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 i
ts 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.
Getting the Delilah system to work as a whole was a job which pushed their resources to the limit. The system was useless unless sender and receiver could keep their multivibrators in time to the microsecond. They spent most of the first half of 1945 in achieving the necessary precision. They also had to test the output of the Delilah key generator, when they had built it, for the evenness over the frequency range which the calculations predicted for it. It was typical of the conditions in which they worked that they had no frequency analyser. Alan would have seen one at Bell Labs, and there was one known to exist at Dollis Hill, but at Hanslope they had to make one for themselves. It provided a challenge of the desert island sort, which Alan as usual enjoyed. After a lot of work they had a device, but when they first tried it out, Alan had to confess ‘It’s a bit of an abortion, isn’t it!’ – so they called it the ABORT Mark I.
To requisition anything at all required an act of skilful and aggressive diplomacy in handling the administrators. All they could obtain was a double-beam oscilloscope and an audio-frequency Hewlett-Packard oscillator. They even had to fight for this, first being fobbed off with an inferior one, and having to demand something better from SCU3’s Controller, Colonel Maltby. For Alan, the process was as baffling as it ever was for Alice in the Looking Glass shop, trying to locate what she needed on the White Queen’s shelves. Dealing with Maltby on the telephone drove Alan to extremes of nervousness, and people remarked upon how his speech, halting at the best of times, was on these occasions an almost indecipherable scrambling operation itself. He hated the showmanship that was required in negotiating for equipment. It was forever his bitter complaint that more adept players – ‘Charlatans’, ‘Politicians’, ‘Salesmen’ – would get their way not through expertise but through clever talk. He still tended to expect reason to prevail as if by magic.
It was a small-scale, homely example of the conflict that permeated the British war effort. But the Delilah project, manifestly too late for the German war, could not possibly expect a high priority, as he must have known. It was not like the work at Bletchley. And so even if angry over what he saw as incomprehensible waste and stupidity, he could also afford to stand aside and see the establishment in a more detached way. In this respect he and Robin Gandy would see things in very much the same light, and they both enjoyed reading Nigel Balchin’s novel The Small Back Room, which had appeared in 1943. This presented with unconcealed bitterness, yet also with a mordant wit, the frustrations felt by young scientists trying to get the war won and over with, and hamstrung by games of one-upmanship and empire-defending. At Hanslope a number of amusing stories were told, fairly or unfairly, about the plots and coups of the upper echelons, but Alan certainly did not suffer from all the tribulations Balchin described, and in particular he was spared the problem of dealing with dead-wood ‘eminent scientists’ who stifled initiative in the name of efficiency. In fact no one took any interest, scientific or otherwise, in the Delilah project. This remained true even when the addition of the key generator showed that he had a means of giving complete speech security with two small boxes of equipment.
The army officers emerged in Balchin’s book as ‘red-tabbed stooges’ who had entered a ‘profession for fools’, but to Alan the army system was less pernicious than ludicrous. He was very fond of Trollope’s novels and kept a stock of them in the Hanslope cottage. He would hold forth on the similarities between the organisation of the Church of England and that of the army; with the help of Robin Gandy and Don Bayley he would seek out parallels between the Barchester machinations and those of the Hanslope hierarchy. They worked out a correspondence between the respective ranks, so that a lieutenant-colonel became a dean, and a major-general a bishop, while a brigadier was pegged at the status of suffragan bishop (the cheapest kind of bishop, Alan explained).
Occasionally there would be episcopal visitations, when Gambier-Parry and Maltby would look in to pay their respects and listen to the Delilah output, but this would be for reasons of form rather than out of real interest, as they had no direct responsibility for the work and only the haziest of notions of what Alan and Don Bayley were up to. Nor was it much use asking, since Alan was quite incomprehensible to them, a fact which was somewhat uncongenial si
nce they claimed some scientific knowledge. The visitors were liable to be treated to a rendering of Winston Churchill’s voice, since they used a gramophone recording of one of his speeches to test the Delilah· It was the broadcast made on 26 March 1944 in which after dwelling rather uncharacteristically on the subject of post-war housing policy, the Prime Minister had turned to more immediate prospects:15
…The hour of our greatest effort is approaching. We march with valiant Allies who count on us as we count on them. The flashing eyes of all our soldiers, sailors and airmen must be fixed upon the enemy on their front. The only homeward road for all of us lies through the arch of victory. The magnificent Armies of the United States are here or are pouring in. Our own troops, the best trained and the best equipped we have ever had, stand at their side in equal numbers and in true comradeship. Leaders are appointed in whom we all have faith. We shall require from our own people here, from Parliament, from the Press, from all classes, the same cool, strong nerves, the same toughness of fibre, which stood us in good stead in those days when we were all alone under the blitz.
With the help of the ABORT Mark I they could check that the Delilah had enciphered Churchill’s phrases into a White Noise – a perfectly even and uninformative hiss. And then, by passing the output into the decipherment process, they could recover:
Alan Turing: The Enigma The Centenary Edition Page 45