Alan Turing: The Enigma (54 page)

^*
J.R.F. Jeffries, Research Fellow in mathematics at Downing College, Cambridge, contracted tuberculosis in early 1941 and died.

^*
For consistency the word ‘radio’ is used henceforth, although at the time this was the American term, English people calling it ‘wireless’, or more formally ‘wireless telegraph’. At the time of Roosevelt’s re-election in 1936, Alan wrote from Princeton ‘all the results are coming out over the wireless (‘radio’ they say in the native language). My method of getting the results is to go to bed and read them in the paper next morning.’

^*
There were complications, but not affecting the account that follows.

^*
The rather tiresome complication introduced by the ring-setting is, unfortunately, required to make sense of what the Poles achieved. It will play no part thereafter.

^*
That is,

^*
Actually 11 pairs gives slightly more ways – not that it makes any difference; 12 or 13 pairs rather less.

^†
i.e
. 26! This is also the number of possible wirings for each rotor of an Enigma.

^*
Questions about the chance of obtaining loops could be posed and answered in the language of probability theory and combinatorial mathematics – very much what Alan, or indeed any Cambridge mathematician, would be well-placed to tackle. One would be lucky to get a loop within one word, as shown in the artificial example; in practice the analyst would have to pick letters out of a longer ‘crib’ sequence. Furthermore one loop would not be enough – far too many rotor positions would satisfy the consistency condition by chance. Three loops would be required – a taller order.

^†
The Bombe, nevertheless, had nothing whatever to do with the Universal Turing Machine. It was more general than the Polish Bombe, which worked on a specific indicator system; but otherwise it could hardly have been less universal, being specific to the Enigma wirings and requiring an absolutely accurate ‘crib’.

^*
Welchman, whose first work had been on the identification of the different key-systems, had devised a way of naming them by colours. ‘Red’ was the general purpose Luftwaffe system; ‘Green’ the Home Administration of the Wehrmacht. Despite these early breaks, ‘Green’ turned out to be an example of where an Enigma system was almost totally unbreakable because it was used properly.

^*
Knox’s work had a very direct pay-off in the battle of Matapan, in March 1941.

^*
Literally, in future parlance, software.

^†
The Yellow was the temporary inter-service system used in Norway.

^*
They might well have worried that the German occupiers would now learn of the successful start to Enigma decryption from a French source. But no such disclosure or discovery was ever made.

^*
She was not a country vicar’s daughter, but that was what they thought.

^*
Though any but a very naive player would be able to do better than this and play so as to exploit the particular weaknesses of the opponent.

^*
More strictly, any ‘zero-sum’ game, one in which the loss of one player would always be the gain of the other.

^†
Less complicated than poker (which in fact is much too complex for a full mathematical analysis), the game of ‘stone, paper, scissors’ illustrates the idea. In this game the optimal strategy, for both players, is a ‘mixed’ strategy, that of choosing the three options randomly and with equal probability. For clearly, if one player departs from randomness, the other can exploit the departure to gain an advantage.

^*
The ‘Foreign’ key-system, used by German vessels in waters such as the Indian Ocean, was
never
broken. Furthermore the ‘Home’ key-system no longer covered the communications of the Mediterranean surface vessels. These, from April 1941, had gone on to a new system which remained immune from decryption for another year.

^*
A reference to punched-card machine work employed on other stages of the process.

^†
Luftwaffe key-system used in Africa.

^*
A reference to the problem of testing the positions at which the Bombe stopped, to eliminate those which had arisen by chance.

^*
The ‘crib’ for 14 March came from a special message sent out both on the (broken) Home key-system, and on the U-boat system, announcing the no doubt vital news that Dönitz had been promoted to the rank of Admiral.

^*
They thought of the tape as reading from left to right, as shown, and so thought of it as having five ‘rows’. This is not the usual terminology, but for consistency it will be used throughout.

^*
Other types of teleprinter-enciphering machine systems remained unbroken.

^*
Nothing to do with testing, but named after its head, a Major Tester.

BRIDGE PASSAGE

Aboard at a ship’s helm,

A young steersman steering with care.

Through fog on a sea-coast dolefully ringing,

An ocean-bell – O a warning bell, rock’d by the waves.

O you give good notice indeed, you bell by the sea-reefs ringing,

Ringing, ringing, to warn the ship from its wreck-place.

For as on the alert O steersman, you mind the loud admonition,

The bows turn, the freighted ship tacking speeds away under her gray sails,

The beautiful and noble ship with all her precious wealth speeds away gayly and safe.

But O the ship, the immortal ship! O ship aboard the ship!

Ship of the body, ship of the soul, voyaging, voyaging, voyaging.

While the Atlantic remained in the dark,
November 1942 proved to be the worst month yet for Allied shipping. But the North African landings drew off part of the U-boat force, and the
Queen Elizabeth
, faster than any U-boat, made her way in safety. Alan disembarked at New York on 13 November, but according to a story he told his mother,
¹
was very nearly refused entry to the United States:

He had on arrival some difficulty over admission as he had been told on no account to take any papers other than those in the Diplomatic Bag which he carried. The triumvirate who confronted him on landing talked of despatching him to Ellis Island. Alan’s laconic comment was, ‘That will teach my employers to furnish me with better credentials.’ After further deliberation and passing of slips of paper, two of the triumvirate outvoted the third member and he was admitted.

Such problems were supposed to be kept under control by W. Stephenson, the Canadian millionaire who directed ‘British Security Coordination’ from Rockefeller Center. Stephenson, originally installed to liaise between the British secret service and the FBI, had made a considerable effort to advance British interests in America by undercover manipulation. Since 1941 his office had expanded to take in the more serious work of channelling
Bletchley’s productions to Washington. But perhaps Alan’s tiresome habit of taking instructions literally had defeated even him.
²
It was certainly a curious greeting for a person who in so many ways was bridging old and new worlds. His primary assignment took him to the enormously expanded capital city, much changed since the sleepy days of 1938, where his opposite numbers in the Navy’s cryptanalytic service, ‘Communications Supplementary Activities (Washington)’, were based.

From Bletchley’s point of view, America was the miraculous land across the rainbow bridge, possessing resources and skilled labour in quantities that desperate Britain could not supply. The CSAW was already closely connected with the most advanced sections of American industry, using Eastman Kodak, National Cash Register, and IBM to plan and build its machinery. As in other ways, Hitler had the effect of adding British ideas to the massive capacity of American business. Again it was Alan Turing’s role to connect the logical and the physical.

But CSAW was certainly not without its own brains, and one of its staff was the brilliant young Yale graduate mathematician, Andrew Gleason. He and another member of the organisation, Joe Eachus, looked after Alan during his period in Washington. Once Alan was taken by Andrew Gleason to a crowded restaurant on 18th Street. They were sitting on a table for two, just a few inches from the next one, and talking of statistical problems, such as that of how best to estimate the total number of taxicabs in a town, having seen a random selection of their licence numbers. The man on the next table was very upset by hearing this technical discussion, which he took to be a breach of ‘security’, and said, ‘People shouldn’t be talking about things like that.’ Alan said, ‘Shall we continue our conversation in
German?’
The man was insulted and told them in no uncertain terms how he had fought in the First World War.

They were all spy-conscious in Washington now, but such anecdotes apart, the central event of Alan’s visit was the breakthrough back into the U-boat Enigma. This was achieved without the possession of faster Bombes; it depended upon a precarious thread of luck, ingenuity, and a German blunder. It went back to the weather signals that in mid-1941 had given them an almost unfairly simple crib each day, thanks to the fact that they were transmitted both in the Enigma, and in the special meteorological cipher. But early in 1942 a change in the system had denied this method to Hut 8. Not until the U-boat capture of 30 October could it be regained. This gave them the cribs, but the difficulty remained that it would take three weeks to work through all the rotor settings, just for one day’s traffic. Here, however, they were saved by a German blunder which, in effect, threw away all the advantage that the fourth wheel offered. For the weather reports, and other routine short signals, the U-boats used their Enigma with the fourth wheel in ‘neutral’ position, thus reducing the cryptanalysts’ problem to the one they had mastered in 1941. This in itself was not fatal for
Germany; the greater mistake lay in the fact that the three rotor settings used for the weather reports were also used for all the other traffic of the day. For this the analysts now needed only to work through 26 possibilities for the fourth wheel, rather than the 26 × 336 × 17576 possibilities that would otherwise have been the case. As a result of this slip, Hut 8 was able to supply decrypted messages from 13 December. It was not a sudden restoration of sight, but more like a return to the period in the spring of 1941. They had weeks in which nothing worked out. But it was sufficiently copious a flow of information for the Tracking Room in the OIC to have by 21 December a clear idea of the location of all eighty-four U-boats at large in the North Atlantic. And this time Hut 8 was not alone. In Washington, Alan Turing was indoctrinating the American analysts into all their methods. Now, when the rotor settings were discovered, they were passed back and forth across the Atlantic, the analysts beginning to communicate directly as indeed the two tracking rooms were also doing.