“You’re talking about the recent writings of Roger Wolcott Sperry on hemispheric specialization?”46
Anna, relieved of carrying the conversation, wondered if she’d regret the inconsequence of her first gambits. Sicozzi and Leonard belonged to the same species. She was prepared for them to talk shop across her plate without any regard for her.
“I often count on my right lobe, the intuitive brain, to solve a problem for me. You work on theoretical computer science, if I’m not mistaken.”
“Cryptanalysis, actually.”
“Your father told me about your research in encryption. You’ve moved away from his own fields of interest.”
“He likes to tell me that he puts my chosen field somewhere between plumbing and automobile repair.”47
Anna decided not to correct this unfair allegation. Calvin Adams always spoke of Leo with undisguised pride. The father had never ventured more than a little irony to squelch his son, who in return savaged his father unmercifully. While Calvin worried that his brilliant son might be wasting his talents on overly “technical” studies, Leo accused him outright of hiding his intellectual barrenness by copping an administrative post. The elder Adams had been an inspired mathematician before accepting the honor and material comfort of his present chronophagic job.
“Calvin described it enthusiastically enough to me.”
Leo, flattered by the Frenchman’s attention, grew loquacious. With two friends, he had been working on a new system for encrypting computer data. He spoke of an “asymmetric encryption” that would allow the exchange of digital information to remain confidential. Although this business of “public key cryptography” was totally obscure to her, Anna listened hungrily. In other circumstances, Leo would never take the trouble to tell her about his research. How many times when they were children had he not grown furious explaining ideas that to him were perfectly clear? Recognizing in his interlocutor the bewildered expression he had so often mocked in Anna, Leo grabbed his notepad to scratch out a quick sketch.
“Imagine a simple lock. Anyone can close it. But only you can open it, as long as you have the key. The combination.”
She thought of her locker at school. At the time, Leo used it for ancillary storage: old socks and controlled substances. No matter how often she changed the combination, he always managed to crack it, showing early signs of his calling.
“Encrypting, or locking, is easy. Anyone can do it. Decryption, or opening the lock, can be done only by the person holding the key. Knowing how to close the lock doesn’t give you any information about how to open it.”
Anna signaled her full attention by laying down her knife and fork.
“Imagine that you send your locker, with the lock unlocked, and that you keep the key.”
She visualized a long line of eighteen-wheelers loaded with lockers traveling across the country in a modern version of the Pony Express. She decided not to share the image with Leo. His humor was not particularly bijective: his touchiness was matched only by his ability to trample on the sensibilities of others.
“I put a message in the box. I lock your padlock. For me, this is an irreversible act. But you will be able to unlock the box when you receive it and retrieve the contents.”
Pierre Sicozzi was scanning the table for a bottle of wine. At the far end, the three graduate students were pouring out the last of the Gevrey-Chambertin. Ernestine, not missing a trick, uncorked a new bottle for Pierre.
“You would need to identify one-way functions that answered the requirements of this asymmetric key. Mathematical operations that are simple but very difficult to reverse.”
Leonard gave a tight-lipped smile, which for him was a sign of rapturous delight.
“Done.”48
“Splendid! Where did the inspiration come from?”
“From pizza. I consume hallucinogenic quantities of it. But to be entirely factual, the idea came to my colleague after a night of drinking.”
“A strong migraine can shut down the left hemisphere.”
“And sometimes both! It all depends on the dose of ethanol consumed. We conduct numerous tests in this department.”
“Could you give me a quick sketch of your results, unless the young lady has reached saturation?”
“Please. It’s so rare to hear Leonard talk about his work.”
She thought of Adele’s theorem. And here she had caught herself red-handed, putting it into practice. She batted her eyelashes. It was the nefarious influence of her red dress.
“Okay. For your sake, I’ll keep it simple.”
She took no offense. She had long ago concluded, though not without bitterness, that she didn’t play in the same league as her childhood friend. He hadn’t been trying to show her up. You don’t boast of an innate talent; you simply don’t suspect others of not possessing it.
“You choose two prime numbers, p and q, and you keep them secret. Their product gives you a variable, N. Do you know what a prime number is?”
“Primes are numbers divisible only by themselves and 1.”
“I’m going to explain it to you with very small primes. If p = 13 and q = 7, then p × q = 91. Your personal value for N is 91. If I want to send you a message, you have to give me this N, your public key. Which is 91. I’ll encrypt my information as a function of this value. Only you will be able to decrypt it.”
“Someone could guess where my N comes from!”
“Multiplying two primes is a one-way function, or almost so. If N is large enough, it’s very difficult to identify the prime factors. In other words, the source of the initial product. Only you will know the values of p and q that define N. That pair of numbers, 13 and 7, will be your private key.”
“How can you guarantee that some little nerd who is good at arithmetic isn’t going to factor my N?”
“To increase the encryption security, you only need to choose an enormous value. If N is around 10 to the 308th power, it would take one hundred million people with their computers more than one thousand years to find that key.”49
“Someone will eventually find a shortcut for identifying prime factors.”
“Mathematicians have been looking for a way to do it for centuries with no success. It’s a very elegant system.”
Leo was so pleased that he almost revealed his teeth.
“We announced a contest in the mathematical games section of Scientific American. We published an encrypted text with a succinct explanation of the encryption process using the key N. The value is on the order of 10 to the 129th power. We were being generous.”
“What does the message say?”
“Break the code! It has something to do with this turkey.”50 Pierre Sicozzi declined the challenge with a smile. He had plenty of other research topics on which he could spend his next thousand years, but he congratulated Leo again for his pioneering work. Anna for her part was concerned about the snake pit into which he was poking his nose. The NSA or some other combination of military initials was going to batten down on him.51 They had already preempted all of the developing networks. Big Brother would never authorize a level of privacy that couldn’t be decrypted in a few hours. When it came to security, History had already made its lesson plain: respect for the fundamental rights of man came a distant second to the national interest. Or, at least, to what certain people saw as the national interest. Turing, the father of computer encryption, had paid for it with his life. She wondered how Mr. Gödel would have reacted to these technological advances. Would he have enjoyed seeing the purity of his ink-based logic transformed in fewer than fifty years into a hidden guerrilla action of bits and bytes?