Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  The traffic in signals was indeed like ‘a thriving trade in pornography and erotica’, inasmuch as what mattered was not so much the guarding of any particular fact, or thing, as the maintenance of the whole subject as something improper for discussion, like ‘dirty talk’. A deeply ingrained fear and embarrassment about the unmentionable was the keynote of all that depended upon the Bletchley work, rather than this or that rule. This was how it worked so well, but it left Alan Turing in an extreme position. It was difficult enough being a mathematician, this being the frightening subject of which even educated people knew nothing, not even what it was, and of which they might proudly boast ignorance. His sexuality might at best elicit a similar condescension, but more likely the associations of evil, tragedy and disease. Above all, it was a matter on which society still demanded silence. Such silence was for him tantamount to an uneasy game of deceit, and he loathed pretence. But as chief consultant to GC and CS, he was living at the heart of yet another imitation game, doing work that did not officially exist. Now there was almost nothing in his life that he could talk about but chess-playing and fir cones.

  Fragments of ordinary life continued. Occasionally he saw his friend David Champernowne, himself now working in the Ministry of Aircraft Production, but of course they never spoke of their work. He had continued to concern himself with Bob’s future, being concerned that he should try for a Cambridge scholarship. This he did, cramming for Latin, but reaching only the standard for an ordinary place. In the circumstances this was quite an achievement, but Bob felt that he had disappointed Alan, in not possessing a feel for abstract ideas. Alan could not possibly afford to send him to Cambridge, so Bob went in autumn 1942 to take the telescoped chemistry course at Manchester University, earning his own keep by stoking the boilers in the Friends Meeting House.

  Bob had a sharp eye, and guessed that Alan, ‘Champ’ and Fred Clayton formed a team working together in Intelligence. He was mistaken in that respect, but right about Alan, though all he knew was that Alan worked at a place called Bletchley. Other people likewise were able to put two and two together. John Turing, while serving in Egypt, found that his superior officer had a brother working at the same town, and they guessed it had to do with ciphers. Mrs Turing guessed correctly too, remembering Alan’s letter about ‘the most general code or cipher’ in 1936, and knowing he worked for ‘the Foreign Office.’ She liked the idea of him being assigned duties once more, although perhaps it was a disappointment that these did not oblige a military haircut. Her long letters sometimes found their way unread into the Hut 8 waste paper basket, Alan telling Peter Hilton ‘Oh, she’s all right.’ She also visited him in autumn 1941. He tried to hint that he was doing an important job, with ‘about a hundred girls’ working for him, but neither she nor indeed anyone else had the faintest idea of how important it was. How could they? The concept of an information processing system, one matching the organisation of an advanced industrial power, had only just been invented.

  Which was now the ordinary and which the extraordinary? Which the reality and which the illusion? The pure mathematician of 1938 had wandered into an amazing position on the board, so that his brain concentrated ideas upon which the struggle for Europe depended. Miranda was playing chess when she saw the brave new world – and here it was in this organisation, a progressive scientist’s dream in which the experts had confounded the Blimps, and forced them to play the modern tune. Far above the heads of its slaves, far above the heads of the British people, the secret technocracy was working like an intelligent machine. There at the centre was the brain of the Alpha Plus who had breathed life into it and nurtured its growth – the unhappy Alpha, cursed with the ability to think for himself, and beginning to be edged out by his own creation.

  The broken Enigma and Fish systems were only just decipherable, and were stretching the fastest minds and the resources of modern science to the limit. They also depended upon luck and sudden, brilliant observations. On 30 October another stroke of fortune, the capture of U-559 off Port Said, at last gave Bletchley the key to the blank Atlantic, just as Alan was preparing to cross it. Thus elements of pure chance, amplified by a youthful will that had thrown off the ‘old fogies’ of the 1930s, had implanted into the British state a fantastic new element. In his central control of the war, Churchill now relied totally upon an unmentionable department, in which no one knew what anyone else was doing, and which made deceit into second nature. Starting with those early discoveries in the outhouses of Bletchley Park, a great explosion of implications had, in silence, proliferated through level after level of military and political organisation. It was a logical chain reaction, whose after-effects no one had time or inclination to consider.

  General Montgomery always put his troops ‘in the picture’. Indeed he was prone to give too much of the ultra-modern picture away, and had to be reprimanded by Churchill. But with that picture integrated effectively into Montgomery’s plans, his troops inflicted defeat at last upon the Afrika Korps. It was the first decisive British victory over German arms in three years of war. On 6 November 1942, General Alexander signalled ‘Ring out the bells!’. The British occupation of Egypt was preserved, its puppet regime saved, the southern German pincer on the Middle East destroyed. Then on 8 November, the Allied forces landed in Morocco and Algeria, achieving complete surprise. It was a first victory for planning and the coordination of Intelligence. The Americans were now back in the Old World – and to British consternation, would treat with the Vichyiste Darlan. But the British could not complain, for they had handed over the torch.

  Alan Turing had boarded the Queen Elizabeth on 7 November.54 As the refitted Monster zigzagged alone towards America, the fighter escort left behind, the King’s First Minister was explaining that he did not intend to preside over the liquidation of the British Empire. Churchill also said that it was only the end of the beginning. But for the goose that laid the greatest golden egg, it was already the beginning of the end.

  * J.R.F. Jeffries, Research Fellow in mathematics at Downing College, Cambridge, contracted tuberculosis in early 1941 and died.

  * For consistency the word ‘radio’ is used henceforth, although at the time this was the American term, English people calling it ‘wireless’, or more formally ‘wireless telegraph’. At the time of Roosevelt’s re-election in 1936, Alan wrote from Princeton ‘all the results are coming out over the wireless (‘radio’ they say in the native language). My method of getting the results is to go to bed and read them in the paper next morning.’

  * There were complications, but not affecting the account that follows.

  * The rather tiresome complication introduced by the ring-setting is, unfortunately, required to make sense of what the Poles achieved. It will play no part thereafter.

  *That is,

  * Actually 11 pairs gives slightly more ways – not that it makes any difference; 12 or 13 pairs rather less.

  † i.e. 26! This is also the number of possible wirings for each rotor of an Enigma.

  * Questions about the chance of obtaining loops could be posed and answered in the language of probability theory and combinatorial mathematics – very much what Alan, or indeed any Cambridge mathematician, would be well-placed to tackle. One would be lucky to get a loop within one word, as shown in the artificial example; in practice the analyst would have to pick letters out of a longer ‘crib’ sequence. Furthermore one loop would not be enough – far too many rotor positions would satisfy the consistency condition by chance. Three loops would be required – a taller order.

  † The Bombe, nevertheless, had nothing whatever to do with the Universal Turing Machine. It was more general than the Polish Bombe, which worked on a specific indicator system; but otherwise it could hardly have been less universal, being specific to the Enigma wirings and requiring an absolutely accurate ‘crib’.

  * Welchman, whose first work had been on the identification of the different key-systems, had devised a way of naming them by colours. ‘Red
’ was the general purpose Luftwaffe system; ‘Green’ the Home Administration of the Wehrmacht. Despite these early breaks, ‘Green’ turned out to be an example of where an Enigma system was almost totally unbreakable because it was used properly.

  * Knox’s work had a very direct pay-off in the battle of Matapan, in March 1941.

  * Literally, in future parlance, software.

  † The Yellow was the temporary inter-service system used in Norway.

  * They might well have worried that the German occupiers would now learn of the successful start to Enigma decryption from a French source. But no such disclosure or discovery was ever made.

  * She was not a country vicar’s daughter, but that was what they thought.

  *Though any but a very naive player would be able to do better than this and play so as to exploit the particular weaknesses of the opponent.

  * More strictly, any ‘zero-sum’ game, one in which the loss of one player would always be the gain of the other.

  † Less complicated than poker (which in fact is much too complex for a full mathematical analysis), the game of ‘stone, paper, scissors’ illustrates the idea. In this game the optimal strategy, for both players, is a ‘mixed’ strategy, that of choosing the three options randomly and with equal probability. For clearly, if one player departs from randomness, the other can exploit the departure to gain an advantage.

  * The ‘Foreign’ key-system, used by German vessels in waters such as the Indian Ocean, was never broken. Furthermore the ‘Home’ key-system no longer covered the communications of the Mediterranean surface vessels. These, from April 1941, had gone on to a new system which remained immune from decryption for another year.

  *A reference to punched-card machine work employed on other stages of the process.

  † Luftwaffe key-system used in Africa.

  * A reference to the problem of testing the positions at which the Bombe stopped, to eliminate those which had arisen by chance.

  * The ‘crib’ for 14 March came from a special message sent out both on the (broken) Home key-system, and on the U-boat system, announcing the no doubt vital news that Dönitz had been promoted to the rank of Admiral.

  *They thought of the tape as reading from left to right, as shown, and so thought of it as having five ‘rows’. This is not the usual terminology, but for consistency it will be used throughout.

  *Other types of teleprinter-enciphering machine systems remained unbroken.

  *Nothing to do with testing, but named after its head, a Major Tester.

  BRIDGE PASSAGE

  Aboard at a ship’s helm,

  A young steersman steering with care.

  Through fog on a sea-coast dolefully ringing,

  An ocean-bell – O a warning bell, rock’d by the waves.

  O you give good notice indeed, you bell by the sea-reefs ringing,

  Ringing, ringing, to warn the ship from its wreck-place.

  For as on the alert O steersman, you mind the loud admonition,

  The bows turn, the freighted ship tacking speeds away under her gray sails,

  The beautiful and noble ship with all her precious wealth speeds away gayly and safe.

  But O the ship, the immortal ship! O ship aboard the ship!

  Ship of the body, ship of the soul, voyaging, voyaging, voyaging.

  While the Atlantic remained in the dark, November 1942 proved to be the worst month yet for Allied shipping. But the North African landings drew off part of the U-boat force, and the Queen Elizabeth, faster than any U-boat, made her way in safety. Alan disembarked at New York on 13 November, but according to a story he told his mother,1 was very nearly refused entry to the United States:

  He had on arrival some difficulty over admission as he had been told on no account to take any papers other than those in the Diplomatic Bag which he carried. The triumvirate who confronted him on landing talked of despatching him to Ellis Island. Alan’s laconic comment was, ‘That will teach my employers to furnish me with better credentials.’ After further deliberation and passing of slips of paper, two of the triumvirate outvoted the third member and he was admitted.

  Such problems were supposed to be kept under control by W. Stephenson, the Canadian millionaire who directed ‘British Security Coordination’ from Rockefeller Center. Stephenson, originally installed to liaise between the British secret service and the FBI, had made a considerable effort to advance British interests in America by undercover manipulation. Since 1941 his office had expanded to take in the more serious work of channelling Bletchley’s productions to Washington. But perhaps Alan’s tiresome habit of taking instructions literally had defeated even him.2 It was certainly a curious greeting for a person who in so many ways was bridging old and new worlds. His primary assignment took him to the enormously expanded capital city, much changed since the sleepy days of 1938, where his opposite numbers in the Navy’s cryptanalytic service, ‘Communications Supplementary Activities (Washington)’, were based.

  From Bletchley’s point of view, America was the miraculous land across the rainbow bridge, possessing resources and skilled labour in quantities that desperate Britain could not supply. The CSAW was already closely connected with the most advanced sections of American industry, using Eastman Kodak, National Cash Register, and IBM to plan and build its machinery. As in other ways, Hitler had the effect of adding British ideas to the massive capacity of American business. Again it was Alan Turing’s role to connect the logical and the physical.

  But CSAW was certainly not without its own brains, and one of its staff was the brilliant young Yale graduate mathematician, Andrew Gleason. He and another member of the organisation, Joe Eachus, looked after Alan during his period in Washington. Once Alan was taken by Andrew Gleason to a crowded restaurant on 18th Street. They were sitting on a table for two, just a few inches from the next one, and talking of statistical problems, such as that of how best to estimate the total number of taxicabs in a town, having seen a random selection of their licence numbers. The man on the next table was very upset by hearing this technical discussion, which he took to be a breach of ‘security’, and said, ‘People shouldn’t be talking about things like that.’ Alan said, ‘Shall we continue our conversation in German?’ The man was insulted and told them in no uncertain terms how he had fought in the First World War.

  They were all spy-conscious in Washington now, but such anecdotes apart, the central event of Alan’s visit was the breakthrough back into the U-boat Enigma. This was achieved without the possession of faster Bombes; it depended upon a precarious thread of luck, ingenuity, and a German blunder. It went back to the weather signals that in mid-1941 had given them an almost unfairly simple crib each day, thanks to the fact that they were transmitted both in the Enigma, and in the special meteorological cipher. But early in 1942 a change in the system had denied this method to Hut 8. Not until the U-boat capture of 30 October could it be regained. This gave them the cribs, but the difficulty remained that it would take three weeks to work through all the rotor settings, just for one day’s traffic. Here, however, they were saved by a German blunder which, in effect, threw away all the advantage that the fourth wheel offered. For the weather reports, and other routine short signals, the U-boats used their Enigma with the fourth wheel in ‘neutral’ position, thus reducing the cryptanalysts’ problem to the one they had mastered in 1941. This in itself was not fatal for Germany; the greater mistake lay in the fact that the three rotor settings used for the weather reports were also used for all the other traffic of the day. For this the analysts now needed only to work through 26 possibilities for the fourth wheel, rather than the 26 × 336 × 17576 possibilities that would otherwise have been the case. As a result of this slip, Hut 8 was able to supply decrypted messages from 13 December. It was not a sudden restoration of sight, but more like a return to the period in the spring of 1941. They had weeks in which nothing worked out. But it was sufficiently copious a flow of information for the Tracking Room in the OIC to have
by 21 December a clear idea of the location of all eighty-four U-boats at large in the North Atlantic. And this time Hut 8 was not alone. In Washington, Alan Turing was indoctrinating the American analysts into all their methods. Now, when the rotor settings were discovered, they were passed back and forth across the Atlantic, the analysts beginning to communicate directly as indeed the two tracking rooms were also doing.

  The decrypts flooded in, at an average rate of 3000 a day, like a newspaper filled with nothing but concise, up-to-date news about the Atlantic operations. Just as the flow began, in early December, the3 ‘irreplaceable’ Winn collapsed from ‘total mental and physical exhaustion’ and ‘what was not of immediate operational importance had to be put on one side for later study and usually, before this could be undertaken … the next crisis was upon us and the study had to be abandoned,’ and so forth. But somehow the joint system managed to keep going, and in the new year became able once more to divert convoys away from known U-boats. The result was that on the other side, they could not understand why their success in sinking Allied shipping had suddenly been reduced to the level of September 1941. Indeed they were sure that U-boat positions were somehow known to the enemy. But the head of the German naval intelligence service at Naval High Command adhered to the opinion that it would be impossible for the enemy to have deciphered the signals. They continued to assume that there was a spy network operating in their bases in occupied France, although nothing could have been further from the truth. And so their faith in machines and experts continued to be matched by distrust of men. There were in fact many other factors involved besides cryptanalysis – the provision of escorts and aircraft patrols, the development of radar and of counter-radar measures, and the fearsome weather of this fourth winter of the war. But the crucial change was that Allied authorities once more knew where the U-boats were.