The top student must be diligent.

Chapter 122 Questions from Turing Award Winners
The RSA encryption algorithm, one of the foundations of cryptography, has been directly and forcibly improved to a level of security that is not inferior to the ECC elliptic encryption algorithm in the solution to the classification sieve attack proposed by the young man in front of him. The difficulty of cracking it has directly reached an exponential level.

According to a public report released by the IEEE yesterday, the number of password bits required for the RSA encryption system has been greatly reduced under the Xiao Sieve attack solution.

In the past, the recommended password bit number for the ECC encryption algorithm was 256 bits, while the recommended bit number for the RSA encryption algorithm was as high as 1024 bits or even 2048 bits.

The higher the number of bits, the lower the efficiency.

Because the higher the number of bits, the more computational effort it takes to crack the password directly, but it also increases the time required to use the password, such as the time to write the password, which takes up a lot of computing power.

At the same time, as the performance of computers on the earth becomes stronger and stronger, the cracking speed becomes faster and faster. In order to ensure security, the RSA encryption algorithm can only continuously increase the number of password bits, which is very inconvenient.

But now...

The report pointed out that when the number of password bits is 277, the difficulty of cracking the RSA encryption algorithm under Xiao Yi's system is equal to that of ECC.

If the number of password bits continues to increase, the difficulty of cracking the RSA encryption algorithm under this system will become increasingly higher than that of ECC encryption.

This means that as computer performance continues to improve, when the recommended password number of ECC is higher than 277 bits, it will no longer have any advantages over RSA.

Therefore, Xiao Yi almost single-handedly made the RSA encryption system secure again, and the RSA system will not be eliminated for a long time in the future.

To some extent, this is equivalent to saving a huge cost for the entire information security field, whether it is people's learning costs or the economic cost of originally planning to replace the RSA encryption system.

Probably, even if quantum encryption becomes completely popular in the future, RSA will still remain strong because of its cost advantage.

Perhaps, decades later, Xiao Yi’s name will also be on the Turing Award?
"Hello everyone, I'm Xiao Yi."

Xiao Yi's voice brought the computer experts present back to their senses.

Then they calmed down and began to listen to the report carefully.

"I am honored to be invited by AMS to give an impromptu speech at this joint mathematics meeting a few days ago."

"I believe that everyone is here for the polynomial expansion method I recently came up with. I do have a lot of ideas about this method."

"Then I will simply pick out some of the ideas that I think are more important and talk about them."

"First, there is the Riemann hypothesis."

Xiao Yi turned around and wrote the expression of the Riemann zeta function on the blackboard.

【Let s be a complex number such that Re(s) is greater than 1, then ζ(s)=∞∑_(n=1)1/n^s】

Hearing what Xiao Yi said, the mathematicians present all had their eyes brightened and sat up straight.

It turned out to be the Riemann hypothesis!
Although they do not think that Xiao Yi has even proved the Riemann hypothesis, if he could say something about his thoughts on the Riemann hypothesis, perhaps it would be able to bring some inspiration to many scholars who are studying the Riemann hypothesis?

These days, thanks to Xiao's work, the mathematics community has approached the critical line theorem of the Riemann hypothesis to 61%. However, after reaching this point, they found that they seemed unable to proceed any further.

They hope Xiao Yi can give some direction.

"I have also read the recent paper that approaches the critical line theorem to 61%." Xiao Yi said, "But in fact, we can still go a little further on this point."

"Just like this."

He then gave a brief demonstration on the blackboard.

He wrote out the last few steps of the 61% paper from memory, and then he simply added a few more steps on top of it.

【ψ_(d=1)(s)=∑_(n≤y1)^2(n)n^(σ01/2)/n^s……】

"Finally, we can easily push the critical line to 62.5%, which is 5/8."

"However, it is difficult to decide how to proceed. I think that the critical line approach method has reached its limit under Xiao's deployment."

There was silence in the audience.

Scholars in the field of mathematics stared at Xiao Yi's few moves that seemed to come easily.

You call this "easy"?
If it was really that easy, would you still have to take action?

As for the scholars in the computer field, they looked confused and impressed.

They had also heard of the Riemann hypothesis.

Although I don’t understand what Xiao Yi’s moves are, anyway, since they are related to the Riemann hypothesis, they must be not simple.

However, Xiao Yi on the stage did not show any emotion about this result, and then said: "In fact, compared to the critical line theorem, I am more interested in another theorem."

"The Bohr-Landau theorem, proved by Harold Bohr and Edmund Landau in 1914, states that for any δ > 0, the fraction of all nontrivial zeros whose distance from the critical line is greater than or equal to δ is infinitesimal."

"In other words, any arbitrarily narrow vertical strip centered on the critical line contains almost all of the nontrivial zeros."

"Although this theorem does not even prove that there is a non-trivial zero on the critical line, I think this theorem is quite interesting."

"Now let's use Xiao's expansion to discuss this theorem..."

Afterwards, Xiao Yi started writing on the blackboard again. This time, it was even more complicated and difficult than the previous method to advance to 62.5%.

When the mathematicians below saw the new things written by Xiao Yi, they gradually started to think about them.

And just like that, time passed quickly.

This speech was indeed as Xiao Yi said, he just gave a simple speech.

Mainly to show the mathematicians who came to attend his report some more advanced uses of Xiao's expansion.

It is almost equivalent to some technical sharing, but does not bring any new results.

After all, new results don't come just because you want them, just like the x^2+1 prime number problem that he discussed with Terence Tao and Maynard. After so many days of discussion, although there has been very positive progress, it is still a long way from the final solution. Even Xiao's expansion cannot play a big role in solving this problem.

Of course, even if it was just some technical sharing, it was already a great surprise for the mathematicians on the scene, especially his new thinking on the Riemann hypothesis, which also gave those mathematicians a lot of ideas.

Xiao Yi did not only talk about things related to the Riemann hypothesis, but also some other aspects, such as the error analysis of calculating the Cauchy principal value integral using the effective integration formula in complex analysis, contour integrals and combinatorial identities.

Or it may be applied in various fields such as harmonic analysis and ergodic theory.

In short, although Xiao Yi spoke very fast, he gave very eye-catching applications in every direction.

For a moment, all the mathematicians present felt even more amazed at the young man in front of them.

How much math has this guy mastered?
Why does it feel like there is nothing he doesn't understand?
And just like that, thirty minutes passed.

"...Okay, that's what I plan to share in this speech. I hope it can give you some thoughts and inspiration."

When the blackboard behind him was filled with writing, Xiao Yi had finally finished saying everything he could.

"Then the next step is the question and answer session. If you have anything else you want to know, you can ask it now. I am happy to communicate with you."

As Xiao Yi spoke, he picked up the water cup and took a sip, but the next moment he almost spit out the water.

Because there were about 100 people raising their hands.

Are you kidding me? So many people want to ask questions?

There are 15 minutes left, enough time for him to answer questions from as many people as he wants.

Forget it, let’s see what they ask first.

Xiao Yi shook his head, then glanced at the people below, and finally pointed to a person sitting in the second row and said, "Sir, you go first."

When Silvio Micali saw that Xiao Yi was pointing at him, his eyebrows raised immediately.

Isn't this a coincidence?

At this time, a staff member handed him a microphone. He then smiled, stood up, and said, "Hello, Mr. Xiao. I am Silvio Micali from the Massachusetts Institute of Technology."

Upon hearing this name, many people in the venue were stunned and then looked over.

Immediately these people were shocked. Isn’t this the Turing Award winner from MIT?
Why did he come to listen to this report?

Micali also raised his question at this time: "In your speech just now, you basically talked about things in the field of pure mathematics, and I am a computer professor, so I want to ask questions about the application of computers."

"During this period, Xiao's development has shown a very strong role in the field of information security. In your paper a few days ago, even the classification sieve attack, which poses a great threat to the RSA encryption algorithm, has been solved. The security of the RSA encryption algorithm has been greatly improved since then."

"And the cross-chain transaction principle you constructed using the principle developed by Xiao also surprised us in the computer industry."

"All these fully demonstrate the important role of Xiaoshi Development in the field of computer security."

“And what I want to say is, if the Xiao expansion is applied to blockchain cryptocurrency and used as part of the digital signature, can it also greatly improve the security of cryptocurrency?”

"Of course, it's not just cryptocurrency, there are all aspects that blockchain can affect. Does Xiao's development also have the opportunity to use its mathematical principles to provide a certain role in information security?"

“Because I also built a blockchain called Algorand, so I would love to hear your thoughts.”

As soon as these words were spoken, the scientists in the lecture hall who were also in the computer field looked at Xiao Yi curiously.

Most of the mathematicians showed puzzled expressions.

WTF?

What paper did Xiao Yi publish a few days ago?
Directly solve the risk of classification screening attack?
Has the security of RSA encryption also been improved?

How come they don't know?
But finally they understood why this Turing Award winner came to attend this report.

It turns out that Xiao's expansion has not only played a huge role in the field of pure mathematics, but has even branched out into applied fields?

Of course, the most confused person in the whole audience was Xiao Yi.

What's going on here?
The participants of this report are not all scholars in the field of pure mathematics?
(End of this chapter)