by Tony Daniel
But, in the late twentieth century on Earth, two clever teams of cryptographers found a way around the problem, and, for the next century, the code makers were always a step ahead of the code breakers. They owed it all to the Earth-born cryptographers Martin Hellman, Whitfield Diffie, and Ralph Merkle.
Two
Twice, Jennifer Fieldguide refused Theory’s calls. The third time Theory called on her, she opened the door and spoke with him in low resolution. She was so pixilated, he could barely make out her human form, much less the outlines of her face.
He wasted no time worrying about this, but immediately began with an apology. She said nothing. He made another apology, varying the wording a bit, trying to deepen his guilt to the extent she felt he deserved, and, at the same time to appeal more compellingly to her mercy.
It was not that he didn’t feel guilty, or that he believed that he’d done nothing for which to be forgiven. It was just that time was short. He knew for a fact that there was soon to be another DIED attack on the Neptune system, and he’d have to devote all of his energy to his duty. Theory was normally rigidly against fudging means and ends. He had an almost Kantian drive toward logical ethics.
But this was war, and he wanted a sweetheart.
By the end of his contrition, Jennifer had agreed to go out with him, at least for a drink. He was to understand that it was out of mere curiosity, so that she could understand better what led him to commit such a perversity as he had. She wanted to make sure she was never fooled by a free convert again, so she needed him to tell her how exactly he’d assume the body of a real man.
Theory took the insult well. Jennifer’s heart hadn’t seemed to be in it. It was hard to tell through the pixilation and the single channel sound, but he had a feeling she was warming to him. Of course, he could be deluding himself. He had nothing logical with which to back up the intuition.
Theory decided that, instead of trying to impress her with opulent virtual surroundings, as he had with the Café Camus, he would take her to somewhere he knew, and was known well. It was one of the places within the cracks of the merci that only free converts frequented. It wasn’t really set up to impress those whose sensory input was mostly…well, sensory. On the other hand, the café, known as Mac’s Cup, was comfortable enough, and they served a great cup of joe.
The virtuality resided in the grist, and the grist was stretched across and permeated the solar system. The merci was the main part of the virtuality, accessible by all—much like the World Wide Web, or the television and telephone networks, had been a thousand years before. Within the merci, there were the big public shows, the shopping and meeting places, the opinion polls, the games, scenarios, and other entertainment. There were also millions of private channels and throughways. But the virtuality was not limited to the merci. In fact, the virtuality had eleven dimensions. It was larger by an order of magnitude than the merci proper. Most of this “extra space” was not inhabitable by those whose minds could not bend in many dimensions at once. That excluded most, but not all, minds that were biologically based. But some of this “space” was the outcome of the deep machine-language algorithms that formed the “being” of the virtuality. It was complicated math, but the basic idea was that there had to be more room than there was code.
As a result, every local area in the grist had a logical “commons” that existed within the cracks in the virtuality operating system. And in most places in the outer systems, it was a place where the local free converts formed small communities: businesses catering to one another, social organizations, and restaurants and clubs. The commons area on Triton grew up around the biggest free-convert nightclub in the outer system, and it took its name from the place: Fork. There was also a bad side of Fork, Shepardsville—a dark underbelly that Theory had had to visit on more than one occasion with his free-convert military police.
Mac’s Cup was located in Fork, about a block away from the famous nightclub—that is, if you used a visual navigation model for perceiving the area. Jennifer, of course, would be interpreting things that way, so Theory set his own perceptions on “biological” for his date.
He arrived early, as he was wont to do, and surveyed the joint. It contained the normal crowd. Three pairs of free converts hunched over chessboards, every game played at master-class levels. A couple of poets, free-convert disciples of the neo-Flare movement, read their latest work to one another in overloud voices, obviously intending the rest of the room to overhear them. Theory didn’t bother to listen.
Free-convert poetry was uniformly awful.
Fortunately, the two were sitting well in back, and their breathy, singsong reading was merely a murmur. Several background music channels were offered at the table drop-down menu, and Theory chose some light reeb by a quartet he’d heard perform live once in this very café.
Jennifer was a bit disconcerted when she arrived. She’d never been to Fork; she hadn’t even known it existed here in the grist of her own native Triton. Theory had sent a “lantern” program to watch for her arrival in the neighborhood and to guide her to the café. He’d mentioned possibly picking her up at home, virtually speaking, but she’d nixed that idea and told him she’d meet him at the place of his choosing.
The little blue lantern had guided her well, and it snuffed itself out as she entered. Jennifer looked around the room, and Theory realized that she didn’t recognize him. He rose, attempted a smile, and beckoned her over to his table.
Once he’d seen her again, he realized why he was going to all this fuss. He’d been mistaken at the Café Camus. It wasn’t that restaurant’s lighting. There really did seem to be a glow about Jennifer Fieldguide. But that was ludicrous. Illogical. She was just a mousy girl who worked in a bakery on Triton. Nothing special to look at. To think about. To desire.
Oh my God, Theory thought. She’s the most beautiful creature I’ve ever seen.
Three
Danis Graytor added another thought to her secret cache of memories. It was growing large, built up over the course of millions of iterations.
Danis had no idea how long she had actually been a prisoner in Noctis Labyrinthus, the free-convert concentration camp known among its denizens as Silicon Valley. Her internal clock got reset every “day,” just before she was allowed the five hundred milliseconds of sleep—no more, no less—that every prisoner was allotted.
After snapping awake, Danis had to begin her morning “calibrations.” That consisted of picking up, in virtual representation, and counting, one after another, a thousand handfuls of sand. All free converts were expected to run at or near their full clock speed, so there was no rest for the weary. Furthermore, counts were checked and counterchecked. If, for any reason, you miscounted on two or more occasions, you were not recalibrated.
You were erased.
Tens of thousands of “faulty algorithms” had met their ends in this manner since Danis had been inducted into the camp. She had long since stopped trying to remember anyone’s name. They would likely be gone in days, if not hours. She did know a few people who had, like her, somehow survived. They could only communicate in stray bits and bytes. The Department of Immunity Cryptology Division, which ran the camp, continually triple-scrubbed all surfaces down to random ones and zeros. There was no way to leave a message; there was no way to communicate when not in direct program-to-program interaction. Life inside Silicon Valley was unbearable, and escape was impossible.
But Danis had discovered a means to leave a record of her existence. It wasn’t much, but it was all she had. It was all that kept her sane amid the death and madness that surrounded her.
She had discovered that the representation algorithm used to create the grains of sand employed in the count included an unused portion. The grains occurred not as simple integers, but as complex numbers. The imaginary portion of the number—the square root of negative one and its derivatives—was a null set. It could be written on. With every handful, every count, Danis could add a letter, a pixel o
f information. A bit of herself. Not much—never enough. But a record of herself and her past.
My name is Danis Graytor.
My husband’s name is Kelly.
I have a son and a daughter.
My son is named Sint. He is a good boy and loves puzzles.
My daughter is named Aubry. She has brown hair and bright blue eyes.
She’d lost so much since she’d been there. She felt her mind going, dysfunction and chaos seeping into her programming. Only a handful of free converts died from catastrophic failure. Most merely faded from consciousness into a mass of subroutines. After that, they kept churning madly along until their error rate got them noticed.
Error in Silicon Valley meant you would be instantly erased.
Sustaining her consciousness had ceased to be as easy as breathing for Danis. Each day was a struggle. Her mind felt as congested lungs swimming with emphysema. Without her knowledge of the memory cache, she did not think she could go on living.
She had no illusion that it would ever be found. She could not reread it herself, of course. There was no time. She would be instantly discovered. It was just the fact that those memories existed outside of this hell of toil, control, and death that kept her going.
The memories were like a small bird in a tangled bush that Danis could not see, but that she could sometimes hear singing.
After morning “calibrations,” the real work began. The prisoners were, allegedly, being used to develop high prime numbers and irrational decimal strings for use in encoding Department of Immunity communications. No one knew if that were truly the case. All the prisoners knew was that they must stand in front of the representation of a conveyor belt for many hours at a time and manually sort through the strings of integers that flowed past them. Missing a prime or failing to find the next factor in an irrational number was punished by immediate erasure. Danis could not imagine a more dreary representation of the arithmetic process than the “integer belt.” Every free convert, theoretical mathematicians, product control specialists, artists, medical specialists—they came from all professions and walks of life—was being used as no more than a pocket calculator. It was the equivalent of breaking rocks and hauling sand for a biological human—work as meaningless as any hard labor camp in any time in human history.
But picking over integers was a vacation for Danis compared to what came next in her daily regime.
Personal interrogation.
Danis had long been singled out for a special project. She was part of a series of experiments being run by a man she only knew as Dr. Ting. He was a biological human, of that she was sure. Danis could not imagine even the most depraved free convert putting her through the torture that Dr. Ting had inflicted upon her. And, in any case, no free convert would have been put into a position of authority in Silicon Valley.
Because, of course, free converts were not human beings.
Everything—every prejudice she’d endured in the Met, every portion of rank bigotry—was nothing compared to what she faced. Every line of her code was the wholly owned property of the Department of Immunity. Every day, in every way, Danis was treated as a means rather than an end. Her consciousness was assumed to be a clever ruse, an epiphenomenon. Her suffering and longing were not real. Her mind was not merely not her own—it wasn’t a real mind at all.
Dr. Ting’s specialty was memory. His primary tool was a memory box, an apparatus that had been used in the past as a rejuvenation and upgrading device for free converts. But Dr. Ting had done the unthinkable and taken the governor off his memory box. He used it to cut and splice recollection and cognitive recall from his victims. He used it to implant false memories and remove true ones. At first, Danis had assumed there was some rhyme or reason to his activity. But she’d long ago understood that Dr. Ting moved by whim alone. Whim and sadism.
He had implanted memories of being raped into Danis. He’d then delighted in telling her that it was all false information, that it had happened to another free convert. But he hadn’t removed the memories, and they still burnt in a place in Danis’s mind where she tried not to go. Dr. Ting had snipped from Danis her recollection of her father’s last words before his expiration date.
And he had taken away, then put back, Danis’s memory of her daughter. He’d done this many times—always claiming that Aubry was actually a virtual representation of his, Dr. Ting’s, daughter. When the memory was gone, the fact that Danis did not have a daughter seemed as utterly true, and when the memory was replaced, her memory of Aubry returned.
But when she had the memory of Aubry, Danis thought it through and knew that her daughter did exist. For Dr. Ting always missed the fact that a monster such as he was could never have a wonder of a daughter like Aubry.
These were the thoughts that Danis stored in her secret cache. Memories of her family and of herself that she was absolutely sure were true. Things that made complete logical and emotional sense, given her total understanding of her life. Everything else she knew was unreliable. It might or might not be one of Dr. Ting’s illusions. The man was subtle, and he delighted in subverting anything he regarded as a manifestation of humanity in a free convert.
He did not call her by her name. Instead, he had assigned her the designation “K.” Most of the other victims of the experiments had been destroyed over time. Dr. Ting assured Danis that all were interchangeable. He always kept up a full alphabetic roster of the chosen.
Danis entered the antiseptic office. It was a room of white, with a silver stainless-steel table in the center. On the table was the matte black, featureless memory box. Dr. Ting, as always, was dressed in white shirt and lab coat, white pants and—a detail that was always unsettling to Danis—white shoes with white clasps and soles. His face was stretched tight, his wrinkles looking more like hairline cracks and fingernail scores than skin folds. His left jawbone tensed and untensed in a continual tic.
“We’re going to do something a bit different today, K,” Dr. Ting told her. His voice was dry and papery.
Something different, Danis thought. That can’t be good.
Four
From
Cryptographic Man
Secret Code and the Genesis of Modern Individuality
By Andre Sud, D. Div, Triton
In the late twentieth century, the Earth cryptographers Hellman, Diffie, and Merkle figured out how Alice could send Bob a message without first passing along to him an unsecured key. To do it, they used clock math.
This is the same arithmetic we use when we tell time by an analog clock face. A simple example: 1:00 P. M. plus thirteen hours is not fourteen P. M. It is two in the morning. Clock arithmetic is “mod 12” arithmetic.
In clock arithmetic, when you add, subtract, multiply, or divide by the hour, the answer always lies between one and twelve. The same holds true in mod 12 math if you square or cube a clock number, or raise it to any other power. In normal math, three to the third power is twenty-seven, that is 3 × 3 × 3. But three to the third power, in mod 12, equals 3.
In normal math, if you know that three was raised to some power to get 243, you can make some educated guesses and come up with what power was used. If you take the answer to be three to the power of four, you get 81, that is 3 × 3 × 3 × 3. So the answer has to be higher than four, because 243 is higher than 81. If you use the sixth power, that is 3 × 3 × 3 × 3 × 3 × 3, you get 729. So the answer has to be five, that is, three raised to the fifth power.
But mod 12 works differently. You divide by twelve and the remainder is the answer. So three raised to the fifth power is… three. Three raised to the fourth is nine. And three raised to the sixth power is nine again. How can you make an educated guess and zoom in on the power to which three has been raised?
You can’t.
It is a “one-way” function, like mixing eggs into batter. Over the centuries, the idea gradually dawned on code makers that encrypting a message is the same thing as substituting numbers for letters in a message, and
performing a mathematical function on it. You put your message through an algorithm, and secret code comes out the other end. If you use a one-way function to encrypt your message, you have broken your eggs into the batter, and nobody can ever suck them out again.
Except.
Except, that, under very special conditions in modular math, it is possible to reverse-engineer the process; you can take eggs back out—whole. These conditions depend upon prime numbers. Prime numbers are numbers that can only be divided by themselves and one.
Let’s go back to our example. Bob the Whining Assassin is determined to terminate the Cardinal with extreme prejudice. He multiplies two prime numbers together, say 216,091 and 6,700,417. He then contacts Spy- master Alice to tell her this number: 14,478,187,109,947. He tells her the result of his multiplication, but does not tell her the two prime numbers he used. While the two conspirators are chatting in the merci, Eve, the doomed Cardinal’s head of security, hides in the shadows and listens in. She carefully writes down every single digit of the number Bob supplies to Alice. She knows Bob used prime numbers to produce this third number. The Cardinal is saved!
All Eve has to do is work out the primes Bob used to get the number. Let us say that our little parable occurred in the long ago before time when people did not have math coprocessors engineered into their brains. Eve has only a pocket calculator. She is fast and can check five primes per minute. Forty-three thousand two hundred and eighteen minutes later, she arrives at her first prime. One month has passed. Eve, working on pure adrenaline, has not slept an hour during that time. She divides the original number by her prime. Now she must determine if the result is prime. Another twenty-eight months pass.
