The top student must be diligent.

Chapter 113 Xiao Polynomial Expansion
As he was thinking about this, Xiao Yi suddenly slapped his head.

"What are you thinking about now... Let's think about this problem first."

“A cross-blockchain encrypted transaction… a sorting sieve… a protocol…”

【Millionaire Problem】.

He wrote these words again on the draft paper.

In the process of solving the millionaire's problem, it is also necessary to first build a protocol and then achieve the solution.

In this process, no third party is involved, ensuring the security of the transaction.

"But...what if one of the two millionaires is dishonest, or both want to know the other's wealth?"

"This makes it a semi-honest model..."

"But there are prime numbers involved..."

“And the most important thing is that this transaction does not occur within the blockchain, but between cross-chains.”

Xiao Yi pinched his eyebrows with a headache.

If it is just a transaction within the blockchain, it would not be so troublesome, but the problem is that this is a transaction between cross-blockchains. Bitcoin is Bitcoin, and Ethereum is ETH, so in cross-chain transactions, it is necessary to implement the process of exchanging Bitcoin for ETH.

Therefore, in addition to ensuring the atomicity of cross-chain transactions as mentioned earlier, security must also be guaranteed.

It is precisely because of the "cross-chain" that problems arise. A third party appears in the process of the transaction, generally speaking, it is a cross-chain trading platform. In the CSGO accessories transaction that everyone is familiar with, NetEase BUFF is equivalent to this cross-chain trading platform.

This process may lead to theft by the trading platform, and of course, hacker attacks, etc. In fact, these two types of things have already happened in the cross-chain transaction process.

This is also the main reason why many parties, including the World Bank, want to make this agreement.

Now, due to the risks brought by the classification screen, according to what Professor Kleinlock said, the investors, that is, the World Bank and other banks, as well as the requirements of the blockchain companies that invested money, the encryption method of this cross-chain protocol also needs an algorithm that can avoid the classification screen attack.

Probably every group around the world participating in this project will have a headache about this requirement.

The same goes for Xiao Yi.

After all, he had just invented the classification sieve, and the classification sieve had become one of his most useful tools. It not only successfully cracked the twin prime conjecture, but has also made good progress on the x^2+1 prime number problem.

As a result, he was asked to come up with something that could make the classification screen ineffective.

Isn't this equivalent to letting yourself deal with your own children?

If the sorting sieve could open its eyes and mouth, it might say to him, "How presumptuous of you!"

"If you ask me, why bother with RSA when all the encryption algorithms are elliptic?"

The elliptic encryption algorithm is ECC, and its mathematical basis comes from the computational difficulty of the elliptic discrete logarithm on the Abelian additive group formed by rational points on the elliptic curve. It is much more difficult to crack it than RSA.

However, Xiao Yi finally sighed. Obviously, this is not realistic, because the mathematical difficulty of ECC is much higher than that of RSA. RSA uses the difficulty of factorizing large prime factors, and anyone with a certain mathematical foundation can understand it. As for ECC, based on the above paragraph, it is estimated that unless you are a mathematics major, how many people can understand it?
Therefore, RSA has already covered the encryption system worldwide because of its simplicity and ease of use. Naturally, it is impossible for ECC to completely replace RSA encryption. Even on some old devices, ECC encryption may cause incompatibility issues because the systems of those old devices do not support ECC encryption.

Taking this into consideration, it is still necessary to know how to classify and screen.

"So, I still have to deal with the theory I came up with myself."

Xiao Yi rubbed his face and said to the sorting screen in his heart: "Sorry, baby."

Then he concentrated again and thought about the problem.

"Well, according to the classification sieve, for the prime factorization of all large numbers, we will be able to separate the number of prime factors and use this to solve the problem..."

Suddenly, Xiao Yi's brows moved.

He remembered the key step in his proof of the twin prime conjecture.

"Oh, by the way, I mentioned in the paper that we can extract the basic group information by using the method of Etale algebraic variety self-conservation theory!"

"And based on this basic group information... we can encrypt from this basic group information!"

"Oh! And the L-function! Don't forget that."

"Use L-function to analyze the complex polynomials, and then use ..."

He wrote a line of formula on the draft paper.

【[Z1Z2]=[Z1][Z2](ReZ1Z2/|Z2|^2……】

After thinking for a while, he started writing again.

[Definition (n)=ΣΣ(r^2+s^2=n)(s/r)...]

And this time, his pen did not stop.

In this way, he wrote more and more things on the draft paper, and finally a gradually unified thinking began to form in his mind.

That thought broke through the previous fog.

It also broke through the obstacles in his mind.

He quickly finished writing on a piece of draft paper, put it aside, and began to deduce quickly on the second piece of draft paper.

While writing the previous step, I already thought about how to write the next few steps in my mind.

The 10th level of [Ruthless Link], with 17 times the efficiency, was also fully utilized at this time.

……

Time passed in the burst of knowledge.

The sun outside the window finally set at the end of the west coast.

When the last ray of afterglow happened to shine on the table under the windowsill, making the surface of the draft paper red.

Xiao Yi stopped writing.
Finally... he found it!
He found out how to deal with his "baby"!
cough cough...

But in short, after the original mathematical information is transformed, he is sure that he has found a way to eliminate the risks brought by the classification screen to cross-chain transactions.

And it doesn’t just stop there!
He suddenly laughed. "I see! It turns out that the hidden information in mathematics can be used in this way!"

"I understand!"

Pick up the draft paper in your hand.

The red sunlight shining in from the window left the paper and made the words on it clearer.

What appeared before him were lines of formulas that might be criticized as weird in the mathematics community and lacked the beauty of mathematics.

However, in fact, during an attempt, he extracted the information of the etale basic group losslessly into the complex domain!
What is the use of this method?

"If we use this method to solve the Siegel-Zero-Point Conjecture..."

Xiao Yi thought that he already had a possible solution to this conjecture.

The Siegel-Zero conjecture involves analysis over the field of complex numbers.

And now he has found the key to the analysis.

but……

It’s quite embarrassing to talk about it.

After all, he is now in Terence Tao's research group, but he found the solution to Zhang Yitang's zero-point conjecture first.

Of course, he also has to thank Zhang Yitang for sharing his results on the Siegel-zero conjecture with him before, so he immediately thought of the idea of ​​using L-function to study this problem. When he meets Zhang Yitang in the future, he must share this matter with him!
Of course, he is not completely sorry to Terence Tao and Maynard.

after all……

At stake is the outcome of a massive $1000 million prize, and they are already in the lead!

"Hopefully, they won't be too surprised when they see it tomorrow."

Xiao Yi smiled slightly.

Putting down the draft paper in his hand, he looked at the afterglow outside the window.

"Hmm~ What a satisfying problem-solving process!"

……

“…When we analytically extend the L function, we get a new complex field polynomial, which contains the private key information that can match the RSA public key.”

"At this point, we just need to perform a simple Fourier transform on it..."

"Okay! All the original information is gone! But the format of the public key and private key has not changed."

"Still only the private key can achieve decryption!"

The next morning.

As the morning sun shone into the office of the UCLA Department of Mathematics, the two mathematicians stared in amazement at what the boy had written on the blackboard.

There was also an old professor from the computer science department nearby, who was completely confused because what was written on the blackboard was a bit incomprehensible to him.

He now really wanted to know what Xiao Yi had written.

As Xiao Yi finished writing, Maynard asked hurriedly: "How to prove it? How to prove that the loss of information after Fourier transform will not make the private key invalid?"

Kleinrock: “No, what are you talking about?”

"Hmm?" Xiao Yi took another look at the process he wrote on the blackboard, and then recalled what he had just said.

He should have made it quite clear, right?

Of course, Tao did understand.

He nodded slightly and said to Maynard, "Pay attention to the form of this polynomial. Although some information is lost after the Fourier transform, it does not affect the decryption of the private key."

Maynard was stunned and looked at the polynomial written on the blackboard again.

Finally, he suddenly realized: "I see! This polynomial... My God, I have never seen such a polynomial expansion before. Is this something you have newly researched?"

Kleinlock: "So what? Explain it to me, please!"

"Well... roughly." Xiao Yi thought about it, then nodded, "It incorporates some of the content of Fourier expansion, but this new expansion is more useful in the field of complex numbers."

"It seems that in the field of complex analysis, there will be a new method called Xiao expansion." Tao exclaimed.

"This new development can reveal the information of the complex field in a more detailed way, and many new things can be extracted from it, which may be helpful for studying the Riemann hypothesis!"

“It’s so unbelievable!”

Maynard also said: "Amazing!"

Recalling when they first arrived at the office this morning, Xiao Yi directly stated that he had found a way to deal with the classification screening problem.

Then, he showed them this wonderful derivation.

This new complex field polynomial...

What a wonderful polynomial!
At first glance, they felt that there was no mathematical beauty in it, but once they understood the polynomial, they found that it was full of beauty!
But right now.

"Oh! Jesus! Professor Kleinlock! What are you doing! Don't jump!"

……

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(End of this chapter)