“What did you just say?”
The White House national security adviser seated in the very front row asked with a frown. Displeasure was plain in his voice.
The generals from the Pentagon were no different. In a national emergency where astronomical sums of money were disappearing every day, no one had the leisure to indulge a joke like this.
“That joke has gone too far, young man! Do we look like people with time to waste?”
A massive four-star general could no longer contain himself and sprang up from his seat, shouting.
A murmur spread throughout the audience. Arrogant, rude, throw him out at once—heated reactions poured out from every corner.
But Seoha stood there, his gaze unwavering.
He had agonized over it for a long time. Whether it was truly right to reveal Kyber’s vulnerability in this place.
Gathered here now were people capable of making important decisions. If he remained silent despite knowing that Kyber could be attacked in the future, and if someone else suffered because of it, Seoha was not confident he could bear that burden.
“Quiet!”
Herbert rose and calmed the audience. The instinct of an old scholar who had spent long years at the forefront of cryptography was telling him that now was the time to listen.
He looked at Seoha and said quietly,
“I trust you are not making a frivolous joke in this atmosphere.”
Seoha nodded.
“If Kyber goes out into the world as it is, chaos like this will come again within a few years.”
It was then.
“That’s impossible!”
Victor, the chief researcher below the stage, rose from his seat, his face gone deathly pale.
“Kyber is a lattice-based cryptosystem built on the Shortest Vector Problem, SVP. It has already been perfectly proven that even Shor’s algorithm on a quantum computer cannot solve it within a feasible time!”
At his shout, every gaze in the hall turned back to Seoha.
Victor’s words were common sense in the field of cryptography.
Finding the shortest vector within a lattice structure caused the number of possibilities to explode exponentially as the dimension increased. It was a problem that even the most powerful supercomputer would need hundreds of millions of years to solve.
“…”
Seoha adjusted his grip on the microphone and looked at Victor. A strange pity lingered in his eyes.
“Yes, that’s correct. In its current state, the lattice problem cannot be solved not only by Shor’s algorithm, but even by the SS algorithm. But the future is different. Even if it isn’t me, someone will notice before long.”
“Notice what?”
Victor’s voice trembled.
Damian’s eyes, seated beside him, shook violently.
“Kyber’s mechanism is excellent. It performs modular operations over a polynomial ring and artificially inserts errors into them.”
Tap.
When Seoha operated the laptop, a complex multidimensional lattice entangled with countless points appeared on the screen.
The audience stared at the display as if possessed.
“In flat Euclidean space, breaking through those errors to find the shortest vector is impossible. As you said, it would require exponential computation. But that is only true as long as the space is flat.”
Tap.
When he pressed the Enter key, the lattice on the screen slowly began to rotate.
“Huh?”
Victor stared blankly.
He had realized what Seoha was trying to do. Yu-Riemann geometry fundamentally dealt with the distortion of dimensions and space. He intended to collapse the very premise of LEW—Learning With Errors—not merely Kyber. But was that truly possible? With human thought?
“B-bring the problem!”
At Herbert’s command, a staff member hurriedly ran up onto the stage. In his hands was a laptop connected to a thick security cable. It contained the most complex Kyber cipher currently in existence, created internally by NIST to measure the limits of next-generation PQC.
Herbert handed it to Seoha with trembling hands.
“This is the master key algorithm that not only NIST, but even the supercomputers of the Department of Defense and the NSA could not so much as scratch. Now, break it. Just as you claimed you could.”
Seoha quietly nodded and connected the laptop to the large screen.
Tatatatatak.
The moment he first recognized the possibility was several months ago, when he broke Team Apex Korea’s lattice cipher.
[b = As + e(mod q)]
Here, e was an error vector drawn from a discrete Gaussian distribution.
Because this error was sufficiently random, an attacker could not recover s. That was the great premise of the LEW method.
However, Seoha had seen the inherent limitation of pseudo-randomness created for efficiency.
Kyber’s error e was generated through a function called SHAKE-256.
A structure that had no choice but to produce the same output if the seed value was the same. That meant it was essentially a problem with a finite answer.
“No matter how I think about it, finding the seed is impossible.”
Damian muttered with a hand on his chin.
SHAKE-256 had already been sufficiently verified for stability. For decades, no one had found a rule in that function.
‘This, at least, is a structural problem.’
Once mixed, the information completely diffused.
What Seoha was trying to do was like dropping a single drop of ink into the sea and then gathering that ink back again.
Damian shook his head.
Seoha closed his eyes.
The surrounding murmurs and doubtful gazes receded like the tide.
Plop.
A single drop of black ink fell into the silent space within his mind. It was crushed by the SHAKE-256 function and spread into the sea of randomness. A seed diluted endlessly, infinitely.
But it was a problem he had already anticipated.
‘Ducky, come out!’
The greedy duck sleeping in Seoha’s depths opened its eyes.
Tatatatatak.
[b = As + e(mod q)]
The inherent limitation of pseudo-randomness.
It was that, for computational efficiency, it used NTT—Number Theoretic Transform. For NTT to function, q had to be a prime number that satisfied specific conditions.
Here, a point of contact arose between LEW cryptography and Yu-Riemann geometry. The necessity of using prime numbers meant it was connected to the zero structure of the Riemann zeta function.
They had stepped into the world of number theory and geometry that Seoha had proven.
‘Why did you call me?’
Ducky looked out over the vast sea of numbers with a languid expression.
‘I’m going to reverse-calculate the seed. I need your help with spatial processing.’
What would happen if the curvature created by prime-number waves were applied to Kyber’s NTT space?
A computation so complex it made the mind grow distant.
Tatatatatak—
“Huh?”
Damian was the first to notice the anomaly.
“He’s folding the space?”
The lattice points he had believed invincible were bending.
Space was torn into countless tiny fragments. And as they folded endlessly, they began tracing the origin of the seed.
Crack—
An attack in a way he had never once imagined.
Damian heard something cracking inside him.
Tatatak.
Each time Seoha’s fingers moved, the once-flat space crumpled and twisted like paper. Space screamed. The lattice structure no one had invaded for decades was caught in the curvature of Yu-Riemann geometry and began converging into a single point.
“The seed was scattered, but it didn’t disappear. If you trace it to the end, it is bound to reveal itself.”
No matter how diluted it became, the moment it possessed a relationship with prime numbers, the seed could not escape Yu-Riemann geometry.
A few years, perhaps a few decades.
But it was only a matter of time. Someone would inevitably discover this someday, and then a crisis like the present one would come again. So it had to be concluded here and now.
‘Done!’
Ink was a particle made in the language of prime numbers. No matter how diluted it became, its essence did not change.
Tatatatak.
Code poured across the screen.
Professor Kim Ji-yoon spoke as if sighing while looking at the display.
“He’s extracting the seed.”
Damian stared at the screen.
He knew that the error elements lay within the residue class of q. Anyone who dealt with cryptography was aware of that. But he had never once thought it could be connected to Yu-Riemann geometry.
‘Is it a difference in depth?’
It was only natural.
After all, someone capable of seeing into mathematics to that depth would never bother making something as trivial as a cipher.
Tap—
When Seoha entered the final key, the screen stopped for an instant.
Everyone in the hall held their breath. A few seconds passed, feeling like an eternity, and then a single line appeared on the screen.
[Seed: 0X4F92···B147]
“This can’t be happening.”
Victor wanted to deny reality. Kyber’s heart—the seed that should have remained sealed forever inside an impregnable vault—had been fully exposed before the audience.
Tatak.
Seoha’s hands did not stop as he entered the next command.
Based on the extracted seed value, the error vector e began to be reverse-calculated. The points of the complexly entangled multidimensional lattice aligned along the Yu-Riemann curvature Seoha had set.
Tap.
The moment Seoha pressed the final key, the massive lattice filling the large screen shattered to pieces as though a glass wall had collapsed.
And at last, the plaintext appeared.
[Unbreakable Shield]
Craaaack, snap—
At last, the shell was completely broken.
Damian felt a shock as if the world were collapsing.
Thud.
The bundle of documents in Director Herbert’s hand fell to the floor.
On the screen, the plaintext of the master key, which NIST had never once disclosed and had believed to be humanity’s final bastion, appeared in stark detail.
He looked at his watch.
“It didn’t even take ten minutes.”
Stagger—
Victor swayed and grabbed the chair.
“My God.”
“Lord. Hast Thou forsaken us?”
Sighs came from the audience.
The generals’ faces hardened. The bankers’ complexions, too, had gone as white as corpses. The cipher they had believed to be the ark that would save humanity had a hole in its bottom before it had even set sail.
But none of this could compare to the shock the cryptographers had received.
How many people in the hall truly understood what it meant? That the life of lattice cryptography had just been severed.
Seoha stared at the ciphertext, then tapped Backspace twice.
[Breakable Shield]
The prefix meaning impossibility vanished from the unbreakable shield.
Silence.
At the moment hope turned into despair, a bleak stillness settled over the hall.
No one spoke.
Tick.
Tick.
Several minutes passed.
Only then did NSA Director Murphy, finally emerging from the shock, look at Seoha and shout,
“Th-the alternative? Is Utopia all right?”
Seoha smiled faintly and said,
“Of course. That is why I came here today.”
Tap.
The screen changed.
A multidimensional geometric maze unfolded on the display, changing its form and space from moment to moment like a living organism. It was like a beautiful aurora rippling across the night sky.
Seoha looked at the audience with resolute eyes and said,
“The word Utopia has two origins. A good place, and a place that exists nowhere. I intend to gift the former to humanity, and the latter to hackers.”
He had no intention of ever forgiving the wicked.