Cryptonomicon (52 page)

“All right,” Alan says, “I agree that the use of thirty-two-letter alphabet suggests a binary coding scheme. And I agree that the binary coding scheme, in turn, lends itself to a sort of treatment in which individual groups of five binary digits are mooshed together to make larger numbers, and that you could even take it to the point of mooshing together all of the data on a whole page that way, to make one extremely large number. But what does that accomplish?”

“I don’t really know,” Waterhouse admits. “I just have an intuition that what we are dealing with here is a new encryption scheme based upon a purely mathematical algorithm. Otherwise, there would be no point in using the thirty-two-letter alphabet! If you think about it, Alan, thirty-two letters are all well and good—as a matter of fact, they are essential—for a teletype scheme, because you have to have special characters like line feed and carriage return.”

“You’re right,” Alan says, “it is extremely odd that they would use thirty-two letters in a scheme that is apparently worked out using pencil and paper.”

“I’ve been over it a thousand times,” Waterhouse says, “and the only explanation I can think of is that they are converting their messages into large binary numbers and then combining them with other large binary numbers—one-time pads, most likely—to produce the ciphertext.”

“In which case your project is doomed,” Alan says, “because you can’t break a one-time pad.”

“That is only true,” Waterhouse says, “if the one-time pad is truly random. If you built up that three-thousand digit number by flipping a coin three thousand times and writing down a one for heads and a zero for tails, then it would be truly random and unbreakable. But I do not think that this is the case here.”

“Why not? You think there were patterns in their one-time pads?”

“Maybe. Just traces.”

“Then what makes you think it is other than random?”

“Otherwise it makes no sense to develop a new
scheme,” Waterhouse says. “Everyone in the world has been using one-time pads forever. There are established procedures for doing it. There’s no reason to switch over to this new, extremely odd system right now, in the middle of a war.”

“So what do you suppose is the rationale for this new scheme?” asks Alan, clearly enjoying himself a great deal.

“The problem with one-time pads is that you have to make two copies of each pad and get them to the sender and the recipient. I mean, suppose you’re in Berlin and you want to send a message to someone in the Far East! This U-boat that we found had cargo on board—gold and other stuff—from Japan! Can you imagine how cumbersome this must be for the Axis?”

“Ahh,” Alan says. He gets it now. But Waterhouse finishes the explanation anyway:

“Suppose that you came up with a mathematical algorithm for generating very large numbers that were random, or at least random-looking.”

“Pseudo-random.”

“Yeah. You’d have to keep the algorithm secret, of course. But if you could get it—the algorithm, that is—around the world to your intended recipient, then they could, from that day forward, do the calculation themselves and figure out the one-time pad for that particular day, or whatever.”

A shadow passes over Alan’s otherwise beaming countenance. “But the Germans already have Enigma machines all over the place,” he says. “Why should they bother to come up with a new scheme?”

“Maybe,” Waterhouse says, “maybe there are some Germans who don’t want the entire German Navy to be able to decipher their messages.”

“Ah,” Alan says. This seems to eliminate his last objection. Suddenly he is all determination. “Show me the messages!”

Waterhouse opens up his attache case, splotched and streaked with salt from his voyages to and from Qwghlm, and draws out two manila envelopes. “These are the copies I made before I sent the originals down to Bletchley Park,” he says, patting one of them. “They are much more legible than the originals—” he pats the other envelope “—which
they were kind enough to lend me this morning, so that I could study them again.”

“Show the originals!” Alan says. Waterhouse slides the second envelope, encrusted with
TOP SECRET
stamps, across the table.

Alan opens the envelope so hastily that he tears it, and jerks out the pages. He spreads them out on the table. His mouth drops open in purest astonishment.

For a moment, Waterhouse is fooled; the expression on Alan’s face makes him think that his friend has, in some Olympian burst of genius, deciphered the messages in an instant, just by looking at them.

But that’s not it at all. Thunderstruck, he finally says, “I recognize this handwriting.”

“You do?” Waterhouse says.

“Yes. I’ve seen it a thousand times. These pages were written out by our old bicycling friend. Rudolf von Hacklheber. Rudy wrote those pages.”

Waterhouse spends much of the next week commuting to London for meetings at the Broadway Buildings. Whenever civilian authorities are going to be present at a meeting—especially civilians with expensive-sounding accents—Colonel Chattan always shows up, and before the meeting starts, always finds some frightfully cheerful and oblique way to tell Waterhouse to keep his trap shut unless someone asks a math question. Waterhouse is not offended. He prefers it, actually, because it leaves his mind free to work on important things. During their last meeting at the Broadway Buildings, Waterhouse proved a theorem.

It takes Waterhouse about three days to figure that the meetings themselves make no sense—he reckons that there is no imaginable goal that could be furthered by what they are discussing. He even makes a few stabs at proving that this is so, using formal logic, but he is weak in this area and doesn’t know enough of the underlying axioms to reach a Q.E.D.

By the end of the week, though, he has figured out that these meetings are just one ramification of the Yamamoto assassination. Winston Spencer Churchill is very fond in
deed of Bletchley Park and all its works, and he places the highest priority on preserving its secrecy, but the interception of Yamamoto’s airplane has blown a gaping hole in the screen of deception. The Americans responsible for this appalling gaffe are now trying to cover their asses by spreading a story that native islander spies caught wind of Yamamoto’s trip and radioed the news to Guadalcanal, whence the fatal P-38s were dispatched. But the P-38s were operating at the extreme limit of their fuel range and would have had to be sent out at precisely the correct time in order to make it back to Guadalcanal, so the Japanese would have to have their heads several feet up their asses to fall for that. Winston Churchill is pissed off in the extreme, and these meetings represent a prolonged bureaucratic hissy fit intended to produce some meaningful and enduring policy shift.

Every evening after the meetings, Waterhouse takes the tube to Euston and the train to Bletchley, and sits up late working on Rudy’s numbers. Alan has been working on them during the daytime, so the two of them, combining their efforts, can almost pound away on it round the clock.

Not all of the riddles are mathematical. For example, why the hell do the Germans have Rudy copying out big long numbers by hand? If the letters do indeed represent big numbers that would indicate that Dr. Rudolf von Hacklheber had been assigned to a job as a mere cipher clerk. This would not be the stupidest move ever made by a bureaucracy, but it seems unlikely. And what little intelligence they’ve been able to gather from Germany suggests that Rudy has in fact been given a rather important job—important enough to keep extremely secret.

Alan’s hypothesis is that Waterhouse has been making an understandable but totally wrong assumption. The numbers are
not
ciphertext. They are, rather, one-time pads that the skipper of U-553 was supposed to have used to encrypt certain messages too sensitive to go out over the regular Enigma channel. These one-time pads were, for some reason, drawn up personally by Rudy himself.

Usually, making one-time pads is just as lowly a job as enciphering messages—a job for clerks, who use decks of
cards or bingo machines to choose letters at random. But Alan and Waterhouse are now operating on the assumption that this encryption scheme is a radical new invention—presumably, an invention of Rudy’s—in which the pads are generated not at random but by using some mathematical algorithm.

In other words, there is some calculation, some equation that Rudy has dreamed up. You give it a value—probably the date, and possibly some other information as well, such as an arbitrary key phrase or number. You crank through the steps of the calculation, and the result is a number, some nine hundred digits long, which is three thousand binary digits, which gives you six hundred letters (enough to cover one sheet of paper) when you convert it using the Baudot code. The nine-hundred-digit decimal number, the three-thousand-digit binary number, and the six hundred letters are all the same abstract, pure number, encoded differently.

Meanwhile, your counterpart, probably on the other side of the world, is going through the same calculation and coming up with the same one-time pad. When you send him a message encrypted using the day’s pad, he can decipher it.

If Turing and Waterhouse can figure out how the calculation works, they can read all of these messages too.

T
HE
D
ENTIST IS GONE, THE DOOR LOCKED, THE
phone unplugged. Randall Lawrence Waterhouse lies naked on the starched, turned-down sheets of his king-sized bed. His head is propped up on a pillow so that he can peer through the vee of his feet at a BBC World Service newscast on the television. A ten-dollar minibar beer is near at hand. It’s six in the morning in America and so rather than a pro basketball game, he has to settle for this BBC newscast, which is strongly geared to South Asian happenings. A long and very sober story about a plague of locusts on the India/Pakistan border follows a piece on a typhoon about
to nail Hong Kong. The king of Thailand is calling in some of his government’s more corrupt officials to literally prostrate themselves before him. Asian news always has this edge of the fantastic to it, but it’s all dead serious, no nods or winks anywhere. Now he’s watching a story about a nervous system disease that people in New Guinea come down with as a consequence of eating other people’s brains. Just your basic cannibal story. No wonder so many Americans come here on business and never really go home again—it’s like stepping into the pages of
Classics Comics.

Someone is knocking on his door. Randy gets up and puts on his plush white hotel bathrobe. He peers through the peephole, half expecting to see a pygmy standing there with a blowpipe, though he wouldn’t mind a seductive Oriental courtesan. But it’s just Cantrell. Randy opens the door. Cantrell is already holding up his hands, palms out, in a cheerful “shut up already” gesture. “Don’t worry,” Cantrell says, “I’m not here to talk about Biz.”

“In that case I won’t break this beer bottle over your head,” Randy says. Cantrell must feel exactly the same way Randy does, which is that so much wild shit happened today that the only way to deal with it is not to talk about it at all. Most of the brain’s work is done while the brain’s owner is ostensibly thinking about something else, so sometimes you have to
deliberately
find something else to think and talk about.

“Come to my room,” Cantrell says. “Pekka is here.”

“The Finn who got blown up?”

“The same.”

“Why is he here?”

“Because there’s no reason not to be. After he got blown up he adopted a technomadic lifestyle.”

“So it’s just a coincidence, or—”

“Nah,” Cantrell says. “He’s helping me win a bet.”

“What kind of bet?”

“I was telling Tom Howard about Van Eck phreaking a few weeks ago. Tom said it sounded like bullshit. He bet me ten shares of Epiphyte stock that I couldn’t make it actually work outside of a laboratory.”

“Is Pekka good at that kind of thing?”

By way of saying yes, Cantrell adopts a serious look and says, “Pekka is writing a whole chapter about it for the
Cryptonomicon.
Pekka feels that only by mastering the technologies that might be used against us can we defend ourselves.”

This sounds almost like a call to arms. Randy would have to be some kind of loser to retreat to his bed after that, so he backs into the room and steps into his trousers, which are standing there telescoped into the floor where he dropped them upon his return from the sultan’s palace.
The sultan’s palace!
The television is now broadcasting a news story about pirates plying the waters of the South China Sea, making freighter crews walk the plank. “This whole continent is like fucking Disneyland without the safety precautions,” Randy observes. “Am I the only person who finds it surreal?”

Cantrell grins, but says, “If we begin talking about surreal, we’ll end up talking about today.”

“You got that right,” Randy says. “Let’s go.”

Before Pekka became known around Silicon Valley as the Finn Who Got Blown Up, he was known as Cello Guy, because he had a nearly autistic devotion to his cello and took it with him everywhere, always trying to stuff it into overhead luggage racks. Not coincidentally, he was an analog kind of guy from way back whose specialty was radio.

When packet radio started to get big as an alternative to sending data down wires, Pekka moved to Menlo Park and joined a startup. His company bought their equipment at used-computer stores, and Pekka ended up scoring a pretty nice nineteen-inch high-res multisync monitor perfectly adequate for his adaptable twenty-four-year-old eyes. He hooked it up to a slightly used Pentium box jammed full of RAM.

He also installed
Finux
, a free UNIX operating system created by Finns, almost as a way of proclaiming to the rest of the world “this is how weird we are,” and distributed throughout the world on the Net. Of course Finux was fantastically powerful and flexible and enabled you, among other things, to control the machine’s video circuitry to the
Nth degree and choose many different scanning frequencies and pixel clocks, if you were into that kind of thing. Pekka most definitely was into it, and so like a lot of Finux maniacs he set his machine up so that it could display, if he chose, a whole lot of tiny little pixels (which displayed a lot of information but was hard on the eyes) or, alternatively, fewer and larger pixels (which he tended to use after he had been hacking for twenty-four hours straight and lost ocular muscle tone), or various settings in-between. Every time he changed from one setting to another, the monitor screen would go black for a second and there would be an audible clunk from inside of it as the resonating crystals inside locked in on a different range of frequencies.

One night at three
A.M
., Pekka caused this to happen, and immediately after the screen went black and made that clunking noise, it exploded in his face. The front of the picture tube was made of heavy glass (it had to be, to withstand the internal vacuum) which fragmented and sped into Pekka’s face, neck, and upper body. The very same phosphors that had been glowing beneath the sweeping electron beam, moments before, conveying information into Pekka’s eyes, were now physically embedded in his flesh. A hunk of glass took one of his eyes and almost went through into his brain. Another one gouged out his voicebox, another zinged past the side of his head and bit a neat triangular hunk out of his left ear.

Pekka, in other words, was the first victim of the Digibomber. He almost bled to death on the spot, and his fellow Eutropians hovered around his hospital bed for a few days with tanks of Freon, ready to jump into action in case he died. But he didn’t, and he got even more press because his startup company lacked health insurance. After a lot of hand-wringing in local newspapers about how this poor innocent from the land of socialized medicine had not had the presence of mind to buy health insurance, some rich high-tech guys donated money to pay his medical bills and to equip him with a computer voicebox like Stephen Hawking’s.

And now here is Pekka, sitting in Cantrell’s hotel room. His cello stands in the corner, dusty around the bridge from
powdered rosin. He is facing a blank wall to which he has duct-taped a bunch of wires in precise loops and whorls. These lead to some home-brewed circuit boards which are in turn hooked up to his laptop.

“Hello Randy congratulations on your success,” says a computer-generated voice as soon as the door is shut behind Randy and Cantrell. This is a little greeting that Pekka has obviously typed in ahead of time, anticipating his arrival. None of the foregoing seems particularly odd to Randy except for the fact that Pekka seems to think that Epiphyte has already achieved some kind of success.

“How are we doing?” Cantrell asks.

Pekka types in a response. Then he cups one hand to his mutilated ear while using his other hand to cue the voice generator: “He showers.” Indeed, it’s possible now to hear the pipes hissing in the wall. “His laptop radiates.”

“Oh,” Randy says, “Tom Howard’s room is right next door?”

“Just on the other side of that wall,” Cantrell says. “I specifically requested it, so that I could win this bet. See, his room is a mirror image of this one, so his computer is only a few inches away, just on the other side of this wall. Perfect conditions for Van Eck phreaking.”

“Pekka, are you receiving signals from his computer right now?” Randy asks.

Pekka nods, types, and fires back, “I tune. I calibrate.” The input device for his voice generator is a one-handed chord-board strapped to his thigh. He puts his right hand on it and makes flopping and groping motions. Moments later speech emerges, “I require Cantrell.”

“Excuse me,” Cantrell says, and goes to Pekka’s side. Randy watches over their shoulders for a bit, understanding vaguely what they’re doing.

If you lay a sheet of white paper on an old gravestone, and sweep the tip of a pencil across it, you get one horizontal line, dark in some places and faint in others, and not very meaningful. If you move downwards on the page by a small distance, a single pencil-line-width, and repeat, an image begins to emerge. The process of working your way down the page in a series of horizontal sweeps is what a
nerd would call raster-scanning, or just rastering. With a conventional video monitor—a cathode-ray tube—the electron beam physically rasters down the glass something like sixty to eighty times a second. In the case of a laptop screen like Randy’s, there is no physical scanning; the individual pixels are turned on or off directly. But still a scanning process is taking place; what’s being scanned and made manifest on the screen is a region of the computer’s memory called the screen buffer. The contents of the screen buffer have to be slapped up onto the screen sixty to eighty times every second or else (1) the screen flickers and (2) the images move jerkily.

The way that the computer talks to you is not by controlling the screen directly but rather by manipulating the bits contained in that buffer, secure in the knowledge that other subsystems inside the machine handle the drudge work of pipelining that information onto the actual, physical screen. Sixty to eighty times a second, the video system says shit! time to refresh the screen again, and goes to the beginning of the screen buffer—which is just a particular hunk of memory, remember—and it reads the first few bytes, which dictate what color the pixel in the upper left-hand corner of the screen is supposed to be. This information is sent on down the line to whatever is actually refreshing the screen, whether it’s a scanning electron beam or some laptop-style system for directly controlling the pixels. Then the next few bytes are read, typically for the pixel just to the right of that first one, and so on all the way to the right edge of the screen. That draws the first line of the grave-rubbing.

Since the right edge of the screen has now been reached, there are no more pixels off in that direction. It is implicit that the next bytes read from memory will be for the leftmost pixel in the second raster-line down from the top. If this is a cathode-ray tube type of screen, we have a little timing problem here in that the electron beam is currently at the right edge of the screen and now it’s being asked to draw a pixel at the left edge. It has to move back. This takes a little while—not long, but much longer than the interval of time between drawing two pixels that are cheek-by-jowl.
This pause is called the
horizontal retrace interval.
Another one will occur at the end of every other line until the rastering has proceeded to the last pixel at the bottom right-hand corner of the screen and completed a single grave-rubbing. But then it’s time to begin the process all over again, and so the electron beam (if there is one) has to jump diagonally all the way up to the upper left-hand pixel. This also takes a little while and is called the
vertical retrace interval.

These issues all stem from inherent physical limitations of sweeping electron beams through space in a cathode-ray tube, and basically disappear in the case of a laptop screen like the one Tom Howard has set up a few inches in front of Pekka, on the other side of that wall. But the video timing of a laptop screen is still patterned after that of a cathode-ray tube screen anyway. (This is simply because the old technology is universally understood by those who need to understand it, and it works well, and all kinds of electronic and software technology has been built and tested to work within that framework, and why mess with success, especially when your profit margins are so small that they can only be detected by using techniques from quantum mechanics, and any glitches vis-à-vis compatibility with old stuff will send your company straight into the toilet.)

On Tom’s laptop, each second of time is divided into seventy-five perfectly regular slices, during which a full grave-rubbing is performed followed by a vertical retrace interval. Randy can follow Pekka and Cantrell’s conversation well enough to gather that they have already figured out, from analyzing the signals coming through the wall, that Tom Howard has his screen set up to give him 768 lines, and 1,024 pixels on each line. For every pixel, four bytes will be read from the video buffer and sent on down the line to the screen. (Tom is using the highest possible level of color definition on his screen, which means that one byte apiece is needed to represent the intensity of blue, green, and red and another is basically left over, but kept in there anyway because computers like powers of two, and computers are so ridiculously fast and powerful now that, even though all of this is happening on a timetable that would strike a human
being as rather aggressive, the extra bytes just don’t make any difference.) Each byte is eight binary digits or bits and so, 1,024 times a line, 4 × 8 = 32 bits are being read from the screen buffer.

Unbeknownst to Tom, his computer happens to be sitting right next to an antenna. The wires Pekka taped to the wall can read the electromagnetic waves that are radiating out of the computer’s circuitry at all times.