Samantha took the notebook from Marcus and read his line again. The fix is one number.
“How many?” she said.
“How many what?” Marcus asked.
“How many signatures before somebody has the key.” She looked at Vlad.
Vlad was back in Doug’s chair. He didn’t answer. He had barely said anything since he came in off the porch, and she was too tired to ask him why.
“Can you work it out?” Marcus asked.
“Not from the log. I’d need their key to check my answer.” She picked up the tablet. “I can make my own key and break it.”
She sat back down on the floor behind the woodstove and plugged the cord in. Cooper came over and lay across her feet again.
The standard had the whole signing algorithm in it. The reference code it came from would make a key as small as sixty-four numbers instead of 1,024, for testing. She wrote one. She shrank its sigma by the same amount nib had, 165.74 over 168.39. It took her twenty minutes. Then she signed ten thousand copies of the word test, took the average of every signature, and laid it next to her key.
Noise.
She signed a hundred thousand. More noise.
“Vlad.”
He opened his eyes.
“Look at this. Tell me what I’m doing wrong.”
He held his hand out without getting up. She gave him the tablet. He scrolled for maybe ten seconds.
“Your tree is wrong,” he said. “The leaves get the small number. Not the top.”
He handed it back and closed his eyes.
Damn. She’d read that section of the standard twice and still gotten it backwards. She fixed it and ran it again.
At four thousand signatures the average looked like noise. At ten thousand there was a shape in the noise. At thirty thousand it looked like her key.
“Fuck,” she said.
“Good fuck or bad fuck?” Seth asked from the kitchen.
“It works.”
“That sounds like a bad fuck.”
PQ1 was sixteen times bigger than her key. She worked it out on the back page of Doug’s notebook and came up with a range of 2.1 to 2.6 million signatures before the key fell out.
If she had to bet, it would be closer to 2.1 million.
She pulled the log back up. Every signature in it had a timestamp. There were seventy-one thousand in the last hour of Vlad’s download. Two hundred and eight thousand at ten, plus almost five hours of that, put the log at a little over half a million. Two million was another twenty hours. Monday, around lunch.
She put the tablet face down on the boards, closed her eyes, and breathed in slowly through her nose until her chest stopped hurting.
“Sam?” Marcus said.
She opened her eyes. “It’s tomorrow.”
“What’s tomorrow?”
“Somebody can have the new key tomorrow. Probably around lunchtime. It takes two to four million signatures, and they’re signing seventy thousand an hour.”
Marcus took his foot off the milk crate. “Who’s somebody?”
“Anybody with the log and a decent computer. They publish the log on purpose.”
Seth came in from the kitchen with a dish towel over his shoulder. “Say it again, but this time for the dumb investor.”
“Every time someone signs something with the new key, the signature gives away a little bit of the key. Enough of them and you have the key.”
“How many do they sign before they’re done?”
“Two point four million.”
“And how many does it take to break the key?”
“Somewhere between two and four million.”
“Then tell them to stop signing,” Seth said.
“If they stop, every device that took the new root still trusts the old one until Day 10. The other side is breaking the old one right now. It’ll take eighty-one hours, and we don’t know when they started.”
“And if they keep going?”
“Then somebody has the new key tomorrow. And on Day 10, the devices stop listening to anything but the new key.”
Cooper lifted his head off her feet, looked at Seth, yawned, and put it back down.
“Who do we give this to?” Samantha asked.
“Eleanor,” said Marcus.
“The address is dead.”
“Then we drive to Boulder.”
“And do what? Knock on her door?” Seth said. “If she is burned, somebody is parked outside her house.”
“Then somebody else,” Marcus said. “There has to be somebody at Ostvik who reads email.”
“Everybody at Ostvik reads email,” Vlad said without opening his eyes. “So does everybody who is watching Ostvik.”
“Whoever it is,” Marcus said, “‘two to four million’ isn’t going to move them. They’ll want one number.”
She hated that he was right.
“Then I’ll get them one,” said Samantha. “Nobody goes anywhere until I have it.”
At four Vlad took the case out to the porch. Samantha went out with him and stood at the rail with her arms crossed. The sun had already gone behind the ridge and it was cold again. Monday lunch was about twenty hours away.
Vlad had the dish up in under a minute. He read the tablet for forty seconds without saying anything.
“Ostvik says nine hundred and forty thousand,” he said. “As of six o’clock in New York.”
Ostvik was signing faster than her seventy-one thousand. Tomorrow morning, then, not lunch.
“They’re ahead of schedule,” she said.
“Yes. They are very happy with themselves.” He powered the dish down. Three minutes and ten seconds.
She couldn’t blame them. Until half past one her own third line had said Accept it only if it also carries a PQ1 signature.
She went back inside and took the notebook off the couch. Under Marcus’s line she wrote Before Monday morning, and underlined it twice.
Then she sat back down behind the stove and started over with a bigger key.