The Bletchley Park Codebreakers (46 page)

If, say, the plain-text is 4,000 characters long, then 4,000 consecutive characters from the chi-stream are used in the course of forming the cipher-text. These letters from the chi-stream will be referred to simply as ‘the chi’ of the message. Tutte’s method exploits a fatal weakness in the design of Tunny which renders the chi amenable to attack. The method depends on knowing the Tunny machine’s wheel-patterns – patterns of cams or ‘pins’ around the circumference of each wheel. The Research Section established what these patterns were in the course of reverse-engineering the machine, and although the Germans changed the patterns from time to time, Bletchley kept on top of the changes thanks to operator errors. What Tutte discovered was that after some massaging, the chi of the message is recognizable on the basis of the cipher text, provided that the wheel patterns are known. Once the message chi has been found it is an easy step to the settings of the chi-wheels, one part of the message’s ‘combination’.

What both Robinson and Colossus did, initially, was use Tutte’s Statistical Method to find the settings of the chi-wheels (other methods came later). Knowing the settings of the chi-wheels gave the codebreakers enough of a head-start that they were able to discover the settings of the psi-wheels by eye, given ‘a knowledge of “Tunny-German” and the power of instantaneous mental addition of letters of the Teleprint alphabet’. Once the settings of all the wheels were known, the codebreakers had the message’s ‘combination’. From there on it was left to clerks to decipher the complete message.

The crucial massaging required by Tutte’s method involves forming what is called the ‘delta’ of a character stream. The delta is the stream that results from adding together each pair of adjacent letters in the original stream. For example, the delta of the short stream MNT is produced by adding M to N and N to T. The last two columns of the following table contain the delta of the stream MNT. The rules for dot-and-cross addition are: dot plus dot is dot, cross plus cross is dot, dot plus cross is cross, cross plus dot is cross.

The idea of the delta is that it tracks changes in the original stream. If a dot follows a dot or a cross follows a cross at a particular point in the original stream, then the corresponding point in the delta has a dot. A dot in the delta means ‘no change’. If, on the other hand, there is a cross followed by a dot or a dot followed by a cross in the original stream, then the corresponding point in the delta has a cross. A cross in the delta means ‘change’. (The whole idea was invented by Turing.)

Tutte’s all-important discovery was that the delta of a message’s cipher-text and the delta of the chi usually correspond somewhat: where the one has a dot, so does the other, more often than not.

Here, then, is Tutte’s method for finding the chi of a given cipher-text when the wheel-patterns are known. Suppose, for the sake of illustration, that the cipher-text is 10,000 characters long. First, form the delta of the cipher-text. Then, use the patterns of the chi-wheels to start generating chi-stream (as we may imagine, by hand with paper and pencil). It is the patterns of the cams around the circumferences of the chi-wheels that determine which letters the chi-mechanism produces, and if these patterns are known it is possible to calculate the entire chi-stream. Generate 10,000 successive characters of the chi-stream. Form their delta, and compare the result with the delta of the cipher-text, counting how many times the two have dots in the same places and how many times crosses in the same places. Add these two scores and record the total. It probably won’t be very good, since the chances are that at the start of the simulated generation of chi-stream, the positions of the chi-wheels were not the same as those used in producing the cipher-text. The five chi-wheels are like the moving parts of a combination lock, and it is only when they are set to the exact combination that the German operator used at the start of enciphering the message that they will produce the chi of the message. The goal of Tutte’s method is to find that combination. So now generate the
next character in the chi-stream, and compare the delta of the 2nd to the 10,001st characters of the stream with the delta of the cipher-text. And so on. Since the motion of the chi-wheels is circular, eventually the complete chi-stream will have been examined. The stretch of chi-stream whose delta matches the delta of the cipher-text more closely than any of the other stretches do (and there may be no more than a 55–60 per cent correspondence) is probably the message chi.

Why do the delta of a message’s cipher-text and the delta of the message chi tend to correspond? At bottom, this is because of the all-or-nothing way in which the psi-wheels move – the great weakness of Tunny. The Tunny machine’s heart, its twelve wheels, stand side by side in a single row, like plates in a dish rack – the five psis, the two motor wheels and the five chis. The chi-wheels all move forward together one step every time a key is pressed at the keyboard, whereas the
psi-wheels
may all move forward one step when the key is pressed or may all stand still. Whether the psi-wheels move or not is determined by the motor wheels (or in some versions of the machine, by the motor wheels in conjunction with yet other complicating features). Whenever a stroke at the keyboard is not accompanied by a movement of the psi-wheels, what is added to the letter produced by the chi-wheels is whatever letter the psi-wheels produced on the last occasion when they did move. It follows that the delta of the letters contributed by the psi-wheels will contain a column consisting of five dots every time the psi-wheels stand still and ‘miss a turn’ (because in this case they contribute the same letter twice, so there is absolutely no change). These columns of dots in the psi’s delta produce the correspondence that Tutte discovered. If instead of the psi-wheels either all moving together or all standing still, the designer had arranged for them to move independently, then the delta of the cipher-text and the delta of the chi would not have tended to correspond and the chink that let Tutte in would not have existed.

Colossus generated the chi-stream electronically. The cipher-text was on a loop of tape on a bedstead. In the case of Heath Robinson, the complete chi-stream was punched on one of its tapes before the search commenced, the other tape carrying the cipher-text. The two tapes ran on the Robinson’s bedstead in such a way that the tape containing the cipher-text was progressively stepped through the chi-tape, one character at a time. In practice, the search would be simplified by punching onto the chi-tape only the dots and crosses
produced by the first and second of the five chi-wheels, resulting in a much shorter tape. Tutte had shown that his method of counting correspondences worked in this case too (and for this reason it was sometimes called the ‘1+2 break in’). Once the settings of the first two chi-wheels had been found, the settings of the others would be chased by the same procedure.

Heath Robinson was effective, but there were problems. Tapes would stretch, causing them to go out of synchronization, would tear, and would come unglued. It was clear that one machine was not going to be anywhere near enough. Newman proposed to order a dozen more Robinsons from the Post Office. Flowers had first been called in, at Turing’s suggestion, when Morell’s group was having difficulty with the design of the combining unit. Flowers had not been involved in the basic design of the Robinson and did not think much of the machine. The difficulty of keeping two paper tapes in synchronization at high speed was a conspicuous weakness. So was the use of a mixture of valves and relays in the counters, because the relays slowed everything down. Flowers suggested a new machine, all electronic, with only one tape. However, opinion at Bletchley was that a machine containing the number of valves that Flowers was proposing – about 2,000 – would not work reliably. In any case, there was the question of how long the development process would take. Newman decided that his section should press ahead with the Robinson, and left Flowers to do as he wished. At Dollis Hill Flowers just got on with building the machine that he could see was necessary. Colossus was entirely his idea.

Colossus I had approximately 1,600 valves and operated at 5,000 characters per second. The later models, containing approximately 2,400 valves, processed five streams of dot-and-cross simultaneously in parallel. This boosted the speed to 25,000 characters per second. By means of repluggable cables and a panel of switches, Flowers deliberately built more flexibility than was strictly necessary into the logic stages of Colossus I. These, like the combining unit of Heath Robinson, did the deltaing and the comparing. As a result of this flexibility, new methods could be implemented on Colossus as they were discovered. Michie and Good soon found a way of using Colossus I to discover the wheel patterns themselves. (Prior to the summer of 1944, the Germans changed the cam patterns of the chi-wheels once every month and the cam patterns of the psi-wheels at first quarterly, then monthly from October 1942. After 1 August 1944
wheel patterns changed daily.) Colossus II, installed shortly before D-Day, was supplied with a special panel for use when breaking wheel patterns. Following the delivery of Colossus II, new Colossi arrived in the Newmanry at roughly six-week intervals.

If Flowers could have patented the inventions that he contributed to Ultra, he would probably have become a very rich man. As it was, the personal costs that he incurred in the course of building the Colossi left his bank account overdrawn at the end of the war. Newman was offered an OBE for his contribution to the defeat of Germany, but he turned it down, remarking to ex-colleagues from Bletchley Park that he considered the offer derisory.

Colossus was far from universal. Nevertheless, Flowers had established decisively and for the first time that large-scale electronic computing machinery was practicable. Even in the midst of the attack on Tunny, Newman was thinking about the universal Turing machine. He showed Flowers Turing’s 1936 paper about the universal computing machine, ‘On Computable Numbers’. (Not being a mathematical logician. Flowers ‘didn’t really understand much of it’.) There is little doubt that by 1944 Newman had firmly in mind the possibility of building a universal Turing machine using electronic technology. It was just a question of waiting until he ‘got out’. In February 1946, a few months after his appointment to the Fielden Chair of Mathematics at the University of Manchester, Newman wrote to the Hungarian–American mathematician John von Neumann (like Newman, considerably influenced by Turing’s 1936 paper, and himself playing a leading role in the computing developments taking place in the US):

The implication of Flowers’ racks of electronic equipment would have been obvious to Turing too. Flowers said that once Colossus was in operation, it was just a matter of Turing’s waiting to see what opportunity might arise to put the idea of his universal computing machine into practice.

Such an opportunity came along in 1945, when John Womersley, head of the Mathematics Division of the National Physical Laboratory (NPL) in London, invited Turing to design and develop an electronic computing machine for general scientific work. Womersley named the proposed computer the Automatic Computing Engine, or ACE – a homage to Babbage.

During the remainder of 1945 Turing designed his electronic stored-program universal machine, completing his technical report, ‘Proposed Electronic Calculator’, before the end of 1945. This was the first relatively complete specification of an electronic stored-program general-purpose digital computer. An earlier document (May 1945), ‘First Draft of a Report on the EDVAC’, written by von Neumann in the US, discussed at length the design of a stored-program computer, but in fairly abstract terms, saying little about programming, hardware details, or even electronics. Turing’s ‘Proposed Electronic Calculator’, on the other hand, contained specimen programs in machine code, full specifications of hardware units, detailed circuit designs, and even an estimate of the cost of building the machine (£11,200). Turing’s ACE and the proposed EDVAC computer differed fundamentally in their design; for example, the EDVAC had what is now called a central processing unit, or cpu, whereas in the ACE, the various logical and arithmetical functions were distributed among different hardware units.

Turing saw that processing speed and memory capacity were the keys to computing, and his design specified a high-speed memory of roughly the same size as the chip memory of an early Macintosh computer (enormous by the standards of his day). Had Turing’s ACE been built as he planned, it would have been in a different league to the other early electronic computers. Unfortunately, delays beyond Turing’s control resulted in the NPL losing the race to build the world’s first electronic stored-program universal digital computer – an honour that went to the University of Manchester, where in Newman’s Computing Machine Laboratory the ‘Manchester Baby’ ran its first program on 21 June 1948.

It was not until May 1950 that a small ‘pilot model’ of the Automatic Computing Engine executed its first program (some months before the EDVAC was working properly). With an operating speed of 1 MHz, the Pilot Model ACE was for some time the fastest computer in the world. DEUCE, the production version of the Pilot Model ACE, was
built by the English Electric Company. Sales of this large and expensive machine exceeded thirty – confounding the suggestion, made in 1946 by Charles Darwin, grandson of the famous naturalist and Director of the NPL, that ‘one machine would suffice to solve all the problems that are demanded of it from the whole country’. The fundamentals of Turing’s ACE design were later employed by Harry Huskey (at Wayne State University, Detroit) in the Bendix G15 computer. The G15 was arguably the first personal computer; over 400 were sold worldwide. DEUCE and the G15 remained in use until about 1970. Another computer deriving from Turing’s ACE design, the MOSAIC, played a role in Britain’s air defences during the Cold War period; other derivatives include the Packard-Bell PB250 (1961).