Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Yet the fight was very far from over. The British improvements were only just keeping pace with the continually growing U-boat strength, and they were at the mercy of the Enigma enciphering system. September 1941, in particular, saw a dramatic increase in sinkings for the few weeks after a small sophistication was introduced into the U-boat signals. They had all along been indicating positions by means of the grid references on their maps, and39

  … not by latitude and longitude. Thus position AB1234 would indicate point, say 55 degrees 30 minutes North, 25 degrees 40 minutes West. This of course presented no problem to us once a portion of a gridded chart had been captured and the whole reconstructed. But in [September] 1941 the Germans started transposing these letters, square AB becoming, for example, XY while a figure would have to be added to or subtracted from the numerals, so that 1234 would appear in the text of the signal as, say, 2345. These transpositions were changed at regular intervals.

  Yet either the Enigma was being read, in which case these precautions were a feeble response, or it was not, in which case they were a waste of time. The rationale lay not in foiling the British cryptanalysts, but in creating a defence against imagined spying and treachery. The cumbersome disguise succeeded in confusing their own officers:

  On one occasion we successfully solved a disguised grid reference and diverted a convoy clear of a waiting patrol line, only to find that the C.O. of one of the U-boats involved had not been as clever as we had and had misinterpreted the disguised grid reference given in his orders and blundered into the convoy in consequence.

  In November 1941 the system was made even more complicated, and gave rise to long periods of uncertainty at Bletchley. They were still on a knife-edge, and were never allowed to forget it.

  It was in the autumn of 1941 that the cryptanalysts finally rebelled against the administrative system. As one of the very few who had the vision, it fell to Alan Turing to force the British government into the modern world. He and the others broke all the rules by writing directly to another man who knew how to break all the rules, and who now had the power to change them:40

  Secret and Confidential

  Prime Minister only

  Hut 6 and Hut 8,

  (Bletchley Park)

  21st October 1941

  Dear Prime Minister,

  Some weeks ago you paid us the honour of a visit, and we believe that you regard our work as important. You will have seen that, thanks largely to the energy and foresight of Commander Travis, we have been well supplied with the ‘bombes’ for the breaking of the German Enigma codes. We think, however, that you ought to know that this work is being held up, and in some cases is not being done at all, principally because we cannot get sufficient staff to deal with it. Our reason for writing to you direct is that for months we have done everything that we possibly can through the normal channels, and that we despair of any early improvement without your intervention. No doubt in the long run these particular requirements will be met, but meanwhile still more precious months will have been wasted, and as our needs are continually expanding we see little hope of ever being adequately staffed.

  We realise that there is a tremendous demand for labour of all kinds and that its allocation is a matter of priorities. The trouble to our mind is that as we are a very small section with numerically trivial requirements it is very difficult to bring home to the authorities finally responsible either the importance of what is done here or the urgent necessity of dealing promptly with our requests. At the same time we find it hard to believe that it is really impossible to produce quickly the additional staff that we need, even if this meant interfering with the normal machinery of allocations.

  We do not wish to burden you with a detailed list of our difficulties, but the following are the bottlenecks which are causing us the most acute anxiety.

  1. Breaking of Naval Enigma (Hut 8)

  Owing to shortage of staff and the overworking of his present team the Hollerith section* here under Mr Freeborn has had to stop working night shifts. The effect of this is that the finding of the naval keys is being delayed at least twelve hours every day. In order to enable him to start night shifts again Freeborn needs immediately about twenty more untrained Grade III women clerks. To put himself in a really adequate position to deal with any likely demands he will want a good many more.

  A further serious danger now threatening us is that some of the skilled male staff, both with the British Tabulating Company at Letchworth and in Freeborn’s section here, who have so far been exempt from military service, are now liable to be called up.

  2. Military and Air Force Enigma (Hut 6)

  We are intercepting quite a substantial proportion of wireless traffic in the Middle East which cannot be picked up by our intercepting stations here. This contains among other things a good deal of new ‘Light blue’† intelligence. Owing to shortage of trained typists, however, and the fatigue of our present decoding staff, we cannot get all this traffic decoded. This has been the state of affairs since May. Yet all that we need to put matters right is about twenty trained typists.

  3. Bombe testing, Hut 6 and Hut 8

  In July we were promised that the testing of the ‘stories’ produced by the bombes* would be taken over by the WRNS in the bombe hut and that sufficient WRNS would be provided for this purpose. It is now late in October and nothing has been done. We do not wish to stress this so strongly as the two preceding points, because it has not actually delayed us in delivering the goods. It has, however, meant that staff in Huts 6 and 8 who are needed for other jobs have had to do the testing themselves. We cannot help feeling that with a Service matter of this kind it should have been possible to detail a body of WRNS for this purpose, if sufficiently urgent instructions had been sent to the right quarters.

  4. Apart altogether from staff matters, there are a number of other directions in which it seems to us that we have met with unnecessary impediments. It would take too long to set these out in full, and we realise that some of the matters involved are controversial. The cumulative effect, however, has been to drive us to the conviction that the importance of the work is not being impressed with sufficient force upon those outside authorities with whom we have to deal.

  We have written this letter entirely on our own initiative. We do not know who or what is responsible for our difficulties, and most emphatically we do not want to be taken as criticising Commander Travis who has all along done his utmost to help us in every possible way. But if we are to do our job as well as it could and should be done it is absolutely vital that our wants, small as they are, should be promptly attended to. We have felt that we should be failing in our duty if we did not draw your attention to the facts and to the effects which they are having and must continue to have on our work, unless immediate action is taken.

  We are, Sir, Your obedient servants,

  A.M. Turing

  W.G. Welchman

  C.H.O’D. Alexander

  P.S. Milner-Barry

  This letter had an electric effect. Immediately upon its receipt, Winston Churchill minuted41 to General Ismay, his principal staff officer:

  ACTION THIS DAY

  Make sure they have all they want on extreme priority and report to me that this had been done.

  On 18 November the chief of the secret service reported that every possible measure was being taken; though the arrangements were not then entirely completed, Bletchley’s needs were being met.

  Meanwhile, another profound change was beginning to affect their work. America’s phoney war, preceding rather than following an official declaration, was reflected not only in the judicious aspirations of the Atlantic Charter, but in the more substantial negotiations with Britain over the sharing of intelligence. Already in 1940 a limited disclosure of cryptanalytic success had been made. This had involved work for Alan, who had gone to extraordinary lengths to devise methods that could be used to explain their decryption of Engima messages at a time when the Bombe was being retain
ed as a British secret. The British doubted the ability of the Americans to keep secrets – and for all that Churchill spoke of the American republic as a rather bigger and better Dominion, the fact was that it was a very different country, one apparently lacking the habits of deference, secretiveness and deviousness, and with powerful elements inimical to British interests. But in the course of 1941, arrangements were made for liaison officers to be attached to Bletchley, and the charade was dropped. The Turing eggs were now for export.

  Germany declared war on the United States on 11 December 1941, four days after the attack on Pearl Harbor. ‘So we had won after all!… England would live, Britain would live; the Commonwealth of Nations and the Empire would live…’, reflected Churchill. But the first effects were disastrous for Britain. The Pacific drew off the American naval vessels which had protected the convoys. And it proved to be an even tougher job selling intelligence to the US Navy than it had been in the British Admiralty. Naval Enigma information had indicated the operation of fifteen U-boats off the American coast at the declaration of war, but the warning had been spurned, and no precautions taken. Enormous shipping losses marked an unhappy start to the Grand Alliance. Then on 1 February 1942, a far greater blow was dealt. The U-boats switched over on to a new Enigma system. The Bombes failed to deliver their prophecies. There was no more ULTRA.

  The black-out of February 1942 meant that the U-boat Enigma analysis had to begin all over again, with the past two years serving as warming-up practice. It was symbolic of the war effort as a whole, the British situation being one that in 1939 would have seemed disastrous beyond belief. The loss of all European allies, the reversal of early gains from Italy, the surrender of Singapore – these and other blows were still offset only by the promise of help from an ill-prepared, inexperienced America. For what it was worth, which was very little, the RAF was gaining superiority over the Luftwaffe in crude bombing capacity. Yet this did not prevent the Scharnhorst and Gneisenau passing Dover in broad daylight. Meanwhile the economy of German Europe, hitherto complacently assessed as ‘taut’, was in reality only just beginning to adapt to full-scale war production. And its principal enemy had only just staved off defeat at the gates of Moscow.

  They had to think impossible things, and to think them before breakfast. An American army had to be created out of almost nothing, and conveyed across the Atlantic to invade a heavily fortified continent dominated by a no less advanced industrial power. But even the preparations for that invasion, let alone its success, were impossible while the Atlantic U-boat fleet was allowed to operate. With Hitler now taking the war seriously, the U-boat force had swollen to a fleet of a hundred larger vessels by January 1942, and was increasing every week. After February, with invisibility restored, they were able to inflict damage that approached disaster levels – half a million tons a month, exceeding the construction rate of the new Allies combined. It would be hard even to stay in the same place, let alone build up to the possibility of a victory.

  Everything had changed. There was no unemployment in Britain now, as there had been in 1940, and now everything was being planned. Indeed, Britain and the United States found themselves planning the entire trading economy of the world outside Axis and Soviet jurisdiction. At Bletchley, the country-house party spirit was gone, replaced by a conscription of the intelligentsia, to be ferried round Buckinghamshire in fleets of buses. The chaos of 1940 and the floundering of 1941 had been sorted out just in time to make use of the ‘cornucopian abundance’. Now the military departments had been forced to swallow their pride and adapt to its output: not sporadic ‘golden eggs’, but the production of an intelligent, integrated organisation which mirrored every level of the enemy system. In 1941 the supply of resources to Bletchley was still regarded as a concession, one that subtracted from the real men’s war of aircraft and guns. Even at the end of the year, the cryptanalysts had been obliged to manage with no more than sixteen Bombes – and this when the breaking into a number of German Army key-systems had rapidly increased their requirements. But their desperate letter to Churchill had brought about a change of attitude. Travis took over the direction from Denniston, and presided over an administrative revolution which at last brought the management of Intelligence into line with its mode of production. Meanwhile the services, recognising the hard fact that Intelligence was dominating Churchill’s control of the war, began to slacken their resistance to Bletchley’s claims.

  But however wonderfully their minds were concentrated, the fact remained that the U-boat Enigma problem now surpassed their means. In 1941, Hut 8 had given sight to the blind, and if this experience had been traumatic, the taking of sight away was an even more cruel blow. More precisely, the Admiralty again became, like Nelson, one-eyed. For only the ocean-going U-boats had adopted the new system. Surface vessels and U-boats in coastal waters continued to use a ‘Home’ key which could still be broken. They therefore had information on the departures from port of U-boats, and knew how many U-boats were at large – data which could be correlated with sightings and Huff-Duff findings. But this was very poor stuff compared with the operational commands and position reports to which they had now become accustomed.

  Within Hut 8 the black-out had a different meaning. The game had been going very enjoyably, and now the Germans had spoilt it by changing the rules. The temptation was to regard the Atlantic problem as a tiresome interruption, and to carry on with the fascinating work of decrypting the signals from European waters. But as they read about the sinkings, and saw the dim, dismal charts, reality penetrated the mathematical game. And much of the fun went out of it.

  What had happened was not only a change in the system for using the Engima machine. It was a change in the machine itself. It had been modified in such a way that it now possessed a space for a fourth rotor. Hitherto, the naval Enigma settings had continued to involve a choice of three rotors out of eight, for which there were 336 possibilities. Had the machine been modified to allow a free choice of four rotors out of nine, the figure would have gone up to 3024 (a ninefold increase) and the setting of the new rotor would have introduced a further twenty-six-fold increase on top of that. But this was not done. There was indeed a new ninth rotor, but it had to stay in its place. It was only the old machine, but with a new rotor attached to the end, capable of twenty-six different settings. It was equivalent to having twenty-six different reflector wirings. Accordingly, the problem had become not 234 times worse, but only twenty-six times worse.

  It was a half-hearted measure, like the encoding of the map references, and was undertaken for the same misguided reason: the internal protection of the U-boat messages. It was not that the Germans feared British cryptanalysis. But even if half-hearted, it was a change that pushed Hut 8 off the knife-edge and into almost total blindness. It was already a fluke that the numbers worked out at all, allowing Bombes that worked in hours rather than weeks. Already the naval Enigma had strained every nerve in the process of achieving decryption in the day or two that was necessary for it to be of convoy-diverting use. Now the twenty-six-fold increase turned every hour into a day, or would require twenty-six Bombes for every one that they had used in 1941, unless ingenuity found another way.

  There was one point of success: they knew the wiring of the new fourth wheel. This was because the new four-rotor Enigmas were not new machines, but modified versions of the old ones. The fourth wheel had been sitting in a ‘neutral’ position on the U-boat machines during late 1941. Once in December a U-boat cipher operator had carelessly let it move out of this position while enciphering a message; Hut 8 had noted the ensuing gibberish, and also spotted the re-transmission of the message on the correct setting. This elementary blunder of repetition, so easy to make while the Germans held complete trust in their machines, had allowed the British analysts to deduce the wiring of the wheel. Armed with this information, they were in fact able to break the traffic for 23 and 24 February and for 14 March – days for which they had particularly clear ‘cribs’ fro
m messages that had also been enciphered in other, breakable, systems.* But it took twenty-six times too long: six Bombes working for seventeen days were employed. This development well illustrated the chanciness of the whole endeavour. Had this enlarged Enigma been adopted from the start, the treasure hunt might never had got off the Polish ground.

  ‘Faster, faster!’, the White Queen now cried. But nothing could make Bombes go twenty-six times faster overnight. There had, in fact, been an opportunity to prepare against the dreadful day, since as early as the spring of 1941 there had been references in the decrypts to the addition of a fourth rotor. The Hut 8 analysts afterwards rebuked themselves for not having impressed this fact with greater force upon the administrators. But in the conditions of 1941 it was quite unrealistic to think in terms of finding resources for bigger and better Bombes to cover a possible future development, when they had to fight to get enough Bombes merely to keep up with the existing traffic. The authorities had thrown away this advantage of foreknowledge. But with the shake-up of late 1941 a more dynamic approach had been taken, and one very important effect of the impending naval Enigma crisis was that at the turn of the year it brought in fresh expertise on the engineering side.

  One obvious approach was that of enlarging the Bombe to include the new fourth rotor spinning through its twenty-six possible positions at extremely high speed. The task of devising such a high-speed rotor system was entrusted to the inventive Cambridge physicist, C.E. Wynn-Williams, who in 1941 was working for the radar research laboratory, the Telecommunications Research Establishment as it became on its move to Malvern in May 1942.