Duffy and Herman solved the problem of key distribution perfectly. From then on, exchanging keys is very simple. Alice and Bob can exchange keys through the speaker at the village head. But the encryption method is still symmetric encryption.
Although DH protocol is convenient to exchange keys, there are still some unsatisfactory troubles. Alice still needs to yell at Bob for a long time to generate the key. When Alice wants to exchange keys, if Bob is sleeping, Alice's love letter can't be sent out.
In their paper, Duffy and Herman pointed out the direction of future encryption methods. The final solution is to design asymmetric encryption through one-way function. Asymmetric encryption means that one key is used to lock and the other key is used to unlock. These two keys are different. The locked key cannot be unlocked. The key to this lock won't open.
Three MIT scientists, Ron Rivest, adi shamir and Leonard Aderman, read Duffy's and Herman's papers, were deeply interested and began to study them. The algorithm that Duffy and Herman failed to solve was born by the three of them.
In 2002, these three masters won the Turing Award for the invention of RSA. But don't think RSA is all they have. These three are real masters, and each of them has a rich academic career. Let's look up at the height of the masters.
Livingstone also invented RC2, RC4, RC5 and RC6 algorithms, as well as the famous MD2, MD3, MD4 and MD5 algorithms. He also wrote a book called Introduction to Algorithms, in which programmers have worn out countless brain cells.
Samol invented Gefei-Fiat-Chamil authentication protocol, and also discovered differential cryptanalysis.
Aderman is even more legendary. He initiated the theory of DNA computing and solved the problem of "traveling salesman" with DNA computer. His student Cohen invented computer virus, so he is the originator of computer virus. He is also a master expert in AIDS immunology and has made outstanding contributions in mathematics, computer science, molecular biology and AIDS research.
From 65438 to 0976, all three people worked in the computer science laboratory of MIT, and their team was perfect. Livingstone and Samol are computer scientists. They keep putting forward new ideas, while Aderman is an extremely clever mathematician who can always find fault with Livingstone and Samol.
A year later, 1977, after a party, Livingstone lay on the sofa to sober up. He tossed and turned and couldn't sleep. Half asleep, suddenly a flash of lightning struck his brain, and he found a way. He wrote a paper all night. The next morning, he handed the paper to Aderman, and Aderman couldn't find any mistakes this time.
In the name of the thesis, these three gentlemen are really modest. Livingstone named it Adleman-Rivest-Shamir, and the great Aderman asked to remove his name because it was an invention of Livingstone. The final result of the dispute is that Aderman ranks third, so this algorithm becomes RSA.
RSA algorithm is based on a very simple number theory fact: it is very easy to multiply two large prime numbers, but it is extremely difficult to factorize their products, so the products can be made public and used as encryption keys.
For example, if two prime numbers are selected, one is 17 159 and the other is 10247, then the product of the two numbers is 175828273. The product 175828273 is the encrypted public key, and (17 159, 10247) is the decrypted private key.
Everyone can get the public key 175828273, but it is very difficult to break the ciphertext by decomposing 175828273 into 17 159 and 10247.
When RSA was published in 1977, mathematician and popular science writer martin gardner published a public key in Scientific American magazine:
1 14 38 1 625 757 888 867 669 235 779 976 146 6 12 0 10 2 18 296 72 1 242 362 562 842 935 706 935 245 733 897 830 597 123 563 958 705 058 989 075 147 599 290 026 879 543 54 1?
Martin offered rewards to readers who cracked this public key. After 17 years,1April 26th, 994, a group of 600 fans claimed to have found the private key. The private key is:
Tel: 349052951084765094914784961990389813341776463849384390820577
Q: 32 769132 993 266 709 549 96190 834 4613177 642 967 992 942 539 798 288 533.
This time, it took 17 years to crack, and only targeted at 129-bit public key. Today, RSA has used 2048-bit public keys, which almost consumes the computing power of computers all over the world and takes billions of years to crack.
The security of RSA depends on the decomposition of large numbers, but whether the difficulty of cracking is equal to the decomposition of large numbers has not been proved theoretically, because it has not been proved that the decomposition of large numbers is a necessary condition for cracking RSA.
RSA still has its weaknesses. RSA calculates large numbers, so whether it is implemented by software or hardware, the fastest situation is many times slower than ordinary symmetric encryption. Speed has always been RSA's shortcoming. Generally speaking, it is only used to encrypt a small amount of data. ?
RSA has another weakness, which will be mentioned later.
In cryptography, American scholars are very busy, and the results are one after another. However, Britain, an old empire, is not completely without achievements in cryptography. After all, it is the hometown of Turing, the country where Turing led cryptographers to defeat the German Enigma encryption machine in Bleicherry Park.
The British invented RSA, but it was buried.
In the 1960s, the British military was also worried about password distribution. 1969, the cryptographer James Ellis was working for the military, and he received the subject of key distribution. He came up with an idea to realize asymmetric encryption with a one-way function, but he couldn't find this function. Many geniuses from the government communication headquarters joined in to find the one-way function. But three years later, these clever heads got nothing, and everyone was a little depressed. Does such a single function exist?
Often at this time, newborn calves are needed to save the scene. Cox is a brave calf. He is a young mathematician, very pure and determined to devote himself to the Muse. Young as he is, he has great advantages. At that time, he knew nothing about this one-way function problem, and he didn't know that the teachers had achieved nothing for three years. So I broke into the minefield.
Faced with such a dangerous minefield, Cox almost jumped over it. The problem was solved in half an hour, and then he went home from work, which didn't take it too seriously. It's just a job given by the leader, which is nothing more than drinking tea and sweeping the floor to solve math problems. He finished it early and can buy freshly baked bread on his way home. He doesn't know that he made history. Cox is a pure mathematician. When he heard the praise from his colleagues, he felt a little embarrassed. In his eyes, mathematics should be useless knowledge as Hardy said. It is a shame that he solved specific problems with mathematics.
Unfortunately, Cox's invention was too early, and the computing power of the computer at that time was too weak to realize asymmetric encryption and decryption. Therefore, the military did not apply asymmetric encryption algorithm. James and Cox have developed the theory of asymmetric encryption to the extreme, but they can't say anything. The military requires that all work content must be kept secret, and they can't even apply for a patent.
Although the military is very strict about the confidentiality of the work results, it does not care much about the work results themselves. Later, the British Communications Headquarters discovered the RSA algorithm in the United States and thought it was great. They just forgot the RSA of James and Cox. The communication headquarters was shocked and pulled its own knowledge base, only to find that its employee Cox had invented a similar algorithm for RSA. Bureaucracy is really a good friend of mankind. It can always make all kinds of jokes for people, although its original intention is to create authoritarianism.
Cox doesn't care about this. He even said, "bury it. I don't want to be an online celebrity. Why do I need fans? " Can those fans eat? "The exact words are not like this, but the meaning expressed is basically the same.
1982, Duffy made a special trip to England to meet James. The two of them admired each other and met each other for a long time. Unfortunately, James still can't reveal their research on RSA. He just told Duffy, "You did better than us." Scientists from all over the world can be better than anyone else, but bureaucrats from all over the world can hardly be better than anyone else. They are neck and neck.
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