• Mathematician Marian Adam Rejewski, 1905
• Mathematician Peter Frank George Twinn, 1916

While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff's Biuro Szyfrów (Cipher Bureau), which he joined full time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptologic "card catalog," derived using his "cyclometer," and the "cryptologic bomb".

Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the fall of France in June 1940, but within months returned to work undercover in Vichy France. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician Henryk Zygalski fled, via Spain, Portugal and Gibraltar, to Britain. There they worked at a Polish Army unit, solving low level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967.

Marian Rejewski was born 16 August 1905 in Bromberg, now Bydgoszcz. His parents were Józef, a cigar merchant, and Matylda, née Thoms. He attended a German speaking Königliches Gymnasium zu Bromberg (Royal Grammar School in Bromberg) and completed high school with his matura in 1923. Rejewski then studied mathematics at Poznań University, graduating on 1 March 1929.

In early 1929, shortly before he graduated, Rejewski began attending a secret cryptology course organized for selected German speaking mathematics students by the Polish General Staff's Cipher Bureau (Biuro Szyfrów). The course was conducted off campus at a military facility and, as Rejewski would discover in France in 1939 during World War II, "was entirely and literally based" on French General Marcel Givièrge's 1925 book, Cours de cryptographie (Course of Cryptography). Rejewski and fellow students Henryk Zygalski and Jerzy Różycki were among the few who could keep up with the course while balancing the demands of their normal studies.

Rejewski graduated with a master's degree in mathematics on 1 March 1929; his thesis was titled, "Theory of double periodic functions of the second and third kind and its applications." A few weeks later, without having completed the cryptology course, Rejewski began the first year of a two year actuarial statistics course at Göttingen, Germany. He would not complete the actuarial - statistics course, for, while home for the summer in 1930, he accepted the offer of a mathematics teaching assistantship at Poznań University.

He also began working part time for the Biuro Szyfrów (Cipher Bureau), which by then had concluded the cryptology course and set up an outpost at Poznań to decrypt intercepted German radio messages. Rejewski worked some twelve hours a week near the Mathematics Institute in an underground vault referred to puckishly as the "Black Chamber".

In the summer of 1932, the Poznań branch of the Cipher Bureau was disbanded. On 1 September 1932, as a civilian employee, Rejewski joined the Cipher Bureau at the General Staff building (the Saxon Palace) in Warsaw, as did Zygalski and Różycki.

Their first assignment was to solve a four - letter code used by the Kriegsmarine (German Navy). Progress was initially slow, but sped up considerably after a test exchange was intercepted — a six - group signal, followed by a four - group response. The cryptologists guessed correctly that the first signal was the question, "When was Frederick the Great born?" followed by the response, "1712."

In late October or early November 1932, while work on the Naval code was still underway, Rejewski was set to work, alone and in secret, on the output of the new standard German cipher machine, the Enigma I, which was coming into widespread use. While the Cipher Bureau had, by later report, succeeded in solving an earlier, plugboard - less Enigma, it had had no success with the Enigma I.

The Enigma machine was an electro - mechanical device, equipped with a 26 letter keyboard and a set of 26 lamps, corresponding to the letters of the alphabet. Inside was a set of wired drums ("rotors" and a "reflector") that scrambled the input. The machine also featured a plugboard to swap pairs of letters. To encipher a letter, the operator pushed the relevant key and noted down which of the lamps lit. Each key press caused one or more rotors to advance, and thus the encipherment varied from one key press to the next.

In order for two operators to communicate, both Enigma machines had to be set up in the same way. The large number of possibilities for setting the rotors and the plugboard combined to form an astronomical number of configurations, each of which would produce a different cipher. The settings were changed daily, with the consequence that the machine had to be "broken" anew each day if the messages were to be read continually.

To decrypt Enigma messages, three pieces of information were needed:

1. A general understanding of how Enigma functioned;
2. The wiring of the rotors;
3. The daily settings: the sequence and orientations of the rotors (of which there were three initially), and the plug connections on the plugboard.

Rejewski had only the first at his disposal, based on information already acquired by the Cipher Bureau.

First Rejewski tackled the problem of finding the wiring of the rotors. To do this, he pioneered the use of pure mathematics in cryptanalysis. Previous methods had largely exploited linguistic patterns and the statistics of natural - language texts — letter - frequency analysis. Rejewski, however, applied techniques from group theory — theorems about permutations — in his attack on Enigma.

These mathematical techniques, combined with material supplied by Captain Gustave Bertrand, chief of French radio intelligence, enabled him to reconstruct the internal wirings of the machine's rotors and non - rotating reflector.

"The solution", writes historian David Kahn, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalysts of all time". Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem that won World War II".

Prior to receiving the French intelligence material, Rejewski had made a careful study of Enigma messages, particularly of the first six letters of messages intercepted on a single day.

For security, each message was encrypted using different starting positions of the rotors, as selected by the operator. This message setting was three letters long. To convey it to the receiving operator, the sending operator began the message by sending the message setting in a disguised form — a six - letter indicator.

The indicator was formed using the Enigma with its rotors set to a common global setting for that day, termed the ground setting, which was shared by all operators.

The particular way that the indicator was constructed, introduced a weakness into the cipher.

For example, suppose the operator chose the message setting KYG for a message. The operator would first set the Enigma's rotors to the ground setting, which might be GBL on that particular day, and then encrypt the message setting on the Enigma twice; that is, the operator would enter KYGKYG (which might come out to something like QZKBLX). The operator would then re-position the rotors at KYG, and encrypt the actual message. A receiving operator could reverse the process to recover first the message setting, then the message itself. 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. Due to the indicator's repetition of the message setting, Rejewski knew that, in the plaintext of the indicator, the first and fourth letters were the same, the second and fifth were the same, and the third and sixth were the same. These relations could be exploited to break into the cipher.

Rejewski studied these related pairs of letters. For example, if there were four messages that had the following indicators on the same day: BJGTDN, LIFBAB, ETULZR, TFREII, then by looking at the first and fourth letters of each set, he knew that certain pairs of letters were related. B was related to T, L was related to B, E was related to L, and T was related to E: (B,T), (L,B), (E,L), and (T,E). If he had enough different messages to work with, he could build entire sequences of relationships: the letter B was related to T, which was related to E, which was related to L, which was related to B (see diagram). This was a "cycle of 4", since it took four jumps until it got back to the start letter. Another cycle on the same day might be AFWA, or a "cycle of 3". If there were enough messages on a given day, all the letters of the alphabet might be covered by a number of different cycles of various sizes. The cycles would be consistent for one day, and then would change to a different set of cycles the next day. Similar analysis could be done on the 2nd and 5th letters, and the 3rd and 6th, identifying the cycles in each case and the number of steps in each cycle.

Using the data thus gained, combined with Enigma operators' tendency to choose predictable letter combinations as indicators (such as girlfriends' initials or a pattern of keys that they saw on the Enigma keyboard), Rejewski was able to deduce six permutations corresponding to the encipherment at six consecutive positions of the Enigma machine. These permutations could be described by six equations with various unknowns, representing the wiring within the entry drum, rotors, reflector and plugboard.

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 soluble without further data. 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 December 9 or 10, 1932, the documents were given to Rejewski. They enabled him to reduce the number of unknowns and solve the wirings of the rotors and reflector.

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."

The settings provided by French Intelligence covered two months which 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. 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.

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 achieve this, but that the method was "imperfect and tedious" and relied on chance. (In 2005, mathematician John Lawrence published a paper arguing that it would have taken four years for this method to have had a reasonable likelihood of success.) Rejewski wrote that "the conclusion is that the intelligence material furnished to us should be regarded as having been decisive to solution of the machine."

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. Rejewski later recalled:

Now we had the machine, but we didn't have the keys and we couldn't very well require Bertrand to keep on supplying us with the keys every month ... The situation had reversed itself: before, we'd had the keys but we hadn't had the machine — we solved the machine; now we had the machine but we didn't have the keys. We had to work out methods to find the daily keys.

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.

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.

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.

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.

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.

However, on November 1 or 2, 1937, the Germans replaced the reflector in their Enigma machines, which meant that the entire catalog had to be recalculated from scratch.

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%.

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 put into effect new rules for enciphering message keys (a new "indicator procedure"), rendering the card - catalog method completely useless. The Polish cryptologists rapidly responded with new techniques.

One was Rejewski's bomba ("bomb"), an electrically powered aggregate of six Enigmas, which made it possible to solve the daily keys in about two hours. Six bombs were built and ready for use by mid November 1938. The bomb method, like the grill method, exploited the fact that the plug connections did not change all the letters. But while the grill method required unchanged pairs of letters, the bomb method required only unchanged letters. Hence it could be applied even though the number of plug connections in this period was five to eight.

But from 1 January 1939 the number of plug connections was increased to seven - to - ten, greatly decreasing the usefulness of the bombs. Moreover, two weeks earlier, on 15 December 1938, the Germans had increased the number of rotors from three to five, thereby increasing the bombs' workload tenfold. Building an additional 54 bombs, in order to increase the number tenfold to 60 from the original 6, would have utterly exceeded the Polish Cipher Bureau's available funds.

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 bomb, though according to Gordon Welchman the cryptanalytic methods embodied by the two machines were different.

Around the same time as the Polish bomb, a manual method was invented by Zygalski, that of "perforated sheets" ("Zygalski sheets"), which, like the card - catalog method, was independent of the number of plug connections. But production of these sheets was very time consuming, so that by 15 December 1938 only one - third of the job had been done.

As it became clear that war was imminent and that Polish resources were insufficient to keep pace with the evolution of Enigma encryption (e.g., due to the prohibitive expense of an additional 54 bombs and due to the Poles' difficulty in producing in time the required 60 series of 26 "Zygalski sheets" each), the Polish General Staff and government decided to let their Western allies in on the secret.

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 Henri Braquenié; Britain, by Alastair Denniston, Alfred Dillwyn Knox and Royal Navy electronics expert Humphrey Sandwith. The Polish hosts included Stefan Mayer, Gwido Langer, Maksymilian Ciężki and the three cryptologists. 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. The British were able to manufacture at least two complete sets of perforated sheets — they sent one to PC Bruno, outside Paris, in mid December 1939 — and began reading Enigma within months of the outbreak of war.

Without the Polish assistance, British cryptologists would, at the very least, have been considerably delayed in reading Enigma. Author 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. Former Bletchley Park cryptologist Gordon Welchman goes further, writing that the Army and Air Force Enigma section, Hut 6, "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... Enigma machine, and of the operating procedures that were in use."

Intelligence gained from solving high level German ciphers — intelligence code - named "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." 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". The availability of Ultra was, at the least, due largely to the earlier Polish breaking of Enigma.

In September 1939, after the outbreak of World War II, Rejewski and his fellow Cipher Bureau workers were evacuated from Poland to Romania, crossing the border on September 17 (the day the Soviet Union invaded eastern Poland).

Rejewski, Zygalski and Różycki managed to avoid being interned in a refugee camp and made their way to Bucharest, where they contacted the British embassy. Having been 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 immediately issued instructions for the three Poles to be assisted in evacuating to Paris.

On 20 October 1939 the three Polish cryptologists resumed work on German ciphers at a joint French - Polish - Spanish radio intelligence unit stationed at Gretz - Armainvillers, forty kilometers northeast of Paris, and housed in the Château de Vignolles (code - named "PC Bruno"). On January 17, 1940, the Poles found the first Enigma key to be solved in France, one for October 28, 1939.

The staff at PC Bruno collaborated by teleprinter with their opposite numbers at Bletchley Park in England. For communications security, the allied Polish, French and British cryptologic agencies used the Enigma machine itself — Bruno closing its Enigma encrypted messages to Britain with an ironic "Heil Hitler!"

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

During September 1940 they returned to work in secret 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 near Uzès, code - named "Cadix". 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). Rejewski may have had little or no involvement in working on German Enigma at Cadix.

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.

On 9 January 1942, Różycki, the youngest of the three mathematicians, died in the sinking of a French passenger ship as he was returning from a stint in Algeria to Cadix in southern France.

By summer 1942 work at Cadix was becoming dangerous, and plans for evacuation were drawn up. Vichy France itself was liable to be occupied by German troops, and Cadix's radio transmissions were increasingly at risk of detection by the Funkabwehr, a German 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 chateau where the cryptologists were operating. The visitors, however, did not enter, and merely investigated — and terrorized — nearby farms. Nonetheless, the order to evacuate Cadix was given, and this was done by 9 November. The Germans occupied the chateau only three days later.

The Poles were split into twos and threes. On 11 November Rejewski and Zygalski were sent to Nice, which was in the Italian occupied zone. They had to flee again after coming under suspicion, constantly moving or staying in hiding, to Cannes, Antibes, Nice again, Marseilles, Toulouse, Narbonne, Perpignan and Ax - les - Thermes, close to the Spanish border.

The plan was to smuggle themselves over the Pyrenees into Spain. On 29 January 1943, accompanied by a local guide, Rejewski and Zygalski began their trek across the Pyrenees, avoiding German and Vichy patrols. Near midnight and near the Spanish border, the guide pulled out a pistol and demanded that they hand over the rest of their money. After being robbed they succeeded in reaching the Spanish side of the border, only to be arrested within hours by security police.

The Poles were sent first to a prison in La Seu d'Urgell until 24 March, then moved to a prison at Lerida. The pair were eventually released on 4 May 1943, after the intervention of the Polish Red Cross, and sent to Madrid. Leaving Madrid on 21 July, they made it to Portugal; from there aboard HMS Scottish to Gibraltar; and thence aboard an old Dakota to RAF Hendon, in north London, arriving on 3 August 1943.

Rejewski and Zygalski were inducted as privates into the Polish Army 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. Bletchley Park also recorded receipt of German Police Decrypts from Boxmoor from October 1945 to July 1944. On 10 October 1943, Rejewski and Zygalski were commissioned second lieutenants; on 1 January 1945 Rejewski, and presumably also Zygalski, were promoted to lieutenant. 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 cypher office where it seems likely that his collaboration with Rejewski and Zygalski continued.

Enigma decryption, however, had become an exclusively British and American domain; the two mathematicians who, with their late colleague, had laid the foundations for Allied Enigma decryption were now excluded from making further contributions to their métier. British cryptologist Alan Stripp suggests that 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. Stripp comments further that "Setting them to work on the Doppelkassetten system was like using racehorses to pull wagons."

On 21 November 1946, Rejewski, having been on 15 November discharged from the Polish Army in Britain, returned to Poland to be reunited with his wife, Irena Maria Rejewska (née Lewandowska, whom Rejewski had married on 20 June 1934) and their son Andrzej (Andrew, born 1936) and daughter Janina (Jeanne, born 1939, who would later follow in her father's footsteps to become a mathematician).

Rejewski [writes Kozaczuk] could after the war have worked in academia and was urged to do so by Prof. [Zdzisław] Krygowski, who proposed a [university] mathematics [position] at Poznań or Szczecin. Rejewski was, however, exhausted psychically, in ill health (in the Spanish prisons he had contracted, among other things, rheumatism...). A grievous blow to him also was, not long after his return, in the summer of 1947, the almost sudden, after five days' illness (poliomyelitis), death of his 11 year old son Andrzej. After that he did not want to part from his wife and daughter, as would have been necessary if he had accepted Krygowski's offer, which might... have promised him a rapid academic career in view of the postwar shortages in personnel, decimated by the enemy. In Bydgoszcz they lived with their fairly well - to - do in - laws (Mrs. Rejewska's father was a dentist).

Rejewski took a position in Bydgoszcz as director of the sales department at a cable manufacturing company, Kabel Polski (Polish Cable).

Between 1949 and 1958, Rejewski was repeatedly investigated by the Polish Security Service but never divulged that he had worked on Enigma; in 1950 they demanded that he be fired from his employment. He then worked briefly as a director at the State Surveying Company, then at the Association of Polish Surveyors. From 1951 to 1954 he worked at the Association of Timber and Varied Manufactures Cooperatives. From 1954 until his retirement on a disability pension in February 1967, he was director of the inspectorate of costs and prices at a Provincial Association of Labor Cooperatives.

In 1969 Rejewski and his family moved back to Warsaw, to the apartment that he had acquired in May 1939 with financial help from his father - in - law. (After the Germans suppressed the 1944 Warsaw Uprising, they had sent Mrs. Rejewska and her children to the west, along with other Warsaw survivors. The family had eventually found refuge with her parents in Bydgoszcz.)

Rejewski understandably took satisfaction from his accomplishments in breaking the German Enigma cipher for nearly seven years (beginning in December 1932) prior to the outbreak of World War II and then into the war, in personal and teleprinter collaboration with Bletchley Park, at least until the 1940 fall of France. In 1942, at Uzès, Vichy France, he wrote a "Report of Cryptologic Work on the German Enigma Machine Cipher." Before his retirement in 1967 a quarter - century later, he began writing his "Memoirs of My Work in the Cipher Bureau of Section II of the [Polish] General Staff," which were purchased by the Military Historical Institute, located in Warsaw.

Rejewski must often have wondered, after the 1940 French debacle, what use Alan Turing (who had visited the Polish cryptologists outside Paris) and Bletchley Park, had ultimately made of the Polish discoveries and inventions. For nearly three decades after the war, little was publicly known due to a ban that had been imposed on 25 May 1945 by British Prime Minister Winston Churchill.

What little was published attracted little attention. Ladislas Farago's 1971 best seller The Game of the Foxes presented a garbled account of Ultra's origins: "Commander Denniston went clandestinely to a secluded Polish castle [!] on the eve of the war [to pick up an Enigma, "the Wehrmacht's top system" during World War II]. Dilly Knox later solved its keying..." Still, this was closer to the truth than most of the British and American accounts that would follow after 1974. Their authors were at a disadvantage: they did not know that the founder of Enigma decryption, Marian Rejewski, was still alive and alert and that historical confabulation was therefore hazardous.

With Gustave Bertrand's 1973 publication of his Enigma, substantial information about the origins of Ultra began to seep out to the broader world public. With F.W. Winterbotham's 1974 best seller The Ultra Secret, the dam began to burst. Still, many authors likewise aspired to best - sellerdom and were not averse to filling gaps in their information with whole - cloth fabrications. Rejewski fought a gallant (if into the 21st century still not entirely successful) fight to get the truth before the public. He published a number of papers on his cryptologic work and contributed generously to articles, books and television programs. 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.

He maintained a lively correspondence with his wartime French host, General Gustave Bertrand, and at the General's bidding began translating Bertrand's Enigma into Polish. A few years before his death, at the request of the Józef Piłsudski Institute of America, Rejewski broke enciphered correspondence of Józef Piłsudski and his fellow Polish Socialist conspirators from 1904. On 12 August 1978, a year and a half before his death, he received the Officer's Cross of the Order of Polonia Restituta.

Rejewski, who had been suffering from heart disease, died of a heart attack at his home on 13 February 1980, aged 74. He was buried with military honors at Warsaw's Powązki Military Cemetery.

In 1979 Rejewski and his colleagues became heroes of Sekret Enigmy ("The Enigma Secret"), a Polish - cryptologists - and - German - spies movie thriller about the Poles' solution of the German Enigma cipher. Late 1980 also saw a Polish TV series with a similar theme, Tajemnice Enigmy ("The Secrets of Enigma").

In 1983, a Polish postage stamp marked the 50th anniversary of the German military Enigma's first solution; the First Day Cover featured likenesses of the three mathematician - cryptologists.

Memorials to the trio have been unveiled at Bletchley Park and the Polish Embassy in the United Kingdom, and at Uzès in France. In Rejewski's home city of Bydgoszcz, a street and school have been named for him, a plaque placed on the building where he had lived, and a sculpture commissioned.

In 2000, Rejewski and his colleagues Zygalski and Różycki were posthumously awarded the Grand Cross of the Order of Polonia Restituta.

On 4 July 2005, Rejewski's daughter Janina Sylwestrzak received on his behalf, from the British Chief of the Defence Staff, the War Medal 1939 – 1945.

In 2005 a postcard was issued, commemorating the centennial of Rejewski's birth.

In 2007 a three - sided bronze monument was dedicated before Poznań Castle. Each side bears the name of one of the three mathematics students who had attended the 1929 cryptology course and subsequently collaborated on breaking the Enigma cipher.

On 1 August 2012 Marian Rejewski posthumously received the Knowlton Award of the U.S. Military Intelligence Corps Association. Rejewski's mathematician daughter Janina accepted the award on behalf of her late father at his home town, Bydgoszcz, on 4 September 2012. Rejewski had been nominated for the award by NATO Allied Command Counterintelligence. The Knowlton Award, named for an American War of Independence military intelligence chief, was established in 1995.

Born in Streatham, South London, Twinn was the son of a senior General Post Office official. After attending Manchester Grammar School and Dulwich College, he graduated in mathematics at Brasenose College, Oxford. He won a scholarship to pursue postgraduate studies in Physics.

Twinn joined GC&CS — Britain's code breaking service — in early 1939, recruited after seeing an advertisement, working first in London before moving to Bletchley Park. He worked with Dilly Knox and Alan Turing on German Enigma ciphers. In early 1942, he became the head of the Abwehr Enigma section.

Twinn was the first British cryptographer to read a German military Enigma message, having obtained vital information from Polish cryptanalysts in July 1939. Twinn stated that, "It was a trifling exercise, but I repeat for the umpteenth time, no credit to me."

He was in the middle of a postgraduate scholarship studying Physics when he saw an advertisement for a job with the government. "I was a bit unsettled," he remembered. "I'd finished my university degree and I didn't quite know what to do." The advertisement indicated that they were looking for mathematicians, but was unclear about what else was involved.

In that unsettled period after the Munich Agreement, international relations between the major European powers were tense and getting tenser.

"They offered me this job at the princely salary of, I think, £275 a year," he said, "which sounded all right to me, and I was taken along on the first day to be introduced to Dilly Knox." He began as an assistant to Alfred Dilwyn (“Dilly”) Knox, who headed a team of code breakers at GC&CS.

An eccentric but brilliant character, Dilly Knox was the first British code breaker to work on the Enigma cipher. Like most GC&CS experts, he was a classicist. But, as war loomed, GC&CS began employing mathematicians, as well as chess players and crossword experts. Twinn was in fact the first mathematician to join the team.

Knox believed in throwing his new recruits in at the deep end. He gave Twinn a mere five minutes’ training before telling him to go and get on with it.

The Enigma machine dated back to 1919, when Hugo Alexander Koch, a Dutchman, patented an invention that he called a secret writing machine. A little later, Arthur Scherbius, an engineer, was experimenting with this and similar machines and became enthusiastic about encryption machines that used rotors. He recommended them to Siegfried Turkel, the director of the Institute of Criminology in Vienna, who also became interested in them.

In the meantime, Koch had set up a company with the hope of selling his encryption machine for commercial use. But industry was not interested. However, in 1926 the German Navy looked at the Koch machine. Senior officers were impressed with it and ordered a large number. The purchase of the device — called Enigma — was kept strictly secret.

The Enigma machine was a very complicated instrument. It had a keyboard, like the ones used on a typewriter, containing all the letters of the alphabet. Each of the 26 letters was connected electrically to one of three rotors, each provided with a ring. Each ring also held the 26 letters of the alphabet. Further electrical connections led from the rotors to 26 illuminated letters.

When an operator, enciphering a message, pressed a key, an electric current passed through the machine and the rotors turned mechanically, but not in unison. Every time a key was pushed, the first rotor would rotate one letter. This happened 26 times until the first rotor had made a complete revolution. Then the second rotor would start to rotate. And so on.

When a key was pressed, a light came on behind the cipher text letter, always different from the original letter in the plain text. The illuminated letters made up the coded message.

The system worked in reverse. The person decoding a cipher message would use an Enigma with identical settings. When he pressed the cipher text letter, the letter in the original plain text message lit up. The illuminated letters made up the original message.

To make the codes more difficult to break, each of the rotors could be taken out and replaced in a different order. Also, the rings on the rotors could be put in a different order each day — for example, on one day the first rotor could be set at B, the next day at F, and so on. The military version of Enigma was provided with a plug board, like an old telephone switchboard. This allowed an extra switching of the letters, both before they entered the rotors and after leaving them. The plug board had 26 holes. Connections were made with wires and plugs. With three rotors and, say, six pairs of letters connected with the plug board, there would be 105,456 different combinations of the alphabet.

In December 1938 the Germans added additional rotors (up to six) and the number of combinations increased dramatically. The Germans believed that messages sent on their most sophisticated Enigma machines were so well coded that they could not be decoded. But Twinn and his colleagues proved them wrong.

In July 1939 GC&CS moved from London to Bletchley Park. The mansion in the park was used by the staff, but many other buildings had to be constructed to accommodate the large number of people who worked for GC&CS during the war. These temporary buildings were known as the “huts”.

About 10,000 people worked at Bletchley. The core group was the small number of cryptanalysts trying to crack the Enigma machine; at the beginning, this group consisted of no more than ten people, with Knox and Twinn in charge.

The British code breakers had been working on the commercial version of Enigma, the easier of the two to break, during the 1920s and 1930s, and they had made much progress in breaking the military version. But Twinn and his colleagues were stymied because they could not work out the order in which the Enigma keys were wired up.

In July 1939, a month or so before the war started, Knox and some others traveled to Poland. Polish cryptologists, some of whom were brilliant, handed over to their British colleagues key information about Enigma, including replica machines.

The British discovered that Enigma machines were wired alphabetically: A to the first contact, B to the second, and so on. This was the order given in the diagram attached to the patent application. But Twinn and his colleagues thought it such an obvious thing to do that nobody considered it worth trying.

In early 1940 Twinn made the first break into Enigma. This could have been done much earlier if only they had tried the alphabetical system detailed in the patent application.

The ability to read German encoded military messages was of inestimable help to the Allies in winning the war. It was achieved largely because of the efforts of Twinn, Knox, Alan Turing (who later became the father of artificial intelligence) and others at Bletchley Park. Turing, a brilliant mathematician, developed a machine called the “bombe”, which sped up the deciphering process by trial and error — a crucial development for the code breakers.

Twinn worked with Turing on breaking the German Naval Enigma. Their success helped allied convoys to avoid German U-boats. Knox worked on the German Army (Abwehr) codes, a task that Twinn took over when Knox became ill. This operation was crucial in the Allied campaign to deceive the Germans about their plans to invade Normandy in June 1944. The work of GC&CS, however, remained one of Britain’s best kept secrets until 1974, nearly 30 years after the end of the war.

Twinn's carried on government work after the war in a number of departments, including, in the late 1960s, as Director of Hovercraft in the Ministry for Technology. Later he became Secretary of the Royal Aircraft Establishment in Farnborough. In the early 1970s, he was the second secretary of the Natural Environment Research Council.

Twinn became interested in entomology, gaining his doctorate from the University of London in the jumping mechanism of click beetles. He co-authored A Provisional Atlas of the Longhorn Beetle (Coleoptera Cerambycidae) (1999), a study of the distribution of a number of beetle species.

Twinn had an interest in music and played the clarinet and viola. Twinn married Rosamund Case, whom he had met at Bletchley Park through his interest in music, in 1944; they had a son and three daughters.