Cryptonomicon

by Neal Stephenson

  To the irritation and bafflement of the German High Command, the Nipponese government has sent a message to them, requesting that, in the event that all of Germany’s European naval bases are lost, the Kriegsmarine should be given orders to continue operating with the Nipponese in the Far East. The message is encrypted in Indigo. It is duly intercepted and read by the Allies.

  In the United Kingdom, Dr. Alan Mathison Turing, considering the war to be effectively finished, has long since turned his attentions away from the problem of voice encryption and into the creation of thinking machines. For about ten months—ever since the finished Colossus Mark II was delivered to Bletchley Park—he has had the opportunity to work with a truly programmable computing machine. Alan invented these machines long before one was ever built, and has never needed hands-on experience in order to think about them, but his experiences with Colossus Mark II have helped him to solidify some ideas of how the next machine ought to be designed. He thinks of it as a postwar machine, but that’s only because he’s in Europe and hasn’t been concerned with the problem of conquering Nippon as much as Waterhouse has.

  “I’ve been working on BURY and DISINTER,” says a voice, coming out of small holes in a Bakelite headset clamped over Waterhouse’s head. The voice is oddly distorted, nearly obscured by white noise and a maddening buzz.

  “Please say it again?” Lawrence says, pressing the phones against his ear.

  “BURY and DISINTER,” says the voice. “They are, er, sets of instructions for the machine to execute, to carry out certain algorithms. They are programmes.”

  “Right! Sorry, I just wasn’t able to hear you the first time. Yes, I’ve been working on them too,” Waterhouse says.

  “The next machine will have a memory storage system, Lawrence, in the form of sound waves traveling down a cylinder filled with mercury—we stole the idea from John Wilkins, founder of the Royal Society, who came up with it three hundred years ago, except he was going to use air instead of quicksilver. I—excuse me, Lawrence, did you say you had been working on them?”

  “I did the same thing with tubes. Valves, as you would call them.”

  “Well that’s all well and good for you Yanks,” Alan says, “I suppose if you are infinitely rich you could make a BURY/DISINTER system out of steam locomotives, or something, and retain a staff of thousands to run around squirting oil on the squeaky bits.”

  “The mercury line is a good idea,” Waterhouse admits. “Very resourceful.”

  “Have you actually gotten BURY and DISINTER to work with valves?”

  “Yes. My DISINTER works better than our shovel expeditions,” Lawrence says. “Did you ever find those silver bars you buried?”

  “No,” Alan says absently. “They are lost. Lost in the noise of the world.”

  “You know, that was a Turing test I just gave you,” Lawrence says.

  “Beg pardon?”

  “This damned machine screws up your voice so bad I can’t tell you from Winston Churchill,” Lawrence says. “So the only way I can verify it’s you is by getting you to say things that only Alan Turing could say.”

  He hears Alan’s sharp, high-pitched laugh at the other end of the line. It’s him all right.

  “This Project X thing really is appalling,” Alan says. “Delilah is infinitely superior. I wish you could see it for yourself. Or hear it.”

  Alan is in London, in a command bunker somewhere. Lawrence is in Manila Bay, on the Rock, the island of Corregidor. They are joined by a thread of copper that goes all the way around the world. There are many such threads traversing the floors of the world’s oceans now, but only a few special ones go to rooms like this. The rooms are in Washington, London, Melbourne, and now, Corregidor.

  Lawrence looks through a thick glass window into the engineer’s booth, where a phonograph record is playing on the world’s most precise and expensive turntable. This is, likewise, the most valuable record ever turned out: it is filled with what is intended to be perfectly random white noise. The noise is electronically combined with the sound of Lawrence’s voice before it is sent down the wire. Once it gets to London, the noise (which is being read off an identical phonograph record there) is subtracted from his voice, and the result sent into Alan Turing’s headphones. It all depends on the two phonographs being perfectly synchronized. The only way to synchronize them is to transmit that maddening buzzing noise, a carrier wave, along with the voice signal. If all goes well, the opposite phonograph player can lock onto the buzz and spin its wax in lockstep.

  The phonograph record is, in other words, a one-time pad. Somewhere in New York, in the bowels of Bell Labs, behind a locked and guarded door stenciled PROJECT X, technicians are turning out more of these things, the very latest chart-topping white noise. They stamp out a few copies, dispatch them by courier to the Project X sites around the globe, then destroy the originals.

  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

  Caveat: they aren’t really random, of course, they just look that way, and that’s why the pseudo-

  Overview of the Problem

  It seems as if it should be easy

  Actually it turns out to be really hard

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

  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)

  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)

  Conclusions

  It’s harder than it looks

  It’s not for the unwary

  It can be done if you keep your wits about you

  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-Randomness, 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/Pufferfish 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.

  LANDFALL

  * * *

  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 Bischoff’s 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.

  Bischoff tries to recognize them as they row closer. It takes a while. There are five in all. Otto has lost his pot-belly and gone much greyer. Rudy is a completely different man: he has long flowing hair ponytailed down his back, and a surprisingly thick, Viking-like beard, and he appears to have lost his left eye somewhere along the way, because he’s got an actual black patch over it!

  “My god,” Bischoff says, “pirates!”

  The other three men he has never seen before: a Negro with dreadlocks; a brown-skinned, Indian-looking fellow; and a red-headed European.

  Rudy is watching a stingray furling and unfurling its meaty wings ten meters straight down.

  “The clarity of the water is exquisite,” he remarks.

  “When the Catalinas come for us, Rudy, then you will long for the old northern murk,” Bischoff says.

  Rudolf von Hacklheber swings his one eye around to bear on Bischoff, and allows just a trace of amusement to show on his face. “Permission to come aboard, Captain?” Rudy asks.

  “Granted with pleasure,” Bischoff says. The dinghy has come alongside the round hull of the submarine, and Bischoff’s crew unrolls a rope ladder to them. “Welcome to the V-Million!”

  “I have heard of the V-1 and the V-2, but…”

  “We could not guess how many other V-weapons Hitler might have invented, and so we chose a very, very large number,” Bischoff says proudly.

  “But Günter, you know what the V stands for?”

  “Vergeltungswaffen,” Bischoff says. “You’re not thinking about it hard enough, Rudy.”

  Otto’s puzzled, and being puzzled makes him angry. “Vergeltung means revenge, doesn’t it?”

  “But it can also mean to pay someone back, to compensate them, to reward them,” says Rudy, “even to bless them. I like it very much, Günter.”

  “Admiral Bischoff to you,” Günter returns.

  “You are the supreme commander of the V-Million—there is no one above you?”

  Bischoff clicks his heels together sharply and holds out his right arm. “Heil Dönitz!” he shouts.

  “What the hell are you talking about?” asks Otto.

  “Haven’t you been reading the papers? Hitler killed himself yesterday. In Berlin. The new Führer is my personal friend Karl Dönitz.”

  “Is he part of the conspiracy too?” Otto mutters.

  “I thought my dear mentor and protector Hermann Göring was going to be Hitler’s successor,” Rudy says, sounding almost crestfallen.

  “He is down in the south somewhere,” Bischoff says, “on a diet. Just before Hitler took cyanide, he ordered the SS to arrest that fat bastard.”

  “But in all seriousness, Günter—when you boarded this U-boat in Sweden, it was called something else, and there were some Nazis on board, yes?” asks Rudy.

  “I had completely forgotten about them.” Bischoff cups his hands around his mouth and shouts down the hatch in the top of the sleek rounded-off conning tower. “Has anyone seen our Nazis?”

  The command echoes down the length of the U-boat from sailor to sailor: Nazis? Nazis? Nazis? but somewhere it turns into Nein! Nein! Nein! and echoes back up the conning tower and out the hatch.

  Rudy climbs up V-Million’s smooth hull on bare feet. “Do you have any citrus fruit?” He smiles, showing magenta craters in his gums where teeth might be expected.

  “Get the calamansis,” Bischoff says to one
of his mates. “Rudy, for you we have the Filipino miniature limes, great piles of them, with more vitamin C than you could ever want.”

  “I doubt that,” Rudy says.

  Otto just looks at Bischoff reproachfully, holding him personally responsible for having been thrown together with these four other men for all of 1944 and the first four months of 1945. Finally he speaks: “Is that son of a bitch Shaftoe here?”

  “That son of a bitch Shaftoe is dead,” Bischoff says.

  Otto averts his glare and nods his head.

  “I take it you received my letter from Buenos Aires?” asks Rudy von Hacklheber.

  “Mr. G. Bishop, General Delivery, Manila, the Philippines,” Bischoff recites. “Of course I did, my friend, or else we would not have known where to meet you. I picked it up when I went into town to renew my acquaintance with Enoch Root.”

  “He made it?”

  “He made it.”

  “How did Shaftoe die?”

  “Gloriously, of course,” Bischoff says. “And there is other news from Julieta: the conspiracy has a son! Congratulations, Otto, you are a grand-uncle.”

  This actually elicits a smile, albeit black and gappy, from Otto. “What’s his name?”

  “Günter Enoch Bobby Kivistik. Eight pounds, three ounces—superb for a wartime baby.”

  There is hand-shaking all around. Rudy, ever debonair, produces some Honduran cigars to mark the occasion. He and Otto stand in the sun and smoke cigars and drink calamansi juice.

  “We have been waiting here for three weeks,” Bischoff says. “What kept you?”

  Otto spits out something that is pretty bad-looking. “I am sorry that you have had to spend three weeks tanning yourselves on the beach while we have been sailing this tub of shit across the Pacific!”