Cryptonomicon

Lawrence looks carefully around the pub. They are the only customers, and he cannot bring himself to believe that Mrs. Ramshaw is a spy. "I thought it might have something to do with--" he says, and nods in the direction of Bletchley Park.

"They are building--I have helped them build--a machine called Colossus."

"I thought I saw your hand in it."

"It is built from old ideas--ideas we talked about in New Jersey, years ago," Alan says. Brisk and dismissive is his tone, gloomy is his face. He is hugging the RCA Radio Tube Manualto himself with one arm, doodling in a notebook with the other. Waterhouse thinks that really the RCA Radio Tube Manualis like a ball and chain holding Alan back. If he would just work with pure ideas like a proper mathematician he could go as fast as thought. As it happens, Alan has become fascinated by the incarnations of pure ideas in the physical world. The underlying math of the universe is like the light streaming in through the window. Alan is not satisfied with merely knowing that it streams in. He blows smoke into the air to make the light visible. He sits in meadows gazing at pine cones and flowers, tracing the mathematical patterns in their structure, and he dreams about electron winds blowing over the glowing filaments and screens of radio tubes, and, in their surges and eddies, capturing something of what is going on in his own brain. Turing is neither a mortal nor a god. He is Antaeus. That he bridges the mathematical and physical worlds is his strength and his weakness.

"Why are you so glum?" Alan says. "What have you been working on?"

"Same stuff, different context," Waterhouse says. With these four words he conveys, in full, everything that he has been doing on behalf of the war effort. "Fortunately, I came upon something that is actually rather interesting."

Alan looks delighted and fascinated to hear this news, as if the world had been completely devoid of interesting things for the last ten years or so, and Waterhouse had stumbled upon a rare find. "Tell me about it," he insists.

"It's a cryptanalysis problem," Waterhouse says. "Non-Enigma." He goes on to tell the story about the messages from U-553. "When I got to Bletchley Park this morning," he concludes, "I asked around. They said that they had been butting their heads against the problem as long as I had, without any success."

Suddenly, Alan looks disappointed and bored. "It must be a one-time pad," he says. He sounds reproachful.

"It can't be. The ciphertext is not devoid of patterns," Waterhouse says.

"Ah," replies Alan, perking up again.

"I looked for patterns with the usual Cryptonomicontechniques. Found nothing clear--just some traces. Finally, in complete frustration, I decided to start from a clean slate, trying to think like Alan Turing. Typically your approach is to reduce a problem to numbers and then bring the full power of mathematical analysis to bear on it. So I began by converting the messages into numbers. Normally, this would be an arbitrary process. You convert each letter into a number, usually between one and twenty-five, and then dream up some sort of arbitrary algorithm to convert this series of small numbers into one big number. But this message was different--it used thirty-two characters--a power of two--meaning that each character had a unique binary representation, five binary digits long."

"As in Baudot code," Alan says (15). He looks guardedly interested again.

"So I converted each letter into a number between one and thirty-two, using the Baudot code. That gave me a long series of small numbers. But I wanted some way to convert all of the numbers in the series into one large number, just to see if it would contain any interesting patterns. But this was easy as pie! If the first letter is R, and its Baudot code is 01011, and the second letter is F, and its code is 10111, then I can simply combine the two into a ten-digit binary number, 0101110111. And then I can take the next letter's code and stick that onto the end and get a fifteen-digit number. And so on. The letters come in groups of five--that's twenty-five binary digits per group. With six groups on each line of the page, that's a hundred and fifty binary digits per line. And with twenty lines on the page, that's three thousand binary digits.

So each page of the message could be thought of not as a series of six hundred letters, but as an encoded representation of a single number with a magnitude of around two raised to the three thousandth power, which works out to around ten to the nine hundredth power."