Root of Unity

by SL Huang

  Her nostrils flared, her color rising, and I wondered if I had just signed my own arrest warrant.

  Someone rapped on the door.

  Jones ignored it for a long moment. Then she swept out of the room without saying another word.

  I slumped in my chair, trying to remain expressionless for the hidden cameras, but not sure I managed. It would be nice if I could learn to keep my goddamn mouth shut sometimes. I seemed to have some sort of opening here I couldn’t figure out how to slot myself into. I had the distinct suspicion an ounce of social grace on my part would have wrapped my involvement in this whole case up in a nice bow for the Feds and assigned myself to their list of people who were unsavory but necessary cogs in society and Not Worth Their Time.

  Instead, I had pissed off one of the lead investigators to the point where she wanted me to rot in jail forever.

  I rested my elbows on the table and pressed the heels of my hands against my eyes. Shit. It was so hard to think right now. My head felt stuffed with cotton, and the wound in my side, despite being properly dressed now, was an increasingly persistent burn. And there was a different sort of twisted discomfort mixed in with everything else, some tangled mess about Arthur and this case and Agent Jones’s assumptions about me.

  I’d expected Jones to step back in after a few minutes and continue her interrogation, but she didn’t. After a while, I put my head down on the table again and tried to sleep, but it worked about as well as it had before. I’d get some alcohol to help with that, once I was off this job. A lot of it. Or some of the good pills. Or both.

  A different agent came by a few hours later with a dinner tray, a hamburger and a bag of crisps and a soda. I ate mechanically while considering the efficacy of trays as weapons, but I wasn’t ready to try busting out yet. How likely was it that I’d torpedoed my chances of walking away from this? I couldn’t tell. The same agent came back to take the tray away when I was done anyway, so I shelved that plan for now.

  Finally, after a very, very lengthy wait, Agent Jones came back. My watch said it was almost the next morning, and I pettily hoped Jones had been forced to be up all night because of me—she was in the same clothes and the bags under her eyes had gouged themselves darker. Then I realized she probably would have been up all night anyway because of the continuing national security crisis and all, and I was just the asshole making everything harder.

  Jones leaned against the wall across from me in the same posture she’d taken before. “Your client is demanding to see you,” she said, after a long moment.

  And they were letting her? “I thought you people weren’t the sort to listen to demands,” I said unwisely. God, I just couldn’t keep quiet.

  Fortunately, Jones ignored me.

  She brought me to another room, one with about the same decor as mine but larger. Halliday was sitting at the table, and Arthur stood propped against it, seemingly casual but with a dangerous air about him. Like a panther on a branch. Arthur tended to pull that look off well—I was pretty sure I, on the other hand, always came off like a particularly aggressive hyena.

  “Professor,” I said. “You all right?”

  “Yes,” she said.

  “What’s going on?”

  Arthur stuck out his hand. “Arthur Tresting. We met before. I’m a friend of Sonya’s.”

  “Right,” I said, shaking his hand stiffly. “Yeah. So what’s going on?”

  “First off, we better assume we’re on tape,” said Arthur, with no animosity about it. “Just so you ladies know.”

  “Yeah,” I said. It was a smart reminder. “Good. Okay. How’d you get them to agree to let us talk?”

  I’d been directing the question at Arthur, but Halliday was the one who answered. “I told them it was the only way they were getting the proof. In a perfect world, they’ll figure out who stole it and contain the information, but if not, they need to have it, too—as fast as possible—so they can work to counter any possible security threats. And the only place it exists now is inside my head. They know it, and I know they know it, and they know I know they know it.”

  “Nice recursive dilemma for them,” I said. “So what do you propose, then?”

  “I propose I give them the proof.” She flicked her eyes to me. Was I imagining it, or had I heard a slight emphasis on the second “I?” It dawned on me that Halliday knew to protect me. Either she’d figured it out, or Arthur had told her.

  Holy crap. It was nice to be surrounded by smart people.

  “I propose I give them the proof,” Halliday repeated, as if steeling herself, “in return for certain considerations.”

  Excellent idea. “They let us all go,” I said. “No further interest. We’ll have to figure out some way of holding them to that once your math is delivered.” I might have leaned a little too heavily on the pronoun, too. Dammit. Hopefully the NSA or whoever wouldn’t analyze too closely.

  “I’ve been recruited before,” said Halliday. “It never appealed to me. But the prospect of consulting with them—I would also be open to negotiating that.”

  More bargaining chips. That was nice of her.

  “I’ve given them a full and honest report of what happened,” said Halliday to me. “That my work was stolen and that I hired you to find it. That I was kidnapped, that some unknown people held me to work on the proof, and that you found a way in and broke us out. They know someone else out there has a copy of the proof, and they’ll be looking for it. It’s therefore of the utmost urgency that I tell them the contents.”

  A “full and honest” report. Heh. I was grateful.

  “They threaten you?” said Arthur.

  Halliday had her hands pressed flat against the table. She looked down at them. “I believe it was implied. But that does not mean it would be their preferred course of action. Although we would be fools not to protect our interests, our government is not the enemy here, and I don’t believe any of us wishes them to be.”

  “What’s the plan, then?” said Arthur.

  “We figure out our demands,” Halliday answered. “We present them. And we make a deal. Quickly, so as to ensure the NSA has whatever mathematical information they need to prevent attacks before they begin happening.”

  “Bet they’ll deal,” said Arthur. “You’re right. They ain’t the bad guys.” I wondered if that remark was directed more at me or at the hidden cameras. Then I wondered if I was looking for reasons to be annoyed with Arthur.

  Halliday pulled over a pad of paper and a pen. “Then what do we want?”

  I tried to organize my thoughts. “I get to protect you. No NSA or DHS looking over your shoulder while you do this. I don’t trust them. I’m your line of defense while you’re writing the proof.”

  She hesitated and then nodded, beginning to write in a flowing script. She understood what I was saying: I’d protect her, and I’d also help her write it.

  “No charges,” said Arthur. “Against any of us involved here.”

  “And if I catch them spying on you or me or sniffing around after my business,” I added to Halliday, “or if they decide you’re a liability because of what you know…”

  “We keep a copy,” said Arthur.

  Smart. It was a move that had worked for us before—make sure there was a way for the information to get out if someone felt it was more expedient to kill us than to worry about letting us live while we had the potential for spilling the knowledge.

  “And I want to be able to speak freely where we do this,” I said. “No spying; I mean it. I’ll bring the tech to check.”

  “Don’t think that’s unreasonable,” said Arthur. “Anything else important?”

  Halliday handed him the list. “I believe we’ve covered it.”

  Chapter 20

  The only thing the Feds refused was us hanging onto a copy of the proof—they claimed they didn’t trust us to keep it secure. I pointed out that, considering it was still missing and uncontained, Halliday was going to be helping them propagate security
overhauls everywhere anyway. They pointed out in turn that the security overhaul meant we wouldn’t be a threat to them and we therefore had no need for leverage.

  I didn’t like it, but considering I’d be able to write the whole damn thing out myself afterward without them being able to stop me, I let it slide. I wasn’t too happy they wouldn’t know I was capable of releasing the proof—that was the point of leverage, after all—but maybe I could tell them later.

  The Feds set up a safe house for Halliday in the mountains. It was some sort of abandoned estate, old but clean and in good repair. The NSA set up shop at a respectful distance, controlling access to the house. We’d been able to dictate that Arthur and I would have the freedom to move in and out—either a mark of how irrelevant they thought we were or how over a barrel we had them; I wasn’t sure which. Halliday herself wasn’t allowed to leave until we had finished, and after that we would set up new provisions for her protection. But right now all anyone was concerned about was getting her proof on paper.

  The first time I drove out through the perimeter, I expected someone to follow me, and I switched cars three times just in case. But nobody was on my tail, and when I came back with an array of bug scanners and went over the whole house for electronic listening devices, we determined the Feds had been as good as their word on that as well. I wasn’t sure whether to be pleased or suspicious. Maybe they had technology I couldn’t detect. Maybe they had some sort of long-distance listening devices that would hear inside the house, even though I’d done the calculations on all standard parabolics and the math said we were safe.

  Or maybe I was paranoid. Dammit, I hated having to trust people I didn’t trust.

  Arthur’s ostensible role in sticking around was to be part of Halliday’s protection in the house with me, but he also ended up helping us liaise with the NSA and DHS agents. He was better at talking to them than I was, that was for sure. Whenever I went by them coming or going, I pasted on a scowl and hoped they wouldn’t try to speak to me.

  Halliday asked for her friend Xiaohu Zhang to be her official NSA contact, especially seeing as how he was a mathematician and all. He turned out to be a bespectacled man with a predilection for sweater vests and perpetually crooked bow ties. He was a genial, soft-spoken guy with a slight pot belly, a ready smile, and stars in his eyes every time he started in on mathematics with Halliday. I sat in the corner and cleaned my guns while they rambled on about her proof and how exciting it would be for the mathematical world once it was finally revealed to the public. Zhang kept asking if she’d written her Abel Prize speech yet.

  He also told us the NSA had made no headway on figuring out who had actually stolen the proof, which was slightly worrying. Fortunately, it not only hadn’t turned up anywhere, but there’d been no whisper of anyone who might be using her methods. The prospect dangled above us, an anvil waiting to be dropped.

  Of course, I thought, Zhang might be lying. I didn’t think he had the duplicity—but then, the NSA might be lying to him.

  Zhang did tell us there was already a mostly-behind-the-scenes revamping of computer security going on across the country. Halliday jumped in on helping with the tail end of it, making sure the concepts in her proof couldn’t be used against it in the same fashion, and with giddy relief—well, what passed for giddy with her—seemed to be confident the crisis was averted. All vital national security concerns had quietly swapped encryption protocols with impressive speed, and anything that could lead to drastic economic consequences was slowly being switched over as well. Whoever had the proof would still have a lot of power once they deciphered it, but the NSA had at least averted the apocalypse. Probably.

  Amusingly, the authorities switched from factorization of semiprimes to using Halliday’s own work on encryption via prime roots of unity. I supposed it wasn’t that ironic for her own work to have come out on top, considering how few people there were in her field. There were whispers in security circles wondering about all the changes, Zhang told us, but the NSA had managed to keep them tamped down enough that the mainstream news media hadn’t picked anything up yet, and people tended not to listen to conspiracy theorists. Even when they were right.

  After the relief part of it, Halliday had an attack of guilt after Zhang revealed—in his absent, slightly dotty way—just how fast the NSA had been able to mitigate possible disaster. “I should have gone to them right away,” she told Arthur and me that night, leaving her food untouched as we ate dinner over the in-progress proof papers. “I was too afraid. But look how quickly…I was stupid. And selfish.”

  “Eat,” said Arthur.

  “Yeah, I don’t want to have to deal with you fainting,” I said. Arthur shot me a look. “What?”

  “Sonya,” he continued, ignoring me, “everyone makes mistakes, right? You know that. None of us was aware of enough to know it was the right call. I ain’t told you to do it neither.”

  “And I didn’t even want Arthur to go to them when you were kidnapped,” I said, tucking in my stew as I spoke. Arthur wasn’t a bad cook.

  “But I should have known,” said Halliday. “This is my world. I should know how it works. I could have talked to Xiaohu, or any other of my friends who consult occasionally. It was too easy to listen to the stories that scared me.”

  “Well, there are a lot of them,” I said. “The NSA is scary.”

  “Not helping, Russell,” said Arthur.

  “Why not? I think you acted perfectly reasonably,” I told Halliday. “I’d recommend hiring me any day over going to the NSA.”

  She fixed me with a wry look. “Do not take this the wrong way, Miss Russell, but your approval of my life choices is not the most comforting of notions.”

  Right.

  “You made a mistake,” Arthur said bracingly, putting a hand on her shoulder. “Humans do that. Okay? Cut yourself a break. Now eat something. Please.”

  She finally obeyed, sipping delicately at a spoonful of stew broth. “I understand what you’re saying, but to be perfectly honest with you both—I’m not sure I deserve this deal we have. I handled this wrong from the start.”

  “You can have your crisis of confidence after we get your proof done,” I said. I spooned up my last bite of stew and pushed away the empty dishes to pick up her latest papers, the ones she and Zhang had been scribbling on during his visit today. “You’re close on this, but you’re going in circles. Come on, the whole point of the graph theory lemma was so clearly to give you a reducing function for f-bar.”

  Halliday dropped her spoon, spattering broth across the pages, and snatched the ones I was holding, her mouth gaping wide. “Yes—of course! How did we not see that!”

  “You weren’t thinking?”

  She brushed me off and snatched at a pen, but Arthur picked it up first and moved it out of her reach. “Eat, Sonya. The proof will be here.”

  “Arthur, no, you don’t understand—I have to get this down—” She pawed around for another writing utensil and started scrawling on the back of one of the proof papers.

  Arthur gave up and glared at me. “Russell, no more talking math at meal times. You gals have got to take care of yourselves.”

  “What are you talking about?” I asked, as innocently as I knew how. “I ate.”

  It took a little over two weeks for Halliday and me to complete the math, and a few more days to smooth it out into something coherent and readable. I kept my contributions limited to heckling and oral explanations so all the handwriting would be hers. Arthur tried to get the NSA to allow Pilar in to typeset the TeX, but the Feds refused to let another civilian have eyes on the proof, so Halliday did it herself. We worked on a computer with no network connection, printed the proof, and then magnetized the hard drive of the computer.

  “You’d think they’d want the digital copy,” I said.

  “Think it’s a security thing,” Arthur answered. “Probably don’t want it digital until it’s behind enough sets of closed doors. Too easy for someone to copy it.”<
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  I didn’t really care. This whole fiasco was over—well, over for us. We’d never figured out who’d stolen Halliday’s work in the first place, but the Feds had been very clear that it was their investigation now and that they would look unkindly on anyone stepping into it. Since the imminent danger to both the country and Halliday’s well-being were over, we’d agreed to let it go, which meant we were done. The Lancer and D.J. were still out there somewhere—their bodies hadn’t been found buried in the building we’d blown up—but the Feds had helped us there, too; they’d continued going after the Lancer with the fury of a thousand avenging angels, and last we’d heard Interpol had reported intelligence he was somewhere in Croatia. I wasn’t convinced we’d seen the last of them, as they probably craved some violent vengeance against us if nothing else. But Halliday’s proof was a whole lot less valuable now, so maybe we wouldn’t be worth the trouble.

  The afternoon we put on the final touches, Halliday and I sat out on the deck of the safe house, staring at the neatly completed proof stacked between us. I was drinking tequila out of the bottle and appreciating the fact that my various recent injuries had all mostly healed. She had a glass of ginger ale.

  “When’s the switchover happening?” I asked. I was exhausted, but something felt…good about finishing this. Complete. Like it had been a job that meant something.

  “Xiaohu’s coming by tomorrow morning, and I’ll be passing it off to him.” Halliday smiled. “He was giddy as a schoolboy when he told me they’d cleared him to take custody. I think a promotion might be in his future.”

  “He seems like a good guy,” I said.

  “Yes. And he reminds me…” She stood and wandered over to the railing. “He reminds me of why we do this. Of how amazing this is, what we are a part of, what we can build. He reminds me to love it. Sometime between the kidnapping and the government custody I had lost that.”

  I stood up and joined her, still suffused with good feeling. “Well, you did it. I…it’s a marvelous result. I don’t think I ever told you that.” I clinked my bottle against her glass. “Congratulations, Professor.”