Alan Turing: The Enigma (61 page)

Alan Turing with two Ferranti engineers at the console of the ‘Mark I’ computer at Manchester, 1951.

Alan Mathison Turing on election of Fellowship of the Royal Society, 1951.

By late 1943, the research had been completed. An inventive telegraph engineer, R.J. Griffith, had been borrowed from Cable and Wireless Ltd to do the detailed design. The manufacture was now going ahead at Hanslope Park, where Griffith was also at work on the problem of generating the key-tapes automatically, by using electronic random noise.

Hanslope Park, with its web of connections
with secret enterprise and electronic cryptographic work, was therefore a natural place for the Turing speech encipherment project to be based. The Post Office Research Station might have housed it, but it was a great deal further from Bletchley than was Hanslope, which was only ten miles to the north. It was a rather strange place, strange for its very appearance of being an ordinary military station, with all the accoutrements of military ranks and language. Quite different from Bletchley Park, where the military had been obliged to adjust to the young Cambridge intelligentsia, here a service mentality was unaffected by the advent of modern technology. Here there was not a civilian cafeteria but an officers’ mess, where framed in passepartout lay the clue, a quotation from
Henry
V:

The King hath note of all that they intend,

By interception which they dream not of

But in fact Gambier-Parry’s staff were working in a dream war themselves, one in which they knew neither the significance of what they were doing, nor what anyone else did. The newcomer would spend many months before being able to work out that the organisation came under the direction of the secret service.

Alan’s first contact with Hanslope Park came in about September 1943, when he cycled the ten miles from Bletchley to inspect the possibilities. A senior ex-Post Office man, W.H. ‘Jumbo’ Lee, was deputed to look after his requirements. Hanslope was not exactly a model of spit-and-polish smartness; some of its uniformed personnel were ‘real soldiers’ but many
were of an unmilitary disposition, transferred straight from the Post Office, Cable and Wireless, and similar organisations. There was, however, a sufficiently military air at Hanslope for a misunderstanding to arise when ‘Jumbo’ Lee introduced Alan to his superior, Major Keen. ‘Dick’ Keen was the top British expert on radio direction-finding, who had written the only textbook on the subject during the First World War, and spent much of the Second on writing a new edition. Alan and ‘Jumbo’ Lee stood together at his door and Keen waved them away, assuming from his appearance that Alan was a cleaner or delivery boy.

Hanslope Park had a precedent for the arrival of a cryptographic project, but whereas Griffith had demanded, and received, a new workshop and adequate staff, Alan simply took what he was given, which was not very much. In fact his project was granted bench-space in a large hut where a number of other research projects were being conducted, and he was offered some mathematical assistance in the form of Mary Wilson, who did direction-finding analysis with Keen. She was a graduate from a Scottish university, and working with Keen had considerably raised the standard from the early days when people said ‘Two fixes are better than three – there is no triangle of error.’ Instead, they were offering to the analysts ellipses on the map which represented the area in which the point of transmission could be asserted to be with such-and-such a probability. But she did not have enough mathematics to understand what Alan wanted when he explained his idea. (He helped her later with the direction-finding work, though expressing a somewhat dim view of her training.) So over the next six months he had to work alone on the project, coming in a couple of days a week, not every week. Two army signalmen were assigned to assemble pieces of electronic equipment under his direction, but that was all.

In mid-March 1944 that there was a distinct change in the Hanslope staffing, with an influx of mathematical and engineering expertise. Such a change was needed. There was, for instance, an occasion when ‘Jumbo’ Lee showed Alan a problem on which they were stuck. It was no more than a trigonometrical series (in connection with aerial design) easily within the grasp of a Cambridge scholarship candidate, but he was most impressed when Alan immediately produced the answer, the more so as Post Office engineers had been laboriously summing it term by term. The authorities had chosen five new young officers, selected from those taking courses at the Army Radio School near Richmond in Surrey. Two of them would take special places in Alan Turing’s life. Indeed, this was a fresh start for him. In 1943, he had met Victor Beuttell over lunch in London, with some of their personal troubles coming out. (Victor had finally rebelled against his father, and joined the RAF.) They would never see each other again; but the personal
rapport
that thereby lapsed was to be found within new friendships.

The first was Robin Gandy, the undergraduate who in 1940 had stoutly
maintained ‘Hands off Finland’ at Patrick Wilkinson’s party in the face of Alan’s quizzical scepticism. His arrival brought to Hanslope a breath of the King’s spirit. He had been conscripted into the ranks in December 1940, with six months on a coastal defence battery, until his mathematical mind had enjoyed more recognition, as he became a radar operator, and then an instructor. After being commissioned into REME, a series of courses, sandwiched with practical experience, had taught him about all the radio and radar equipment used by the British forces.

The second was yet another Donald. This was Donald Bayley, who came from a quite different background, that of Walsall Grammar School (where Alan’s friend James Atkins had taught him mathematics) and Birmingham University, where he had graduated in electrical engineering in 1942. He also had been commissioned into REME and had likewise shot ahead in all the courses.

Both were introduced to the large ‘laboratory’ hut where the research projects were in progress, and found Alan at work there. If civilians from Cambridge were apt to find him unusually careless in appearance, his divergences from respectability were very much more noticeable at military Hanslope. With holes in his sports jacket, shiny grey flannel trousers held up with an ancient tie, and hair sticking out at the back, he became the cartoonist’s ‘boffin’ – an impression accentuated by his manner of practical work, in which he would grunt and swear as solder failed to stick, scratch his head and make a strange squelching noise as he thought to himself, and yelp when shocked by the current that he forgot to turn off before soldering the joints in his ‘bird’s nest’ – so they called it – of electronic valves.

But Robin Gandy was struck in another way on about the first day that he set to work investigating the effectiveness of high-permeability cores in the transformers of the radio receivers. There were two engineers in his section, who started the tedious task of testing the things, when Alan pottered in, and decided that it should all be solved from theoretical principles – in this case, it being an electromagnetic problem, from Maxwell’s equations. These he wrote down at the top of his paper, just as though it were some contrived Tripos question instead of one from real life, and eventually performed a
tour de force
of partial differential equations to get an answer.

Donald Bayley was impressed in a similar way by the speech encipherment project, which at Hanslope became known as the
Delilah
. Alan had offered a prize for the best name, and awarded it to Robin for his suggestion of Delilah, the biblical ‘deceiver of men’. It made full use of his experience in cryptanalysis, and as Alan would explain, was designed to meet the basic condition that even if the equipment were compromised, it would still provide complete security. Yet the system he had conceived on board the
Empress of Scotland
a year earlier was essentially very simple.
¹⁰
It was a mathematician’s design, and one which had depended upon Alan asking ‘But why not?’

What he had done was to consider
the roomful of equipment which made up the X-system, and to ask what were the crucial features which made it into a secure speech cipher. The Vocoder was
not
essential, although it had been the starting point of the project. Nor was the business of quantising the output amplitudes into a number of discrete levels. By jettisoning these he reduced the number of ideas involved to two: the fact that it
sampled
the speech at a succession of moments in time, and the fact that it used
modular
addition, like a one-time pad.

The Delilah was based on these two ideas from the beginning, while in the X-system they had arrived by a back-door route. The point about sampling was that it removed the redundancy of the continuous sound wave. Any sound signal could be represented by a curve such as:

The point was that it would be unnecessary to transmit the whole curve. It would be sufficient to communicate the knowledge of certain points on the curve, provided that the recipient could thereupon perform the exercise of ‘joining the dots’ to reconsitute the curve. This could be done, at least in principle, provided that it was known how sharply the curve was allowed to wiggle in between the points. Since sharp wiggles would correspond to high frequencies, it followed that provided there was a limit on the frequencies contained in the signal, then a sequence of discrete points, or samples, of the curve, taken at regular intervals, would contain
all
the information of the signal. Since telephone channels did in any case cut off high frequencies, the restriction on allowed ‘wiggling’ of the curve was no real restriction at all, and in fact a rather small number of samples could be shown to suffice to convey the signal.

The idea was well-known to communication engineers. In the X-system, it was the practice to sample each of the twelve 25 Hz channels fifty times a second. These figures were illustration of a general result, that it was necessary to sample at a rate of twice the maximum variation in frequency of the sound, or bandwidth. There was an exact mathematical result to this effect, proved as early as 1915 but which Shannon had re-stated
¹¹
and discussed with Alan at Bell Labs. If, for instance, the sound signal were restricted to frequencies less than 2000 Hz, then a sample taken 4000 times a second would be exactly enough to reconstitute the signal. There would be precisely one curve of the stated frequency restriction that passed through all the sampled points. Alan described and proved this result to Don Bayley as the ‘Bandwidth theorem’. His ‘Why not?’ had come in asking why this elegant fact could not be made the pivot on which to turn the whole encipherment process.

The figure of 2000 Hz was in
fact the one he intended to use, and his encipherment process would start with the speech signal being sampled 4000 times a second. The Delilah would then have to effect the addition of these sampled speech amplitudes to another stream of key amplitudes. The addition would be done in modular fashion, meaning that while speech sample amplitude of 0.256 units and key amplitude 0.567 units would be added to give 0.823 units, the addition of 0.768 and 0.845 would give 0.613, not 1.613. The result of all this would be a train of sharp ‘spikes’, of heights varying between zero and one unit
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