from Amazon?â
Ben let out a hard-edged laugh. âItâs like the guy said this morning. Encryption doesnât just protect credit card numbers. Itâs how they keep
everything
on computer networks secure. People buying stocks. Wire transfers. Itâs how they control water systems. Airplanes and missiles. Nuclear power plants, for all I know.â
Water systems.
Nuclear power plants.
The stock market.
Smiles was getting a bigger picture now, and as he did, something heavy settled over his body.
âYou could see all those things?â Smiles said. âHow?â
ââCause I can generate private keys.â
Smiles closed his eyes, trying to catch up.
âThe gate and the door, remember that? Thatâs how public-key cryptography works, but itâs just an analogy. Your dadâs the one who actually made it work electronically. Without his system, you couldnât exchange secret messages over the Internet with people you didnât trust completely. It was a total revolution, and itâs all based on primes.â
Smiles nodded, more to calm Ben down than anything. âSo instead of keys, they use prime numbers somehow,â he ventured.
â
Yes, exactly!
â
âChill. Just break it down.â
Ben pointed to what heâd written before:
3 Ã 7 = 21
âThree and seven are primes. Because theyâre primes, theyâre the
only
two numbers that you can multiply together to get 21.â
âOkay.â
âSo 21 is my public keyâit opens my gate. And 3 and 7 are my private keys. They open my door.â
âOkay,â Smiles said, feeling a foreign twinge of pride within himself for keeping up.
âSo say you want to send me your credit card number. You type it in the computer, and then the encryption program scrambles it up using a formula based on my public key, 21. The way the encryption is written, the only way to undo it is to know the two numbers that when multiplied together equal 21. Which only I know, âcause theyâre my private keys.â
âAnd even though people know that your public key is 21, itâs hard to figure out that your private keys are 3 and 7?â
âRight! But thatâs what I figured out today, how to do this . . .â He underlined:
213 Ã 7
âItâs always been impossible to do in a short time with really huge numbers. Itâs called factoring. The only way that people can do it is to basically try random combinations to see if you get the public key when you multiply them together. With the big numbers they use, it takes forever to try all the possible combinations.â
âForever? Even with computers?â
Ben nodded. âThe sun would burn out before you would get the private keys to a really long public key. Literally. Itâll be faster when quantum computing gets here, but for now it takes forever. When your dad started Alyce, he did this thing to prove how good his system was. He put a number out there, the product of two prime numbers. He challenged anyone to find the two prime factors within ten years. Somebody actually figured it out, but it took them twelve years. Now, with my algorithm, I can do it in under a second.â
âWhich means you can unscramble the messages.â
âYeah.â Ben sat back in his chair, spent. âWith my algorithm, I can figure out all the private keys in the world.â
Smiles really needed to stretch his legs, but he was glued to the bed. âIf somebody got your formula, they could, like, wreck the stock market, couldnât they?â
âThey could do anything,â Ben said. âSmiles, this algorithmâthe government would consider it an instrument of war. They would actually consider it illegal to possess. Didnât you hear that guy talking about the NSA?â
Smiles nodded.
âThey donât even want people talking about little research discoveries. But this
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