machines away because one mathematician writes a paper?' He stares at his cigarette a while longer, then puts it to his lips, draws on it tastefully, holds the smoke in his lungs, and finally exhales it slowly through his vocal cords whilst simultaneously causing them to emit the following sounds: 'I knew that there must be people working for the enemy who would figure this out. Turing. Von Neumann. Waterhouse. Some of the Poles. I began to look for signs that they had broken the Enigma, or at least realized its weaknesses and begun trying to break it. I ran statistical analyses of convoy sinkings and U-boat attacks. I found some anomalies, some improbable events, but not enough to make a pattern. Many of the grossest anomalies were later accounted for by the discovery of espionage stations and the like.
'From this I drew no conclusion. Certainly if they were smart enough to break the Enigma they would be smart enough to conceal the fact from us at any cost. But there was one anomaly they could not cover up. I refer to human anomalies.'
'Human anomalies?' Root asks. The phrase is classic Root-bait.
'I knew perfectly well that only a handful of people in the world had the acumen to break the Enigma and then to cover up the fact that they had broken it. By using our intelligence sources to ascertain where these men were, and what they were doing, I could make inferences.' Von Hacklheber stubs out his cigarette, sits up straight, and drains a half-shot of schnapps, warming to the task. 'This was a human intelligence problem-not signals intelligence. This is handled by a different branch of the service-' and he's off again talking about the structure of the German bureaucracy. Terrified, Shaftoe flees from the room, runs outside, and uses the outhouse. When he gets back, von Hacklheber is just winding up. 'It all came down to a problem of sifting through large amounts of raw data-lengthy and tedious work.'
Shaftoe cringes, wondering what something would have to be like in order to qualify as lengthy and tedious to this joker.
'After some time,' von Hacklheber continues, 'I learned, through some of our agents in the British Isles, that a man matching the general description of Lawrence Pritchard Waterhouse had been stationed to a castle in Outer Qwghlm. I was able to arrange for a young lady to place this man under the closest possible surveillance,' he says dryly. 'His security precautions were impeccable, and so we learned nothing directly. In fact, it is quite likely that he knew that the young woman in question was an agent, and so took added precautions. But we did learn that this man communicated through one-time pads. He would read his encrypted messages over the telephone to a nearby naval base whence they would be telegraphed to a station in Buckinghamshire, which would respond to him with messages encrypted using the same system of one-time pads. By going through the records of our various radio intercept stations we were able to accumulate a stack of messages that had been sent by this mysterious unit, using this series of one-time pads, over a period of time beginning in the middle of 1942 and continuing up to the present day. It was interesting to note that this unit operated in a variety of places:
Malta, Alexandria, Morocco, Norway, and various ships at sea. Extremely unusual. I was very interested in this mysterious unit and so I began trying to break their special code.'
'Isn't that impossible?' Bischoff asks. 'There is no way to break a one-time pad, short of stealing a copy.'
'That is true in theory,' von Hacklheber says. 'In practice, this is only true if the letters that make up the one-time pad are chosen perfectly randomly. But, as I discovered, this is not true of the one-time pads used by Detachment 2702-which is the mysterious unit that Waterhouse, Turing, and these two gentlemen all belong to.'
'But how did you figure this out?' Bischoff asks.
'A few things helped me. There was a lot of depth-many messages to work with. There was consistency- the one-time pads were generated in the same way, always, and always exhibited the same patterns. I made some educated guesses which turned out to be correct. And I had a calculating machine to make the work go faster.'
'Educated guesses?'
'I had a hypothesis that the one-time pads were being drawn up by a person who was rolling dice or shuffling a deck of cards to produce the letters. I began to consider psychological factors. An English speaker is accustomed to a certain frequency distribution of letters. He expects to see a great many e's, t's, and a's, and not so many z's and q's and x's. So if such a person were using some supposedly random algorithm to generate the letters, he would be subconsciously irritated every time a z or an x came up, and, conversely, soothed by the appearance of e or t. Over time, this might skew the frequency distribution.'
'But Herr Doctor von Hacklheber, I find it unlikely that such a person would substitute their own letters for the ones that came up on the cards, or dice, or whatever.'
'It is not very likely. But suppose that the algorithm gave the person some small amount of discretion.' Von Hacklheber lights another cigarette, pours out more schnapps. 'I set up an experiment. I got twenty volunteers- middle-aged women who wanted to do their part for the Reich. I set them to work drawing up one-time pads using an algorithm where they drew slips out of a box. Then I used my machinery to run statistical calculations on the results. I found that they were not random at all.'
Root says, 'The one-time pads for Detachment 2702 are being created by Mrs. Tenney, a vicar's wife. She uses a bingo machine, a cage filled with wooden balls with a letter stamped on each ball. She is supposed to close her eyes before reaching into the cage. But suppose she has become sloppy and no longer closes her eyes when she reaches into it.'
'Or,' von Hacklheber says, 'suppose she looks at the cage, and sees how the balls are distributed inside of it, and
Bischoff's not buying it. 'But it will still be mostly random!'
'Mostly random is not good enough!' von Hacklheber snaps. 'I was convinced that the one-time pads of Detachment 2702 would have a frequency distribution similar to that of the King James Version of the Bible, for example. And I strongly suspected that the content of those messages would include words such as Waterhouse, Turing, Enigma, Qwghlm, Malta. By putting my machinery to work, I was able to break some of the one-time pads. Waterhouse was careful to burn his pads after using them once, but some other parts of the detachment were careless, and used the same pads again and again. I read many messages. It was obvious that Detachment 2702 was in the business of deceiving the Wehrmacht by concealing the fact that the Enigma had been broken.'
Shaftoe knows what an Enigma is, if only because Bischoff won't shut up about them. When von Hacklheber explains this, everything that Detachment 2702 ever did suddenly makes sense.
'So, the secret is out then,' Root says. 'I assume you made your superiors aware of your discovery?'
'I made them aware of absolutely nothing,' von Hacklheber snarls, 'because by this time I had long since fallen into a snare of Reichsmarschall Hermann Goring. I had become his pawn, his slave, and had ceased to feel any loyalty whatsoever towards the Reich.'
The knock on Rudolf von Hacklheber's door had come at four o'clock in the morning, a time exploited by the Gestapo for its psychological effect. Rudy is wide awake. Even if bombers had not been pounding Berlin all night long, he would have been awake, because he has neither seen nor heard from Angelo in three days. He throws a dressing gown over his pajamas, steps into slippers, and opens the door of his flat to reveal, predictably, a small, prematurely withered man backed up by a couple of classic Gestapo killers in long black leather coats.
'May I proffer an observation?' says Rudy von Hacklheber.
'But of course, Herr Doktor Professor. As long as it is not a state secret, of course.'
'In the old days-the early days-when no one knew what the Gestapo was, and no one was afraid of it, this four in the morning business was clever. A fine way to exploit man's primal fear of the darkness. But now it is 1942, almost 1943, and everyone is afraid of the Gestapo. Everyone. More than they are of the dark. So, why don't you work during the daytime? You are stuck in a rut.'
The bottom half of the withered man's face laughs. The top half doesn't change. 'I will pass your suggestion up the chain of command,' he says. 'But, Herr Doktor, we are not here to instill fear. We have come at
