Chapter 195
Translator: Dreamscribe
"What did you just say?"
The White House national security advisor, seated in the front row, frowned as he asked. The displeasure in his voice was unmistakable.
The generals from the Pentagon felt the same. In a national emergency where astronomical sums were vanishing every single day, nobody had the patience to humor a joke like this.
"That joke's gone too far, young man! Do we look like we have time to waste?"
A four-star general couldn't hold back and shot up out of his seat, shouting.
Murmuring spread through the audience. Heated reactions came pouring in, calling him arrogant, calling him disrespectful, demanding he be thrown out that instant.
But Seo-ha stood there with an unwavering look in his eyes.
He had agonized over it for a long time. Whether revealing Kyber's vulnerability here, in this room, was really the right thing to do.
Gathered in this place were the people with the power to make the decisions that mattered. If he stayed silent knowing Kyber could be attacked one day, and if someone else got hurt because of that silence, Seo-ha wasn't confident he could live with it.
"Quiet, all of you!"
Herbert rose and settled the hall. The instincts of an old scholar who had spent decades at the front line of cryptography were telling him that now was the time to listen.
He looked at Seo-ha and spoke quietly.
"I'll trust that you didn't make a pointless joke in an atmosphere like this."
Seo-ha nodded.
"If Kyber goes out into the world as it is, chaos like this will come back around within a few years."
That was when it happened.
"Impossible!"
Victor, the chief researcher, stood up below the podium, his face drained white.
"Kyber is lattice-based cryptography built on the Shortest Vector Problem (SVP). It's already been proven, perfectly, that not even a quantum computer running Shor's Algorithm can solve it in any feasible amount of time!"
At his shout, every eye in the hall swung back to Seo-ha.
What Victor said was common sense in the field of cryptography.
Finding the shortest vector inside a lattice structure meant the number of possible cases exploded exponentially as the dimensions rose. Even the finest supercomputer would need hundreds of millions of years of calculation to crack it.
"...."
Seo-ha adjusted his grip on the microphone and looked at Victor. A strange sort of pity lingered in his eyes.
"Yes, that's correct. As things stand, the lattice problem can't be solved by Shor, or even by the SS algorithm. But the future is a different story. Even if it isn't me, before long someone is going to notice."
"Notice what?"
Victor's voice trembled.
Beside him, Damian's pupils shook violently.
"Kyber's mechanism is excellent. It performs modular arithmetic over a polynomial ring and inserts artificial error into it."
Tap.
Seo-ha worked the laptop, and a complex multidimensional lattice, countless points tangled together, rose onto the screen.
The audience watched the display as though spellbound.
"In flat Euclidean space, punching through that error to find the shortest vector is impossible. It would take exponential computation, exactly as you said. But that's only true so long as the space is flat."
Tap.
He pressed the enter key, and the lattice on the screen slowly began to rotate.
"Huh?"
Victor's expression went blank.
He had realized what Seo-ha was about to do. Yu-Riemann Geometry fundamentally dealt with the distortion of dimension and space. He intended to tear down not Kyber, but the very premise of the LWE, Learning With Errors, approach itself. But was that truly possible? By human thought?
"B..bring the problem!"
At Herbert's order, a staff member rushed up onto the podium. In his hands was a laptop with a thick security cable attached to it. It held the most complex Kyber cipher in existence, one NIST had built internally to measure the limits of next-generation PQC.
Herbert handed it to Seo-ha with shaking hands.
"This is a master key algorithm that not NIST, nor the Department of Defense, nor the NSA's supercomputers have ever managed to so much as scratch. Go on. Break it. Just as you claim you can."
Seo-ha nodded quietly and linked the laptop to the large screen.
Clack clack clack clack.
The first moment he had recognized the possibility was a few months earlier, 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 that error was sufficiently random, an attacker couldn't recover s. That was the grand premise of the LWE approach.
But Seo-ha had seen the essential limitation of the pseudo-random values that had been created for the sake of efficiency.
Kyber's error e was generated through a function called SHAKE-256.
A structure that had no choice but to produce identical output when the seed value was identical. That meant it was, in essence, a problem with a finite answer.
"No matter how I think about it, finding the seed is impossible."
Damian muttered, one hand on his chin.
SHAKE-256's stability had already been thoroughly verified. For decades, no one had found any rule governing the function.
'This one thing is a structural problem.'
Once it had been mixed, the information diffused completely.
What Seo-ha was trying to do was drop a single drop of ink into the ocean and then gather that ink back up again.
Damian shook his head.
Seo-ha closed his eyes.
The murmuring around him and the doubt-laden stares receded like an outgoing tide.
Plop.
Into the silence that fell over the space inside his head, a single drop of black ink descended. It was crushed by the SHAKE-256 function and spread out into a sea of randomness. A seed, diluted on and on without limit.
But it was a problem he had already anticipated.
'Ducky, come out!'
The greedy duck slumbering in Seo-ha's depths opened its eyes.
Clack clack clack clack.
[b = As + e(mod q)]
The essential limitation of pseudo-random values.
It was that they used the NTT (Number Theoretic Transform) for computational efficiency. For the NTT to work, q had to be a prime satisfying certain specific conditions.
And there, a point of contact formed between LWE-style ciphers and Yu-Riemann Geometry. Having to use primes meant being connected to the zero structure of the Riemann Zeta Function.
They had stepped into the world of number theory and geometry that Seo-ha had proven.
'Why'd you call me?'
Ducky gazed out at the vast sea of numbers with a languid expression.
'I'm going to invert the seed. I need your help with the spatial processing.'
What would happen if the curvature made by the waves of the primes were applied to Kyber's NTT space?
Computation complex enough to leave the mind reeling.
Clack clack clack clack-
"Huh?"
Damian was the first to notice the anomaly.
"He's folding the space?"
The points of the lattice everyone had believed invincible were bending.
The space tore into countless tiny pieces. And those pieces folded endlessly, beginning to trace the seed back to its origin.
Crack-
An attack by a method no one had ever conceived of.
Damian heard the sound of something fracturing inside himself.
Clack clack.
Every time Seo-ha's fingers moved, the flat space crumpled and twisted like paper. The space screamed. A lattice structure no one had breached in decades was caught up in the curvature of Yu-Riemann Geometry and began converging to a single point.
"The seed was scattered, but it didn't disappear. Chase it all the way down and it has to show itself in the end."
No matter how diluted it was, from the moment it held a relationship with the primes, the seed could not escape Yu-Riemann Geometry.
A few years, maybe a few decades.
But it was only a matter of time. Someone would find this someday, without fail, and then a crisis like this one would come around again. So it had to be settled here and now.
'Got it!'
The ink was a particle made from the language of primes. No matter how diluted, its essence didn't change.
Clack clack clack.
Code came pouring across the screen.
Professor Kim Ji-yoon looked at the display and spoke as though letting out a sigh.
"He's extracting the seed."
Damian stared at the screen.
He had known the error elements sat within the residue system of q. Anyone who handled cryptography was aware of that. But the thought that it connected to Yu-Riemann Geometry had never once crossed his mind.
'Is it a difference of depth?'
It was only natural.
There was no way someone who could look into mathematics that deeply would be building something as trivial as a cipher.
Tap-
Seo-ha entered the final key, and the screen froze for an instant.
Everyone in the hall held their breath. A few seconds that felt like an eternity passed, and a single line surfaced on the display.
[Seed : 0X4F92...B147]
"This can't be happening."
Victor wanted to deny reality. Kyber's heart, the seed that should have been sealed inside an impregnable vault forever, had been laid bare in front of an audience.
Clack clack.
Seo-ha's hands didn't stop, entering the next command.
Based on the extracted seed value, the error vector e began to be inverted. The intricately tangled points of the multidimensional lattice aligned themselves along the Yu-Riemann curvature Seo-ha had set.
Tap.
The moment Seo-ha pressed the last key, the enormous lattice that had filled the large screen shattered into pieces like a collapsing glass wall.
And at last, the ciphertext appeared.
[Unbreakable Shield]
Crrrack, snap-
At last, the shell had broken apart completely.
Damian felt a shock like the world collapsing.
Thud.
The bundle of documents in Director Herbert's hand dropped to the floor.
On the screen, the plaintext of the master key that NIST had never once made public, the one they had believed to be humanity's last bastion, was exposed for all to see.
He looked at his watch.
"It didn't even take ten minutes."
Stagger-
Victor reeled and grabbed hold of a chair.
"Good Lord."
"God. Have You forsaken us?"
Sighs rose from the audience.
The generals' faces hardened. The bank presidents had gone as white as corpses. The cipher they had believed to be the ark that would save humanity had a hole in its hull before it ever set sail.
But none of that compared to the shock the cryptographers had received.
How many of the people in that hall properly understood what it meant? That the life of lattice-based cryptography had just been cut short.
Seo-ha stared at the ciphertext for a moment, then hit backspace twice, tap tap.
[Breakable Shield]
From the shield that couldn't be broken, the prefix that had meant impossibility was gone.
Silence.
At the moment hope turned to despair, a bleak stillness hung over the hall.
No one said a word.
Tick.
Tick.
A few minutes passed.
Only then did Murphy, the NSA Director, pull himself out of his shock and call out to Seo-ha.
"The..the alternative? Would Utopia be safe?"
Seo-ha smiled brightly and said,
"Of course. That's exactly why I came here today."
Tap.
The screen switched over.
A labyrinth of multidimensional geometry unfolded across the display, changing its shape and its space moment by moment like a living, breathing organism. It looked like a beautiful aurora rippling across a night sky.
Seo-ha looked at the audience with resolute eyes and said,
"Utopia has two etymologies. A good place, and a place that exists nowhere. To humanity I intend to give the former, and to hackers, the latter."
He had no intention whatsoever of forgiving the wicked.
*****
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