Codebreakers Victory

by Hervie Haufler

  The machines were built. They worked well when the trios that included the identical letter were free of substitutions introduced by the plugboard. To produce results irrespective of the plugboard connections, Zygalski devised what became known as Zygalski Sheets, sheets of cardboard about two feet square. Each sheet was divided into a grid of small squares representing horizontal and vertical alphabets. For each of the six rotor orders, a set of 26 sheets was prepared, 156 in all. The complex procedure involved cutting holes in the grids where a repeat of plaintext letter and cipher letter from that day's indicators was possible. Zygalski and his coworkers used razor blades to cut out thousands of holes. By stacking the sheets over a light source and shifting them systematically, they found places where the light shone through, indicating a rotor order, and a few trial runs on a replica Enigma could determine whether or not this order was the right one. If it was not, gibberish appeared. If it was, the men read the German message. Together with the bombes, the Zygalski Sheets put the Poles back in the business of speedily deciphering the German traffic, which was now so voluminous that a new rank of Enigma-using technicians had to be added to the Cipher Bureau.

  By the winter of 1937-38 the Poles were deciphering about seventy-five percent of the messages passed to them by their intercept stations. In all, during those five years after they first broke through in 1933, they read about one hundred thousand of Germany's military transmissions. They were able to inform Poland's government and military leaders about the German mobilization plans, the order of battle of the German forces and the output of their armaments industry.

  Passing the Torch to the French and British

  In December 1938, the Poles' entire operation again came to a screeching halt. Once more the Germans changed their system, and this time the change was, from the cryptanalysts' point of view, catastrophic.

  The Germans put into service two additional rotors. As mentioned earlier, the Enigma had slots for only three code wheels at a time. To have the three chosen from the five available, however, multiplied the number of code wheel orders ten times, a huge additional cryptanalytic burden.

  The Poles were confident they could solve the new system, but to do it they would need not 6 bombes but 60, and not 156 Zygalski Sheets but 1,560. These requirements simply outran the Cipher Bureau's resources. In addition, the Nazi drums of war were beating ever more loudly, and the Poles could see that time was running short.

  Even though they could still read the messages of the Nazi Party's intelligence service, which continued to use the old keying system, the Poles came to a momentous decision. They would pass on to their allies, who now included the British, the knowledge they had acquired about the Enigma and the machines they had developed to break its output.

  On July 24, 1939, the French delegates, including Bertrand and an aide, along with three top intelligence officials from Britain, arrived in Warsaw. They were taken to the building the Poles had created for their cryptanalysis crew outside the city. "At that meeting," as Rejewski depicted it, "we told everything that we knew and showed everything that we had." Ironically, the common language for their meeting was German.

  The head of the Cipher Bureau, Lieutenant Colonel Gwido Langer, showed the visitors around the facility. Then he took them into a room in which several objects under covers rested on tables. Like an artist unveiling a new creation, Langer whisked off the covers. Under them were Polish clones of Enigmas. Everyone recognized what they were, yet they could not believe that the Poles had built the machines on their own. Bertrand called it "un moment de stupeur" "a moment of stupor."

  Among the English party was Dillwyn "Dilly" Knox. Back in England, Knox had been wrestling fruitlessly with the Enigma, and he had a question for his Polish hosts: in what sequence had the Germans ordered their connections in the entry rotor? When told they were wired in alphabetical order, he blinked in disbelief. Something so obvious had never entered his mind. According to one report, later that evening when he was in a taxi with Bertrand returning to their hotel, he chanted happily, "Nous avons le QWERTZU, nous marchons ensemble'1'': "We have the QWERTZU, we march together."

  Lariger led the way to another room. Here, lined up, were the six bombes. Langer switched on the machines and demonstrated how they worked. Rejewski answered questions. Zygalski explained his perforated sheets. Bertrand's moment of stupeur deepened.

  Alastair Denniston, chief of the British delegation, wanted to telephone London right away to have technicians fly in to size up the specifications for the Enigmas and the bombes. That wouldn't be necessary, the Poles told him. They were ready to ship Enigmas by diplomatic pouch to Paris, where one could be forwarded to England, and to supply technical drawings of the bombes as well as samples of the Zygalski Sheets.

  The conference ended, as Kahn has described it, "in an atmosphere of warmth, astonishment, gratitude, and anticipation."

  The disclosure came none too soon. Just five weeks later, the German blitzkrieg overran the armies of Poland. The Cipher Bureau had to quickly destroy its files and smash its machinery. The cryptographic team also needed to escape, for in their heads was information the Gestapo might well extract by methods of torture.

  Rejewski and his mates headed south and soon crossed the border into Romania. At the French consulate in Bucharest, the code name for Captain Bertrand brought a quick passage. Making their way through Yugoslavia and Italy, they joined up with Bertrand at his headquarters outside Paris. Soon, with British help that included providing new stacks of Zygalski Sheets, they were back to tackling the Enigma.

  The Poles were not again to become the leaders in the attack on the Enigma, but before their flight they had shown what no one else, least of all the Germans, believed possible. The Enigma could be beaten and the secret contents of its messages divulged.

  3

  Britain Takes Over the Cryptologic War

  Britain's cryptanalysts were busily making up for their years of halfhearted attempts to crack the machine. The Government Code and Cypher School (GC&CS)—a deliberately understated title—was moved out of crowded and bomb-vulnerable London. For its new home, the chief of the Secret Intelligence Service, eccentric millionaire Hugh Sinclair, had purchased the Bletchley Park estate in the town of Bletchley, a homely manufacturing and railway hub fifty miles to the northwest in Buckinghamshire. In August 1939, Alastair Denniston, picked by Sinclair to head up GC&CS, had investigated the accommodations at Bletchley Park. Even though the mansion was an architectural monstrosity, Denniston saw that the Park had other virtues. Chief among them was that it was located on a main rail line out of London and another line that connected Bletchley to both Oxford and Cambridge. Convinced, he made BP the GC&CS headquarters just before England was plunged into war against Germany.

  British progress in cryptology owes much to Denniston. During the Great War, he was a bright young man in Britain's Room 40. He could have pursued a much more lucrative career elsewhere, but he stayed with the agency. With World War II approaching, he led the way in making changes that proved critical to BP's success. He realized, as the Poles had a decade earlier, that the new cryptology demanded different mind-sets, individuals with advanced mathematical skills, puzzle solvers, chess players, bridge addicts. He began tracking down such individuals, mainly in Cambridge and Oxford, and recruiting them. He launched a cryptography course to begin their training. Most important, he was a persuasive advocate for having most of Britain's cryptologic program centered in Bletchley. He knew that the kind of brains that excel in cryptanalysis are not common, and to have them joined in collaboration at one place was a distinct advantage. The Germans had bright analysts, but there were so many chiefs contending for Hitler's favor, with each zealously guarding his own turf, that the available brainpower was too fragmented ever to mount a coherent and consistent codebreaking program.

  Denniston was not particular about his recruits' backgrounds. He combed the military; he used his old-boy contacts among the universities; he brought
in civilians; he tapped the Wrens (Women's Royal Navy Service) and Waafs (Women's Auxiliary Air Force) for legions of young women. BP became a melting pot of cryptologic expertise. When the war began, three of Britain's master chess players were attending an international Chess Olympiad in Buenos Aires. They promptly caught the blacked-out, unconvoyed Alcantara for home and joined Denniston's team at Bletchley.

  GC&CS denizens formed a society ruled by meritocracy. Military rank didn't count. No saluting or other military hocus-pocus was tolerated. Everybody went by first names or nicknames. The only way to gain respect was by doing a superlative piece of work.

  Most brilliant, and most eccentric, of the lot was Alan Turing. He had a strange and wonderful combination of talents: he was a mathematical and theoretical genius, yet he could descend from his visionary cloud to become the most practical mechanic. To look back at those times is to marvel at how fortuitous it was that this man became the pivotal figure in the conquest of the Enigma.

  Turing's powerful and independent mind made him, as a schoolboy, intolerant of conventional classroom teaching. Frequently he neglected regular studies because his real attention was given to probing advanced mathematical theorems on his own. Adding to his drive to excel was his memory of an ardent friendship with a fellow student, Christopher Morcom. When Morcom died of tuberculosis while still in school, Turing resolved to achieve what he believed his friend would have achieved if he had lived.

  Morcom had won a scholarship to Cambridge. Turing followed suit by attending Cambridge and being elected to a fellowship at the university's King's College when he was twenty-two. He was also sure Morcom would have sought stimulus by searching out the university's outstanding academic scions. Turing was strongly influenced, first, by David Hilbert, who raised the question, did there exist a definitive method which could, in principle, be applied to any mathematical assertion and produce a correct decision as to whether it was provable? Hilbert believed there was no such thing as an unsolvable mathematical problem.

  The second Cambridge lecturer who most influenced Turing's thinking was Maxwell H. A. "Max" Newman, who asked if there wasn't a mechanical process that could put mathematical theorems to the test.

  From this point on, Turing—in the words of his biographer Andrew Hodges—"dreamed of machines." In the early summer of 1935, when he was just twenty-three years old, he saw his answer. He created a theoretical "universal machine"—afterward known as the Turing machine—that could, by using the binary system that later became the basis for digital computers, replicate logical human thought. The Turing machine could also write a verdict as to whether a specific assertion was or was not provable. This, together with his work on determining computable versus non-computable numbers, proved Hilbert wrong: there could be unsolvable problems.

  The world of advanced mathematics was then centered in Princeton, New Jersey. There men such as Albert Einstein, Alonzo Church and Kurt Godel provided leadership in probing into mathematical unknowns. In 1936, Turing went to Princeton University and benefited from exchanging ideas with the older masters. While there he indulged both his theoretical and his mechanical bents in, as though by predestination, cryptology. He worked on a cryptographic system for which he needed an electrical multiplier. To build it he had to construct his own electrical relays.

  Princeton Ph.D. in hand, and his multiplier in his luggage, Turing returned to Britain in July 1938 and soon afterward wound up at Bletchley Park. There, in the summer of 1939, spirits were animated by the knowledge that the Poles had broken the Enigma. Turing led BP's attack.

  To him the German machine was a practical application of his theoretical machines. The Poles were right: to defeat the Enigma required counter-Enigmas. Yet the Poles were also wrong: their machines attacked the German machine through the message key indicators, and in his estimation, that was not the right way to go as indicators could be changed overnight, sending the codebreakers back to square one.

  With astonishing speed Turing created an English bombe that took little from the Poles except the machine's name. Turing's bombe passed over the indicators; it sought to extract the key from the message itself.

  Turing and Welchman Team Up

  Brilliant as he was, to make his bombe effective, Turing had to have help from a colleague, Gordon Welchman. A lecturer in mathematics at Cambridge, Welchman had a frustrating time when he first came to Bletchley Park. Denniston assigned him to join Dilly Knox's small group at work in the BP building known as the Cottage. But Knox seemed to take a dislike to him and banished him to another building. There Welchman was told to study some German army messages and draw whatever information and patterns he could through an external examination. Welchman soon went beyond those parameters. On his own he realized the vulnerability of the double enciphering of the message key and independently evolved an equivalent of the Zygalski Sheets. When he reported his work to Knox, Welchman was dismayed to find that he had simply been duplicating the efforts of another BP associate and Cambridge alumnus, John Jeffreys, who had produced Bletchley's version of the Polish sheets.

  Welchman's fortunes changed when he teamed up with Turing. Turing's approach to cracking the Enigma was to work with "cribs," or what Welchman called the "probable words" in a message. Since military parlance was highly standardized and repetitious, one could presume that certain words or phrases would appear in the text. The Poles had made rudimentary use of the technique by searching for messages that began with ANX. Turing meant to use his bombes to carry the method much further by finding longer passages embedded in the message itself.

  The British were aided, as the Poles had been, by German overconfidence in the security of their machine. The Germans could have made the use of cribs far more difficult if not impossible. All they needed to do was to add random bits of nonsense into their message beginnings and/or endings, or to insert Xs into long words, or to translate officers' titles into coded references—any such steps would have prevented accurate cribs from being applied. But they remained punctilious about spelling out honorifics and titles, and they continued to use repetitive phrases without any masking.

  Turing's bombe, possessing the power of at least twelve Polish bombes, was designed to run an automatic test to determine whether a specific crib was contained in the message. He, however, had a limited view of what could be obtained even when his bombe succeeded. Essentially, he meant to look for the same sorts of closed letter loops that had been at the center of the Poles' technology. Turing's loops, however, had the great advantage of being drawn from cribs within the message rather than from its indicator. His bombe used the loops to detect incorrect positions and, by rejecting them, to arrive at the correct settings.

  When it was built, though, this first bombe did not work well. To seek out merely small strings of letters did not produce enough rejections. There were many "Stops" that were found to be false only by hand testing. It was a slow and uncertain process.

  Then Turing showed his plans to Welchman. In a flash of inspiration, Welchman saw that they didn't have to settle for closed loops. "By interconnecting the scramblers in a completely new way," he wrote in his memoir, The Hut Six Story, "one could increase the effectiveness of the automatic test by a very large number."

  His new method involved adding to Turing's bombe the circuitry of what Welchman called a "diagonal board"—a matrix of terminals in a square in which the twenty-six letters of the alphabet were arranged horizontally, with another twenty-six vertically. His scheme capitalized on the reciprocal nature of the Enigma's plugboard connections. That is, if A is connected with Z and becomes Z in the encipherment, then the reverse is also true: Zbecomes A. His change ruled out false stops that the plugboards could make in Turing's bombe. The insertion of the diagonal board, as Welchman described it, "greatly reduced the number of runs that would be needed to insure success in breaking an Enigma key by means of a crib."

  Turing, Welchman wrote, was incredulous at first, "but when he had studied my diagram he agr
eed that the idea would work, and became as excited about it as I was."

  Turing's earlier design had guided the British Tabulating Machine Company in producing the first BP bombe. Now an improved design incorporating Welchman's diagonal board was put into production. The conversion benefited from Turing's mechanical bent. To do their required switching jobs, the bombes needed fast-working electrical relays. Turing drew from his electric multiplier to suggest designs for the bombes.

  Patricia Bing, a teletypist who worked for Turing, later recalled how fellow workers at BP quickly adjusted to the unconventional ways of the man they began referring to as "the Prof." They understood that Turing thought little of his appearance or the impression he made. His clothes were a mess; his chewed-up fingernails most often had crescents of dirt beneath them; he could show up at BP entirely unaware that he was wearing two odd shoes. To control his allergies in pollen season he donned a gas mask when riding his bike. The bike had a bad habit of periodically throwing its chain; instead of taking the time to fix it he would count off the number of revolutions and stop just in time to make an adjustment. Bing remembered seeing Turing arrive on his bike and then "scuttle past us giggling girls, eyes downcast, as though in fear he might have to speak to one of us before he disappeared into his office." The papers he wrote and the designs he produced were made almost unintelligible by scratch-outs and inkblots. When invasion threatened, he melted down a collection of silver coins into ingots, buried them and then, when the crisis had passed and it was time to dig them up, could not remember where they were buried.

  In the hunt to unlock the Enigma, though, the Germans never dreamed they would be up against a man of Turing's genius. In those few months between the outbreak of the war and early 1940, he had analyzed the machine, discerned the chinks in its supposedly impenetrable armor and, with Welchman's help, devised the countermeasures that would defeat it.