Neal Stephenson - Cryptonomicon

They would not be having this conversation at all, except that a couple of years ago Alan went to Greenwich Village and worked at Bell Labs for a few months, while Lawrence was on Qwghlm. H.M. Government sent him there to evaluate this Project X thing and let them know whether it was truly secure. Alan decided that it was—then went back home and began working on a much better one, called Delilah.

What the hell does this have to do with dead Chinese abacus slaves?

To Lawrence, staring through the window at the spinning white-noise disk, the connection could hardly be clearer. He says, “Last I spoke to you, you were working on generating random noise for Delilah.”

“Yes,” Alan says absently. That was a long time ago, and that whole project has been BURIED in his memory storage system; it will take him a minute or two to DISINTER it.

“What sorts of algorithms did you consider to create that noise?”

There is another five-second pause, then Alan launches into a disquisition about mathematical functions for generating pseudorandom number sequences. Alan had a good British boarding-school education, and his utterances tend to be well-structured, with outline form, topic sentences, the whole bit:

PSEUDO-RANDOM NUMBERS

I. Caveat: they aren't really random, of course, they just look that way, and that's why the pseudo

II. Overview of the Problem

A. It seems as if it should be easy

B. Actually it turns out to be really hard

C. Consequences of failure: Germans decrypt our secret messages, millions die, humanity is enslaved, world plunged into an eternal Dark Age

D. How can you tell if a series of numbers is random

1, 2, 3,… (A list of different statistical tests for randomness, the advantages and disadvantages of each)

III. A bunch of stuff that I, Alan Turing, tried

A, B, C,… (A list of different mathematical functions that Alan used to generate random numbers; how almost all of them failed abjectly; Alan's initial confidence is replaced by surprise, then exasperation, then despair, and finally by guarded confidence as he at last finds some techniques that work)

IV. Conclusions

A. It's harder than it looks

B. It's not for the unwary

C. It can be done if you keep your wits about you

D. In retrospect a surprisingly interesting mathematical problem deserving of further research

When Alan finishes with this perfectly structured whirlwind tour of the Surprising World of Pseudo-Randonmess, Lawrence says, “How about zeta functions?”

“Didn't even consider those,” Alan says.

Lawrence's mouth drops open. He can see his own semitransparent reflection in the window, superimposed on the spinning phonograph, and he sees that he has got a sort of mildly outraged look on his face. There must be something conspicuously nonrandom about the output of the zeta function, something so obvious to Alan that he dismissed it out of hand. But Lawrence has never seen any such thing. He knows that Alan is smarter than he is, but he's not used to being so desperately far behind him.

“Why… why not?” he finally stammers.

“Because of Rudy!” Alan thunders. “You and I and Rudy all worked on that damn machine at Princeton! Rudy knows that you and I have the knowledge to build such a device. So it is the first thing that he would assume we would use.”

“Ah.” Lawrence sighs. “But leaving that aside, the zeta function might still be a good way of doing it.”

“It might,” Alan says guardedly, “but I have not investigated it. You're not thinking of using it, are you?”

Lawrence tells Alan about the abaci. Even through the noise and the buzz, he can tell that Alan is thunderstruck. There is a pause while the technicians at each end flip over their phonograph records. When the connection is reestablished, Alan's still very excited. “Let me tell you something more,” Lawrence says.

“Yes, go ahead.”

“You know that the Nipponese use a plethora of different codes, and we still have only broken some of them.”

“Yes.”

“There is an unbroken cipher system that Central Bureau calls Arethusa. It's incredibly rare. Only thirty-some Arethusa messages have ever been intercepted.”

“Some company code?” Alan asks. This is a good guess; each major Nipponese corporation had its own code system before the war, and much effort has gone into stealing code books for, and otherwise breaking, the Mitsubishi code, to name one example.

“We can't figure out the sources and destinations of Arethusa messages,” Lawrence continues, “because they use a unique site code system. We can only guess at their origins by using huffduff. And huffduff tells us that most of the Arethusa messages have originated from submarines. Possibly just a single submarine, plying the route between Europe and Southeast Asia. We have also seen them from Sweden, from London, Buenos Aires, and Manila.”

“Buenos Aires? Sweden?”

“Yes. And so, Alan, I took an interest in Arethusa.”

“Well, I don't blame you!”

“The message format matches that of Azure/Pufferfish.”

“Rudy's system?”

“Yes.”

“Nice work on that, by the way.”

“Thank you, Alan. As you must have heard by now, it is based on zeta functions. Which you did not even consider using for Delilah because you were afraid Rudy would think of it. And this raises the question of whether Rudy intended us to break Azure/Pufferfish all along.”

“Yes, it does. But why would he want us to?”

“I have no idea. The old Azure/Puffeffish messages may contain some clues. I am having my Digital Computer generate retroactive one-time pads so that I can decrypt those messages and read them.”

“Well, then, I shall have Colossus do the same. It is busy just now,” Alan says, “working on Fish decrypts. But I don't think Hitler has much longer to go. When he is finished, I can probably get down to Bletchley and decrypt those messages.”

“I'm also working on Arethusa,” Lawrence says. “I'm guessing it all has something to do with gold.”

“Why do you say that?” Alan says. But at this point the tone arm of the phonograph reaches the end of its spiral groove and lifts off the record. Time's up. Bell Labs, and the might of the Allied governments, did not install the Project X network so that mathematicians could indulge in endless chitchat about obscure functions.

The sailing ship Gertrude wheezes into the cove shortly after sunrise, and Bischoff cannot help but laugh. Barnacles have grown so thick around her hull that the hull itself (he supposes) could be removed entirely, and the shell of barnacles could be outfitted with a mast and canvas, and sailed to Tahiti. A hundred-yard-long skein of seaweed, rooted in those barnacles, trails behind her, making a long greasy disturbance in her wake. Her mast has evidently been snapped off at least once. It has been replaced by a rude jury-rigged thing, a tree trunk that has received some attention from a drawknife but still has bark adhering to it in places, and long dribbles of golden sap like wax trails on a candle, themselves streaked with sea salt. Her sails are nearly black with dirt and mildew, and rudely patched, here and there, with fat black stitches, like the flesh of Frankenstein's monster.

The men on board are scarcely in better shape. They do not even bother to drop anchor—they just run Gertrude aground on a coral head at the entrance to the cove, and call it a day. Most of Bischoffs crew has gathered on the top of V-Million, the rocket-submarine; they think it's the most hilarious thing they've ever seen. But when the men on Gertrude climb into a dinghy and begin rowing towards them, Bischoff's men remember their manners, and stand at attention, and salute.