Intelligence in War: The Value--And Limitations--Of What the Military Can Learn About the Enemy (25 page)

AD = SPNP
^-1
MLRL
^-1
M
^-1
PN
^-1
p
^-3
NP MLRL
^-1
M
^-1
p N
^-1
p- S
^-1

The other two were equally complex and, he writes, “the first part of our task [was], essentially, to solve this set of equations in which the left sides, and on the right side only the permutation P and its powers are known, while the permutations S, L, M, N, R are unknown. In this form, the set is certainly insoluble.”
¹⁶

“Therefore,” Rejewski goes on, “we seek to simplify it. The first step is purely formal and consists in replacing the repeated product MLRL
^-1
? M
^-1
. . . with the single letter Q. We have thereby temporarily reduced the number of unknowns to three, namely S, N, Q.”

Non-mathematicians will be unable to follow Rejewski’s subsequent pages of equations. They conclude, however, as follows: “the method described above for [recovering] N could be applied by turns to each rotor, and thus the complete inner structure of the Enigma machine could be reconstructed.”
¹⁷

That was the Polish triumph: the penetration of the Enigma secret by pure mathematical reasoning. During the thirties, the Poles also managed to keep abreast of successive German refinements of Enigma, both electromechanical and procedural, and they succeeded in manufacturing duplicates of the Enigma machine. As its transmissions became more difficult to break, they also devised an electromechanical device (the “bombe,” apparently so-called after its ticking, which was thought to resemble that of an infernal machine) which tested solutions of encrypts faster than was possible by paper methods. Meanwhile they shared their knowledge with the French cryptanalytic service, France being Poland’s principal ally. The French themselves, through a financially corrupt German informant, known as Asché (French pronunciation of HE, the initials of his cover name), were acquiring documents which revealed many of Enigma’s operating secrets; Asché, the brother of a general, appears eventually to have been unmasked and to have been shot for treason in 1943.
¹⁸
The Poles and the French certainly worked together closely on German ciphers throughout the thirties: latterly the French were also co-operating with the British Government Code and Cipher School (GCCS) located at Bletchley Park. During the period 24–25 July 1939, just before Germany’s invasion of Poland, French and British officials visited Warsaw, where the Poles passed them each a reconstructed model of the Enigma machine.

BREAKING ENIGMA AGAIN

By then the Poles were no longer able to read Enigma intercepts, because of mechanical complications—particularly the introduction of two extra discs, increasing the possible number of disc orders from six to sixty—and procedural changes. Nevertheless, they were able to pass to the British reconstructed machines which reproduced the internal wiring of the discs, which to their annoyed consternation was foolishly simple, A being wired to B and so on. They also introduced to the British—who had hit upon the idea themselves—the concept of subjecting intercepts to treatment by punched sheets. Rejewski, besides being a pure mathematician, also had a practical bent and had grasped, from his theoretical understanding of how Enigma worked, that there would be repetitions in the permutations and that those could be identified by representing encrypted letters as perforations in large sheets of paper. Given enough intercepts, and overlaid sheets, their arrangement on a light-table would reveal repetitions, when they occurred, by light shining through. Repetitions would support disc-settings though not prove them; those would have to be established by subsequent work.

The British decryption operation, though eventually far larger than the Polish, proceeded on the whole by a different method: to use Calvocoressi’s distinction, it depended more upon mechanical aids than mathematical theory, though many mathematicians worked at Bletchley and it owed its start to the Polish mathematical endeavour. Gordon Welchman, one of the most gifted of the Bletchley mathematicians, who came from a Cambridge fellowship to Bletchley Park right at the beginning of the war, distinguished four periods in its early history: (1) the preparatory period, ending with the making of complete sets of the perforated sheets in early 1940; (2) the period of dependence on the sheets, ending on 10 May 1940, when the Germans ceased to encrypt the second three-letter group which communicated the setting; (3) a subsequent period when the cryptanalysts were largely dependent on exploiting German operators’ carelessness in procedure; and (4) from September 1940 when Bletchley began to acquire its own bombes, similar in principle to those devised in the thirties by the Poles.
¹⁹

Welchman divides the development of his own thinking about how to decrypt the Enigma intercepts into ten steps, spread over several months. It was not officially his concern, since he had been set to study German radio call signs. That was necessary but routine work and Welchman’s acute mathematical mind began almost involuntarily to engage with the letter groups on the intercepts he was passed. The first three steps he describes had to do with speculation about whether the two three-letter groups in the preliminaries always contained pairs of encrypts of the same letter three positions apart (as the rotor turned). When he decided that they did, he moved to a calculation of probabilities of how often paired letters would appear, establishing a number which he thought manageable (Step 4). He next concluded that the Germans’ military Enigma was much less complex than they—and the British—thought, because the plugboard did not in practice increase the number of permutations to be tested. “With only the 60 wheel [rotor] orders and 17,576 ring [rim] settings to worry about, we are down to a million possibilities. In fact we have reduced the odds against us by a factor of around 200 trillion. This was Step 5 and quite a gain!”
²⁰
Step 6 was a further calculation of probabilities while Step 7 was his independent perception of how perforated sheets could eliminate many unfruitful possibilities. Steps 8, 9 and 10 led him to see how the sheets should be used; “if we could find twelve females [fruitful pairings] on the Red [war] and Blue [training] key for a particular day, we could confidently expect to discover that key after an average of 780 stackings [superimposing the perforated sheets on the light-table] . . . so in great excitement I hurried to tell . . . Dilly about it. Dilly was furious.”
²¹

Dilly Knox, son of the Bishop of Manchester and brother of E.V. (Evoë), editor of
Punch,
and Ronnie, a famous Roman Catholic convert priest, had been a fellow of King’s College, Cambridge, was a veteran of Room 40 and had spent all his subsequent life as a government cryptanalyst. On the establishment of the Government Code and Cipher School at Bletchley Park in August 1939 he became principal assistant to Commander Alastair Denniston, another Room 40 veteran who was now GCCS’s head.
²²
Eccentric and solitary, he was quite unsuited to the task. “Neither an organisation man nor a technical man,” in Welchman’s words, Knox belonged to an earlier age of code-breaking when puzzles were dissolved by flashes of inspiration rather than rigorous analysis. He had tried his hand at Enigma but had concluded that “there were simply too many unknown factors that had to be solved simultaneously. Although Knox had worked out a mathematical procedure for recovering the daily settings, it depended on first knowing the internal rotor wirings, and there just seemed to be no way of isolating that part of the equation.”
²³
In short, what Rejewski had achieved, Knox could not. He was simply not a good enough mathematician. No wonder that, with his introverted temperament, he flew into a rage when his clever young subordinate Welchman arrived to claim that he could see a way through the thickets that had defeated him.

Had Welchman been easily put upon, things might have rested there, Enigma might have taken months longer to crack and the Battle of Britain and the Battle of the Atlantic proved even harder to survive. Fortunately Welchman was not to be browbeaten. Though told to go back and get on with his compilation of call signs, he went to the Deputy Director, Commander Edward Travis, but, sensibly, not simply to complain but to present a plan of organisation and action. Welchman had perceived the first lesson in winning bureaucratic battles: present an alternative scheme. He expressed his fear that, once the Phoney War went hot, Bletchley would be overwhelmed by a volume of vital radio traffic it would be unable to read. To cope with the oncoming rush, he proposed dividing Bletchley Park’s growing staff into five sections working in shifts twenty-four hours a day: a Registration Room to do traffic analysis; an intercept Control Room to direct the listening stations to the most promising senders; a Machine Room to co-ordinate the work of the first two; a Sheet-stacking Room, under the Machine Room’s control; a Decoding Room to deal with any messages that yielded to decryption. Welchman also proposed increasing the number of listening centres, to include one operated by the air force which would listen out for Luftwaffe messages; the principal listening station, in an old fort at Chatham, was, though very efficient, operated by the army.
²⁴

Travis not only accepted Welchman’s scheme but persuaded Denniston to instigate it, so that Bletchley, just in time, was already operating effectively when the storm broke on 10 May 1940. There was another fortuitous event. Bletchley already knew about the bombe, from the Poles. It now acquired bombes of its own. The original design was the work of Alan Turing, another Cambridge mathematics don who had been recruited at the same time as Welchman. Turing was Welchman’s intellectual superior. Indeed, he was one of the foremost mathematicians in the world, who, as a visiting fellow at Princeton in 1936, had written the theory of the digital computer, a universal calculating machine which did not yet exist; computers bear the alternative name of “Turing machines.”
²⁵
Turing’s design for a bombe was being developed by the British Tabulating Machine Company, whose products were largely punched-card devices. Turing’s was electromechanical, of much greater speed and power, but Welchman proposed an alteration in the design which allowed possible, but wrong, Enigma settings to be eliminated much faster.

The bombes could not, of course, test every possible Enigma setting, which would have required the calculating speed of a large modern computer. Welchman, but also Turing and others, had realised that parts of many Enigma intercepts were formal and repeated: the full name and rank of the addressee, for example, or the title of the originating headquarters. These might be guessed and came to be called “cribs” (an English public-school term for an illegal guide to a Latin or Greek translation). The bombe method depended upon guessing a crib and testing letter substitutions, by repetitive mathematical process, within the cycle of 17,576 positions in which the rotors could be set. It proved very fruitful.

The crib method, however, would not have worked unless the German operators had revealed clues to the setting by carelessness, laziness or error. “The machine would have been impregnable if it had been used properly,” in Welchman’s opinion.
²⁶
It was used properly by the operators of a number of branches of the German armed forces and government. Three naval Enigma keys, including the important key code-named Barracuda by Bletchley and used for high-level signals during fleet operations, were never broken; Pink, the high-level Luftwaffe key, was broken only after a year of use and thereafter only rarely; Green, the German army home administration key, was broken only thirteen times during the war and then with some prisoner of war help (“such was the security of Enigma when properly used”); Shark, the Atlantic U-boat key, proved unbreakable between February and December 1942, a crucial period in the Battle of the Atlantic; the Gestapo key, used from 1939 to 1945, was not broken at all.
²⁷

The pattern of breaks was not random. The Gestapo seems, not unnaturally, to have taken great care; the German army and navy, which had long-established signal branches, made use of well-trained and experienced operators; the weakness lay most obviously with the Luftwaffe, a new service founded only in 1935. Its operators were probably younger and less experienced. A Luftwaffe key was the first to be broken by Bletchley, which thereafter broke almost all Luftwaffe keys intercepted, sometimes on the first day they were identified.

Bletchley called two forms of mistake made by German operators—each was the product of laziness—the “Herivel tip” and “Sillies” (or “Cillies”). John Herivel’s tip was the result of a brainwave. He guessed that an operator, after setting the rotor rims, would place them in their slots with the selected letters uppermost. These letters might then form the first three letters of the encrypt, thus revealing the rotor setting which, for the first few years of the war, remained unchanged throughout the day. The “Herivel tip” often yielded a result, which greatly shortened decryption.
²⁸

“Sillies” were another form of laziness, suggested to a careless operator by the arrangement of the keyboard. Required to choose three letters for his first group, he might, instead of tapping at random, run his finger down a diagonal and then the alternative diagonal, on a QWERTZ keyboard (the later German arrangement) producing QAY and WSX. Because this was a silly thing to do, the crib offered was called by the Bletchley cryptanalysts “a silly,” hence “sillies.” Other sillies were short German girls’ names, perhaps that of the operator’s sweetheart, EVA or KAT. Some of the laziest sillies really were silly, ABC or DDD, though their use was quickly stamped out by higher authority; while the habit lasted it provided, nevertheless, numbers of breaks.