Chapter 187
Translator: Dreamscribe
Joseph still wore the look of a man who hadn't recovered from the shock. Back at his lodgings, his expression grim, he took out his laptop and opened the encrypted communications channel.
Tap, tap-
[Report on Yu Seo-ha's Activities and the Status of Next-Generation PQC Development]
-Recipient: NSA Senior Researcher David
David. I thought your assessment of him was an exaggeration. But it may be that even you have underestimated Seo-ha. His capacity for thought lies far outside the human range. What I witnessed was......
(section omitted)
Not a single cryptographic system humanity has ever built is safe before him. If Seo-ha slips beyond our control, I am afraid even to imagine the catastrophe it would bring upon national security.
I request that we cooperate fully with the new PQC development he is leading, and that, at the same time, his surveillance and protection classification be urgently raised to Tier Zero.
Joseph's hands trembled.
Click-
When he pressed the Enter key, a message appeared confirming that the mail had been sent successfully. In his eyes, lit by the glow of the monitor, the marks of fear were unmistakable.
"This is the best I can do."
Joseph muttered to himself.
That overwhelming intellectual violence, dismantling ciphers with an innocent expression as though he were simply taking out the trash. And yet Seo-ha seemed utterly unaware that he was a bomb capable of destroying, in a single stroke, the digital civilization humanity had built up.
***
[Apex Lab KOREA - Director Yu Seo-ha]
"I hear Mr. Yu Seo-ha was your student, Professor. It must feel strange for you."
Lee Hyun-seok, Minister of Science and ICT, glanced at Professor Kim Ji-yoon, who had come along, as he asked. Ji-yoon smiled faintly and shook her head.
"In the world of mathematics, the word 'student' isn't used so lightly. Seo-ha is no one's student."
"How complicated."
"Yes. It's a delicate matter, too. But Seo-ha will have plenty of students of his own before long."
Rumors that Seo-ha would soon be appointed to a faculty position had spread all through academia.
Most likely after his discharge from the military.
She had heard that the Ivy League universities were losing sleep over him.
Knock knock!
She had been told he was inside, but there was no answer.
One more knock.
Knock knock!
Creak-
Ji-yoon carefully opened the door.
There stood Seo-ha by the window. He was wearing headphones and gazing at the blackboard. Ji-yoon stole a glance at the equations.
Lattices, probability, complexity, and curves whose meaning she couldn't grasp, along with a few short lines of text.
[Are being hard to solve and being beautiful a contradiction?]
A question every mathematician who studies cryptography has pondered at least once.
Ji-yoon's face took on a wistful look. Five years ago, she had found her own answer to this question.
That yes, it was a contradiction.
Every beautiful cipher she knew of fell short in terms of performance and efficiency.
Elliptic Curve Cryptography (ECC), used in blockchain and secure communications, is mathematically very elegant but has almost no quantum resistance.
'What conclusion will you reach?'
Her thoughts were tangled.
Alongside the hope that he might have a different answer to offer, there coexisted a petty feeling that even Seo-ha would ultimately be helpless against it.
When the Minister, who had waited a few seconds, made to call out to Seo-ha, Ji-yoon raised a hand to stop him.
Time passed.
One minute.
Two minutes.
Scribble.
As if he had realized something, Seo-ha suddenly began drawing a graph on the blackboard. The lines expanded and contracted in turn, forming a bizarre pattern. Ji-yoon tried to understand it, but she couldn't make out its meaning.
"Oh? Professor!"
Stretching himself, he noticed the two people standing in the doorway.
Ji-yoon smiled and offered a greeting.
"Hello, Seo-ha. This is Minister Lee Hyun-seok of the Ministry of Science and ICT."
Seo-ha's face stiffened for a moment. Then, after thinking for about two seconds, he hurriedly flung off his headphones.
"Sir!"
A knife-sharp posture, the boot-camp conditioning not yet fully worn off. Ji-yoon looked on with an impressed expression.
"Oh my! Director Yu! There's no need for that. I'm not a soldier."
The Minister laughed heartily and took Seo-ha's hand.
"Be at ease. I've heard you went through your training very diligently."
Trickle.
Ben, who now handled secretarial duties as well, came in and set out black tea. It was a top-grade batch Morris had flown in from England.
"Ahem, ahem! I heard about what happened a few days ago. They tell me you cracked the cipher the researchers made."
Perhaps too eager to wait, the Minister was the one to bring up the main subject first.
Joseph's report had reached the NSA at two in the morning.
Director Murphy, having read it, convened an emergency meeting that morning. It was a vice-ministerial-level gathering attended by officials from NIST, the financial sector, and the Department of Defense.
The United States had planned to apply three PQC systems, Kyber among them, to financial institutions and military communications within the next ten years. The Department of Defense alone had already allocated hundreds of billions of dollars in budget...... and they could not ignore the possibility that this very foundation might be shaken.
"It was possible because it was still in the early stages of development. LWE isn't that weak."
Seo-ha's expression said it was no big deal.
Perhaps his insides were burning, for Minister Lee lifted his cup and gulped down the hot black tea.
'It would have been nice if he'd gone into engineering......'
To him, a former engineer, Seo-ha was plainly squandering his talent.
If this brilliant mind were put toward developing cutting-edge technology, just how much economic value could it create?
"So what are you planning to do from here?"
Ji-yoon asked, pulling a chair up in front of him and sitting down.
"Professor."
"Yes?"
"I think I'm someone who doesn't really suit cryptography."
A vein stood out at the Minister's temple.
'What in the world is this nonsense?!'
To smash to pieces a cipher that dozens of experts had labored over, and then to say this......
But he summoned superhuman patience and held his tongue. He had been warned many times over that Seo-ha greatly disliked being pressured.
"Why did you come to think that?"
Ji-yoon asked, watching him as if to coax him along.
"A cipher is basically like a math problem you set for an unspecified crowd of people, isn't it?"
"You could see it that way."
"But you have to give them a problem that can't be solved within the given conditions."
Seo-ha frowned.
RSA is based on the idea that factoring very large numbers into primes is difficult. Realistically, beyond anything one could ever manage. On a home computer, it would take thousands of years, perhaps hundreds of millions of years or more.
Seo-ha's paper had dramatically reduced the computation time of this problem by narrowing the range of the prime arrangement.
"That's right. That's the core concept of modern cryptography."
"LWE comes down to the same idea. Mixing in noise to make the computation a nuisance. Making the problem so complicated that no one wants to solve it. Honestly, I think it's a fairly sound approach. The lattice problem will probably stay safe for decades to come."
Ji-yoon nodded.
"Cryptographers, myself included, think that's the best option we have right now."
"But someday the lattice problem is bound to become easy to solve too. Once a groundbreaking algorithm appears, or a far more powerful computer shows up. In the end, I'd say it's an approach with a fixed lifespan."
Why worry now about a future decades away!
The Minister's face flushed red.
Ji-yoon set down her black tea and gazed intently at Seo-ha. She had sensed in his attitude the hesitation peculiar to mathematicians.
Seo-ha could surely produce a cipher that met NIST's requirements this very instant. But he wasn't doing so.
It was because he valued mathematical integrity. Just then, a thought flickered through Ji-yoon's mind.
'Integrity?'
Calming her trembling heart, she asked.
"Are you, by any chance, grappling with the P≠NP problem?"
P≠NP, or P=NP, one of the Millennium Prize Problems.
P is the set of problems a computer can solve quickly. NP is the set of problems that are quick to verify but difficult to solve.
In other words, if you define the P≠NP problem in a single sentence, it goes like this.
'This problem has an answer that's easy to check, but you will not be able to solve it easily.'
And most existing cryptographic systems are built upon the assumption that this proposition is true.
The existence of problems that cannot be solved efficiently. In a sense, this is also a question about the essential limits of humanity.
Seo-ha nodded with an awkward smile.
"Ah!"
Only now did Ji-yoon understand.
The reason Seo-ha had shown no particular interest in cryptography. It was because the grand premise of cryptography had never been proven.
To Seo-ha, who had a case of mathematical perfectionism, it must have felt like building a house upon sand.
Ji-yoon asked in an urgent voice.
"Don't tell me you mean to solve P≠NP first?"
It hadn't been long at all since he'd solved the Riemann Hypothesis.... The thought that Seo-ha was about to throw himself at another impossible problem left Ji-yoon aghast. Seo-ha waved his hands with a smile.
"No. Of course not. I'm not that out of touch with reality."
If the Riemann Hypothesis is the holy grail of number theory, then 'P Not Equal NP' could be called cryptography itself. Some ten-odd years ago, there had been a large-scale survey of mathematicians.
Mathematicians overwhelmingly regard 'P≠NP' as true.
Eighty-three percent agreed with this conjecture, while only nine percent of mathematicians answered that 'P=NP' was likely correct. It could hardly be otherwise, for if P=NP were to hold, then in every field, pharmacology, biotechnology, mathematics, computer engineering, nuclear fusion, and more, the world would become something entirely different from what it is now.
Ji-yoon wanted confirmation. In a trembling voice, she asked Seo-ha.
"Seo-ha. Do you think P equals NP is correct?"
Tick-tock, tick-tock.
Silence fell.
It was only a few seconds, but to Ji-yoon that span felt dozens of times longer.
"No."
Seo-ha said firmly.
"P is not NP."
Ji-yoon let out a sigh of relief.
If Seo-ha had given the opposite answer, it would have meant the world could change on the scale of heaven and earth being overturned. That was how much Ji-yoon trusted Seo-ha.
"Then there's no problem with making a cipher, is there?"
Seo-ha believes that an essential difficulty exists. If so, then it should be possible to build a cipher that makes use of it.
"Yes! Actually, I have something I've already sketched out. Would you like to see it?"
Rustle.
This was the purpose of today's visit to the lab. A flicker of tension crossed the Minister's face.
What Seo-ha handed over was a single sheet of paper. Ji-yoon took it and began to read.
"Noncommutative algebra cryptography...."
"As expected of you, Professor. You recognize it."
This was a matter that had already been settled among cryptographers long ago.
Some twenty years back, when Braid Group Cryptography first appeared, academia had stirred for a while. A noncommutative structure in which the result changes depending on order, like the braiding of strands of hair.
From an attacker's point of view, the number of possible cases grew explosively, so in theory it looked impregnable.
But in less than four years, this cipher collapsed. The attackers had converted the noncommutative structure into a commutative one.
Seo-ha knew all of this and still chose a noncommutative structure. With an innocent smile, he said.
"Don't worry. I'm going to build the structure using Riemannian geometry."
Ji-yoon raised her head and looked at the blackboard once more.
A form in which graceful curves were geometrically, dizzyingly intertwined. She thought it was truly beautiful.
[Are being hard to solve and being beautiful a contradiction?]
Seo-ha was declaring, firmly.
That it was by no means a contradiction.
Creak- click.
The door closed, and Seo-ha was alone once more.
His expression turned cold.
'Why did you lie? You're planning to solve P≠NP.'
Seo-ha rose from his seat and looked at the Duck Mask on his desk.
"Because I think it's a solvable problem. But I'm not ready yet. It might take years."
'Tch!'
"How about being satisfied with a cipher? You seem to like it quite a bit."
'Ah, that's right. The truth is, you want someone to challenge you too. There'll be plenty of fools who walk fearlessly into the abyss.'
Ducky laughed, making a grotesque sound.
Seo-ha put the headphones he'd taken off back on his head. From the player flowed Han Gyeo-ul's performance.
*****
For 30 or more extra chapters, you can check out my Patreon here --> patreon.com/dreamscribe
If you enjoy this novel, please review and rate it at Novelupdates. Thanks! 😊
To receive the latest update notifications or report mistakes, join our Discord server linked below.