The Cipher by John C. Ford

from Amazon?”
    Ben let out a hard-edged laugh. “It’s like the guy said this morning. Encryption doesn’t just protect credit card numbers. It’s how they keep
everything
on computer networks secure. People buying stocks. Wire transfers. It’s how they control water systems. Airplanes and missiles. Nuclear power plants, for all I know.”
    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.
    â€œYou could see all those things?” Smiles said. “How?”
    â€œâ€™Cause I can generate private keys.”
    Smiles closed his eyes, trying to catch up.
    â€œThe gate and the door, remember that? That’s how public-key cryptography works, but it’s just an analogy. Your dad’s the one who actually made it work electronically. Without his system, you couldn’t exchange secret messages over the Internet with people you didn’t trust completely. It was a total revolution, and it’s all based on primes.”
    Smiles nodded, more to calm Ben down than anything. “So instead of keys, they use prime numbers somehow,” he ventured.
    â€œ
Yes, exactly!
”
    â€œChill. Just break it down.”
    Ben pointed to what he’d written before:
    3 × 7 = 21
    â€œThree and seven are primes. Because they’re primes, they’re the
only
two numbers that you can multiply together to get 21.”
    â€œOkay.”
    â€œSo 21 is my public key—it opens my gate. And 3 and 7 are my private keys. They open my door.”
    â€œOkay,” Smiles said, feeling a foreign twinge of pride within himself for keeping up.
    â€œSo 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, ’cause they’re my private keys.”
    â€œAnd even though people know that your public key is 21, it’s hard to figure out that your private keys are 3 and 7?”
    â€œRight! But that’s what I figured out today, how to do this . . .” He underlined:
    213 × 7
    â€œIt’s always been impossible to do in a short time with really huge numbers. It’s 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€œForever? Even with computers?”
    Ben nodded. “The sun would burn out before you would get the private keys to a really long public key. Literally. It’ll 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€œWhich means you can unscramble the messages.”
    â€œYeah.” Ben sat back in his chair, spent. “With my algorithm, I can figure out all the private keys in the world.”
    Smiles really needed to stretch his legs, but he was glued to the bed. “If somebody got your formula, they could, like, wreck the stock market, couldn’t they?”
    â€œThey could do anything,” Ben said. “Smiles, this algorithm—the government would consider it an instrument of war. They would actually consider it illegal to possess. Didn’t you hear that guy talking about the NSA?”
    Smiles nodded.
    â€œThey don’t even want people talking about little research discoveries. But this