my scientific age

Chapter 200 The Age of Asymmetric Cryptography!
What is fiat currency?
In the future, it will be too sloppy to use as toilet paper.

By the first ten days of May, the exchange rate of silver dollar and fiat currency in Peiping area had reached the level of 1:1.8, showing a clear downward trend. The wealthy exchanged their family property and cash flow into U.S. dollars, British pounds, silver dollars, small yellow croakers and other stores of value, reducing the fiat currency. Holding, but the people who lack information channels and economic knowledge do not understand what the fall of fiat currency means.

If it weren't for the current full-scale war of resistance, coupled with the peg to the British pound and the U.S. dollar, the fiat currency would have fallen into toilet paper long ago.

"Inflation, the economy is deteriorating, and the state is very serious. Forget it, let's not mention these. The question about your treatment will be resolved at the time of admission. How are you doing these days?" Hua Luogeng naturally knew what Yu Hua said. Meaning, pointed out the current situation, but there was nothing he could do, so he shook his head.

As a mathematician, Hua Luogeng certainly understands that there are economic problems closely related to mathematics, but he can't do anything about it. Hua Luogeng can solve mathematical problems, but cannot solve the economic difficulties faced by the National Government.

This is determined by national strength, not by one person, and can be changed.

The most important thing is that when dealing with economic problems, the national government does not like to seek the root cause of the problem, but likes to solve the problem who raises the problem, and adopts the means of printing money.

If the money is not enough, the printing is over.

"Fortunately, every day at three o'clock, I help my juniors and juniors solve some elementary math problems and help them with their studies." Yu Hua smiled and briefly summarized.

Hua Luogeng nodded and asked, "How is the study of knowledge?"

"Nothing left. In addition, the student has a new idea about cryptography." Yu Hua replied.

Hua Luogeng was a little curious and interested, his face was a little serious, his right leg was put down, his posture was leaning forward, and he looked serious: "Oh? Let's hear it."

People's never-ending pursuit of communication security has made cryptography develop rapidly since its birth. However, today, the seemingly mysterious cryptography has fallen into a quagmire, and the pace of progress has become more and more difficult.

Hua Luogeng was curious about Yu Hua's ideas in the field of cryptography.

For scholars, ideas come from inspiration. A sudden inspiration often means a directional breakthrough in a field.

In Hua Luogeng's mind, Yu Hua, who had completed the three courses of advanced mathematics, real variable functions, and mathematical analysis before officially entering Tsinghua University, already belongs to a new scholar.

'Scholar' for student status.

"Throughout the past and present, no matter what method we use to encrypt the key and improve the password, the password transmission mode has not changed, and the symmetric encryption algorithm is used, that is, the sender: chooses a certain encryption rule, encrypts the information, and the receiver : Use the same encryption rule to decrypt the information. This encryption algorithm has a core weakness, that is, the sender must tell Party B the encryption rule, that is, the key, otherwise the decryption cannot be achieved.”

Yu Hua pondered for a while, sorted out the words, and said: "The key storage and transmission of the symmetric encryption algorithm has become the most troublesome problem. When I deciphered the Japanese army's red secret system, I realized this biggest weakness. I'm very curious, can we change this symmetrical way of information transmission?"

"A few days ago, I had a sudden inspiration."

Hua Luogeng's face became serious, and his eyes were fixed on Yu Hua. He faintly felt that a major change in the field of cryptography was about to take place. As a cryptography expert, of course, he understood the biggest weakness of current cryptography.

No matter how advanced the ciphers of various countries are and how rigorous and difficult key encryption is, key storage and transmission will always be the biggest weakness.

It is because of this weakness that the battle between the decipherers and the coders has always been the coders' disadvantage, until the emergence of the Enigma code machine, which led to the coders gaining the upper hand.

But this is the power of machines, not the power of intelligence.

If improvements can be made in the way the password is passed, or a breakthrough can be made, this will solve the problem at the root.

Is it possible to achieve this?

"The first step: the sender generates two keys, one is the public key and the other is the private key. The public key is fully transparent and open, and anyone can obtain it, while the private key is kept secret. The second step, the recipient obtains After the sender's public key, it is then used to encrypt the message. In the third step, the sender gets the encrypted message and decrypts it with the private key."

Yu Hua's voice was steady and clear, and he carefully stated the concept of the asymmetric encryption algorithm system: "Theoretically, the information encrypted by the public key can only be decrypted by the private key, so as long as the private key is not leaked, the communication is safe, because encryption and decryption Using different encryption rules, as long as there is a certain correspondence between the two rules, this way, the key transmission link is directly avoided. This encryption method can realize the secure key of the communication parties in the non-secure channel. exchange, which is used to encrypt subsequent communication messages, which I call an asymmetric encryption algorithm."

The asymmetric encryption algorithm system was proposed by Leif Moko in 1974 and then improved by the scholar Whitfield Diffie. This is a cryptographic system born in the 70s and successfully opened the door to modern cryptography. The foundation of computer communication security in later generations comes from the asymmetric encryption algorithm system.

This statement is no exaggeration, because the famous RSA encryption algorithm in later generations is one of the most widely circulated asymmetric encryption algorithms.

Bank card passwords, QQ passwords, WeChat passwords, game account passwords... But wherever there is a computer network, there is the RSA algorithm.

The public key encryption algorithm is a revolutionary achievement in the history of cryptography.

The reason why he introduced the concept of public key encryption is that Yu Hua intends to use it to gain fame in the academic world and further package himself. The basis of public key encryption algorithms, including RSA encryption algorithm, its mathematical principle is number theory.

This will be his first 'result' in the field of number theory.

Of course, Yu Hua is not going to eat this achievement alone. First, the knowledge reserve and mathematical level are not enough, and second, it is too conspicuous.

The idea was put forward by him, and he and his master Hua Luogeng worked together to make the results. In this way, it would not make people suspicious, but also deepen the weight of geniuses and increase their influence, killing two birds with one stone.

As for this kind of behavior similar to stealing the academic achievements of later generations, there are moral problems...

unimportant.

I'm sorry, Mr. Moko.

I'm sorry, Mr. Diffie.

Yu Hua silently said sorry in his heart.

"A public key... This is a wildly imaginative idea. It's very good. The introduction of the public key has greatly improved the difficulty of cracking the entire password process. It is simply the introduction of a few variables and Factors can increase the difficulty of deciphering by several orders of magnitude." Hua Luogeng thought carefully about the concept of public key encryption algorithm given by Yu Hua, the expression of the whole person changed from serious to solemn, a storm had already set off in his mind, he was completely attracted by Yu Hua's idea Shocked.

This is change.

The change of the password transmission method, the breakthrough of the root level!

Unconstrained, subverting cognition.

Hua Luogeng never thought that he could encrypt and decrypt without directly passing the key.

The public key can be known to everyone, and the private key is only mastered by the sender. In this case, how to decipher it?
If it is said that the Japanese red secret system that used the principle of matrix mathematics before, the difficulty of deciphering is 10, then the difficulty of deciphering the cryptographic system based on the public key encryption algorithm will be 1000!

Hua Luogeng, an expert in ciphering, has come up with several encryption algorithms based on mathematical principles in an instant. Moreover, in order to ensure password strength, in addition to using public key encryption, traditional encryption algorithms can also be combined with public key encryption. The encryption method used together.

First use a set of cryptographic systems to encrypt important information, and then use public key encryption algorithm to encrypt.

How to decipher this?

The difficulty of deciphering is so high that it is simply outrageous.

In theory, it is computationally impossible to derive the decryption key by knowing the encryption key. In other words, this is a completely new and perfect encryption mechanism.

The Enigma machine, which is said to be impossible to crack, is also so fragile in front of this encryption mechanism.

The perfect encryption of the mechanism!
At this moment, Hua Luogeng's scalp was numb. He already understood the whole concept of public key encryption algorithm. He looked at Yu Hua with surprise and admiration.

After three days of separation, Yu Hua, who had not seen him for a long time, not only brought him full marks in seven subjects, but also brought him a big surprise.

"Have you thought about which mathematical principle is used for the public key and the private key?" Hua Luogeng took a deep breath, regained his composure, and asked Yu Hua in the tone of a scholar.

The mathematical principle adopted by the public key and the private key is the core key. It must satisfy both the public encryption key and the self-mastered decryption private key.

"Not yet, the student's knowledge reserve is not enough, how about the decomposition of large prime numbers?" Yu Hua shook his head and answered truthfully, for the asymmetric encryption algorithm system, he only understands the basic principles and RSA algorithm principles, and other things are pitiful.

There is no way. Zhihu big guys often go to the United States. Brothers at station B check in everywhere for nostalgia. Brother Tieba has tossed the dog's head all day long. There is not much to explain the uncommon and unpopular knowledge in the field of pure numbers and cryptography.

The mathematical principles applied to public key encryption algorithms are nothing but an RSA algorithm.

"The decomposition of large prime numbers is feasible as the underlying algorithm, with high security, and basically will not be cracked, but there is a corresponding defect, that is, the amount of calculation is very large, which leads to a great increase in the time of encryption and decryption operations. Decomposition with large prime numbers The length of the key is doubled, the encryption time of the public key is roughly increased by four times, and the decryption time of the private key is eight to ten times, and the timeliness cannot meet the demand.”

When Hua Luogeng heard the idea given by Yu Hua, he fell into thought, weighed it carefully, and shook his head: "Theoretically speaking, large prime number decomposition is particularly suitable for this public key encryption mechanism, but from a practical point of view, the two do not match. Unless there is a special machine like an Enigma machine that assists human calculations, or performs self-operation, generates public and private keys and decrypts private keys, otherwise, it is difficult to be effectively applied.”

Timeliness.

This is the mathematical principle of the decomposition of large prime numbers, and there is a serious problem.

Mathematically speaking, the decomposition of large prime numbers fits perfectly with the asymmetric encryption algorithm system. The larger the two prime numbers, the higher the security.

The problem is that the larger the prime number, the more difficult it is to compute.

Assuming two large prime numbers are 100009921 and 10009933, how difficult is the factorization of these two large prime numbers?
The astronomically large prime numbers mean extremely high computational difficulty, and the timeliness of human computing cannot meet the needs of 'efficient' communication at all.

The simplest reason is to assume that the Ninth Army of No. 20 is facing the Japanese attack and is under too much pressure. They want to retreat and request to withdraw into the city within one day, and use the asymmetric encryption system based on the decomposition of large prime numbers into the underlying mathematical principles to send a message to the Nationalist Government. The request, from the time the request is received by the National Government, to when the other party makes a decision, encrypts the information with the public key, and feeds it back to the No.20 Ninth Army.

Due to the high difficulty of calculation, the decryption of the private key of the No.20 Ninth Army may take two days.

The request to withdraw into the city within one day, and the decryption time is as long as two days. How can this be done?
For the military field that attaches great importance to communication efficiency, the large prime number decomposition algorithm is completely unacceptable.

In addition, if the asymmetric encryption algorithm system is to be used, the quality requirements of the personnel in the communication department are higher, especially the mathematical level, the discrimination of prime numbers and the decomposition of large numbers, which are by no means ordinary people can do, and the minimum requirements must be universities. Graduates are considered student level.

And how many college graduates are there in the country?
If you want to use the large prime number decomposition, which can be done manually, you must use the power of the machine, a special machine similar to the Enigma machine, to assist the human calculation.

Or, design a machine that can calculate by itself, and hand over this large amount of repetitive computing work to this self-calculating machine.

"Timeliness..." Yu Hua pondered and suddenly realized that he had made a classic mistake - Dong Shi imitated frown.

According to number theory, it is relatively simple to find two large prime numbers, but it is extremely difficult to factorize their product. Based on this, the RSA encryption algorithm of later generations is based on this, and the product of two large prime numbers is disclosed as a public key encryption algorithm.

The basis for the later RSA encryption algorithm to use large prime number decomposition is because of the rapid development of computers, computers with millions or even tens of millions of operations per second can meet the needs of the RSA encryption algorithm.

Obviously, the large prime number decomposition given by myself is not suitable for the current era.

In the entire Republic of China, except for him, it is impossible to factorize large prime numbers in a very short time. If it is some super prime numbers, such as [-] million units or even one billion units, the entire calculation process will be particularly difficult.

As expected of the master, it is amazing.

Although his idea was rejected, Yu Hua was not angry. Instead, he admired it and pondered: "Students are limited in their ability. Apart from the decomposition of large prime numbers, I haven't thought of any other good solutions for now."

If you want to use an asymmetric encryption system, you must find a set of mathematical principles that conform to the characteristics of the current era as the core foundation, which is the key.

"This is not urgent, take your time, such as calculus, Riemann function and discrete logarithm, etc., can be used as the core basis of this system, but Master wants to ask you a question, have you thought about asymmetric encryption system Is there any impact after the announcement?" Hua Luogeng shook his head gently and replied.

The basic feature of calculus is reciprocal operation, which meets the needs of asymmetric encryption systems, as well as Riemann functions, discrete logarithms, etc.

Finding mathematical principles is not a problem, the problem is the impact of the announcement of the asymmetric encryption system.

After hearing this, Yu Hua replied: "The cryptographic society has made breakthrough progress, students will gain academic reputation, and the cryptographic systems of various countries will be rapidly updated to the era of asymmetric cryptography, thereby greatly improving communication security and anti-deciphering difficulty."

Breakthroughs in cryptography will quickly reflect in real life, because people's pursuit of information security is almost a perverted obsession.

No one wants their message to be deciphered.

It is foreseeable that with the announcement of the achievement of the asymmetric encryption system, the encryption systems of various countries in the world will immediately enter the era of asymmetric encryption from the era of symmetric encryption.

During this process, Yu Hua, the founder, will gain a great reputation.

"Have you ever thought about the situation after the Japanese entered the era of asymmetric encryption?" Hua Luogeng asked seriously.

(End of this chapter)