The top student must be diligent

"Don't worry, we all know that there is only a risk of being cracked. It is still a long way to go to truly crack it. After all, even if we use the sieve method to crack it, it will take a lot of time." Tao Zhexuan was not scared. He waved his hand and said, "But we are still very happy to give them a headache."

People like them who study pure mathematics are often asked what applications their research has, which often causes friction between the pure mathematics community and other fields.

For example, after Zhang Yitang made a breakthrough in the twin quality conjecture, Google once invited him to give a speech, but he refused because he was afraid that after the speech, others would ask him what the use of his results was.

Similarly, after Perelman proved the Poincare conjecture, he was invited by various universities to give speeches to explain his proof.

As a result, someone asked him what applications he had after he solved this method. Upon hearing this question, Perelman immediately became furious and said why someone asked such a stupid question. In the end, he couldn't stand it and went back to Russia directly.

In short, those who work on pure mathematics and those who work on applications are basically not on the same page.

Of course, this has also formed a temperament of some pure mathematicians. The less they can use the things they come up with, the more they are satisfied, and they think that this is the real [pure mathematics].

Hearing the discussion of the professors in front of him, Xiao Yi shook his head helplessly.

This is not his intention. He would never have thought that if he came up with a classification sieve, it would bring the risk of cryptography being cracked.

"Okay, don't gloat over the misfortune. I also want to ask you how to solve this problem. This kind of thing involving pure mathematics will eventually fall on the heads of you pure mathematicians."

Professor Kleinlock said.

Then the three mathematicians also calmed down and waited for Kleinlock's explanation.

"Well... to explain what a multi-party security algorithm is, let's start with a classic problem."

"That is the millionaire problem. Do you know this problem?"

Tao Terence nodded. He also has some research on computers. More than a decade ago, he had come up with something called information acquisition guidance theory. In simple terms, this is a digital compression imaging technology. In the end, this technology was widely used in various fields such as the information field, which fully demonstrated his strong ability in applied mathematics.

However, Xiao Yi and James Maynard seemed a little embarrassed.

The latter was okay, saying that he had heard of this, "I remember the person who asked this question was a Turing Award winner."

"Haha, yes." Kleinrock nodded and said, "Speaking of which, this Turing Award winner is also Chinese like Xiao Yi. His English name is Andrew Yao, and his Chinese name seems to be Yao Qizhi."

"In short, the millionaire problem is, suppose there are two millionaires named Alice and Bob, and now they want to compare who is richer, but they don't want to reveal how much money they have to each other. In this case, how should they compare their wealth?"

As he said, Kleinrock also wrote a description on the blackboard.

[Suppose Alice and Bob's assets are i and j respectively, and the size of i and j is between 1 million and 10 million, then how to make the other party not know the specific number of i or j, and realize the comparison of the size of i and j? 】

Looking at this problem, Tao Zhexuan knew how to solve it, but Maynard and Xiao Yi began to think about it.

This problem also looks interesting.

After a while, the two of them had some time to think, but Kleinrock did not think of asking them to answer on the spot, and then he said: "Okay, we can solve this problem later..."

"Wait."

However, at this time, Xiao Yi spoke, "I think this problem may be solved in this way."

Then he walked to the blackboard, picked up a pen and started writing.

[Let M be a set of all elements that are N-bit non-negative integers, and QN is the permutation group from M to M. ]

"If my design is correct, as long as they compare according to the following protocol, they can complete the wealth comparison while keeping their assets confidential."

"First, Alice randomly selects an element Ea from QN as a public key and tells it to Bob, while keeping the inverse Da of Ea as a private key for herself."

"Then, Bob randomly selects an N-bit integer x and uses the public key given by Alice to calculate k=Ea(x)..."

As Xiao Yi began to narrate, the three people next to him fell silent.

They looked at each other and were a little caught off guard by the scene in front of them.

Especially James Maynard.

Although, if you really study this problem carefully, it won't be difficult for him. As a mathematical modeling problem, its difficulty is just that.

After all, this problem has been completely concrete. In terms of abstraction, it is too simple compared to the problems in analytic number theory that Maynard studied.

However, it was impossible for him to react so quickly and start to give a solution directly.

Looking at what Xiao Yi had written on half of the blackboard, Maynard experienced for the first time what was called [dimensionality reduction strike].

Perhaps when he showed his students what was called [top mathematical logical thinking] before, his students also felt the same way, right?

It was simply amazing!

Kleinrock's reaction was similar to Maynard's. Originally, he had not thought of asking them to solve the problem on the spot when he asked this question. He had left a few minutes just to let them get a little familiar with the problem.

As a result, who would have thought that after just a few minutes, the young man had already started writing.

Forgive him for not being particularly good at mathematics as a computer scientist, at least compared to these mathematicians, after all, there is a saying that only people who are really good at mathematics can always be rooted in pure mathematics, and people who are not good at mathematics will change careers early.

However, Xiao Yi's "good mathematics" was a little too good to be true.

"Step 4, Alice randomly generates an N/2-bit prime number p, and calculates Zu = yu mod p, where u = 1, 2, ..., 10."

"Then we ensure that at least two of all zu are not equal, otherwise re-select p to calculate..."

"Alice re-marks the prime number p and [z1, z2, ..., zi, zi+1]... as..."

"Bob checks the zj`, if zj` = x mod p, then i is greater than or equal to j, otherwise i is less than j."

After writing the last stroke on the blackboard, Xiao Yi turned around and reviewed it from beginning to end. He nodded with satisfaction, put down the pen, turned around and said to the three people next to him.

"In this way, the comparison of Alice and Bob's wealth is completed, and except when the wealth of both parties is equal, they have not exposed their real wealth to each other."

"Professor Kleinrock, my method should be OK, but I don't know how to write the specific program." Xiao Yi said modestly: "I don't know anything about programming."

However, what puzzled him was that the three professors in front of him were a little silent at this time.

After a moment, Kleinrock whispered to Tao Zhexuan: "Are all of you who are good at mathematics like this? Treat the difficult problems in our computer field as... addition and subtraction within 100?"

Tao Zhexuan waved his hands repeatedly: "Uh... That's not the case, but you know, there will always be some special situations in this world, and some low-probability events will occur. Xiao Yi is such a low-probability event, you know."

Chapter 112 Build a blockchain?

Maynard also said faintly: "Professor Kleinrock, I feel like you are saying that my mathematics is not good."

He didn't come up with the answer so quickly!

"No, no!" Kleinrock waved his hands to explain.

Just kidding, his math is really bad!

"Three professors, what are you talking about?" Xiao Yi, who was standing next to him, saw the three of them whispering after he solved the problem, and asked.

"Ah, we are saying that your solution is perfect!"

"Yes, yes."

"That's right!"

The three responded quickly.

"Ahem, of course, the millionaire problem is just an entry-level problem for our ultimate goal. It is mainly to help you understand the logic of a multi-party security algorithm, and this millionaire problem is just a two-party security algorithm. We can also expand it to n people to compare wealth."

Kleinrock felt that he needed to save some face for the computer.

But soon Xiao Yi replied: "If it is expanded to n people, the problem is not big. Just use the protocol I just used for repeated comparisons, and it can be completed in the end."

"Of course, considering the larger the n, repeated comparisons will also be a bit troublesome, um..."

Then Xiao Yi started writing on the blackboard again.

Soon, he put down the pen again and clapped his hands, "Done."

"In the end, it's just a matter of Boolean functions. If you program them and input all these numbers, you can get the result for n people."

"Well... Although I haven't studied programming, it's probably just a matter of if statements, right?"

Xiao Yi said with a little outsider.

Kleinrock finally gave up.

Tao Zhexuan and Maynard beside him patted the old man on the shoulder.

"Why bother?" Tao Zhexuan shook his head.

He is not even 18 years old this year, you can't beat him.

"Okay, okay." Kleinrock accepted the reality.

After all, he is 85 years old, and he has to look at it.

"The logic of multi-party secure computing is almost like this."

"I will now formally explain to you the goal of this topic."

Kleinrock knocked on the blackboard, as if he was going to class.

"Blockchain promotes secure and atomic transactions between mutually distrustful parties on the chain."

"However, at present, although there are multiple blockchains with different interfaces and security properties, in this multi-blockchain world, due to the lack of cross-chain communication and the generality of computing, there are always problems in actual operation."

"The current cross-chain communication bridge has a variety of low-level interfaces, which makes it difficult to develop portable applications, and the current multi-chain atomic transaction method is limited to cryptocurrency exchange."

"Therefore, our goal is to develop a new protocol that should guarantee the atomicity of cross-chain transactions."

"In this regard, I think LayerZero cross-chain bridge as a prototype would be a good idea..."

As Professor Kleinrock talked, they gradually entered the core point.

Although Xiao Yi did not understand computers, fortunately, his current understanding ability can be said to be far beyond that of ordinary people, so he roughly understood the final requirements.