The Magdeburg Sting 1936
Marian Adam Rejewski; (16 August 1905 - 13 February 1980) was a Polish mathematician and cryptologist who, in 1932, solved the Enigma machine, the main cipher device then in use by Germany. The success of Rejewski and his colleagues jump-started British reading of Enigma in World War II, and the intelligence so gained, code-named "Ultra", contributed decisively to the defeat of Nazi Germany.
While studying mathematics at Poznań University, Rejewski attended a secret cryptology course conducted by the Polish General Staff's Cipher Bureau, which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and set Rejewski to work on the problem in late 1932. After only a few weeks, he had deduced the secret internal wiring of the Enigma. Rejewski and two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski's contributions included devising the cryptology "card catalog", derived using his "cyclometer", and "bomba".
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 Żygalski fled via Spain to Britain. There they worked at a Polish Army unit, solving german ciphers. In 1946, Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptology work until 1967.
Education and early work with Polish Cipher Bureau
Marian Rejewski was born August 16, 1905, in 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 Bydgoszcz) and completed high school in 1923. Rejewski then studied mathematics at Poznań University, graduating on March 1, 1929.
In early 1929, shortly before he graduated, Rejewski started attending a secret cryptology course, organized by the Polish General Staff's Cipher Bureau (Biuro Szyfrów), for selected German-speaking mathematics students. Rejewski and fellow students Henryk Żygalski 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". He began the first year of a two-year actuarial statistics course at Göttingen, Germany, which he was not to complete, for, while home for the summer in 1930, Rejewski accepted an offer of a mathematics teaching assistant position at Poznań University. At the same time, he also began working part-time for Cipher Bureau, which had by then concluded the cryptology course and had 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 place referred to as the "Black Chamber".
In the summer of 1932, the Poznań branch of Cipher Bureau was disbanded. On September 1, 1932, as a civilian employee, Rejewski joined Cipher Bureau at the General Staff building (the Saxon Palace) in Warsaw, as did Żygalski and Różycki. Their first assignment was to work out a four-letter code used by the Kriegsmarine, the German Navy. Progress on solving this system was initially slow, but sped up considerably after a coded message exchange was received-a short test signal apparently in the form of a question and answer. The cryptologists guessed correctly that the question was, "When was Frederick the Great born?"
The Enigma machine, solved by Rejewski in 1932, was widely used by Germany's military services to secure their communications.
In October 1932, while work on the Naval code was still underway, Rejewski was set to work, alone and in secret, on the output of new standard of German communications; the cipher machine Enigma I, which was coming into widespread use. While Cipher Bureau had, by later report, succeeded in solving an earlier, plug-board-less Enigma, it had had no success with the Enigma I.
To decrypt the Enigma messages, four pieces of information were needed:
- The understanding of how Enigma functioned
- The wiring of rotors
- The wiring of final reflector
- The daily settings:
- the number, sequence and orientations of rotors
- the plugs connections on plug-board
Rejewski had only the first at his disposal, based on the Enigma machine already acquired by Cipher Bureau.
Solution of the Enigma wiring
A cycle formed by the first and fourth letters of a set of indicators. Rejewski exploited these cycles to deduce the Enigma rotor wiring in 1932, and thereafter to solve the daily message settings.
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 the material supplied by French military intelligence, enabled him to reconstruct the internal wiring of the machine's rotors and non-rotating reflector. "The solution", historian David Kahn writes, "was Rejewski's own stunning achievement, one that elevates him to the pantheon of the greatest cryptanalyst of all time". Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem that won World War II".
Rejewski studied the first six letters of all the Enigma messages intercepted on a single day. For security, each message sent on Enigma was encrypted using a different starting position of the three rotors, chosen by the operator. This was termed the message setting, and was three letters long. To convey this to the receiving operator, a sending operator began each message by sending the message setting in a disguised form - a six-letter indicator. The indicator was formed using the Enigma with the rotors set to a common global setting for that day, termed the ground setting, shared by all operators. Unfortunately for the Germans, the particular way the indicator was constructed introduced a fundamental weakness into the system.
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 reposition 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 plain-text 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. 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 A F W A, 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 operator's tendency to choose predictable letter combinations as indicators (such as girl-friends' initials or a pattern of keys that they saw on the Enigma keyboard), Rejewski was able to deduce six permutations corresponding to the enciphering 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 plug-board.
Assistance from French Intelligence
At this point Rejewski ran into difficulty: the large number of unknowns made the equations complex. He would later comment in 1980, that it was still not known whether such a set of six equations was solvable without further data. But he was assisted by cryptographic documents that a section of the French intelligence organization (the Deuxième Bureau), under future general Gustave Bertrand, had obtained and passed on to the Polish Cipher Bureau. The documents had been procured from a traitor in the German cipher office, Hans-Thilo Schmidt, and included the Enigma settings for the months of September and October 1932. On December 9 or 10, 1932, the documents were given to Rejewski, who used their information to eliminate the effect of the plug-board from the equations. With the reduced number of unknowns, solving the equations became a tractable problem.
Another obstacle had to be overcome, however. The military Enigma had been modified from the commercial Enigma, of which Rejewski 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 the alphabetical order: "ABCDEF..." This new wiring sequence foiled British code breakers 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 wiring of two rotors could be recovered by the same method. This simplified the analysis, and by the end of the year, the wiring of all three rotors and the reflector had been recovered. An example message in an Enigma instruction manual provided a sequence of plain-text and corresponding cipher-text enciphered at a given setting; this helped Rejewski eliminate remaining ambiguity from the wiring.
There has been speculation as to whether the rotor wiring 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".
Methods for solving the daily Enigma settings
After Rejewski had determined the wiring in the remaining rotors, he was joined in early 1933 by Różycki and Żygalski 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 plug-board'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, increasing the number of plug-board connections. 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-board 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. The 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 Cipher Bureau's German section was reading a remarkable 75% of Enigma intercepts, and according to Rejewski, with only a minimal increase in personnel, this could easily have been increased to 90%.
Rejewski's bomba and Żygalski's sheets
In 1937 Rejewski, along with the German section of Cipher Bureau, transferred to a secret facility near Pyry in the Kabaty Woods south of Warsaw. On September 15, 1938, new rules for enciphering message keys (a new "indicator procedure") were put into effect by the Germans, making the techniques then in use obsolete. The Polish cryptanalysts rapidly responded with new techniques. One was Rejewski's "bomba", an electrically powered aggregate of six Enigmas, which enabled the daily keys to be solved in about two hours. Six "bombas" were built and ready for use by mid-November 1938. The "bomba" exploited the fact that the plug-board connections did not affect all the letters; therefore, when another change to German operating procedure occurred on 1 January 1939, increasing the number of plug-board connections, the usefulness of the machines 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", although the cryptanalytic methods embodied by the two machines were very different.
A manual method was invented around the same time by Żygalski, that of "stack of perforated sheets" ("Żygalski sheets"), which was independent of the number of plug-board connections. However, application of both the "bomba" and "Żygalski's 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 "bombes" was beyond the Biuro's financial ability-that many "bombes" would have cost fifteen times their entire annual equipment budget. The following month, things became even worse when the number of plug-board cables increased from six to ten. Instead of twelve letters being swapped before entering the rotor scrambler, there were now twenty swapped letters, reducing the effectiveness of the "bomba" and increasing the number of possible plug-board settings by more than a thousandfold.
Results given to the British and French
The Poles' gift of Enigma decryption to their Western allies, a month 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 cryptanalysts. 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 code-breakers 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 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 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." 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 due in large part to the early Polish work on Enigma.
Work in France
In September 1939 after the outbreak of World War II, Rejewski and his fellow Cipher Bureau workers were evacuated from Poland to Romania. Rejewski, together with Żygalski 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 code name). The French army officer on duty called Paris for instructions and immediately had the three mathematicians evacuated to France. They arrived in Paris by the end of September.
On 20 October, they resumed their work on German ciphers at a joint French-Polish-Spanish radio intelligence unit stationed at Château de Vignolles, forty kilometers northeast of Paris, code-named "PC Bruno". Enigma keys were being broken again by December 1939 or January 1940. The staff at PC Bruno collaborated by teletype with their opposite numbers at Bletchley Park in England. For communications security the allied Polish, French and British cryptology agencies used the Enigma machine itself closing Bruno's Enigma-encrypted messages to Britain with an ironic "Heil Hitler!". On 24 June 1940, Bruno was disbanded after Germany's victory in the Battle of France, and Rejewski and his colleagues were evacuated 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 plug-board). Rejewski may have had little or no involvement in working on German Enigma at Cadix.
In early July 1941, Rejewski and Żygalski were asked to try solving messages enciphered on the secret Polish Lacida cipher machine, which was used to 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 a 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 January 9, 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, the 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.
Escape from France
The Poles were split into groups of twos or threes. Rejewski and Żygalski were sent to Nice on 11 November, which was in a zone occupied by the Italians. 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 Aix-les-Thermes, close to the Spanish border.
The plan was to smuggle themselves over the Pyrenees across into Spain. Accompanied by a local guide, Rejewski and Żygalski began their trek through the Pyrenees on 29 January 1943. They avoided German and Vichy patrols, but near midnight and near the border, their guide pulled out pistol and demanded them to hand over the rest of their money.
Despite being robbed, they succeeded in reaching the Spanish side of the border, only to be arrested by Spanish security police within hours. The Poles were sent first to a prison in Séo de Urgel until 24 March, then moved to a prison at Lerida. The pair were eventually released on 4 May, 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 Britain, arriving 3 August 1943.
Work in Great Britain
On 16 August Rejewski and Żygalski were inducted as privates into the Polish Army and employed at cracking German SS and SD hand ciphers at Boxmoor. The SS and SD ciphers were largely based on the Doppelkassettenverfahren system (a double cassette scheme). On October 10, 1943, Rejewski was commissioned a second lieutenant, and on January 1, 1945, he was promoted to lieutenant.
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 the opportunity of making further contributions to their craft. British code-breaker 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 observance of the "need-to-know" principle. Stripp comments further that "setting them to work on the Doppelkassetten system was like using the racehorses to pull wagons".
Postwar life and recognition
On November 21, 1946, Rejewski, having been 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 two children, Andrzej (born 1936) and Janina (born 1939, who would follow in her father's footsteps to become a mathematician). One option now open to Rejewski was to resume teaching mathematics at University in Poznań or Szczecin, as suggested by his old Poznań University professor, Zdzisław Krygowski. Taking a university post, however, would have entailed yet another separation from his family and his elderly in-laws, with whom the Rejewski family was now living in Bydgoszcz. A grievous blow to Rejewski, too, soon after his return, was the death in summer 1947 of his 11-year old son Andrzej from poliomyelitis. Instead, Rejewski took a position in Bydgoszcz as a supervisor in the sales section of a cable manufacturing plant; Kabel Polski.
The communist Poland Interenal Security Service (UB) repeatedly investigated him between 1949 and 1958, but never had found out about his history of success with Enigma. In 1950, they demanded that he be fired from his employment. Thereafter, he worked briefly at the State Surveying Company as a supervisor, then at the Union of Surveyors of Poland. Between 1951 and 1954 he was employed at the Branch Union of Timber and Varied Manufactures Cooperative. From 1954 until his retirement in February 1967, he worked as a bookkeeper at the Provincial Union of Labor Cooperatives.
Until this point, Rejewski had remained silent about his prewar and wartime work. Shortly after his retirement, he wrote a memoir of his work on Enigma and deposited it at the Military Historical Institute. In 1969, he moved back with his family to Warsaw. When the role of prewar Poland in the Enigma solving emerged in 1973, Rejewski published a number of papers on his cryptology work and contributed generously to articles, books and television programs the world over on the subject. He maintained a lively correspondence with general Gustave Bertrand, author of the first book published on Enigma (1973), which Rejewski at Bertrand's suggestion began translating into Polish. A few years before his death, Rejewski broke enciphered correspondence of Józef Piłsudski and his fellow Polish Socialist conspirators from 1904. On 12 August 1978, he received the Officer's Cross of the Order of Polonia Restituta. Rejewski, who had been suffering for some time from heart disease, died of a heart attack at his home on February 13, 1980, aged 74, and was buried with military honors at Warsaw's Powiązki Cemetery.
The story of Rejewski and his co-workers has been celebrated both in Poland and abroad. He was decorated with a number of Polish medals, both before and after World War II, and after the Enigma story had become public knowledge. In 2000, Rejewski and his colleagues Żygalski and Różycki were posthumously awarded the Grand Cross of the Order of the Rebirth of Poland. On July 4, 2005, Rejewski's daughter received the War Medal 1939-1945 on his behalf, presented by the British Chief of the Defense Staff.
A plaque at Bletchley Park, unveiled in 2002. The English side reads: This plaque commemorates the work of Marian Rejewski, Jerzy Różycki and Henryk Żygalski, mathematicians of the Polish intelligence service, in first breaking the Enigma code. Their work greatly assisted the Bletchley Park code breakers and contributed to the Allied victory in World War II.
Finally, after 57 years, the polish mathematicians essential contribution to the WW II allies' victory was officially recognized!
In exchange, allies give Poland, in Yalta, to the soviet monster; Joseph Stalin.
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