The Lock That Runs One Way

The padlock came apart in Maya's hands, which was not supposed to happen.

Her aunt Rina looked up from the key grinder. "That one's dead. Somebody forgot the combination and got angry at it."

Maya turned the pieces over. Four numbered wheels, a little cam, a spring. She spun the wheels and watched the cam rise and fall. "So there's no way to open it if you forget?"

"You try all the numbers. Zero zero zero zero. Zero zero zero one. On up." Rina held a blank key against the grinding wheel and sparks came off orange. "Ten thousand tries. A person could do it in an afternoon if they were stubborn."

"You're stubborn."

"I'm expensive," Rina said. "There's a difference."

Rain ran down the window in sheets. Maya laid the four wheels in a row on the counter. Ten thousand felt like a lot and also felt like nothing. She had watched a computer at school count to a million while the teacher was still explaining the assignment.

"What if the lock had more wheels," she said.

"More wheels, more tries. Five wheels is a hundred thousand. Six is a million."

"So you just add wheels until nobody can be stubborn enough."

Rina shrugged, not really listening now, absorbed in the key. "That's the whole business. Make the trying take longer than the thief has patience for."

Maya spun a wheel. It was a satisfying thing, the click of it, but it bothered her. If a computer could count to a million, you would need a lock with an enormous number of wheels. And a lock like that would take forever to open even when you did know the number. That seemed wrong. Every day her mother bought things on her phone in about four seconds. Nobody was standing there spinning wheels.

"Aunt Rina. When Mom buys shoes online. There's a little lock in the corner of the screen."

"Mm."

"What's it locking?"

"The numbers. Her card. So the shoe people get them and nobody in between does."

Maya frowned at the four dead wheels. "But everybody in between can see the message going by. It's not like a letter in an envelope. It's more like shouting across a room."

Rina turned off the grinder. The shop went quiet except for the rain. "You'd have to ask the shoe people how they do it. It's math, not metal. Out of my department."

Math, not metal. Maya sat with that.

A metal lock was symmetric. The same secret closed it and opened it. If you knew how to lock, you knew how to unlock. Which meant you could never tell a stranger how to lock a message to you, because telling them how to lock it would tell them how to open it too. And you had to tell them across a crowded shouting room where everyone was listening.

She picked up a pen from the counter and a receipt off the spike.

There had to be a kind of lock that worked one way. Easy to close. Hard to open. Where knowing how to close it told you nothing at all about how to open it.

"Aunt Rina, is there any sum that's easy going forward and impossible going backward?"

"Backward how?"

"Like. I give you two numbers, you multiply them, that's easy. But I give you the answer and I ask which two numbers made it."

Rina thought about it while she swept filings into her palm. "Little numbers, easy. What's six? Two times three, anybody can see it."

"But big ones." Maya wrote a number on the receipt. Then another. She was picking numbers that couldn't be split, the stubborn ones, the ones only one and themselves went into. Seven. Eleven. Then bigger. "If I hand you a huge number, and I promise it's exactly two of these stubborn numbers multiplied together, and I ask you which two."

"I'd start dividing and see what fit."

"You'd try things. Like the wheels." Maya's pen stopped. "You'd have to try things."

Rina tipped the filings into a bin. "Sure. And there's no shortcut, is there. Multiplying, you just do it. Un-multiplying, you hunt."

That was it. That was the whole shape of it, sitting on the counter between them.

Multiplying two enormous stubborn numbers took a computer no time at all. But handed the result, a computer had to hunt for the two pieces, and if the numbers were huge enough, the hunt was so long that all the computers on Earth working together since the Earth was made would not have finished. Not a hundred thousand tries. Not a million. A number so large it made a million look like nothing, the way a million made ten look like nothing. That was a lock that ran one way. The shoe people could shout the huge number across the crowded room, shout it to everyone. Here is how to lock a message to me. Go ahead. And everyone in between could hear it and it did them no good, because locking was the easy direction and opening meant hunting for the two stubborn pieces, and only the shoe people knew those, because they were the ones who multiplied them in the first place.

You could hand a stranger the lock and the whole world could watch you do it, and the message was still safe, because the safety wasn't in hiding the lock. It was in the hunt nobody could finish.

"The little lock on the screen isn't hiding anything," Maya said slowly. "It's showing everybody. It's showing everybody the answer and it doesn't matter."

Rina looked at her, then at the receipt covered in stubborn numbers. "You lost me a while back."

"Multiplying is easy," Maya said. "That's the whole trick. It's easy on purpose. Because backward is the wall."

The rain had thinned to almost nothing. Outside, a phone in someone's pocket was buying something, telling the world its lock, and the world could not open it.

Maya spun the four dead wheels, all the way around, and let them click to a stop on a number that meant nothing to anyone.