Alan Turing: The Enigma (63 page)

Every month or so there was a Mess Night at which dress uniform, or in Alan’s case a dinner jacket, would be required, and at which pheasant might be on the menu. This he would enjoy, for although generally so austere he liked to live it up occasionally, dancing vigorously with the ladies of the ATS afterwards. There was plenty of social gossip and intrigue, which Alan rather liked hearing about, and discussing with Mrs Lee and Mary Wilson. Sometimes his own rather glamorous position as the mysterious Prof, coupled with his unthreatening friendly way with the women members of staff, aroused a mild jealousy. In this respect, he kept his own secret.

It was the first time in his life that he had mixed with ordinary people for any length of time, people picked out neither by social class nor by a special kind of intellect. It was a typical Turing irony that this should happen at an establishment working for the secret service. He liked its unpretentiousness, and perhaps the escape from the intellectual pressure at Bletchley. He certainly had the pleasure of being a large fish in a small pond. This liking was reciprocated. There was an occasion when he was invited to a drinking-party organised by the Other Ranks. For some reason it did not come off, but he was still very pleased: partly at breaching social class barriers, but surely also because of the allure, felt almost inescapably by a homosexual of his background, of that vast unknown England of working-class men.

In the evenings most of the officers would play billiards or drink in the bar, and sometimes Alan did too. But Donald Bayley, Robin Gandy and Alan Wesley had the idea of doing something more mind-improving, and asked Alan to give a course of lectures on mathematical methods. They found a place upstairs in the mansion, which in the winter of 1944 was a singularly cold classroom, and retired thither, somewhat to the amazement of the less zealous. Alan wrote out notes, which the others would copy, mainly on Fourier analysis and related material using the calculus of complex numbers. He illustrated his discussion of the idea of ‘convolution’ – the blurring or spreading out of one function in a way defined by some other function – with the example of a mushroom fairy ring.

It was not only the mushroom which currently reflected his interest in
biological form; on his return from runs he would often show examples of the Fibonacci numbers to Don Bayley, producing fir cones as he had in 1941. He was still sure there had to be a reason for it. And he found time for mathematical study of his own, taking up von Neumann’s
Mathematical Foundations of Quantum Mechanics
again. In the evening there might also be chess, or card games, which he enjoyed, although these also brought out his most childish side in which – just as when a little boy – if he thought that someone else had cheated or changed the rules, he would storm out and slam the door. Such behaviour also typified his dealings with authority, which he still naively expected to maintain literal truth-telling and constancy of policy.

It was like the last two terms at school, staying on after having won a scholarship, without any clear function but accorded a gratifying respect. In August 1944, at about the same time as he came to live at the Hanslope mess, a small extension was built on to the large laboratory hut, and one of the four ten-foot by eight-foot rooms in it was allocated for work on Delilah. This gave him a more self-contained world in which to experiment, read, and think for the future. It was an odd position for ‘the top cryptanalyst in England’, waiting for his opponent to concede the game now dragging on and on. The Delilah project made more sense now that he had a qualified engineer to sort it out, but even this had been something of an accident. Don Bayley had not been assigned to it, but had been obliged to enveigle his way into participation, and there were always pressures on him to forsake it for other duties. Alan was irritated when this happened and would sometimes help in getting them out of the way.

Once, for instance, his advice was sought on the question of whether the ‘wide-band’ amplifiers, used in the process of distributing signals from a single large aerial to several different receivers, were introducing an element of noise into the system. He devised some experiments for testing them and did a little theoretical analysis. For this there was an outing to Cambridge, to search for appropriate literature on thermal noise. They had the privilege of an official car, and Don Bayley was rather pleased at being able to make a first visit to Cambridge. Before they went, Alan told the others not to call him ‘Prof’ while they were there.

Alan certainly enjoyed working together with his assistant in this way, but it meant being involved in what was very small stuff compared with his role in naval Enigma, or in Anglo-American liaison. Don knew that he had worked in cryptanalysis, and had been to America, but virtually nothing else. Alan did not supply any more to go on, and it was particularly striking at Hanslope, where with most people a few leading questions and a suggestion of already knowing more than was really the case would usually prise out further details. This method did not work with the Prof.
^*
It was
not simply the government’s secrets that he protected with a uniquely rigid silence, but all personal confidences too. He treated all promises with a perhaps rather annoying literalness, as sacrosanct pieces of his own mind. (He often complained of politicians that they never kept their promises.) It left his colleague very puzzled as to his status. Alan showed himself slightly put out when after a short while he was taken to be one of the SCU3 staff, and made it clear he considered himself something rather better. But he had no discernible superior to whom to report, and no one ever came to see the progress of the Delilah.

There were a few social visits by his Bletchley colleagues, and evidence of one piece of Bletchley work on which he was consulted. This was to do with the design of a new Enigma-type machine which Gordon Welchman was currently organising. It was to encipher Baudot-code messages, and so had rotors with thirty-two rather than twenty-six contacts. This he also described to Shaun Wylie, explaining how he had been shown the proposed machine and complained that it had a period of only 32 × 32 × 32. Meeting resistance, he had embarked on cranking through the settings by hand, only to discover that it was even worse – the period was only 32 × 32. His algebraic work on this problem stimulated some pure-mathematical offshoots which he kept for himself.
¹⁴

There was some cryptographic consultation at Hanslope too, perhaps more typical of the work he had been doing since returning from America. He was asked to check that the Rockex key-tapes that were being generated by electronic noise were, in fact, sufficiently random. Unprotected by the buffer of a Hut 4 or a Hugh Alexander in such dealings with the military, there were often failures of communication. Speaking too technically about ‘the imaginary part of the error’, he found the top brass had stopped listening. What he perceived as incompetence and stupidity would often send him into a black mood. In that case he would often take off for a run round the large field at the south of the Hanslope Park mansion to work off his feelings.

There was another issue which created argument and frustration, this time in the Delilah hut itself. Alan suddenly dropped into the conversation, with apparent casualness, the fact that he was a homosexual. His young Midlands assistant was both amazed and profoundly upset. He had heard mention of homosexuality only through jokes at school (which he was not the sort of person to find amusing) and through the vague allusions to ‘grave charges’ employed by the popular Sunday newspapers reporting court cases. It was not only what Alan told him that he found repellent, but the unapologetic attitude.

But it was the attitude of a Cambridge background that was as different from Don Bayley’s as mathematics from engineering. Alan’s assistant had equally firm, clear views, and said rather sharply that he had never before met anyone who not only admitted to what he considered at best distasteful A few lines from Alan Turing’s attack on the problem of designing rotor wirings, showing his use of group theory. The extract might be thought to show also the influence of Timothy the cat on his work, but in fact this was typical of his typewriting standard. and at worst disgusting propensities, but who seemed to think it perfectly natural and almost to be proud of it. Alan in turn was upset and disappointed by this reaction, which he described as only too typical of society at large. But this was, perhaps, one of the very few times that he had ever directly sampled the opinions of society at large. The reality, whether he liked it or not, was that most ordinary people would think of his feelings as alien and nauseating. His own attitudes having hardened since before the war – perhaps since breaking the engagement, but surely also because of increased confidence in himself after the work he had done – he did not drop the subject in embarrassment, but continued to argue in such a way that the exchange became quite heated. The progress of the Delilah was jeopardised.

Alan had ridden roughshod over fundamental
differences. But he managed to overcome the difficulties in a way that did not mean either of them backing down. Don Bayley was able to cope by regarding it as another Turing eccentricity, and by weighing it against the advantage of working on such high-level ideas with a person whom in other ways he had come to like, and thought he knew quite well. So the Delilah survived the revelation. By the end of 1944, the equipment which did the sampling of the speech signal, and which processed the enciphered samples, was finished. They had proved it to work satisfactorily by setting up both a transmitting and a receiving end within the laboratory, and feeding both with an identical ‘key’, in the form of random noise from a radio receiver working with its aerial removed. It remained to design and build a system for feeding identical key to terminals that would in practice be far apart.

In principle the Delilah could have used a one-time key recorded on gramophone records as the X-system did, analogous to the ‘one-time pad’ for telegraph transmissions. But Alan had chosen to devise a system which, though as good as ‘one-time’, would not require the shipping of thousands of tapes or records, but would instead allow sender and receiver to generate the identical key simultaneously at the time of transmission.

It was in this aspect of the Delilah that his cryptanalytic experience came into play. The work they had done so far constituted the mechanism for ‘adding on’ to speech. The crucial question of
what
to add was the one on which he had spent much of his time since 1938. In this he could act as the mathematical Cambridge and Bletchley figure, rather than someone who had joined in, somewhat awkwardly and embarrassingly, with the expanding world of electronic engineering.

Although he could not say, nor even hint, the task amounted to creating something like the Fish key generator. It had to be deterministic, for otherwise it could not be produced identically at two independent ends. But it had to be sufficiently devoid of pattern or repetition, to be as secure as something truly ‘random’, such as electronic noise. Any kind of mechanism would, inevitably, have
some
pattern to it; the job was to make sure that it
was one that the enemy cryptanalyst could not possibly detect. So in doing this for the Delilah, he was finally scoring off the half-hearted efforts of German cryptography. In fact, he was doing very much better, for the Delilah key would have to be supplied in sequences of hundreds of thousands of numbers. It was like enciphering not telegraph messages, but
War and Peace
.

The idea of generating a key for speech encipherment in this way was not entirely new. The X-system was not always used with one-time gramophone records for the key. There was an alternative, called ‘the threshing machine’. But this only had to produce a stream of digits at a rate of 300 a second, and was only used for testing or for low-status signals. The Delilah was much more demanding.

The generator had to be electronic, and the basic unit he used was the ‘multivibrator’ – a pair of valves possessing the property of locking into an oscillation between ‘on’ and ‘off, with a length which would be some integral multiple of a basic period. His key generator made use of the outputs of eight such multivibrators, each locked into a different mode of oscillation. But that was just the beginning. These outputs were fed into several circuits with non-linear elements, which combined them in a complicated way. He had worked out a circuit design which ensured that the energy of the output would be spread as evenly as possible over the whole frequency range, and he explained to Donald Bayley with the aid of Fourier theory that this would endow the amplitude of the resulting output with the necessary degree of ‘randomness’ for cryptographic security.

There had to be some variability in the circuits, or else the generator would produce the same noise over and over again. This was allowed for by making the interconnections required for the combination of the eight multivibrator outputs to pass through the wirings rather like those of an Enigma, with rotors and a plugboard. So a setting of this ‘Enigma’ would serve to define a particular sequence of key, in a way that both sender and receiver could agree upon in advance. With the rotors fixed in position, the key would not repeat itself for about seven minutes. In practical operation, speech in one direction of transmission could be limited to this time and a new key sequence started off on reversing the direction of transmission. This could be done simply by stepping on the rotors. There were enough rotor and plugboard positions for the resulting system to be as safe – according to his theory – as a genuinely random one-time key.