Rejewski had no idea of the day key, and he had no idea which message keys were being chosen, but he did know that they resulted in this table of relationships. Had the day key been different, then the table of relationships would have been completely different. The next question was whether there existed any way of determining the day key by looking at the table of relationships. Rejewski began to look for patterns within the table, structures that might indicate the day key. Eventually, he began to study one particular type of pattern, which featured chains of letters. For example, in the table, A on the top row is linked to F on the bottom row, so next he would look up F on the top row. It turns out that F is linked to W, and so he would look up W on the top row. And it turns out that W is linked to A, which is where we started. The chain has been completed.

With the remaining letters in the alphabet, Rejewski would generate more chains. He listed all the chains, and noted the number of links in each one: [image]

So far, we have only considered the links between the 1st and 4th letters of the six-letter repeated key. In fact, Rejewski would repeat this whole exercise for the relationships between the 2nd and 5th letters, and the 3rd and 6th letters, identifying the chains in each case and the number of links in each chain.

Rejewski noticed that the chains changed each day. Sometimes there were lots of short chains, sometimes just a few long chains. And, of course, the letters within the chains changed. The characteristics of the chains were clearly a result of the day key setting-a complex consequence of the plugboard settings, the scrambler arrangement and the scrambler orientations. However, there remained the question of how Rejewski could determine the day key from these chains. Which of 10,000,000,000,000,000 possible day keys was related to a particular pattern of chains? The number of possibilities was simply too great.

It was at this point that Rejewski had a profound insight. Although the plugboard and scrambler settings both affect the details of the chains, their contributions can to some extent be disentangled. In particular, there is one aspect of the chains which is wholly dependent on the scrambler settings, and which has nothing to do with the plugboard settings: the numbers of links in the chains is purely a consequence of the scrambler settings. For instance, let us take the example above and pretend that the day key required the letters S and G to be swapped as part of the plugboard settings. If we change this element of the day key, by removing the cable that swaps S and G, and use it to swap, say, T and K instead, then the chains would change to the following: their contributions can to some extent be disentangled. In particular, there is one aspect of the chains which is wholly dependent on the scrambler settings, and which has nothing to do with the plugboard settings: the numbers of links in the chains is purely a consequence of the scrambler settings. For instance, let us take the example above and pretend that the day key required the letters S and G to be swapped as part of the plugboard settings. If we change this element of the day key, by removing the cable that swaps S and G, and use it to swap, say, T and K instead, then the chains would change to the following: [image]

Some of the letters in the chains have changed, but, crucially, the number of links in each chain remains constant. Rejewski had identified a facet of the chains that was solely a reflection of the scrambler settings.

The total number of scrambler settings is the number of scrambler arrangements (6) multiplied by the number of scrambler orientations (17,576) which comes to 105,456. So, instead of having to worry about which of the 10,000,000,000,000,000 day keys was a.s.sociated with a particular set of chains, Rejewski could busy himself with a drastically simpler problem: which of the 105,456 scrambler settings was a.s.sociated with the numbers of links within a set of chains? This number is still large, but it is roughly one hundred billion times smaller than the total number of possible day keys. In short, the task has become one hundred billion times easier, certainly within the realm of human endeavor.

Rejewski proceeded as follows. Thanks to Hans-Thilo Schmidt's espionage, he had access to replica Enigma machines. His team began the laborious ch.o.r.e of checking each of 105,456 scrambler settings, and cataloguing the chain lengths that were generated by each one. It took an entire year to complete the catalogue, but once the Biuro had acc.u.mulated the data, Rejewski could finally begin to unravel the Enigma cipher.

Each day, he would look at the encrypted message keys, the first six letters of all the intercepted messages, and use the information to build his table of relationships. This would allow him to trace the chains, and establish the number of links in each chain. For example, a.n.a.lyzing the 1st and 4th letters might result in four chains with 3, 9, 7 and 7 links. a.n.a.lyzing the 2nd and 5th letters might also result in four chains, with 2, 3, 9 and 12 links. a.n.a.lyzing the 3rd and 6th letters might result in five chains with 5, 5, 5, 3 and 8 links. As yet, Rejewski still had no idea of the day key, but he knew that it resulted in 3 sets of chains with the following number of chains and links in each one: establish the number of links in each chain. For example, a.n.a.lyzing the 1st and 4th letters might result in four chains with 3, 9, 7 and 7 links. a.n.a.lyzing the 2nd and 5th letters might also result in four chains, with 2, 3, 9 and 12 links. a.n.a.lyzing the 3rd and 6th letters might result in five chains with 5, 5, 5, 3 and 8 links. As yet, Rejewski still had no idea of the day key, but he knew that it resulted in 3 sets of chains with the following number of chains and links in each one: 4 chains from the 1st and 4th letters, with3, 9, 7 and 7 links.

4 chains from the 2nd and 5th letters, with2, 3, 9 and 12 links.

5 chains from the 3rd and 6th letters, with 5, 5, 5, 3 and8 links.

Rejewski could now go to his catalogue, which contained every scrambler setting indexed according to the sort of chains it would generate. Having found the catalogue entry that contained the right number of chains with the appropriate number of links in each one, he immediately knew the scrambler settings for that particular day key. The chains were effectively fingerprints, the evidence that betrayed the initial scrambler arrangement and orientations. Rejewski was working just like a detective who might find a fingerprint at the scene of a crime, and then use a database to match it to a suspect.

Although he had identified the scrambler part of the day key, Rejewski still had to establish the plugboard settings. Although there are about a hundred billion possibilities for the plugboard settings, this was a relatively straightforward task. Rejewski would begin by setting the scramblers in his Enigma replica according to the newly established scrambler part of the day key. He would then remove all cables from the plugboard, so that the plugboard had no effect. Finally, he would take a piece of intercepted ciphertext and type it in to the Enigma machine. This would largely result in gibberish, because the plugboard cablings were unknown and missing. However, every so often vaguely recognizable phrases would appear, such as alliveinbelrin-presumably, this should be "arrive in Berlin." If this a.s.sumption is correct, then it would imply that the letters R and L should be connected and swapped by a plugboard cable, while A, I, V, E, B and N should not. By a.n.a.lyzing other phrases it would be possible to identify the other five pairs of letters that had been swapped by the plugboard. Having established the plugboard settings, and having already discovered the scrambler settings, Rejewski had the complete day key, and could then decipher any message sent that day. the scrambler settings, Rejewski had the complete day key, and could then decipher any message sent that day.

Rejewski had vastly simplified the task of finding the day key by divorcing the problem of finding the scrambler settings from the problem of finding the plugboard settings. On their own, both of these problems were solvable. Originally, we estimated that it would take more than the lifetime of the universe to check every possible Enigma key. However, Rejewski had spent only a year compiling his catalogue of chain lengths, and thereafter he could find the day key before the day was out. Once he had the day key, he possessed the same information as the intended receiver and so could decipher messages just as easily.

Following Rejewski's breakthrough, German communications became transparent. Poland was not at war with Germany, but there was a threat of invasion, and Polish relief at conquering Enigma was nevertheless immense. If they could find out what the German generals had in mind for them, there was a chance that they could defend themselves. The fate of the Polish nation had depended on Rejewski, and he did not disappoint his country. Rejewski's attack on Enigma is one of the truly great accomplishments of crypta.n.a.lysis. I have had to sum up his work in just a few pages, and so have omitted many of the technical details, and all of the dead ends. Enigma is a complicated cipher machine, and breaking it required immense intellectual force. My simplifications should not mislead you into underestimating Rejewski's extraordinary achievement.

The Polish success in breaking the Enigma cipher can be attributed to three factors: fear, mathematics and espionage. Without the fear of invasion, the Poles would have been discouraged by the apparent invulnerability of the Enigma cipher. Without mathematics, Rejewski would not have been able to a.n.a.lyze the chains. And without Schmidt, codenamed "Asche," and his doc.u.ments, the wirings of the scramblers would not have been known, and crypta.n.a.lysis could not even have begun. Rejewski did not hesitate to express the debt he owed Schmidt: "Asche's doc.u.ments were welcomed like manna from heaven, and all doors were immediately opened."

The Poles successfully used Rejewski's technique for several years. When Hermann Goring visited Warsaw in 1934, he was totally unaware of the fact that his communications were being intercepted and deciphered. As he and other German dignitaries laid a wreath at the Tomb of the Unknown Soldier next to the offices of the Biuro Szyfrow, Rejewski could stare down at them from his window, content in the knowledge that he could read their most secret communications. As he and other German dignitaries laid a wreath at the Tomb of the Unknown Soldier next to the offices of the Biuro Szyfrow, Rejewski could stare down at them from his window, content in the knowledge that he could read their most secret communications.

Even when the Germans made a minor alteration to the way they transmitted messages, Rejewski fought back. His old catalogue of chain lengths was useless, but rather than rewriting the catalogue he devised a mechanized version of his cataloguing system, which could automatically search for the correct scrambler settings. Rejewski's invention was an adaptation of the Enigma machine, able to rapidly check each of the 17,576 settings until it spotted a match. Because of the six possible scrambler arrangements, it was necessary to have six of Rejewski's machines working in parallel, each one representing one of the possible arrangements. Together, they formed a unit that was about a meter high, capable of finding the day key in roughly two hours. The units were called bombes bombes, a name that might reflect the ticking noise they made while checking scrambler settings. Alternatively, it is said that Rejewski got his inspiration for the machines while at a cafe eating a bombe bombe, an ice cream shaped into a hemisphere. The bombes effectively mechanized the process of decipherment. It was a natural response to Enigma, which was a mechanization of encipherment.

For most of the 1930s, Rejewski and his colleagues worked tirelessly to uncover the Enigma keys. Month after month, the team would have to deal with the stresses and strains of crypta.n.a.lysis, continually having to fix mechanical failures in the bombes, continually having to deal with the never-ending supply of encrypted intercepts. Their lives became dominated by the pursuit of the day key, that vital piece of information that would reveal the meaning of the encrypted messages. However, unknown to the Polish codebreakers, much of their work was unnecessary. The chief of the Biuro, Major Gwido Langer, already had the Enigma day keys, but he kept them hidden, tucked away in his desk.

Langer, via the French, was still receiving information from Schmidt. The German spy's nefarious activities did not end in 1931 with the delivery of the two doc.u.ments on the operation of Enigma, but continued for another seven years. He met the French secret agent Rex on twenty occasions, often in secluded alpine chalets where privacy was guaranteed. At every meeting, Schmidt handed over one or more codebooks, each one containing a month's worth of day keys. These were the codebooks that were distributed to all German Enigma operators, and they contained all the information that was needed to encipher and decipher messages. In total, he provided codebooks that contained 38 months' worth of day keys. The keys would have saved Rejewski an enormous amount of time and effort, shortcutting the necessity for bombes and sparing manpower that could have been used in other sections of the Biuro. However, the remarkably astute Langer decided not to tell Rejewski that the keys existed. By depriving Rejewski of the keys, Langer believed he was preparing him for the inevitable time when the keys would no longer be available. He knew that if war broke out it would be impossible for Schmidt to continue to attend covert meetings, and Rejewski would then be forced to be self-sufficient. Langer thought that Rejewski should practice self-sufficiency in peacetime, as preparation for what lay ahead. containing a month's worth of day keys. These were the codebooks that were distributed to all German Enigma operators, and they contained all the information that was needed to encipher and decipher messages. In total, he provided codebooks that contained 38 months' worth of day keys. The keys would have saved Rejewski an enormous amount of time and effort, shortcutting the necessity for bombes and sparing manpower that could have been used in other sections of the Biuro. However, the remarkably astute Langer decided not to tell Rejewski that the keys existed. By depriving Rejewski of the keys, Langer believed he was preparing him for the inevitable time when the keys would no longer be available. He knew that if war broke out it would be impossible for Schmidt to continue to attend covert meetings, and Rejewski would then be forced to be self-sufficient. Langer thought that Rejewski should practice self-sufficiency in peacetime, as preparation for what lay ahead.

Rejewski's skills eventually reached their limit in December 1938, when German cryptographers increased Enigma's security. Enigma operators were all given two new scramblers, so that the scrambler arrangement might involve any three of the five available scramblers. Previously there were only three scramblers (labeled 1, 2 and 3) to choose from, and only six ways to arrange them, but now that there were two extra scramblers (labeled 4 and 5) to choose from, the number of arrangements rose to 60, as shown in Table 10 Table 10. Rejewski's first challenge was to work out the internal wirings of the two new scramblers. More worryingly, he also had to build ten times as many bombes, each representing a different scrambler arrangement. The sheer cost of building such a battery of bombes was fifteen times the Biuro's entire annual equipment budget. The following month the situation worsened when the number of plugboard cables increased from six to ten. Instead of twelve letters being swapped before entering the scramblers, there were now twenty swapped letters. The number of possible keys increased to 159,000,000,000,000,000,000.

In 1938 Polish interceptions and decipherments had been at their peak, but by the beginning of 1939 the new scramblers and extra plugboard cables stemmed the flow of intelligence. Rejewski, who had pushed forward the boundaries of crypta.n.a.lysis in previous years, was confounded. He had proved that Enigma was not an unbreakable cipher, but without the resources required to check every scrambler setting he could not find the day key, and decipherment was impossible. Under such desperate circ.u.mstances Langer might have been tempted to hand over the keys that had been obtained by Schmidt, but the keys were no longer being delivered. Just before the introduction of the new scramblers, Schmidt had broken off contact with agent Rex. For seven years he had supplied keys which were superfluous because of Polish innovation. Now, just when the Poles needed the keys, they were no longer available. the day key, and decipherment was impossible. Under such desperate circ.u.mstances Langer might have been tempted to hand over the keys that had been obtained by Schmidt, but the keys were no longer being delivered. Just before the introduction of the new scramblers, Schmidt had broken off contact with agent Rex. For seven years he had supplied keys which were superfluous because of Polish innovation. Now, just when the Poles needed the keys, they were no longer available.

The new invulnerability of Enigma was a devastating blow to Poland, because Enigma was not merely a means of communication, it was at the heart of Hitler's blitzkrieg strategy. The concept of blitzkrieg ("lightning war") involved rapid, intense, coordinated attack, which meant that large tank divisions would have to communicate with one another and with infantry and artillery. Furthermore, land forces would be backed up by air support from dive-bombing Stukas, which would rely on effective and secure communication between the front-line troops and the airfields. The ethos of blitzkrieg was "speed of attack through speed of communications." If the Poles could not break Enigma, they had no hope of stopping the German onslaught, which was clearly only a matter of months away. Germany already occupied the Sudetenland, and on April 27, 1939, it withdrew from its nonaggression treaty with Poland. Hitler's anti-Polish rhetoric became increasingly vitriolic. Langer was determined that if Poland was invaded, then its crypta.n.a.lytic breakthroughs, which had so far been kept secret from the Allies, should not be lost. If Poland could not benefit from Rejewski's work, then at least the Allies should have the chance to try and build on it. Perhaps Britain and France, with their extra resources, could fully exploit the concept of the bombe. chance to try and build on it. Perhaps Britain and France, with their extra resources, could fully exploit the concept of the bombe.

Table 10 Possible arrangements with five scramblers. Possible arrangements with five scramblers.

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Figure 43 General Heinz Guderian's command post vehicle. An Enigma machine can be seen in use in the bottom left. ( General Heinz Guderian's command post vehicle. An Enigma machine can be seen in use in the bottom left. (photo credit 4.2) On June 30, Major Langer telegraphed his French and British counterparts, inviting them to Warsaw to discuss some urgent matters concerning Enigma. On July 24, senior French and British crypta.n.a.lysts arrived at the Biuro's headquarters, not knowing quite what to expect. Langer ushered them into a room in which stood an object covered with a black cloth. He pulled away the cloth, dramatically revealing one of Rejewski's bombes. The audience were astonished as they heard how Rejewski had been breaking Enigma for years. The Poles were a decade ahead of anybody else in the world. The French were particularly astonished, because the Polish work had been based on the results of French espionage. The French had handed the information from Schmidt to the Poles because they believed it to be of no value, but the Poles had proved them wrong.

As a final surprise, Langer offered the British and French two spare Enigma replicas and blueprints for the bombes, which were to be shipped in diplomatic bags to Paris. From there, on August 16, one of the Enigma machines was forwarded to London. It was smuggled across the Channel as part of the baggage of the playwright Sacha Guitry and his wife, the actress Yvonne Printemps, so as not to arouse the suspicion of German spies who would be monitoring the ports. Two weeks later, on September 1, Hitler invaded Poland and the war began.

The Geese that Never Cackled For thirteen years the British and the French had a.s.sumed that the Enigma cipher was unbreakable, but now there was hope. The Polish revelations had demonstrated that the Enigma cipher was flawed, which boosted the morale of Allied crypta.n.a.lysts. Polish progress had ground to a halt on the introduction of the new scramblers and extra plugboard cables, but the fact remained that Enigma was no longer considered a perfect cipher.

The Polish breakthroughs also demonstrated to the Allies the value of employing mathematicians as codebreakers. In Britain, Room 40 had always been dominated by linguists and cla.s.sicists, but now there was a concerted effort to balance the staff with mathematicians and scientists. They were recruited largely via the old-boy network, with those inside Room 40 contacting their former Oxford and Cambridge colleges. There was also an old-girl network which recruited women undergraduates from places such as Newnham College and Girton College, Cambridge. Room 40 contacting their former Oxford and Cambridge colleges. There was also an old-girl network which recruited women undergraduates from places such as Newnham College and Girton College, Cambridge.

The new recruits were not brought to Room 40 in London, but instead went to Bletchley Park, Buckinghamshire, the home of the Government Code and Cypher School (GC&CS), a newly formed codebreaking organization that was taking over from Room 40. Bletchley Park could house a much larger staff, which was important because a deluge of encrypted intercepts was expected as soon as the war started. During the First World War, Germany had transmitted two million words a month, but it was antic.i.p.ated that the greater availability of radios in the Second World War could result in the transmission of two million words a day.

At the center of Bletchley Park was a large Victorian Tudor-Gothic mansion built by the nineteenth-century financier Sir Herbert Leon. The mansion, with its library, dining hall and ornate ballroom, provided the central administration for the whole of the Bletchley operation. Commander Alastair Denniston, the director of GC&CS, had a ground-floor office overlooking the gardens, a view that was soon spoiled by the erection of numerous huts. These makeshift wooden buildings housed the various codebreaking activities. For example, Hut 6 specialized in attacking the German Army's Enigma communications. Hut 6 pa.s.sed its decrypts to Hut 3, where intelligence operatives translated the messages, and attempted to exploit the information. Hut 8 specialized in the naval Enigma, and they pa.s.sed their decrypts to Hut 4 for translation and intelligence gathering. Initially, Bletchley Park had a staff of only two hundred, but within five years the mansion and the huts would house seven thousand men and women. central administration for the whole of the Bletchley operation. Commander Alastair Denniston, the director of GC&CS, had a ground-floor office overlooking the gardens, a view that was soon spoiled by the erection of numerous huts. These makeshift wooden buildings housed the various codebreaking activities. For example, Hut 6 specialized in attacking the German Army's Enigma communications. Hut 6 pa.s.sed its decrypts to Hut 3, where intelligence operatives translated the messages, and attempted to exploit the information. Hut 8 specialized in the naval Enigma, and they pa.s.sed their decrypts to Hut 4 for translation and intelligence gathering. Initially, Bletchley Park had a staff of only two hundred, but within five years the mansion and the huts would house seven thousand men and women.

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Figure 44 In August 1939, Britain's senior codebreakers visited Bletchley Park to a.s.sess its suitability as the site for the new Government Code and Cypher School. To avoid arousing suspicion from locals, they claimed to be part of Captain Ridley's shooting party. ( In August 1939, Britain's senior codebreakers visited Bletchley Park to a.s.sess its suitability as the site for the new Government Code and Cypher School. To avoid arousing suspicion from locals, they claimed to be part of Captain Ridley's shooting party. (photo credit 4.3) During the autumn of 1939, the scientists and mathematicians at Bletchley learned the intricacies of the Enigma cipher and rapidly mastered the Polish techniques. Bletchley had more staff and resources than the Polish Biuro Szyfrow, and were thus able to cope with the larger selection of scramblers and the fact that Enigma was now ten times harder to break. Every twenty-four hours the British codebreakers went through the same routine. At midnight, German Enigma operators would change to a new day key, at which point whatever breakthroughs Bletchley had achieved the previous day could no longer be used to decipher messages. The codebreakers now had to begin the task of trying to identify the new day key. It could take several hours, but as soon as they had discovered the Enigma settings for that day, the Bletchley staff could begin to decipher the German messages that had already acc.u.mulated, revealing information that was invaluable to the war effort.

Surprise is an invaluable weapon for a commander to have at his disposal. But if Bletchley could break into Enigma, German plans would become transparent and the British would be able to read the minds of the German High Command. If the British could pick up news of an imminent attack, they could send reinforcements or take evasive action. If they could decipher German discussions of their own weaknesses, the Allies would be able to focus their offensives. The Bletchley decipherments were of the utmost importance. For example, when Germany invaded Denmark and Norway in April 1940, Bletchley provided a detailed picture of German operations. Similarly, during the Battle of Britain, the crypta.n.a.lysts were able to give advance warning of bombing raids, including times and locations. They could also give continual updates on the state of the Luftwaffe, such as the number of planes that had been lost and the speed with which they were being replaced. Bletchley would send all this information to MI6 headquarters, who would forward it to the War Office, the Air Ministry and the Admiralty. Britain, the crypta.n.a.lysts were able to give advance warning of bombing raids, including times and locations. They could also give continual updates on the state of the Luftwaffe, such as the number of planes that had been lost and the speed with which they were being replaced. Bletchley would send all this information to MI6 headquarters, who would forward it to the War Office, the Air Ministry and the Admiralty.

In between influencing the course of the war, the crypta.n.a.lysts occasionally found time to relax. According to Malcolm Muggeridge, who served in the secret service and visited Bletchley, rounders, a version of softball, was a favorite pastime: Every day after luncheon when the weather was propitious the cipher crackers played rounders on the manor-house lawn, a.s.suming the quasi-serious manner dons affect when engaged in activities likely to be regarded as frivolous or insignificant in comparison with their weightier studies. Thus they would dispute some point about the game with the same fervor as they might the question of free will or determinism, or whether the world began with a big bang or a process of continuing creation.

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Figure 45 Bletchley's codebreakers relax with a game of rounders. Bletchley's codebreakers relax with a game of rounders.

Once they had mastered the Polish techniques, the Bletchley crypta.n.a.lysts began to invent their own shortcuts for finding the Enigma keys. For example, they cottoned on to the fact that the German Enigma operators would occasionally choose obvious message keys. For each message, the operator was supposed to select a different message key, three letters chosen at random. However, in the heat of battle, rather than straining their imaginations to pick a random key, the overworked operators would sometimes pick three consecutive letters from the Enigma keyboard (Figure 46), such as QWE or BNM. These predictable message keys became known as cillies cillies. Another type of cilly was the repeated use of the same message key, perhaps the initials of the operator's girlfriend-indeed, one such set of initials, C.I.L., may have been the origin of the term. Before cracking Enigma the hard way, it became routine for the crypta.n.a.lysts to try out the cillies, and their hunches would sometimes pay off.

Cillies were not weaknesses of the Enigma machine, rather they were weaknesses in the way the machine was being used. Human error at more senior levels also compromised the security of the Enigma cipher. Those responsible for compiling the codebooks had to decide which scramblers would be used each day, and in which positions. They tried to ensure that the scrambler settings were unpredictable by not allowing any scrambler to remain in the same position for two days in a row. So, if we label the scramblers 1, 2, 3, 4 and 5, then on the first day it would be possible to have the arrangement 134, and on the second day it would be possible to have 215, but not 214, because scrambler number 4 is not allowed to remain in the same position for two days in a row. This might seem a sensible strategy because the scramblers are constantly changing position, but enforcing such a rule actually makes life easier for the crypta.n.a.lyst. Excluding certain arrangements to avoid a scrambler remaining in the same position meant that the codebook compilers reduced by half the number of possible scrambler arrangements. The Bletchley crypta.n.a.lysts realized what was happening and made the most of it. Once they identified the scrambler arrangement for one day, they could immediately rule out half the scrambler arrangements for the next day. Hence, their workload was reduced by half. in the same position meant that the codebook compilers reduced by half the number of possible scrambler arrangements. The Bletchley crypta.n.a.lysts realized what was happening and made the most of it. Once they identified the scrambler arrangement for one day, they could immediately rule out half the scrambler arrangements for the next day. Hence, their workload was reduced by half.

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Figure 46 Layout of the Enigma keyboard. Layout of the Enigma keyboard.

Similarly, there was a rule that the plugboard settings could not include a swap between any letter and its neighbor, which meant that S could be swapped with any letter except R and T. The theory was that such obvious swappings should be deliberately avoided, but once again the implementation of a rule drastically reduced the number of possible keys.

This search for new crypta.n.a.lytic shortcuts was necessary because the Enigma machine continued to evolve during the course of the war. The crypta.n.a.lysts were continually forced to innovate, to redesign and refine the bombes, and to devise wholly new strategies. Part of the reason for their success was the bizarre combination of mathematicians, scientists, linguists, cla.s.sicists, chess grandmasters and crossword addicts within each hut. An intractable problem would be pa.s.sed around the hut until it reached someone who had the right mental tools to solve it, or reached someone who could at least partially solve it before pa.s.sing it on again. Gordon Welchman, who was in charge of Hut 6, described his team as "a pack of hounds trying to pick up the scent." There were many great crypta.n.a.lysts and many significant breakthroughs, and it would take several large volumes to describe the individual contributions in detail. However, if there is one figure who deserves to be singled out, it is Alan Turing, who identified Enigma's greatest weakness and ruthlessly exploited it. Thanks to Turing, it became possible to crack the Enigma cipher under even the most difficult circ.u.mstances.

Alan Turing was conceived in the autumn of 1911 in Chatrapur, a town near Madras in southern India, where his father Julius Turing was a member of the Indian civil service. Julius and his wife Ethel were determined that their son should be born in Britain, and returned to London, where Alan was born on June 23, 1912. His father returned to India soon afterward and his mother followed just fifteen months later, leaving Alan in the care of nannies and friends until he was old enough to attend boarding school.

In 1926, at the age of fourteen, Turing became a pupil at Sherborne School, in Dorset. The start of his first term coincided with the General Strike, but Turing was determined to attend the first day, and he cycled 100 km unaccompanied from Southampton to Sherborne, a feat that was reported in the local newspaper. By the end of his first year at the school he had gained a reputation as a shy, awkward boy whose only skills were in the area of science. The aim of Sherborne was to turn boys into well-rounded men, fit to rule the Empire, but Turing did not share this ambition and had a generally unhappy schooling.

His only real friend at Sherborne was Christopher Morcom, who, like Turing, had an interest in science. Together they discussed the latest scientific news and conducted their own experiments. The relationship fired Turing's intellectual curiosity, but, more importantly, it also had a profound emotional effect on him. Andrew Hodges, Turing's biographer, wrote that "This was first love...It had that sense of surrender, and a heightened awareness, as of brilliant color bursting upon a black and white world." Their friendship lasted four years, but Morcom seems to have been unaware of the depth of feeling Turing had for him. Then, during their final year at Sherborne, Turing lost forever the chance to tell him how he felt. On Thursday, February 13, 1930, Christopher Morcom suddenly died of tuberculosis.

Turing was devastated by the loss of the only person he would ever truly love. His way of coming to terms with Morcom's death was to focus on his scientific studies in an attempt to fulfill his friend's potential. Morcom, who appeared to be the more gifted of the two boys, had already won a scholarship to Cambridge University. Turing believed it was his duty also to win a place at Cambridge, and then to make the discoveries his friend would otherwise have made. He asked Christopher's mother for a photograph, and when it arrived he wrote back to thank her: "He is on my table now, encouraging me to work hard."

In 1931, Turing gained admission to King's College, Cambridge. He arrived during a period of intense debate about the nature of mathematics and logic, and was surrounded by some of the leading voices, such as Bertrand Russell, Alfred North Whitehead and Ludwig Wittgenstein. At the center of the argument was the issue of undecidability undecidability, a controversial notion developed by the logician Kurt G.o.del. It had always been a.s.sumed that, in theory at least, all mathematical questions could be answered. However, G.o.del demonstrated that there could exist a minority of questions which were beyond the reach of logical proof, so-called undecidable questions. Mathematicians were traumatized by the news that mathematics was not the all-powerful discipline they had always believed it to be. They attempted to salvage their subject by trying to find a way of identifying the awkward undecidable questions, so that they could put them safely to one side. It was this objective that eventually inspired Turing to write his most influential mathematical paper, "On Computable Numbers," published in 1937. In that, in theory at least, all mathematical questions could be answered. However, G.o.del demonstrated that there could exist a minority of questions which were beyond the reach of logical proof, so-called undecidable questions. Mathematicians were traumatized by the news that mathematics was not the all-powerful discipline they had always believed it to be. They attempted to salvage their subject by trying to find a way of identifying the awkward undecidable questions, so that they could put them safely to one side. It was this objective that eventually inspired Turing to write his most influential mathematical paper, "On Computable Numbers," published in 1937. In Breaking the Code Breaking the Code, Hugh Whitemore's play about the life of Turing, a character asks Turing the meaning of his paper. He replies, "It's about right and wrong. In general terms. It's a technical paper in mathematical logic, but it's also about the difficulty of telling right from wrong. People think-most people think-that in mathematics we always know what is right and what is wrong. Not so. Not any more."

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Figure 47 Alan Turing. ( Alan Turing. (photo credit 4.4) In his attempt to identify undecidable questions, Turing's paper described an imaginary machine that was designed to perform a particular mathematical operation, or algorithm. In other words, the machine would be capable of running through a fixed, prescribed series of steps which would, for example, multiply two numbers. Turing envisaged that the numbers to be multiplied could be fed into the machine via a paper tape, rather like the punched tape that is used to feed a tune into a Pianola. The answer to the multiplication would be output via another tape. Turing imagined a whole series of these so-called Turing machines Turing machines, each specially designed to tackle a particular task, such as dividing, squaring or factoring. Then Turing took a more radical step.

He imagined a machine whose internal workings could be altered so that it could perform all the functions of all conceivable Turing machines. The alterations would be made by inserting carefully selected tapes, which transformed the single flexible machine into a dividing machine, a multiplying machine, or any other type of machine. Turing called this hypothetical device a universal Turing machine universal Turing machine because it would be capable of answering any question that could logically be answered. Unfortunately, it turned out that it is not always logically possible to answer a question about the undecidability of another question, and so even the universal Turing machine was unable to identify every undecidable question. because it would be capable of answering any question that could logically be answered. Unfortunately, it turned out that it is not always logically possible to answer a question about the undecidability of another question, and so even the universal Turing machine was unable to identify every undecidable question.

Mathematicians who read Turing's paper were disappointed that G.o.del's monster had not been subdued but, as a consolation prize, Turing had given them the blueprint for the modern programmable computer. Turing knew of Babbage's work, and the universal Turing machine can be seen as a reincarnation of Difference Engine No. 2. In fact, Turing had gone much further, and provided computing with a solid theoretical basis, imbuing the computer with a hitherto unimaginable potential. It was still the 1930s though, and the technology did not exist to turn the universal Turing machine into a reality. However, Turing was not at all dismayed that his theories were ahead of what was technically feasible. He merely wanted recognition from within the mathematical community, who indeed applauded his paper as one of the most important breakthroughs of the century. He was still only twenty-six.

This was a particularly happy and successful period for Turing. During the 1930s he rose through the ranks to become a fellow of King's College, home of the world's intellectual elite. He led the life of an archetypal Cambridge don, mixing pure mathematics with more trivial activities. In 1938 he made a point of seeing the film Snow White and the Seven Dwarfs Snow White and the Seven Dwarfs, containing the memorable scene in which the Wicked Witch dunks an apple in poison. Afterward his colleagues heard Turing continually repeating the macabre chant, "Dip the apple in the brew, Let the sleeping death seep through."

Turing cherished his years at Cambridge. In addition to his academic success, he found himself in a tolerant and supportive environment. h.o.m.os.e.xuality was largely accepted within the university, which meant that he was free to engage in a series of relationships without having to worry about who might find out, and what others might say. Although he had no serious long-term relationships, he seemed to be content with his life. Then, in 1939, Turing's academic career was brought to an abrupt halt. The Government Code and Cypher School invited him to become a crypta.n.a.lyst at Bletchley, and on September 4, 1939, the day after Neville Chamberlain declared war on Germany, Turing moved from the opulence of the Cambridge quadrangle to the Crown Inn at Shenley Brook End.

Each day he cycled 5 km from Shenley Brook End to Bletchley Park, where he spent part of his time in the huts contributing to the routine codebreaking effort, and part of his time in the Bletchley think tank, formerly Sir Herbert Leon's apple, pear and plum store. The think tank was where the crypta.n.a.lysts brainstormed their way through new problems, or antic.i.p.ated how to tackle problems that might arise in the future. Turing focused on what would happen if the German military changed their system of exchanging message keys. Bletchley's early successes relied on Rejewski's work, which exploited the fact that Enigma operators encrypted each message key twice (for example, if the message key was YGB, the operator would encipher YGBYGB). This repet.i.tion was supposed to ensure that the receiver did not make a mistake, but it created a c.h.i.n.k in the security of Enigma. British crypta.n.a.lysts guessed it would not be long before the Germans noticed that the repeated key was compromising the Enigma cipher, at which point the Enigma operators would be told to abandon the repet.i.tion, thus confounding Bletchley's current codebreaking techniques. It was Turing's job to find an alternative way to attack Enigma, one that did not rely on a repeated message key. formerly Sir Herbert Leon's apple, pear and plum store. The think tank was where the crypta.n.a.lysts brainstormed their way through new problems, or antic.i.p.ated how to tackle problems that might arise in the future. Turing focused on what would happen if the German military changed their system of exchanging message keys. Bletchley's early successes relied on Rejewski's work, which exploited the fact that Enigma operators encrypted each message key twice (for example, if the message key was YGB, the operator would encipher YGBYGB). This repet.i.tion was supposed to ensure that the receiver did not make a mistake, but it created a c.h.i.n.k in the security of Enigma. British crypta.n.a.lysts guessed it would not be long before the Germans noticed that the repeated key was compromising the Enigma cipher, at which point the Enigma operators would be told to abandon the repet.i.tion, thus confounding Bletchley's current codebreaking techniques. It was Turing's job to find an alternative way to attack Enigma, one that did not rely on a repeated message key.

As the weeks pa.s.sed, Turing realized that Bletchley was acc.u.mulating a vast library of decrypted messages, and he noticed that many of them conformed to a rigid structure. By studying old decrypted messages, he believed he could sometimes predict part of the contents of an undeciphered message, based on when it was sent and its source. For example, experience showed that the Germans sent a regular enciphered weather report shortly after 6 A.M A.M. each day. So, an encrypted message intercepted at 6:05 A.M A.M. would be almost certain to contain wetter, the German word for "weather." The rigorous protocol used by any military organization meant that such messages were highly regimented in style, so Turing could even be confident about the location of wetter within the encrypted message. For example, experience might tell him that the first six letters of a particular ciphertext corresponded to the plaintext letters wetter. When a piece of plaintext can be a.s.sociated with a piece of ciphertext, this combination is known as a crib crib.

Turing was sure that he could exploit the cribs to crack Enigma. If he had a ciphertext and he knew that a specific section of it, say ETJWPX, represented wetter, then the challenge was to identify the settings of the Enigma machine that would transform wetter into ETJWPX. The straightforward, but impractical, way to do this would be for the crypta.n.a.lyst to take an Enigma machine, type in wetter and see if the correct ciphertext emerged. If not, then the crypta.n.a.lyst would change the settings of the machine, by swapping plugboard cables, and swapping or reorienting scramblers, and then type in wetter again. If the correct ciphertext did not emerge, the crypta.n.a.lyst would change the settings again, and again, and again, until he found the right one. The only problem with this trial and error approach was the fact that there were 159,000,000,000,000,000,000 possible settings to check, so finding the one that transformed wetter into ETJWPX was a seemingly impossible task. ciphertext emerged. If not, then the crypta.n.a.lyst would change the settings of the machine, by swapping plugboard cables, and swapping or reorienting scramblers, and then type in wetter again. If the correct ciphertext did not emerge, the crypta.n.a.lyst would change the settings again, and again, and again, until he found the right one. The only problem with this trial and error approach was the fact that there were 159,000,000,000,000,000,000 possible settings to check, so finding the one that transformed wetter into ETJWPX was a seemingly impossible task.

To simplify the problem, Turing attempted to follow Rejewski's strategy of disentangling the settings. He wanted to divorce the problem of finding the scrambler settings (finding which scrambler is in which slot, and what their respective orientations are) from the problem of finding the plugboard cablings. For example, if he could find something in the crib that had nothing to do with the plugboard cablings, then he could feasibly check each of the remaining 1,054,560 possible scrambler combinations (60 arrangements 17,576 orientations). Having found the correct scrambler settings, he could then deduce the plugboard cablings.

Eventually, his mind settled on a particular type of crib which contained internal loops, similar to the chains exploited by Rejewski. Rejewski's chains linked letters within the repeated message key. However, Turing's loops had nothing to do with the message key, as he was working on the a.s.sumption that soon the Germans would stop sending repeated message keys. Instead, Turing's loops connected plaintext and ciphertext letters within a crib. For example, the crib shown in Figure 48 Figure 48 contains a loop. contains a loop.

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Figure 48 One of Turing's cribs, showing a loop. One of Turing's cribs, showing a loop.

Remember, cribs are only guesses, but if we a.s.sume that this crib is correct, we can link the letters WE, eT, tW as part of a loop. Although we know none of the Enigma machine settings, we can label the first setting, whatever it is, S. In this first setting we know that w is encrypted as E. After this encryption, the first scrambler clicks around one place to setting S+1, and the letter e is enciphered as T. The scrambler clicks forward another place and encrypts a letter that is not part of the loop, so we ignore this encryption. The scrambler clicks forward one more place and, once again, we reach a letter that is part of the loop. In setting S+3, we know that the letter t is enciphered as W. In summary, we know that In setting S,Enigma encrypts w as E.

In setting S+1, Enigma encrypts e as T.

In setting S+3, Enigma encrypts t as W.

So far the loop seems like nothing more than a curious pattern, but Turing rigorously followed the implications of the relationships within the loop, and saw that they provided him with the drastic shortcut he needed in order to break Enigma. Instead of working with just one Enigma machine to test every setting, Turing began to imagine three separate machines, each dealing with the encipherment of one element of the loop. The first machine would try to encipher w into E, the second would try to encipher e into T, and the third t into W. The three machines would all have identical settings, except that the second would have its scrambler orientations moved forward one place with respect to the first, a setting labeled S+1, and the third would have its scrambler orientations moved forward three places with respect to the first, a setting labeled S+3. Turing then pictured a frenzied crypta.n.a.lyst, continually changing plugboard cables, swapping scrambler arrangements and changing their orientations in order to achieve the correct encryptions. Whatever cables were changed in the first machine would also be changed in the other two. Whatever scrambler arrangements were changed in the first machine would also be changed in the other two. And, crucially, whatever scrambler orientation was set in the first machine, the second would have the same orientation but stepped forward one place, and the third would have the same orientation but stepped forward three places.

Turing does not seem to have achieved much. The crypta.n.a.lyst still has to check all 159,000,000,000,000,000,000 possible settings, and, to make matters worse, he now has to do it simultaneously on all three machines instead of just one. However, the next stage of Turing's idea transforms the challenge, and vastly simplifies it. He imagined connecting the three machines by running electrical wires between the inputs and the outputs of each machine, as shown in to check all 159,000,000,000,000,000,000 possible settings, and, to make matters worse, he now has to do it simultaneously on all three machines instead of just one. However, the next stage of Turing's idea transforms the challenge, and vastly simplifies it. He imagined connecting the three machines by running electrical wires between the inputs and the outputs of each machine, as shown in Figure 49 Figure 49. In effect, the loop in the crib is paralleled by the loop of the electrical circuit. Turing pictured the machines changing their plugboard and scrambler settings, as described above, but only when all the settings are correct for all three machines would the circuit be completed, allowing a current to flow through all three machines. If Turing incorporated a lightbulb within the circuit, then the current would illuminate it, signaling that the correct settings had been found. At this point, the three machines still have to check up to 159,000,000,000,000,000,000 possible settings in order to illuminate the bulb. However, everything done so far has merely been preparation for Turing's final logical leap, which would make the task over a hundred million million times easier in one fell swoop.

Turing had constructed his electrical circuit in such a way as to nullify the effect of the plugboard, thereby allowing him to ignore the billions of plugboard settings. Figure 49 Figure 49 shows that the first Enigma has the electric current entering the scramblers and emerging at some unknown letter, which we shall call L shows that the first Enigma has the electric current entering the scramblers and emerging at some unknown letter, which we shall call L1. The current then flows through the plugboard, which transforms L1 into E. This letter E is connected via a wire to the letter e in the second Enigma, and as the current flows through the second plugboard it is transformed back to L into E. This letter E is connected via a wire to the letter e in the second Enigma, and as the current flows through the second plugboard it is transformed back to L1. In other words, the two plugboards cancel each other out. Similarly, the current emerging from the scramblers in the second Enigma enters the plugboard at L2 before being transformed into T. This letter T is connected via a wire to the letter t in the third Enigma, and as the current flows through the third plugboard it is transformed back to L before being transformed into T. This letter T is connected via a wire to the letter t in the third Enigma, and as the current flows through the third plugboard it is transformed back to L2. In short, the plugboards cancel themselves out throughout the whole circuit, so Turing could ignore them completely.

Turing needed only to connect the output of the first set of scramblers, L1, directly to the input of the second set of scramblers, also L1, and so on. Unfortunately, he did not know the value of the letter L1, so he had to connect all 26 outputs of the first set of scramblers to all 26 corresponding inputs in the second set of scramblers, and so on. In effect, there were now 26 electrical loops, and each one would have a lightbulb to signal the completion of an electrical circuit. The three sets of scramblers could then simply check each of the 17,576 orientations, with the second set of scramblers always one step ahead of the first set, and the third set of scramblers two steps ahead of the second set. Eventually, when the correct scrambler orientations had been found, one of the circuits would be completed and the bulb would be illuminated. If the scramblers changed orientation every second, it would take just five hours to check all the orientations. 26 electrical loops, and each one would have a lightbulb to signal the completion of an electrical circuit. The three sets of scramblers could then simply check each of the 17,576 orientations, with the second set of scramblers always one step ahead of the first set, and the third set of scramblers two steps ahead of the second set. Eventually, when the correct scrambler orientations had been found, one of the circuits would be completed and the bulb would be illuminated. If the scramblers changed orientation every second, it would take just five hours to check all the orientations.

Only two problems remained. First, it could be that the three machines are running with the wrong scrambler arrangement, because the Enigma machine operates with any three of the five available scramblers, placed in any order, giving sixty possible arrangements. Hence, if all 17,576 orientations have been checked, and the lamp has not been illuminated, it is then necessary to try another of the sixty scrambler arrangements, and to keep on trying other arrangements until the circuit is completed. Alternatively, the crypta.n.a.lyst could have sixty sets of three Enigmas running in parallel.

The second problem involved finding the plugboard cablings, once the scrambler arrangement and orientations had been established. This is relatively simple. Using an Enigma machine with the correct scrambler arrangement and orientations, the crypta.n.a.lyst types in the ciphertext and looks at the emerging plaintext. If the result is tewwer rather than wetter, then it is clear that plugboard cables should be inserted so as to swap w and t. Typing in other bits of ciphertext would reveal other plugboard cablings.

The combination of crib, loops and electrically connected machines resulted in a remarkable piece of crypta.n.a.lysis, and only Turing, with his unique background in mathematical machines, could ever have come up with it. His musings on the imaginary Turing machines were intended to answer esoteric questions about mathematical undecidability, but this purely academic research had put him in the right frame of mind for designing a practical machine capable of solving very real problems.

Bletchley was able to find 100,000 to turn Turing's idea into working devices, which were dubbed bombes because their mechanical approach bore a pa.s.sing resemblance to Rejewski's bombe. Each of Turing's bombes was to consist of twelve sets of electrically linked Enigma scramblers, and would thus be able to cope with much longer loops of letters. The complete unit would be about two meters tall, two meters long and a meter wide. Turing finalized the design at the beginning of 1940, and the job of construction was given to the British Tabulating Machinery factory at Letchworth. would be about two meters tall, two meters long and a meter wide. Turing finalized the design at the beginning of 1940, and the job of construction was given to the British Tabulating Machinery factory at Letchworth.

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Figure 49 The loop in the crib can be paralleled by an electrical loop. Three Enigma machines are set up in identical ways, except that the second one has its first scrambler moved forward one place (setting S + 1), and the third has its scrambler moved forward two further places (setting S + 3). The output of each Enigma is then connected to the input of the next one. The three sets of scramblers then click around in unison until the circuit is complete and the light illuminates. At this point the correct setting has been found. In the diagram above, the circuit is complete, corresponding to the correct setting. The loop in the crib can be paralleled by an electrical loop. Three Enigma machines are set up in identical ways, except that the second one has its first scrambler moved forward one place (setting S + 1), and the third has its scrambler moved forward two further places (setting S + 3). The output of each Enigma is then connected to the input of the next one. The three sets of scramblers then click around in unison until the circuit is complete and the light illuminates. At this point the correct setting has been found. In the diagram above, the circuit is complete, corresponding to the correct setting.

While waiting for the bombes to be delivered, Turing continued his day-to-day work at Bletchley. News of his breakthrough soon spread among the other senior crypta.n.a.lysts, who recognized that he was a singularly gifted codebreaker. According to Peter Hilton, a fellow Bletchley codebreaker, "Alan Turing was obviously a genius, but he was an approachable, friendly genius. He was always willing to take time and trouble to explain his ideas; but he was no narrow specialist, so that his versatile thought ranged over a vast area of the exact sciences."

However, everything at the Government Code and Cypher School was top secret, so n.o.body outside of Bletchley Park was aware of Turing's remarkable achievement. For example, his parents had absolutely no idea that Alan was even a codebreaker, let alone Britain's foremost crypta.n.a.lyst. He had once told his mother that he was involved in some form of military research, but he did not elaborate. She was merely disappointed that this had not resulted in a more respectable haircut for her scruffy son. Although Bletchley was run by the military, they had conceded that they would have to tolerate the scruffiness and eccentricities of these "professor types." Turing rarely bothered to shave, his nails were stuffed with dirt, and his clothes were a ma.s.s of creases. Whether the military would also have tolerated his h.o.m.os.e.xuality remains unknown. Jack Good, a veteran of Bletchley, commented: "Fortunately the authorities did not know that Turing was a h.o.m.os.e.xual. Otherwise we might have lost the war."

The first prototype bombe, christened Victory Victory, arrived at Bletchley on March 14, 1940. The machine was put into operation immediately, but the initial results were less than satisfactory. The machine turned out to be much slower than expected, taking up to a week to find a particular key. There was a concerted effort to increase the bombe's efficiency, and a modified design was submitted a few weeks later. It would take four more months to build the upgraded bombe. In the meantime, the crypta.n.a.lysts had to cope with the calamity they had antic.i.p.ated. On May 1, 1940, the Germans changed their key exchange protocol. They no longer repeated the message key, and thereupon the number of successful Enigma decipherments dropped dramatically. The information blackout lasted until August 8, when the new bombe arrived. Christened August 8, when the new bombe arrived. Christened Agnus Dei Agnus Dei, or Agnes Agnes for short, this machine was to fulfill all Turing's expectations. for short, this machine was to fulfill all Turing's expectations.

Within eighteen months there were fifteen more bombes in operation, exploiting cribs, checking scrambler settings and revealing keys, each one clattering like a million knitting needles. If everything was going well, a bombe might find an Enigma key within an hour. Once the plugboard cablings and the scrambler settings (the message key) had been established for a particular message, it was easy to deduce the day key. All the other messages sent that same day could then be deciphered.

Even though the bombes represented a vital breakthrough in crypta.n.a.lysis, decipherment had not become a formality. There were many hurdles to overcome before the bombes could even begin to look for a key. For example, to operate a bombe you first needed a crib. The senior codebreakers would give cribs to the bombe operators, but there was no guarantee that the codebreakers had guessed the correct meaning of the ciphertext. And even if they did have the right crib, it might be in the wrong place-the crypta.n.a.lysts might have guessed that an encrypted message contained a certain phrase, but a.s.sociated that phrase with the wrong piece of the ciphertext. However, there was a neat trick for checking whether a crib was in the correct position.

In the following crib, the crypta.n.a.lyst is confident that the plaintext is right, but he is not sure if he has matched it with the correct letters in the ciphertext.

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One of the features of the Enigma machine was its inability to encipher a letter as itself, which was a consequence of the reflector. The letter a could never be enciphered as A, the letter b could never be enciphered as B, and so on. The particular crib above must therefore be misaligned, because the first e in wetter is matched with an E in the ciphertext. To find the correct alignment, we simply slide the plaintext and the ciphertext relative to each other until no letter is paired with itself. If we shift the plaintext one place to the left, the match still fails because this time the first s in sechs is matched with S in the ciphertext. However, if we shift the plaintext one place to the right there are no illegal encipherments. This crib is therefore likely to be in the right place, and could be used as the basis for a bombe decipherment: therefore likely to be in the right place, and could be used as the basis for a bombe decipherment: [image]

The intelligence gathered at Bletchley was pa.s.sed on to only the most senior military figures and selected members of the war cabinet. Winston Churchill was fully aware of the importance of the Bletchley decipherments, and on September 6, 1941, he visited the codebreakers. On meeting some of the crypta.n.a.lysts, he was surprised by the bizarre mixture of people who were providing him with such valuable information; in addition to the mathematicians and linguists, there was an authority on porcelain, a curator from the Prague Museum, the British chess champion and numerous bridge experts. Churchill muttered to Sir Stewart Menzies, head of the Secret Intelligence Service, "I told you to leave no stone unturned, but I didn't expect you to take me so literally." Despite the comment, he had a great fondness for the motley crew, calling them "the geese who laid golden eggs and never cackled." head of the Secret Intelligence Service, "I told you to leave no stone unturned, but I didn't expect you to take me so literally." Despite the comment, he had a great fondness for the motley crew, calling them "the geese who laid golden eggs and never cackled."

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Figure 50 A bombe in action. ( A bombe in action. (photo credit 4.5) The visit was intended to boost the morale of the codebreakers by showing them that thei