A month passed.
The traces of attack strategies vanished from the whiteboard in the lobby. Instead, the researchers spent their days studying Utopia in depth.
“The more I look at Utopia, the more remarkable it is. Noncommutativity is more fragile than you’d think. The mechanism for converting it into commutativity isn’t that difficult.”
“Right. For example, if space is homogeneous, an attacker can pick up the pattern. But in Yu-Riemannian geometry, the very concept of homogeneity doesn’t exist. Even between the same two points, the distance isn’t the same. Everything changes depending on curvature.”
“It seems like it would require an enormous amount of computation. How on earth did they maintain efficiency?”
It was not because cryptographers were fools that they had not implemented a system like this. Cryptography had to run in reality, in the end. Inserting noise was the product of a compromise that arose while pursuing optimal function and efficiency.
Hyeongju stepped forward, pushing up his glasses with his index finger.
“That is precisely why Director Yu hated artificial noise. Existing LEW-style encryption made the system heavy by raising the degree and generating noise. But there are no impurities in Utopia. Since it is pure geometry with the obstacles removed, the basic operations themselves become astonishingly light.”
One researcher raised a hand and objected.
“But the curvature of the space changes constantly. The derived noncommutative operations themselves should place an enormous burden on the system, shouldn’t they?”
Hyeongju spoke with his shoulders puffed up, as though it were his own achievement. Thanks to the common denominator that was Professor Kim Jiyun, he felt a one-sided inner closeness toward Seoha.
“That is where another masterpiece from Team Apex shines. Do you remember ST Compression, developed by Seoha and Theo?”
“Ah! Don’t tell me they applied that to the key mechanism of the encryption?”
“That’s right. For a user with a legitimate key, this structure isn’t heavy at all. Because the key itself serves as a compressed milestone, allowing them to pinpoint the shortest route to the destination with only a few operations, even within a complex space where curvature changes.”
“My God… Then if an attacker without the key wants to find it…”
“The attacker doesn’t know the range. In a space where the curvature changes with every step, they must wander the maze while directly calculating every infinitely derived noncommutative operation.”
To an attacker, it was a hellish maze where even computing for the age of the Earth would not be enough; to the owner with the key, it was a passage as light and elegant as a feather. That was the encryption Seoha had devised: Utopia.
For a while, the researchers could not continue speaking. One researcher murmured quietly, as if sighing.
“That’s unfair.”
“…”
“…”
No one said it aloud, but they were all thinking the same thing.
Kim Jihye, the senior researcher from Seoul National University, said with a sullen face,
“I always thought the concept of talent was somewhat vague. Whether there really exists something that effort can never catch up to… or perhaps it’s merely a difference in time. Starting earlier, or having a better environment.”
The people around her nodded.
“There’s certainly that aspect to it.”
“Jihye, you must have heard that you were talented your entire life, so I suppose you’d feel that way even more.”
She was one of the geniuses whose name was widely known not only in the industry, but in society as well. After all, she had been the only person to achieve a perfect score in the year of the notoriously brutal CSAT.
“I think this may be the first time I’ve seen it. The existence of a human being that simply cannot be explained by factors like time or environment. And…”
She tried to continue, then bit her lip.
Theodore Ranford.
The second-in-command of Apex Lab, who co-developed ST Compression with Seoha. Even if Yu Seoha was treated as an exception, what exactly was different between him and her? When it came to studying, she had confidence in herself as well. In all her life, she had never thought there was anything she could not accomplish in her field. But the moment she dissected Utopia, she instinctively understood.
‘I can’t make this. No matter how much time I have, no matter how perfect an environment I’m given.’
An intellect so impossibly high that she could not reach it even if she repeated her life countless times.
What was even more shocking was that cryptography was not his field of specialty. Merely by studying it intensively for a few short months, he and the team had created Utopia.
She looked at Theo.
Yu Seoha had seemed like a person from another world from the very beginning. He did not even feel like someone who could be used as a point of comparison. But Theo was different. He was someone who had walked a path similar to the way Jihye had lived. A being she felt she could understand, yet could not explain—that was Theo. Suddenly, a thought occurred to her.
‘Could the environment called Seoha have changed him?’
Jihye pondered whether her own life had lacked challenges.
And the people beside her had their eyes shining.
‘The person most deeply involved in Utopia’s design after Seoha.’
Min Jaehyeok, one of the Korean-side researchers, sipped his coffee and glanced sideways. He was a scholarship student from Korea’s largest corporation, and had infiltrated this place to steal the original encryption. However, Utopia’s very structure rendered any attempt at theft meaningless.
Even if he took it, he could not implement it. To design encryption on the same level, one had to understand Yu-Riemannian geometry and ST Compression as deeply as they did.
‘There’s no way such a person exists.’
Something visible, yet impossible to steal. That absurd reality made him laugh hollowly. So he had no choice but to turn his eyes toward people.
Jaehyeok set down his coffee cup. He had to rewrite his report. From the beginning.
* * *
Ding—
Theo looked down at his phone.
“Oh! Another one?”
Recently, contact from headhunters had increased noticeably.
Theo’s smartphone screen was filled with messages.
[Let’s arrange a meeting first. I hear they intend to offer a blank check.]
[Five times your current annual salary, stock options separate, and full authority over team formation guaranteed. You may continue your partnership with Director Yu.]
[This is a research institute under the Ministry of National Defense. I would like to discuss the details in person. Please understand that, for security reasons, I cannot say more than this.]
He indifferently scrolled through the flood of messages.
Overt courtship from the massive capital and state institutions that moved the Republic of Korea. It was on an entirely different level from when he had been in the United States.
“Aha!”
Thinking about it, it was only natural.
It seemed they had defined the three years that Seoha and the team would be in Korea as the golden time for recruiting key personnel.
Theo shook his head and trudged down the hallway.
After walking for a while, he heard the faint sound of a piano from afar. It came from a makeshift practice room that had been hastily built at Seoha’s special request. When he pushed open the soundproof door and entered, a gentle piano melody drifted softly into his ears.
‘He’s playing the piano again.’
Theo leaned against the wall and waited quietly.
Several years had passed since he met Seoha.
By now, Theo had come to understand him to some extent. Seoha sought out the piano whenever his mind was troubled. Theo guessed that it was like a ritual for organizing the equations overflowing in his head. Especially during the Riemann Hypothesis, the symptom had grown so severe that he had been listening to music constantly.
‘But why now?’
Theo tilted his head.
The work here was not actually all that difficult for Seoha. In a sense, it was like a vacation to resolve his military service. The Utopia system had already been designed, and even the complex curvature calculations that the researchers were analyzing in astonishment would have been about as difficult for Seoha as a morning walk.
He usually sank into himself like this only when he was touching the origin of the universe, or dealing with problems humanity had failed to solve for hundreds of years.
“Don’t tell me?”
The words slipped out before he knew it.
Just then, Seoha, who had finished playing, turned around.
“When did you get here, Theo?”
“Just now.”
Seoha’s expression looked as if he were deeply contemplating something. Theo became certain that his guess was correct.
“What problem are you thinking about these days?”
Seoha looked troubled. Then he gave a faint smile.
“If it’s you, Theo, I think I can tell you.”
“If possible, I’d prefer it to be a Millennium Problem.”
“Huh?”
Seoha’s eyes widened.
“Looks like I got it right. There aren’t many problems in the world that can make you serious. It has to be at least that much for us to get motivated too, doesn’t it?”
Theo chuckled.
‘I’ve come a long way too.’
From a mathematician known only to those in the know, to a precious talent receiving love calls from leading companies and organizations all over the world. And now, a member of the first team in history to challenge a second Millennium Problem.
All of this was possible because Seoha was there. If the headhunters had known that, they would not have bothered making such useless efforts.
‘You can achieve enough to go down in history even without Director Yu.’
He sneered inwardly.
Idiots. The problem is that Seoha wouldn’t be there.
Seoha stared at him and asked,
“Theo, do you believe there is a clear rule to the arrangement of prime numbers?”
“Hmm.”
He thought for a moment, then shook his head.
“No. At least, I don’t think there is a rule in a form we can understand. If I had to put it into words… randomness pretending to hide order in an extremely clever way?”
“Hahaha!”
Seoha clutched his stomach and laughed.
“Randomness pretending to have a rule… That’s such a Theo explanation. I think the same. There is an essential chaos in this universe. Not complete chaos, but not a clear order either. I believe this is connected to the ‘P equals NP’ problem. And dealing with encryption has only made me think so even more.”
Theo laughed cheerfully.
“You really are hopeless. They told you to make encryption, and you were poking at a Millennium Problem. Isn’t that an illness?”
At the joking remark, Seoha’s expression turned serious.
His gaze turned toward the doll placed on top of the piano. Then, after hesitating for a moment, he spoke with difficulty.
“Theo.”
“Yeah?”
“Actually, there’s a very naughty duck living inside me.”
“A duck?”
“Yes. That duck has been with me since I was very young, and it’s an incredibly curious one.”
Theo rubbed his chin.
‘Is this a metaphor? No, Seoha doesn’t usually speak this way.’
Seoha was the incarnation of logic. He should not have liked vague expressions… Theo decided to listen a little longer.
“And?”
“That duck loves numbers and order. And it’s extremely greedy. Greedy enough to gobble up even the Riemann Hypothesis in one bite and pat its belly afterward. Now, it wants other food.”
‘It’s a metaphor.’
“That’s quite an excessively greedy duck.”
Seoha’s expression was lonely.
“I don’t think I’ll ever escape this cycle in my lifetime. So if you receive a good offer, don’t hesitate over it. Because my greed might make you unhappy, Theo.”
Seoha knew very well that the fate he carried could wear down the people around him. But Theo, too, was not a human being within the normal range.
“What do you think would be the greatest misfortune that could befall me?”
“What would that be?”
Theo spoke with firm eyes.
“Hearing about your future achievements from the TV or newspapers at home. If you add the fact that I had absolutely no share in them, that would make it perfect. Just thinking about it makes me feel like I want to die.”
Seoha’s eyes widened.
“Huh?”
Theo patted him on the shoulder.
“So let’s not say anything useless. Though if I’m no longer of any help, I’ll gladly accept it.”
Seoha said in a choked voice,
“There isn’t a mathematician as wonderful as you anywhere in the world, Theo.”
“…”
On the way back to his lodging alone, a hot sense of elation rose from deep within his heart.
The team would run again.
Theo felt as though he had glimpsed Seoha’s secret. An intellectual hunger that could never be filled. Perhaps that was the price of the blessing God had bestowed upon Seoha.
“But why a duck, of all things?”
Even Theo, who knew Seoha better than anyone, could not figure that out at all.