with the letters in the machine, likewise permutation S; in other words, the entire cipher key.[49]

However, application of both the bomba and Zygalski sheets was complicated by yet another change to the Enigma machine on 15 December 1938. The Germans had supplied Enigma operators with an additional two rotors to supplement the original three, and this increased the complexity of decryption tenfold. Building ten times as many bombas (60 would now be needed) was beyond the Cipher Bureau's ability—that many bombas would have cost fifteen times its entire annual equipment budget.[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." Zygalski's perforated ("Zygalski") sheets, writes Rejewski, "like the card-catalog method, was independent of the number of plug connections. But the manufacture of these sheets, [...] in our [...] circumstances, was very time-consuming, so that by 15 December 1938, only one-third of the whole job had been done. [T]he Germans' [introduction of rotors] IV and V [...] increased the labor of making the sheets tenfold [since 60, or ten times as many, sets of sheets were now needed], considerably exceeding our [...] capacities."[51]

2002 plaque, Bletchley Park, "commemorat[ing] the work of Marian Rejewski, Jerzy Różycki, and Henryk Zygalski, mathematicians of the Polish intelligence service, in first breaking the Enigma code [sic: it was a cipher]. Their work greatly assisted the Bletchley Park code breakers and contributed to the Allied victory in World War II."

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.[53] The Polish methods were revealed to French and British intelligence representatives in a meeting at Pyry, south of Warsaw, on 25 July 1939. 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. The Polish hosts included Cipher Bureau chief Gwido Langer, the Bureau's German-Section chief Maksymilian Ciężki, the Bureau's General-Staff-Intelligence supervisor Stefan Mayer, and the three cryptologists Rejewski, Różycki and Zygalski.[54]

The Poles' gift of Enigma decryption to their Western allies, five weeks before the outbreak of World War II, came not a moment too soon. Knowledge that the cipher was crackable was a morale boost to Allied cryptologists.[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.[Note 9]

Without the Polish assistance, British cryptologists would, at the very least, have been considerably delayed in reading Enigma. Hugh Sebag-Montefiore concludes that substantial breaks into German Army and Air Force Enigma ciphers by the British would have occurred only after November 1941 at the earliest, after an Enigma machine and key lists had been captured, and similarly into Naval Enigma only after late 1942.[59]

Intelligence gained from solving high-level German ciphers—intelligence codenamed Ultra by the British and Americans—came chiefly from Enigma decrypts. While the exact contribution of Ultra intelligence to Allied victory is disputed, Kozaczuk and Straszak note that "it is widely believed that Ultra saved the world at least two years of war and possibly prevented Hitler from winning."[60] The English historian Sir Harry Hinsley, who worked at Bletchley Park, similarly assessed it as having "shortened the war by not less than two years and probably by four years".[61] The availability of Ultra was due to the earlier Polish breaking of Enigma; Gordon Welchman, head of Bletchley Park's Hut 6 (which solved German Army and Air Force Enigma ciphers), writes: "Hut 6 Ultra would never have gotten off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military version of the commercial Enigma machine, and of the operating procedures that were in use."[62][Note 10]

On 5 September 1939 the Cipher Bureau began preparations to evacuate key personnel and equipment from Warsaw. Soon a special evacuation train, the Echelon F, transported them eastward, then south. 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. The vehicle was confiscated at the border by a Romanian officer, who separated the military from the civilian personnel. Taking advantage of the confusion, the three mathematicians ignored the Romanian's instructions. They anticipated that in an internment camp they might be identified by the Romanian security police, in which the German Abwehr and SD had informers. The mathematicians went to the nearest railroad station, exchanged money, bought tickets, and boarded the first train headed south. After a dozen or so hours, they reached Bucharest, at the other end of Romania. There they went to the British embassy. Told by the British to "come back in a few days", they next tried the French embassy, introducing themselves as "friends of Bolek" (Bertrand's Polish code name) and asking to speak with a French military officer. A French Army colonel telephoned Paris and then issued instructions for the three Poles to be assisted in evacuating to Paris.[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).[65]

As late as 3–7 December 1939, when Lt. Col. Langer and French Air Force Capt. Henri Braquenié visited London and Bletchley Park, the British asked that the Polish cryptologists be made available to them in Britain. Langer, however, took the position that they must remain where the Polish Army in exile was forming—on French soil.[66]

On 17 January 1940 the Poles found the first Enigma key to be solved in France, one for 28 October 1939.[67] The PC Bruno staff collaborated by teleprinter with counterparts at Bletchley Park in England. For their mutual communications security, the Polish, French, and British cryptologic agencies used the Enigma machine itself. Bruno closed its Enigma-encrypted messages to Britain with an ironic "Heil Hitler!"[68]

In the first months of 1940, Alan Turing—principal designer of the British cryptological Bombe, elaborated from the Polish bomba—would visit Bruno to confer about Enigma decryption with the three Polish cryptologists.[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.[71]

Some three months later, in September 1940, they returned to work covertly in unoccupied southern, Vichy France. Rejewski's cover was as Pierre Ranaud, a lycée professor from Nantes. A radio-intelligence station was set up at the Château des Fouzes, code-named Cadix, near Uzès. Cadix began operations on 1 October. Rejewski and his colleagues solved German telegraph ciphers, and also the Swiss version of the Enigma machine (which had no plugboard).[72] Rejewski may have had little or no involvement in working on German Enigma at Cadix.[Note 11]

In early July 1941, Rejewski and Zygalski were asked to try solving messages enciphered on the secret Polish Lacida cipher machine, which was used for secure communications between Cadix and the Polish General Staff in London. Lacida was a rotor machine based on the same cryptographic principle as Enigma, yet had never been subjected to rigorous security analysis. The two cryptologists created consternation by breaking the first message within a couple of hours; further messages were solved in a similar way.[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.[76] By summer 1942 work at Cadix was becoming dangerous, and plans for evacuation were drawn up. Vichy France was liable to be occupied by German troops, and Cadix's radio transmissions were increasingly at risk of detection by the German Funkabwehr, a unit tasked with locating enemy radio transmitters. 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. The visitors, however, did not enter, and merely investigated nearby farms, badly frightening their occupants. Nonetheless, at Bertrand's suggestion French intelligence ordered the evacuation of Cadix. The order was carried out on 9 November, the day after the Allied "Operation Torch" landings in North Africa. Three days later, on 12 November, the Germans occupied the chateau.[77]

The Poles were split into groups of two and three. On 11 November 1942 Rejewski and Zygalski were sent to Nice, in the Italian-occupied zone. After coming under suspicion there, they had to flee again, moving or hiding constantly. Their trek took them to Cannes, Antibes, back to Nice, then on to Marseilles, Toulouse, Narbonne, Perpignan, and Ax-les-Thermes, near the Spanish border.[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. Near midnight, close to the Spanish border, the guide pulled out a pistol and demanded that they hand over their remaining money.[79]

After being robbed, Rejewski and Zygalski succeeded in reaching the Spanish side of the border, only to be arrested within hours by security police.[80] They were sent first to a prison in La Seu d'Urgell, then on 24 March transferred to a prison at Lerida. On 4 May 1943, after having spent over three months in Spanish prisons, on intervention by the Polish Red Cross the pair were released and sent to Madrid.[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.[83]

Marian Rejewski, second lieutenant (signals), Polish Army in Britain, in late 1943 or in 1944, 11 or 12 years after he first broke Enigma

Rejewski and Zygalski were inducted as privates into the Polish Armed Forces on 16 August 1943 and were posted to a Polish Army facility in Boxmoor, cracking German SS and SD hand ciphers. The ciphers were usually based on the Doppelkassettenverfahren ("double Playfair") system, which the two cryptologists had already worked on in France.[84] British cryptologist Alan Stripp suggests that "Setting them to work on the Doppelkassetten system was like using racehorses to pull wagons."[85] On 10 October 1943, Rejewski and Zygalski were commissioned second lieutenants;[86] on 1 January 1945 Rejewski, and presumably also Zygalski, were promoted to lieutenant.[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.[77]

Enigma decryption, however, had become an exclusively British and American domain; the Polish mathematicians who had laid the foundations for Allied Enigma decryption were now excluded from making further contributions in this area.[88] By that time, at Bletchley Park, "very few even knew about the Polish contribution" because of the strict secrecy and the "need-to-know" principle.[85]

The main source used for this article was Kozaczuk (1984).

• Bertrand, Gustave (1973), Enigma ou la plus grande énigme de la guerre 1939–1945 [Enigma: the Greatest Enigma of the War of 1939–1945] (in French), Paris: Librairie Plon
• Bloch, Gilbert; Deavours, C. A. (July 1987), "Enigma before Ultra: Polish Work and the French Contribution", Cryptologia, 11 (3): 142–155, doi:10.1080/0161-118791861947
• Brzezinski, Zbigniew (2005), "The Unknown Victors", in Ciechanowski, Jan Stanislaw (ed.), Marian Rejewski 1905–1980, Living with the Enigma secret (1st ed.), Bydgoszcz: Bydgoszcz City Council, pp. 15–18, ISBN 978-83-7208-117-9
• Farago, Ladislas (1971), The Game of the Foxes: The Untold Story of German Espionage in the United States and Great Britain during World War II, New York: Bantam Books, OCLC 2371136
• Hinsley, Harry (1993b), "The influence of Ultra in the Second World War", in Hinsley, F. H.; Stripp, Alan (eds.), Codebreakers: The Inside Story of Bletchley Park, Oxford: Oxford University Press, p. 2, ISBN 978-0-19-820327-8
• Hinsley, Harry (19 October 1993), "The Influence of Ultra in the Second World War", University of Cambridge History Research Group, archived from the original on 22 June 2011, retrieved 5 February 2015
• Jakóbczyk, Stanisław; Stokłosa, Janusz, eds. (2007), Złamanie szyfru Enigma. Poznański pomnik polskich kryptologów [The Breaking of the Enigma Cipher: the Poznań Monument to the Polish Cryptologists] (in Polish), Poznań: Wydawnictwo Poznańskiego Towarzystwa Przyjaciół Nauk, ISBN 978-83-7063-527-5
• Kahn, David (1991), Seizing the Enigma: The Race to Break the German U-boat Codes, 1939–1943, Houghton Mifflin Co., ISBN 978-0-395-42739-2
• Kahn, David (1996), The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet (2nd ed.), New York: Scribner, ISBN 978-0-684-83130-5
• Kasparek, Christopher; Woytak, Richard (January 1982), "In Memoriam Marian Rejewski", Cryptologia, 6 (1): 19–25, doi:10.1080/0161-118291856740
• Kozaczuk, Władysław (1967), Bitwa o tajemnice: Służby wywiadowcze Polski i Rzeszy Niemieckiej 1922–1939 [Secret Battle: The Intelligence Services of Poland and the German Reich, 1922–1939] (in Polish), Warsaw: Książka i Wiedza
• Kozaczuk, Władysław (1979), W kręgu Enigmy [In the Circle of Enigma] (in Polish), Warsaw: Książka i Wiedza (Kozaczuk's Polish-language book that was later elaborated into the English-language Kozaczuk (1984).)
• Kozaczuk, Władysław (1984), Kasparek, Christopher (ed.), Enigma: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two, Frederick, MD: University Publications of America, ISBN 978-0-89093-547-7. (The standard reference on the Polish part in the Enigma-decryption epic. This English-language book is substantially revised from the Polish-language Kozaczuk (1979), with additional documentation, including many substantive chapter notes and papers by, and interviews with, Marian Rejewski.)
• Kozaczuk, Władysław (July 1990), "A New Challenge for an Old Enigma-Buster", Cryptologia, 14 (3): 204–216, doi:10.1080/0161-119091864913
• Kozaczuk, Władysław; Straszak, Jerzy (2004), Enigma: How the Poles Broke the Nazi Code, New York: Hippocrene Books, ISBN 978-0-7818-0941-2
• Lawrence, John (April 2004), "The Versatility of Rejewski's Method: Solving for the Wiring of the Second Rotor", Cryptologia, 28 (2): 149–152, doi:10.1080/0161-110491892836, S2CID 205486319
• Lawrence, John (July 2005a), "A Study of Rejewski's Equations", Cryptologia, 29 (3): 233–247, doi:10.1080/01611190508951300, S2CID 205487467
• Lawrence, John (October 2005b), "Factoring for the Plugboard – Was Rejewski's Proposed Solution for Breaking the Enigma Feasible?", Cryptologia, 29 (4): 343–366, doi:10.1080/0161-110591893924, S2CID 205486402
• Mahon, A. P. (June 1945), The History of Hut Eight: 1939–1945, archived from the original on 7 March 2016, retrieved 12 February 2019, 117 pp., PRO HW 25/2
• Polak, Wojciech (2005), "Marian Rejewski in the Sights of the Security Services", in Ciechanowski, Jan Stanisław (ed.), Marian Rejewski, 1905–1980: Living with the Enigma Secret, Bydgoszcz: Bydgoszcz City Council, pp. 75–88, ISBN 978-83-7208-117-9
• Rejewski, Marian (1980), "An Application of the Theory of Permutations in Breaking the Enigma Cipher", Applicationes Mathematicae, 16 (4): 543–559, doi:10.4064/am-16-4-543-559
• Rejewski, Marian (July 1981), "How Polish Mathematicians Deciphered the Enigma" (PDF), Annals of the History of Computing, 3 (3): 213–234, doi:10.1109/MAHC.1981.10033, S2CID 15748167; has afterwords by I. J. Good and Cipher A. Deavours; also appears as Rejewski (1984d)
• Rejewski, Marian; Kasparek, Christopher (January 1982), "Remarks on Appendix 1 to British Intelligence in the Second World War by F. H. Hinsley", Cryptologia, 6 (1): 75–83, doi:10.1080/0161-118291856867
• Rejewski, Marian (1984c), "Summary of Our Methods for Reconstructing Enigma and Reconstructing Daily Keys, and of German Efforts to Frustrate Those Methods", in Kozaczuk, Władysław (ed.), Enigma, pp. 241–245, ISBN 978-0-89093-547-7, Appendix C
• Rejewski, Marian (1984d), "How the Polish Mathematicians Broke Enigma", in Kozaczuk, Władysław (ed.), Enigma, pp. 246–271, ISBN 978-0-89093-547-7, Appendix D
• Rejewski, Marian (1984e), "The Mathematical Solution of the Enigma Cipher", in Kozaczuk, Władysław (ed.), Enigma, pp. 272–291, ISBN 978-0-89093-547-7, Appendix E. Covers much the same ground as Rejewski 1980.
• Rejewski, Marian, interview (transcribed by Christopher Kasparek) in Woytak, Richard (1999), Werble historii [History's Drumroll], edited by and with introduction by Stanisław Krasucki, illustrated with 36 photographs, Bydgoszcz, Poland, Związek Powstańców Warszawskich w Bydgoszczy [Association of Warsaw Insurgents in Bydgoszcz], ISBN 83-902357-8-1, pp. 123–143. A more complete transcript of the interview, highlights of which earlier appeared in Woytak, Richard A. (1982). "A Conversation with Marian Rejewski". Cryptologia. 6: 50–60. doi:10.1080/0161-118291856830., and as Appendix B to Kozaczuk, Władysław, Enigma, pp. 229–240.
• Sebag-Montefiore, Hugh (2000), Enigma: the Battle for the Code, London: Weidenfeld and Nicolson, ISBN 978-0297842514
• Stripp, Alan (2004), "A British Cryptanalyst Salutes the Polish Cryptanalysts", in Kozaczuk, Władysław; Straszak, Jerzy (eds.), Enigma: How the Poles Broke the Nazi Code, New York: Hippocrene Books, pp. 123–125, ISBN 978-0-7818-0941-2, Appendix E
• Turing, Dermot (2018). X, Y & Z: The Real Story of How Enigma Was Broken. Gloustershire England: History Press. ISBN 978-0-7509-8782-0. OCLC 1029570490.
• Welchman, Gordon (1982), The Hut Six Story: Breaking the Enigma Codes, New York: McGraw-Hill, ISBN 978-0070691803
• Welchman, Gordon (January 1986), "From Polish Bomba to British Bombe: the Birth of Ultra", Intelligence and National Security, 1 (1): 71–110, doi:10.1080/02684528608431842
• Winterbotham, F. W. (1974), The Ultra Secret, New York: Dell
• Woytak, Richard (1984), "A Conversation with Marian Rejewski", in Kozaczuk, Władysław (ed.), Enigma, pp. 229–240, ISBN 0-89093-547-5, Appendix B