Tetraktys | Ari Juels | Talks at Google

Steve: Welcome everyone. I’d like to welcome our speaker today, Ari Juels. Ari is the head of RSA Laboratories which is part of EMC and he’s written a fiction book about a young cryptographer who stumbles upon a plot involving ancient cults and a lot of intrigue And a little background of Ari. He’s actually a, has a background in Latin literature and mathematics and graduated as a Ph.D. from Berkeley, and surprisingly his main character is also a Ph.D. from Berkeley with a background in classics So I’d like to just turn it over to Ari and welcome him to speak about his book [applause] Ari Juels: Thank you, Steve, and thanks to all of you for coming today Many first time novelists support themselves with day jobs and I’m no exception. As Steve mentioned I work as the Chief Scientist of RSA Labs, the research arm of RSA, a company that some of you are probably familiar with My lab’s research is on computer security and cryptology, encryption and other techniques for protecting computer systems So my day job is like that of many of you in the audience. But I want to stress that my novel isn’t written for computer scientists It’s written for readers; for ordinary readers So there’s a tiny bit of math in the book, but not very much and there are only two lines of pseudo code in the entire novel I am going to talk to you a little bit about computer security and cryptology because they loom large into ‘Tetraktys’. But of course I’m not wearing my RSA labs hat and I’m not gonna talk about research I’m gonna talk to you instead about a collision of worlds between ideas in modern cryptology and the vision of a philosopher in ancient Greece At first glance, computer security and the ancient world don’t seem to have much to do with one another. But by the end of this talk I hope you’ll see how these two worlds are coming together and how in the light and heat of that collision the adventure and mystery story ‘Tetraktys’ was born Probably the first question for most of you in the audience is, “What in blazes does the word ‘Tetraktys’ mean?” And, and of course I’ll get to that I feel that book talks for fiction at least are kind of a tricky proposition. When a bakery wants you to buy a cake they give you a sample But a book isn’t like a cake; one bite of a cake tastes like the rest of the cake. But one chapter in a book doesn’t taste, as it were, like all of the others So what I would like to do instead, is to try to entice you with something more atmospheric Call it the aroma of the book I am going to read some sample passages, but I’m gonna give you a good deal of background for the story and a little bit of visual support in the form of just a few slides I’m pretty sure I’m not the first novelist to use Power Point and this may be a somewhat dangerous thing, but I hope you’ll bear with me Okay. So our story begins with some strange computer infiltrations. We’re not talking about vanilla hackers stealing credit card numbers or about foreign powers spying on corporations like the Aurora attacks that you’ve been dealing with here at Google. It’s much stranger than that The book opens with a passage about an Assistant Secretary of State named Helen Abel and she’s simply having a little problem with her calendar So let me read the first chapter to you. I’ve truncated it a bit [pause] “Helen Abel, Assistant Secretary of State for European Affairs, looked gradually into the distance from a 17th century chateau She visually traced the sandy avenue that ran the access of the vast gardens. Beneath her lay two garden beds embroidered with green arabesques of faultless symmetry; low trimmed hedges winding amid a soil of rich, reddish brown. These great carpets led from the terrace of the chateau to the center of the gardens where circular fountains sent aloft a towering plume of water. Beyond lawn stretched smooth and green around basins in which rings of jets gave forth aqueous crowns. Near the horizon, the Grand Canal spread its thin mirror of water under a tiny portico Still further in the distance, visible as a notch in the trees, was yet another rectangular lawn thrusting the strict ethic of geometry into the surrounding forest up toward the sky The only inhabitants of the garden were statues disposed here and there in decorous solitude; French ghosts of Roman copies of Greek originals; gods and heroes, Diana, Venus, Jove and Apollo, stone animated with the memory of motion She’d been leaning into the huge monitor on her desk to immerse herself as thoroughly as possible. She now tilted back into the chair behind her smoky glass helm and looked again at the screen. She really shouldn’t be spending so much time fussing with these videos

On vacation in France the previous week after a Summit she’d fantasized about a woman, what a woman of her status might have been centuries ago. Not a senior bureaucrat, but a great and noble lady. She’d looked at costumes, jewelry, palaces and gardens and spent many thousands of dollars on antiques and reproductions in Paris She’d even bought an 18th Century tiara set with diamonds and sapphires. While other tourists were only able to look uncomprehendingly and snap photos, she had beheld her own reflection in the glass cases of the museum aptly superimposed upon the jewels, dresses and other treasures within But now it was back to work. She had a staff meeting in an hour. She turned to the black viper-like microphone rising from the pool of glass that was her desk. ‘Calendar’ she commanded The garden dissolved from the monitor giving way to the page of a calendar scattered with flags and icons, somewhat like a military map. A warning message highlighted by a gaudy red bar blinked at the top of the screen and a window popped up: “Reminder missed appointment.” What appointment could she have missed? Had she simply neglected to click on reminders early in the week or did her admin screw up again? She spoke again in the direction of the viper “Go to missed appointment.” The screen turned a gray blur; a sound like pouring rain saturated the speakers; the calendar software made page turning noises with each traversed week; and the weeks now whished stormily backwards In the corner the year was still displayed, but the last digit dropped quickly, three, two one, zero, nine, eight; the second digit also moved backward though more slowly ‘Stop,’ Secretary Abel shouted. The year stood at 1965; the week was empty of meeting. ‘Go to missed appointment,’ she repeated in annoyance Hand it to Microsoft that was one hell of a bug or worse could it be a virus? The furious patter of flipped pages resumed She watched the slowly receding decade digit, 1950s, 1940s, 1930s; the century was rounded and then 1890s, 1880s, 1870s. ‘Stop,’ she cried again, freezing the year at 1872 ‘Christ,’ she thought, ‘maybe it was something worse than a bug.’ She spoke more loudly and precisely, ‘Go to missed appointment.’ The vertiginious backward sweep resumed This time she watched in bewildered passivity It had never occurred to her to wonder, ‘how far back do these calendars actually go?’ 1830s, 1820s, 1780s, 1770s, 1760s; the noise ceased abruptly and a page appearing, appeared displaying the week of 10th June 1754 and fixed itself on the screen A new message appeared, ‘Missed appointment Should the Office Assistant schedule a new one?’ In fact several appointments over the course of the week were marked as missed The latest of these on a Friday evening flashed She had enough French to read, ‘Ball at the residence of Monsieur deCarzeneau Saint-Germain-des-Pres.’ Saint-Germain-des-Pres was a station in the Paris Metro, that she knew. She had no idea who Monsieur deCarzeneau was She explored nearby entries on the calendar looking for evidence of a bug in the software There were so many appointments that it seemed as though somebody else’s life had been accidentally grafted into an unlikely part of her calendar ‘This was like finding a hidden passageway in an old house,’ she thought. ‘Rather fun, actually.’ It soon became clear why the ball along with many other social engagements had been missed It appeared that the owner of this portion of the calendar had become bedridden with a long illness. The ministrations of a Doctor Dachmoi and a Doctor Parre had began in April of 1754. They’d progressed from regular to frequent over the course of May. By the beginning of June, these doctors were in constant attendance Had Secretary Abel’s historical medical French been richer she would have deciphered descriptions of a vigorous regimen of cupping, bleedings, and the administration of poisonous metals These medical rigors culminated on the 15th of June when the patient had her last appointment in the book. This was annotated ‘la mort’, death. The 15th of June she observed was her birthday. The fun took an unnerving turn She went further back; there were dozens of trivial engagements which seemed vaguely but impalpably to trigger memories. Then on the 18th of December 1730 there was Aunt Jean’s funeral. Could she remember the day, the weather? Was the low hanging gray sky a post-dated symbolic trick of memory? Her sister to whom she hadn’t spoken in three years called to tell her that Aunt Jean was dead. Two weeks later a lawyer hired by her sister called to tell her that there was a crazed boyfriend of sorts in the picture, and she remembered her disgust at how the word ‘boyfriend’ was used to describe the 80 year old man The lawyer was trying to pry the old woman’s legacy away from this interloper. The boyfriend wanted to funnel it to a church Times had been difficult in these early days when she was getting her Master’s Degree The aunt had been a wealthy widow, a fragile octogenarian Even while her aunt was living, she had never been entirely successful fending off daydreams of an inheritance. She almost never saw the old woman who refused to leave the Bronx where Helen herself certainly wasn’t gonna go The aunt had sent fifty dollar checks in garish greeting cards on Helen’s birthday and on holidays. Helen had always sent back dutiful thank yous. She simply hadn’t noticed that

nothing had come from Aunt Jean for a year and a half Her sister having gone to clean out the apartment and called her again. The old woman it turned out had been a miser and a packrat and had lived in squalor. The apartment was a morass of burned out light bulbs, moldy wallpaper, broken radiators, crumbling plaster, heaps of old newspaper waiting to catch fire, mice and tattered doilies, amid a miasma of dust, furniture polish and urine Helen had felt unspeakably guilty and had palliated her guilt by telling herself that the old woman had never asked for her help The calendar, however, made a firmer accusation In a matter of fact way, like a reminder for a lunch appointment, which it was, the entry read, ‘Poisoning of Aunt Jean.’ ‘No,’ she protested out loud. ‘No, I know what that means. That’s a lie.’ She shook her head ‘It wasn’t my fault,’ she said to herself ‘If she’d ever asked for help ever, I would have helped her.’ She dug angrily deeper into the calendar What other accusations were there? She read and reread the calendar entries trying to ferret out all of the secret correspondences If a history of the grand dame matched her own, then she had only two more years to live Her antecedent had died at the age of 49 Her meeting was beginning in a matter of minutes Bewildered and exhausted and paying little attention to what she was doing, she made her way back to her own era Instead of keying the current date into the computer, she held down the forward arrow key with her index finger. The weeks advanced; the years hastened by, 1750s, 1760s, 1770s, 1780s. She traversed the blank corridors devoid of appointments of the late 18th, the 19th, the early and mid-20th century. From Aunt Jean’s funeral and the balls, fetes and deaths, back to her own epic Rounding her birthday in the year 1970 she came upon the following entry: ‘an. 1970 – an 1754 = 215 = 63 hic incipit saeclum vitae novum. [Here begins a new cycle of life.] Reincarnate.'” [sound of pages turning] Attacks like this against Secretary Abel multiply as the story gathers pace. There are strange references to reincarnation, numerology, like the game here with dates that Helen Abel came across, and vegetarianism. The attacks become so serious and widespread that the National Security Agency gets involved. And what do they find? They trace the attacks to what seems to be a cult of followers of the ancient philosopher Pythagoras who was active in the sixth century B.C. So you see a, a bust of him here Now we tend to think of Pythagoras as the fellow who discovered the Pythagorean theorem which, which in fact he probably didn’t, but you’ll remember we learn about this theorem in school; it’s a theorem about right triangles You see it here; a2 + b2 = c2 But Pythagoras was actually much, much more than just a small torment to junior high school students. He really was a philosopher in the broadest sense of the word. And in fact he’s even credited with coining the very word “philosophy.” He and his followers created one of the earliest notions of a political utopia and actually seized control of a city in southern Italy to try to realize this, this vision But getting back to mathematics. It was a very strange affair in Pythagoras’ day. It was in many ways more like sorcery than science We don’t have a terribly accurate picture of what Pythagoras and his followers were like, but in some ways they weren’t all that different from the people you might come across say across the Bay in Berkeley For instance, they were probably vegetarian; they believed in reincarnation. In fact they believed in transmigration of souls; this idea that you might die and wake up a cow or a house cat. And they wore unusual clothing Pythagoras, for instance, wore a white robe and a gold diadem. And Pythagoras himself may actually have claimed to be an incarnation of the god Apollo They had other habits we can’t begin to understand and probably never will. Some of their maxims have come down to us. Some are sensible, like for instance, one of their maxims was “Eat not in the chariot.” In other words, don’t eat while you’re driving. Others are just weird and foreign, particularly if you’re vegetarian, like keep away from the vinegar bottle; an inscrutable one that They considered it a crime to throw stones into fountains and they said, “No matter you do, don’t ever, ever catch a cuttlefish.” Really strange stuff But one thing they believed in makes them a lot like us, given how our world is pervaded by computing. In particular, they believed above all in the primacy of number. They believed that numbers were the fabric of the universe and they believed this in a way that resonates particularly well in our digital world [pause] So this idea about the supremacy of number was encapsulated in a sacred symbol for the Pythagoreans called the Tetraktys; you see it up here The tetra part as you may have guessed means four. There’s really no good translation for the full word ‘Tetraktys’, perhaps the best translation is something like the essence of fourness

Anyway you see it’s a pyramid of ten dots aligned in four rows. This one symbol for the Pythagoreans embodied the foundations of the universe So let’s start with music, for instance. We number the rows as here. And now look at the ratios that those numberings define; the three different ratios defined by the Tetraktys Well, let’s start with a ratio 1:2. If you take a string and pluck it; let’s suppose it produces the note C; and then you take that string and you exactly double its length, you’ll again get the note C, only it will be one octave lower. So the ratio 1:2 in the Tetraktys defines the octave Similarly the ratio 2:3 defines the interval of a fifth; roughly speaking that’s a span of five keys on the piano. And 3:4 defines an interval of a fourth; roughly a span of four keys on the piano. That’s in a, a differently tempered world but I won’t get into that So with this reasoning the Tetraktys encapsulated the basics of, of music and consequently the idea of the harmony of the spheres; the resonant substance of the cosmos, the universe The Tetraktys also encapsulates the basics of geometry and I’ll just go through this very quickly The first row is, is a point; zero dimensions The second row contains two dots; you connect them you get a line; that’s one dimension The third row contains three, they form a triangle; two dimensions. And the fourth contains four dots; if you connect them up like this you get a pyramid; three dimensions So all of the known dimensions of our universe, the ones that we experience at any rate, are encapsulated in the Tetraktys. So you can think of the Tetraktys as being a little like our periodic chart in chemistry or perhaps even a little like string theory, only much cruder and, and much more powerful [pause] So the Pythagoreans are the villains in our story, if they really are villains, which isn’t at all clear. Now of course the National Security Agency isn’t accustomed to dealing with incarnations of the god Apollo, so they bring in an un, unusual young man named Ambrose Jerusalem Ambrose is finishing up his doctorate in computer science just across the Bay in, in Berkeley, but he’s unusual in that he was home schooled by his father, a classical archeologist. A really intense guy who would even taste the dirt and artifacts to make sure that they were authentic Ambrose is exactly what the NSA needs because he straddles these two worlds; the worlds of computer science and antiquity To give you a sense of what Ambrose is like, I’m gonna read another passage. This is a passage in which Ambrose has been approached by the NSA, and he’s remembering the things that his father told him when he was a child; the things about Pythagoras in particular And again I’ve truncated the, the chapter somewhat here [pause] [sound of pages turning] “Outside of the two crowded tourist seasons—midsummer, and a space of two weeks around the peak of the fall foliage—Dorington was a picture-book specimen of rural New England. Even as natives of the region, if not the town, Dr. Jerusalem and his nine-year-old son felt a sense, a heightened sense of charm as they walked a dirt road away from the town center. The town consisted of a clutch of white, wooden buildings: a clapboard post office, a general store, and a patterned New England church with a single steeple atop a square base.  (Savoring the irony, Dr. Jerusalem pointed out that such churches were modeled on the architectural template of an English Catholic.) The ground was still sodden in late afternoon The trees turned forth cold, luxuriant greenery touched here and there with hints of autumn Ambrose’s photojournalist’s vest—his favorite piece of clothing, with the pockets of the many treasures—was just warm enough The bleak weather seemed to embalm the isolated houses in a way that brought a cozy pleasure to him. There could be no vain scrambling to find one’s destiny, here. It lay not more than five feet from the fireplace, as in ancient years. His father frequently set Ambrose ruminating on civilizations tens of centuries old, on the frenetically unfolding, spreading, and splintering empires of the Mediterranean. Several times together they had visited archaeological sites. Now, as then Ambrose ran his mind over the traces of antiquity. The jewelweed and blank yellow and copper leaves scattered on the forest floor, the broken stone walls and raw timber of old buildings evoked, if they did not resemble, the altars and groves of ancient Greece or Italy They approached the edge of a pasture enclosed in wire, in which horses grazed. Dr. Jerusalem bounced the back of his hand on the top wire, the ends of which stretched between white plastic cylinders on wooden posts. ‘Not electrified,’

he said. A dappled gray horse came over to them, and Dr. Jerusalem stroked it under the forelock. The animal awkwardly tilted its head up and down, as if unsure how to nod approval and enjoy the scratching at the same time. Dr. Jerusalem encouraged Ambrose to pat the horse’s head Ambrose said, ‘It’s an intelligent horse.’ ‘Yes she is. A beautiful mare,’ his father replied stroking her head. ‘There’s soul in those eyes.’ ‘Maybe there’s a person trapped in the horse like in the story I read by Apuleius. He was turned into an ass though. That’s like a donkey.’ Dr. Jerusalem laughed, ‘Yes, so maybe this is some Russian empress who according to the great wheels of cosmic justice was reincarnated as a mare.’ He chuckled at his private joke ‘Reminds me of Xenophanes’ story about Pythagoras and the dog. Have I ever told it to you?’ ‘I don’t think so,’ Ambrose said seriously ‘Pythagoras was the ancient philosopher who coined the word “philosophy.” He also invented—or at least popularized—the Pythagorean Theorem Yes, I know you know that already. Well, the Pythagoreans thought of numbers a little like we might think of gods. Pythagoras himself was a bit of a loon.’ ‘How?’ Ambrose asked in surprise ‘Well, one story goes like this: He was walking down the street in Kroton—in southern Italy—one day, when he saw a man kicking a dog. Normally, this wouldn’t have bothered anyone in the ancient Greek world. But Pythagoras was different “Stop,” he shouted at the rogue. “Stop that at once! This dog is a friend!” Pythagoras explained that the dog was a reincarnated friend from a previous life. He recognized him by his bark.’ ‘Did he take the dog home?’ ‘A very good question. But that’s the whole story. My guess is that Pythagoras had probably collected too many friends at home as it was, and I doubt his wife appreciated it—although Theano herself was also a formidable philosopher I’m sure the dog kicker was stunned, and left his dog alone for at least a few days.’ ‘How cruel!’ said Ambrose. ‘Pythagoras should have taken the dog home with him. Is that why he didn’t eat animals?’ ‘You mean why he was vegetarian?’ ‘Yes.’ ‘That may be a myth. But almost everything about Pythagoras is a myth, Ambrose. All we know with anything approaching certainty is that he was some kind of genius—and that he abstained from eating beans and ox hearts It’s not impossible that he was a vegetarian, though.’ Father and son fell silent. An old pickup truck with a wood-railed cargo space drove by, forcing Ambrose and his father to the edge of the road. Damp, colored leaves glistened on the forest floor like the shiny coat of an exotic, broad-backed creature. Ambrose mused, ‘I wonder whether I’d remember if I’d been a horse in another life.’ ‘Do you?’ Dr. Jerusalem asked. ‘What would you remember?’ ‘I don’t know. Maybe my pasture. And people petting me. And how hay tastes.’ ‘I’ve raised a confirmed Pythagorean then Do you know the Pythagoreans tried more or less just that?’ ‘What do you mean?’ ‘They used to perform exercises to improve their memories. Every evening, Ambrose, they would try to recall all of the events that had occurred over the course of the day. Imagine it. They’d try to recollect finer and finer details: faces, clothing, what they ate, whom they saw. A word that a friend deftly pulled out of a hat in a conversation on philosophic doctrine in the morning. An odor that wafted with the midday breeze near the western entrance to the agora. Variations in the shapes of the clouds during the afternoon before a storm broke. How the texture of their tunics felt from hour to hour. Then they’d try to extend their recollections to more and more distant times: previous days, weeks, and years. They hoped, eventually—they claimed in certain cases, as Pythagoras did—to recall events from former lives.’ Again they walked for a long time in silence The sun set and the sky began to glow. Ambrose tried forcing on himself a consciousness of the texture of his clothing. He attuned himself to the places where it touched, brushed, or lay lightly on his skin. He felt his stomach rumble. As he turned his attention upward to the orange evening sky, he felt a ghostly attraction to the place—or rather, its tutelary spirit—a desire to embrace it, to sleep by its side. He didn’t know what this meant, and he could not articulate it. He could only experience the bagful of sensations and submit to a feeling that was too grand and tenuous, predicated too glimmeringly on a slant of light, for him to possess He felt as if his father would glibly discouraging something important. But he had no way to protest ‘So do you think the feelings are lies? Are they bad?’ ‘No, not bad, Ambrose. Quite the opposite They’re too important to be badly handled The successors to the Pythagoreans went wrong They tried to reduce them to a superstitious system, to explain these poetic and highly individual experiences in terms of a simplistic universal, like reincarnation or numbers I can’t prove it, but the original Pythagoreans to my mind clearly believed in living in the world. Memory—historical, personal—of course it’s the substance of life. Without that depth of perception, we’re Cyclopes, one-eyed monsters. But today we replace our human memories with computer memories, with exomemories and exominds. That spells the death of nostalgia, the loosening of the deep

cord with which an ancient ruin or this spot of countryside resonates in you, Ambrose Recall that “memory” in Greek was the mother of the muses.’ ‘I know.’ ‘The world is placing less and less value on such things. Fewer and fewer people with memory these days. Memory has been shunted off to a nursing home. The muses will follow soon. I have you learn poetry by heart to nourish your spirit and your mind—to glue it to your soul, Ambrose. That’s just one reason I’m educating you yourself. Do you understand?’ ‘I think so.’ ‘Do you know the famous poem by Frost about the two paths that “diverged in a yellow wood”? The Pythagoreans called it the Furca Pythagorica, the Pythagorean Fork. They represented it by the letter upsilon. Upsilon resembles our capital letter Y, right? It’s forked. You will face the Furca Pythagorica many times in your life, Ambrose. I’ve led you down a different branch of the fork than nearly anyone else will follow.’ Ambrose looked at the road behind them which lay straight as far as the eye could see He held up two fingers as though in a sign of victory ‘What happened to them?’ he asked. ‘To the Pythagoreans? They chose the wrong branch?’ ‘The Pythagoreans were the original utopians, Ambrose. Bringers of the gods’ fire to Earth, if you will. The first aristocrats in the true sense of the word. I don’t mean lazy snobs from privileged families with a ‘de’ or ‘von’ in their names. Just the opposite I mean that they tried to create a community of aristoi, the ‘best’—noble, wise, elect guardians of civilization. It was too much. Most of Pythagoras’s followers couldn’t understand. Pythagoras had unearthly mental gifts and vision. He was strange; he was godlike Some of his early followers forgot what they learned. Plato, Augustine, More, Jefferson—they all owed a debt to Pythagoras. They remembered some of the important teachings. But too many have forgotten.’ Dr. Jerusalem stopped and put his hand on Ambrose’s shoulder. ‘I sometimes lose sight of how young you are. But this is one of the burdens I’ll have to place on your shoulders We’ll make sure that you don’t forget entirely. You’ll be rooted in other times and places. It ‘s the only way to understand your own. You’ll be one of the last with the gift of a classically educated mind, Ambrose The barbarians are again sweeping over the land, and it’s time to retreat to Hibernia—to bide our time across the sea. Perhaps the aristoi will come again. But perhaps you’ll be alone.’ [pause] [sound of pages turning] Now where does the mathematical view of the Pythagoreans come together with modern cryptology? In other words, why is Ambrose at the right intersection of ideas? The NSA believes that the cult of Pythagoreans has used its mathematical prowess to break a cryptographic algorithm known as RSA; many of you are probably familiar with it. Named after its inventors at MIT in 1977, Rivest, Shamir and Adleman. Here’s a picture dating from that decade obviously. Some of you will see a nice little joke on the blackboard there Most of you in this audience probably know that RSA is a real algorithm used in nearly every computing system in the world today It operates, for instance, when you send your credit card information over the Internet and a little lock appears in the corner of your browser, as, as here So breaking RSA would compromise computing systems in a devastating way. It would basically undermine the whole trust infrastructure of the Internet. In fact at this very moment about a mile away at the Moscone Center, the RSA Conference is taking place. This is a huge industry conference staged every year by the company RSA, and Rivest, Shamir and Adleman are probably there at this, this very moment Now you see here the basic formula; one of them for RSA m = cd mod pq. It looks a little like e=mc2, right? It’s got the same sort of simplicity and, and elegance Now the Pythagoreans believed in the power of a very particular type of mathematics, based on integers. And closest in spirit to what we would call number theory today. Mathematicians who specialized in this area used to pride themselves on studying the most useless form of math. They believed that their discipline enjoyed a kind of peerless intellectual purity We know that calculus is useful, but they asked themselves, “What possible use could there be for things like prime numbers?” Well Pythagorean ideas about numbers and their supremacy; all this numerological gobblygook seems little silly at first blush, but Pythagoreans were even writing prayers to numbers like their Tetraktys. But the earth shook under the feet of those number theorists a few decades ago. Prime numbers suddenly found a use; protecting secrets, cryptology So these number theorists found themselves whisked away from their ivory towers into the fortress of the NSA Now Ambrose realizes that as computing gravitates toward the center of our universe and cryptography

spreads, the whole Pythagorean idea of prowess in number theory, of secrecy and so forth, doesn’t seem so far off base any longer. Pythagoras said famously that the universe is number and he meant it in a mystical way. Well cryptology directly links the knowledge of numbers with the unraveling of secrets and control of what we might even think of as divine forces, in a loose sense. So it gives body to the mysticism [pause] As many of you know, to break the RSA algorithm all you have to do is solve the following very simple problem. I randomly picked two numbers, call them P and Q. I generate them behind my back and I multiply them behind my back. Now these are prime numbers; they’re divisible only by themselves and one, as, as many of you know So we’ll call the product of these two integers N. So now what I do is I give you N and your task is to figure out the original P and Q, as it were to split this number N When P and Q are very big, and so therefore when N is very big, this problem is believed to be very hard; and by big I mean really big. Here’s, here’s an example of what N might look like in the real world So this is the cornerstone of the RSA algorithm; this problem of factoring as it’s called And this is the problem that the NSA thinks that the Pythagoreans have solved in order to crack the RSA algorithm As the story gathers pace, messages like the one that Secretary Abel came across multiplied Other powerful people start to be menaced So how do Ambrose and the NSA sleuth out the identities of the Pythagoreans? They use a number of techniques: there’s classical scholarship; there’s gumshoe sleuthing; and computer forensics also come into play So let me read a last bit from the book. This, this bit needs a little bit of explanation The messages left by the Pythagoreans like the one left for Secretary Abel have been essentially flawless, but Ambrose and the NSA noticed a typo in one of them. In one message the word “Syracuse,” like the name of the town in upstate New York, which is also the name of an, a city in the ancient world, Greek city, is misspelled. Somehow the letter “e” dropped off the end and they ended up with Syracus instead of Syracuse It’s a tiny, tiny clue, but it turns out to be critical So in this passage there’s a conversation taking place between Ambrose and Rochelle his supervisor at the NSA [pause] [sound of pages turning] “Ambrose prepared another list of books and they again sent out to the library. In the meantime he read about the history of Huron and the City of Syracuse extracting what he could from the reference books on hand. Rochelle searched the Web to learn some rudiments ‘Look here. I found a portrait,’ she announced, swiveling her monitor to show Ambrose photographs of the two sides of a silver coin on auction The reverse depicted a galloping cavalryman carrying a sphere. The obverse showed a beardless man in profile with a prominent round chin and a small ear; his curly mass of hair bound in a slender band tied from behind ‘He looks young for a king.’ ‘That’s thanks to Alexander the Great. He started the vogue in boyish looks for conquerors.’ ‘Apart from that,’ Rochelle said, ‘every Website has the same historical snippet on Huron Nothing more than you told me. Any luck on your end?’ ‘No. Not yet.’ ‘Really, Ambrose. Are we chasing our tails? Can one letter really mean all that much anyway? Syracuse, Syracus. Is it really such a big deal? Couldn’t it just be a spelling error or a typo?’ ‘It could be a typo. In that case it may not mean much, but every other piece of writing we’ve seen from the neo-Pythagoreans or that I have at least, has been more or less flawless.’ ‘True. But a typo?’ ‘That doesn’t answer your question, does it?’ ‘Can a single letter be important?’ ‘Yes, absolutely.’ ‘There’s a town in northern Italy called Cortona Ancient tradition asserts that the tomb of Pythagoras lies there. But Pythagoras probably never visited northern Italy. It was a mistake Somebody confused Cortona with Cratona, the Latin name for the City of Crotone in southern Italy.’ ‘In classical literature these little errors are everything. For example, the original name of the author The Aeneid was Vergil, that’s spelled v-e, but then in the Middle Ages when he was believed to be a magician of some kind, it became Virgil, v-i. You can tell a Brit from an American by his spelling For instance, the Brit spells it v-e, while the American spells it v-i Where it gets especially interesting is in Medieval manuscripts. Everyone has spelling

errors and they’re like differences in DNA; they mark time and pedigree and they allow philologists to date manuscripts and place them at a kind of family tree.’ ‘So you’re hoping that this missing “e” may be our key DNA marker? Was Syracuse every spelled Syracus by the Greeks?’ ‘No. I’ve looked it up in Little and Scott There were several variance on the name in Greek, the Ionian Syracusi,’ Ambrose said He continued, ‘And also the Doric and others I’m pretty sure that Syracus is the modern German spelling, but I just can’t see any reason for writing Syracus in English.’ ‘I see. So to put it in your terms, the word Syracus is a mutation of some kind.’ ‘Well, yes,’ Ambrose replied. ‘I suppose you could say that.’ ‘But that makes it distinctive, you see?'” [pause] The NSA ends up plunging into various types of computer forensics to figure all of this out and actually a remarkable thing happened while I was writing this story. I was making up certain forensic techniques in Tetraktys to track down the Pythagoreans as it were, when this patent suddenly surfaced describing exactly the techniques I was developing in this fictional context. Only I hadn’t filed that patent; it was the NSA. So it’s just one of these wonderful coincidences I guess I, I happened to, to divine what the, what the NSA was up to as I was writing this story As the story evolves, the Pythagoreans gradually infiltrate many parts of the world online and off. Lottery numbers get changed; airline schedules are modified; and some great event seems to be coming to a head But it’s not clear whether the Pythagoreans are a malevolent or benign force. After all these are the people who tried to establish Utopia many years ago; the bringing a certain beauty to the world and reviving classical ideals Ambrose as you can imagine with his background, has a yearning for these things. So he has to grapple with what’s real and what’s not And whether he may be working for the NSA to try to hunt down and destroy a group that may be older and wiser than we are and could bring a certain order and moral force to the world So who are these Pythagoreans and how do they break the RSA algorithm? And what does ancient Greece tell us about our own evolving digital world and authenticity? These, these are the questions at the heart of ‘Tetraktys’ So I hope that after hearing me speak today, you’ll accept my invitation to join Ambrose on his, on his journey and explore the mystery Thank you very much [applause] Steve: If you have questions, please use the mic in the middle of the room [pause] male voice in audience: This is a somewhat standard question for people who have very, very busy schedules and pretty big day jobs How were you able to carve out time to, to welcome your muse? Ari Juels: That’s a, that’s a great question So the first answer is that it took me over 10 years to write the book The second answer is that to some extent I don’t remember and I often wonder in fact if I just happened to encounter some genie; picked up a bottle on the beach or something and made a deal. I said “Okay, you can erase 10 years of my life if a book will just pop out.” And, and that happened. Because I really don’t have a strong recollection of how on earth I squeezed my writing time in [pause] male voice in audience: In your book you reference the NSA and the interactions there and in the panel you’d chaired earlier this week at the RSA conference. There’s a really interesting cultural contrast between the representative from the NSA and the other members of the panel How does that, what is your characterization of the NSA culture and how does that play out in terms of the book? Is that, is that a part of the book or is that really secondary? Ari Juels: Well, I don’t have intimate knowledge of the culture of the NSA, of course very few people outside the NSA do. So to some extent I, I had to try to make guesses. As I mentioned, I made at least one happy technical guess. I don’t know whether the cultural guesses that I made were accurate Some of the elements of the book are, are certainly farfetched, but there, there certainly is a sharp difference between the academic perspective and the, and the NSA perspective And I think the little that I know has probably percolated into the book, but I’m not sure I can give you a crisp characterization [pause] female voice in audience: Thank you, Ari Ari Juels: Okay. Thank you very much [applause]