Gift for SiggyKlim for ZEcret Santa 2017. I hope you enjoy Alice and Hazuki being cool, and have a great Christmas.

Please excuse the smallness of my primes. Turns out I didn't have the access to 19 industrial grade primes I'd need to do this properly.

25th November, 2029

Alice knew that, technically speaking, Hazuki Kashiwabara fell under the purview of the 'If I tell you, I'll have to shoot you' Protocol. She also didn't much care. After the Nonary Game she had been kidnapped for and with both her daughters working for the Special Office of Internal Security, Hazuki already knew most of everything worth knowing, and knew why it was important to keep it all secret. More importantly, Hazuki was actually a really useful lady to have around. You didn't just find her sort of genius standing by the side of the road. So Alice didn't much care for anyone saying she wasn't allowed to invite her friend into the Office whenever she felt like.

Of course, when an officer of the SOIS doesn't care for something, it doesn't actually matter.

So, one blatantly forged ID badge later, Hazuki was comfortably situated in Alice's office, swinging the swivel-chair by the computer gently around. Alice settled for lounging on the sofa opposite. One of the key tenets of SOIS operations was matching intelligence assets to the task they were best suited for, and despite the electronic warfare training all agents went through Alice could be confident that with Hazuki at the computer there was little more she could contribute.

"So how are Nona and Ennea doing these days?" Hazuki asked. After nearly losing her two daughters a decade before, that question was always her first when she and Alice met.

"Overseas, at the moment," Alice replied. She followed it up with her usual thin smile that said, 'and you don't need to know anything more.'

"'Overseas'? Really?" Hazuki scoffed, "Wasn't this supposed to be the office of internal security?"

Folding her arms and smirking, Alice said, "America's internal security starts as far as possible from our borders. The earlier we catch the bastards, the safer we all are."

"Yup, I guess so." With that, Hazuki swung around in her chair, half way towards the keyboard. "So what's up today, Alice? Who are we going to hack apart this time?"

Alice shrugged. "Maybe I just wanted to talk to an old friend."

"You know, for a top secret agent of the most clandestine agency in the world, your lies are just awful. If you just wanted to chat, there are plenty of cafés around here where we could have met. About half of which are entirely staffed by patsies of yours, if you really needed to discuss something confidential."

"That's not true!" Alice exclaimed. She held her mock-outraged expression for a couple of seconds, then relaxed. "After Light quit his harpist job, we haven't got any leverage on his replacement yet. That makes the number of cafés we control half-minus-one by my count, thank you."

Hazuki chuckled lightly. Then, she continued, "Still, I know I'm right. We wouldn't be meeting here if you didn't need my skills. So tell me, Alice: what's up?"

"Nothing world-ending," Alice said, getting to the point, "Just this mafia group that's resurfaced. The one that tried to take over the Las Vegas strip a couple of years back. We thought that we'd eradicated them back then, but it looks like we only managed to weed out all the stupid." Annoyed as Alice was that the previous mission hadn't been a complete success, it wasn't a complete washout. At the very least, it had been a relatively proving ground for Light and Clover to win their spurs.

"Smart mafiosos? Rue the day." Hazuki gestured avidly towards the computer she was sitting at and said, "Just general hacking disruption, then? Or are you after something in particular?"

Alice considered it. "We'd like to know where they are getting their money from. They couldn't have recovered this fast without outside help."

Hazuki grinned. "Can do."

o - 0 - O - 0 - o

After five minutes of preparation, Hazuki was ready to go. Alice had done her part, aiming the computer at the closest thing the Office had to an entry-point to the gang's computer network; now she could step back and just let Hazuki get to work. Hazuki cracked her knuckles and stretched out her back, ready to type.

Hazuki glanced at Alice.

Alice nodded.

The hacking began.

Green lines of code swept across the screen as Hazuki's fingers swept across the keyboard. The screen flashed with one window full of data then another; Hazuki gave each only a moments glance, absorbing the information then dismissing the window in favour of the next. Each snippet of data informed the next piece of code, and without quite understanding what was going on Alice could feel them spiralling in and in towards their target. At the very least, Hazuki was grinning in anticipation.

And then the screen went blank.

"No!" Hazuki gasped. She slammed her hands onto the desk, rattling the keyboard.

Alice stared at the dark empty screen. "W-What happened?!"

"I was this close," Hazuki hissed. She tapped the left mouse button a couple of times, bring the last few windows of data and code back onto the screen. "Look here. This group has set up their network by using a regularly updating schedule of private and public cryptography keys for an RSA system. After random intervals each computer in the network chooses a new private key, constructs the new public key, and distributes it to all the other trusted computers on the network. I had just set up a buffer-overflow past their final layer of defences, and I was this close to injecting code that would trick those computers into thinking we were part of the trusted network, when someone human noticed and scrubbed us out."

Alice knew far more than the basics of computer security and infiltration, but even so she'd never heard of a cryptosystem complicated as that. "What's with that? Surely that's a bit excessive, especially compared to what this group had the last time we beat them."

Hazuki let out a wry bitter chuckle, then said, "It's probably worth it, if they knew we were after them. It was reasonably well-programmed, at least, and it had to have been the reason your in-house guys couldn't break in. Even if you brought all your processing power to bear, you couldn't break through. I found out that this was the public key just before we were kicked out –" Hazuki elegantly indicated a number – 599725548175349234588407 – at the bottom of the window she had restored "– but by the time you can get SOIS' supercomputers into action to factorise it, they'll have already moved onto another key.

"God help us. So even though we know it's 599746013723 times 999 965876309, we still can't…" Alice trailed off.

Hazuki sat there, frozen by complete disbelief.

Alice snapped her fingers in front of Hazuki's face. "Hello? Hazuki Kashiwabara? Are you still with us?"

Hazuki murmured, "That's… That's not possible."

"Thank god. I thought I was going to have to say that Seven had called you an old lady."

Alice's flippant comment went nowhere. Hazuki still stared at her, but her eyes showed none of the anger they should have. To be honest, Alice was rather concerned.

"Hazuki…? Lotus?"

"That's completely impossible," Hazuki said again. She turned back to the computer screen, furiously typed some code; she stopped and turned back to Alice only when another number had appeared on the screen. "Alice," she said, concern filling her voice, "Can you look at this, please?"

Alice looked at the number: '724677698895304108732301'. "It's 803065408993 times 902389382957," she replied.

Hazuki pressed 'enter' on the keyboard; another number appeared. "And this?"

Alice didn't need to study '668089868878852858021373' for even a second. "769945710559 times 876710358947."

Hazuki murmured again, "It's completely impossible…" She tapped out a long string on the keyboard, then pressed enter again.

Alice stared at the number '90591875222471336864959701060623807145969394309'. "What the hell, Hazuki?"

"Thank goodness." Hazuki sighed, her relief almost filling the room. "You can't actually solve –"

"It's obviously 324270473809 times 465783271379 times 599886421037 times 999836357587. Why are you wasting my time with simple things like this?"

"What the HELL?!"

o - 0 - O - 0 - o

Once Hazuki had recovered, she explained. "Alice… every single bit of computer security in the entire world depends on our inability to easily factorise primes. We can produce numbers in a couple of minutes that can't be broken in centuries. Shouldn't be broken in centuries. But you were doing it instantly."

Alice shrugged. "I've told you. I've always been good at math."

"I know. But this isn't just 'good-at-math' good at math. This is 'you could walk into any bank in the world and walk out with all their money' good at math." Hazuki paused, staring at Alice inquisitively. "Alice… Are you an esper?

"Huh?"

"I should have realised with Nona and Ennea," Hazuki said, "I should have noticed the signs, when they started to get twice as good at school tests without needing to revise, and when one of them would know all the spoilers for a series that only the other had watched. If I'd noticed, maybe I could have protected them, or at least worked out why they had been taken. I decided that I would be more observant next time. So, Alice: are you an esper?"

Alice folded her arms sternly. "No. I'm not."

At that moment, Clover leaned through the office door, her pink hair bouncing eagerly as swung on the doorframe. "Yep she is!"

"Clover!" Alice snapped.

"What? We've known all year: me, Light, all of us! Anyway, see you later!" Clover swung away and skipped down the corridor before Alice could reply.

Alice scowled, but she couldn't avoid the truth. Everyone she'd demonstrated it to had been convinced that there was something extraordinary about her mathematical abilities. She hadn't become a highly-ranked officer of SOIS by failing to look past her own biases. She took a deep breath and accepted the facts in front of her. "Interesting. I'm sure there's some way the Office can use this."

Hazuki nodded slightly. "You can break pretty much any encryption in the world. I'm sure your bosses will find something for you to do. But…" She trailed off, glaring at her computer screen. "Doesn't help us much with this, though. The mafia group we were trying to hack were updating their keys too regularly. By the time I've given you one, you've factorised it, and I've hacked in, they'll already have changed to another one. That's for every single one of the 37 nodes of their network. And even if I do break through, the person who caught me last time will probably force me out again. If we could automate your ability, of course I could hack them. But…"

'If we could automate your ability.' Alice thought about those words, and a spark lit in her mind. She was still getting used to the idea of being an esper herself, but she was comfortably familiar with esper abilities as a concept and in practice. She had recruited Light and Clover, Nona and Ennea, and all the rest of the Nonary Game espers. She had trained them, seen them in action, carried them through their first missions. Mentoring those espers and making them useful to SOIS and the country had been the declared goal of the unit she led. But it hadn't been the only goal.

"I think I have an idea."