It's something that will hurt your butt even if you use it as toilet paper in the future.
By early May, the exchange rate between silver dollars and French currency in the Beiping area had reached 1:1.8, showing a clear downward trend. Rich people were exchanging their property and cash flow into U.S. dollars, pounds, silver dollars, small yellow croakers and other hedging items.
Reduce fiat currency holdings, but people who lack information channels and lack economic knowledge do not understand what the decline in fiat currency means.
If the current full-scale war of resistance had not yet broken out, and it was pegged to the British pound and the US dollar, the French currency would have been reduced to toilet paper.
“Inflation, economic deterioration,
The state of the country is very severe,
Forget it, let's not mention this. Regarding your treatment, it will be resolved when you enroll in school. How have you been these days?" Hua Luogeng naturally knew the meaning after hearing Yu Hua's words. He pointed out the current situation, but was unable to do anything and could only shake his head.
As a mathematician, Hua Luogeng certainly understood the economic problems that were closely related to mathematics, but he was powerless to solve them. Hua Luogeng could solve mathematical problems, but he could not solve the economic difficulties faced by the National Government.
This is determined by national strength and cannot be changed by one person's efforts.
The most important thing is that when dealing with economic problems, the National Government does not like to find the root of the problem. Instead, it likes to solve the people who raised the problem and resort to printing money.
There is not enough money,
Printing is done.
"fine,
Every day at three o'clock and one line, I help my juniors and juniors solve some elementary mathematics problems and tutor them in their studies." Yu Hua smiled and summarized briefly.
Hua Luogeng nodded and asked, "How is your academic study going?"
"Not missing. 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. He lowered his right leg and leaned forward with a serious look: "Oh? Tell me and listen."
People's never-ending pursuit of communication security has led to rapid development of cryptography since its birth. However, today, the seemingly mysterious cryptography has fallen into a quagmire, and its progress has become increasingly difficult.
Hua Luogeng was curious about Yu Hua's thoughts in the field of cryptography.
For scholars, ideas come from inspiration, and a sudden inspiration often means a directional breakthrough in a field.
In Hua Luogeng’s heart,
Yu Hua, who has completed three courses of advanced mathematics, real variable functions, and mathematical analysis before officially entering Tsinghua University, is already a new scholar.
‘scholar’ as a student.
"Throughout ancient times and modern times, no matter what method we use to encrypt the key or improve the password, the password transmission mode has not changed. The symmetric encryption algorithm is used, that is - the sender: chooses a certain encryption rule to encrypt the information, and the receiver
: Use the same encryption rule to decrypt information. This encryption algorithm has a core weakness, that is, the sender must tell Party B the encryption rules, that is, the key, otherwise decryption cannot be achieved."
Yu Hua pondered for a while, sorted out his words, and said: "The key storage and transmission of the symmetric encryption algorithm has become the most troublesome problem. I was aware of this biggest weakness when I deciphered the Japanese army's red secret system. I’m particularly curious, can this symmetrical information transmission method be changed?”
"A few days ago, I suddenly had inspiration."
Hua Luogeng's face became serious and he stared at Yu Hua. He vaguely felt that a major change in the field of cryptography was about to occur. As a cryptography expert, he certainly understood the biggest weakness of current cryptography.
No matter how advanced the passwords in various countries are and how rigorous and difficult the key encryption is, key storage and transmission will always be the biggest weakness.
It is precisely because of this weakness that the battle between decipherers and coders has always been at a disadvantage. It was not until the emergence of the Enigma machine that the coders gained the upper hand.
However, this is the power of machines, not the power of intelligence.
If the password transmission method can be improved or a breakthrough can be made, this will solve the root cause of the problem.
Is it possible?
"The first step: the sender generates two keys, one is the public key and the other is the private key. The public key is completely transparent and public and can be obtained by anyone, while the private key is kept confidential. The second step is for the recipient to obtain The sender's public key is then used to encrypt the information. In the third step, the sender obtains the encrypted information and uses the private key to decrypt it."
Yu Hua's voice was steady and clear, and he carefully explained the concept of the asymmetric encryption algorithm system: "Theoretically, only the private key can decrypt the information encrypted by the public key. So as long as the private key is not leaked, the communication is safe because encryption and decryption are Using different encryption rules, as long as there is a certain correspondence between the two rules, this directly avoids the key transfer link. This encryption method can realize secure key transfer between the communicating parties in the non-secure channel. Exchange 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 1970s and successfully opened the door to modern cryptography. , the foundation of computer communication security in later generations is derived 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... wherever there is a computer network, the RSA algorithm can be found.
The public key encryption algorithm can be said to be a revolutionary achievement in the history of cryptography development.
The reason why Yu Hua introduced the concept of public key encryption was to gain fame in the academic world and further package himself. The basis of public key encryption algorithms, including the RSA encryption algorithm, is based on number theory.
This will be his first 'result' in the field of number theory.
Of course, Yu Hua was not prepared to take this achievement alone. First, his knowledge reserve and mathematical level were insufficient, and second, it was too conspicuous.
He came up with the idea, and he and his master Hua Luogeng would work together to create the results. In this way, it would not only make people suspicious, but also deepen the genius' personality and increase his influence, killing two birds with one stone.
As for the moral problems of this kind of behavior that is similar to stealing the academic achievements of future generations...
unimportant.
Sorry, Mr. Mokou.
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 this public key has greatly improved the difficulty of cracking the entire password link. Just simply introduce a few variables and
Factors can increase the difficulty of deciphering by several orders of magnitude." Hua Luogeng carefully thought about the concept of public key encryption algorithm given by Yu Hua. His expression changed from serious to dignified. There was already a storm in his mind. He was completely attracted by Yu Hua's idea.
Shocked.
This is change.
Changes in password transmission methods, breakthroughs at the root level!
Unbridled and unconstrained, subverting cognition.
Hua Luogeng never expected that encryption and decryption could be performed without directly transferring the key.
Everyone can know the public key, but only the sender has the private key. In this case, how to decipher it?
Gulu
If the difficulty of deciphering the Japanese red cipher system that used the principle of matrix mathematics was 10, then the difficulty of deciphering the cryptosystem based on public key encryption algorithms will be 1000!
As a cryptography expert, Hua Luogeng has already figured out several encryption algorithms based on mathematical principles in an instant. Moreover, in order to ensure the strength of the password, in addition to using public key encryption, traditional encryption algorithms can also be used in combination with public key encryption.
An encryption method that can be used together.
First use a cryptographic system to encrypt important information, and then use a public key encryption algorithm to encrypt it.
How to decipher this?
The difficulty of deciphering is simply outrageous.
Theoretically, it is computationally impossible to derive the decryption key from a known encryption key. In other words, this is a new and perfect encryption mechanism.
The Enigma machine, which is said to be impossible to crack, also appears so fragile in the face of this encryption mechanism.
Perfect encryption of the mechanism!
At this moment, Hua Luogeng's scalp was numb. He already understood the concept of the entire public key encryption algorithm. He looked at Yu Hua with his eyes, full of surprise and admiration.
After three days of separation, Yu Hua, who had not seen him for a long time, not only gave him perfect scores in seven subjects, but also gave him a big surprise.
"Have you thought about which mathematical principle is used for public keys and private keys?" Hua Luogeng took a deep breath, regained his composure, and asked Yu Hua in a scholar's tone.
The mathematical principles used by public keys and private keys are the core key, which must satisfy both the public encryption key and the self-controlled 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 knew the basic principles and the RSA algorithm principle, and there was very little else.
There is no other way. The big guys on Zhihu often go to the United States, and the brothers at Station B check in and miss each other. The guys on Tieba spend all their time trying to figure out how to learn about experience, pure mathematics, cryptography, and other rare and unpopular knowledge. They really don’t explain much.
The mathematical principles applied to public key encryption algorithms are nothing more than an rsa algorithm.
"The decomposition of large prime numbers is feasible as the underlying algorithm, has high security, and will basically not be cracked. However, there are corresponding flaws. That is, the amount of calculation is very large, which leads to a greatly increased encryption and decryption operation time. Decomposition of large prime numbers
If the key length is doubled, the public key encryption time will be roughly four times increased, and the private key decryption time will be about eight to ten times, and the timeliness cannot meet the demand."
After hearing the idea given by Yu Hua, Hua Luogeng fell into thinking, weighed it carefully, and shook his head: "Theoretically, 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-calculation to generate public and private keys and private key decryption, otherwise it will be difficult to be effectively applied."
Timeliness.
This is a serious problem in the mathematical principle of decomposition of large prime numbers.
From a mathematical mechanism perspective, the decomposition of large prime numbers perfectly fits 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 the calculation becomes.
Assume that the two large prime numbers are 100009921 and 10009933 respectively. How difficult is it to factor these two large prime numbers?
Astronomically large prime numbers mean extremely high computational difficulty and the timeliness of human calculations, which are completely unable to meet the needs of ‘efficient’ communication.
The simplest theory is that assuming that the 29th Army is facing a Japanese attack, the pressure is too great, and it wants to retreat. It requires that it be withdrawn into the city within one day. It uses an asymmetric encryption system based on the decomposition of large prime numbers into underlying mathematical principles to issue a message to the National Government.
From the moment the request is received by the National Government to the other party making a decision, the information is encrypted with the public key and fed back to the 29th Army.
Due to the high computational difficulty, the private key decryption process of the 29th Army may take two days.
The request is to evacuate the city within one day, but 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.
Also, if an asymmetric encryption algorithm system is to be used, higher quality requirements are required for communication department personnel, especially mathematics. Prime number discrimination and large number decomposition are definitely not something ordinary people can do. The minimum requirements are university graduates.
Those who graduate are considered students.
And how many college graduates are considered students in the country?
If you want to use large prime number decomposition, it can be done manually. You must use the power of a machine, a special machine similar to the Enigma machine, to assist human calculations.
Or, design a machine that can perform self-computing and hand over this large amount of repetitive calculation work to this self-computing machine.
"Timeliness..." Yu Hua thought thoughtfully and suddenly realized that he had made a classic mistake - imitating others.
According to number theory, it is relatively simple to find two large prime numbers, but it is extremely difficult to factor their product. The later rsa encryption algorithm is based on this point, and the product of two large prime numbers is disclosed as a public key encryption algorithm.
The basis for the later generations of RSA encryption algorithm to use large prime number decomposition is due to the rapid development of computers, with computers having millions or even tens of millions of operations per second, which can meet the needs of the RSA encryption algorithm.
Obviously, the decomposition of large prime numbers I gave is not suitable for the current situation.
The entire Republic of China, except for him, was simply unable to factor large prime numbers in a very short time. If it were some extremely large prime numbers, such as one hundred million units or even one billion units, the entire calculation process would be particularly difficult.
As expected of the master, he is awesome.
Although his idea was rejected, Yu Hua was not angry. Instead, he was extremely impressed and muttered: "The student's level is limited. Apart from the decomposition of large prime numbers, I haven't thought of any other good methods yet."
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. This is the key.
"Don't rush, take your time. Calculus, Riemann functions, discrete logarithms, etc. can all be used as the core foundation of this system. However, Master wants to ask you a question. Have you ever thought about an asymmetric encryption system?
Is there any impact after the announcement?" Hua Luogeng shook his head slightly and replied.
The basic feature of calculus is reciprocal operation, which meets the needs of asymmetric encryption systems. The same is true for Riemann functions, discrete logarithms, etc.
Finding mathematical principles is not the problem, the problem is the impact after the asymmetric encryption system is announced.
After hearing this, Yu Hua replied: "There will be breakthrough progress in the cryptography society. Students will gain academic reputations. Cryptosystems in various countries will be quickly updated to the asymmetric cryptography era, thereby greatly improving communication security and the difficulty of preventing deciphering."
Breakthroughs in cryptography will quickly be reflected in real life, because people have an almost perverted obsession with the pursuit of information security.
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 asymmetric encryption era from the symmetric encryption era.
In this process, Yu Hua, as the founder, will gain great reputation.
"Have you ever thought about the situation after the Japanese entered the asymmetric encryption era?" Hua Luogeng asked seriously.