Chapter 63 Genius is always special (Thanks to the boss Shi Zhongyinyu for the reward)
In the office, when Han Hua asked this sentence, Wang Donglai knew that he recognized the quality of this paper.
"Tutor, I did write this paper myself, and I translated the English version just last night."
Wang Donglai looked confident and said to Hanhua very seriously.
“I’m sorry, the quality of this paper is very high, I just don’t believe it would be written by a new student.”
After Hanhua finished speaking to Wang Dong with a hint of apology, he opened the plagiarism check website in the browser and started to check for plagiarism.
He actually didn’t really believe that this would be a paper that a freshman could write.
Clear organization, rigorous logic, clear data, and concise writing.
Even if a senior student writes such a paper, it requires talent and enough sweat to polish it to this level.
And where is Wang Donglai?
He is just a freshman who has just entered school. Excluding the two weeks of military training, the actual study time is only more than a week.
With all the best in mind, the classes I took at Tangdu Jiaotong University could not exceed fifty lessons.
As a result, such a freshman could write such a paper. Hanwha's first reaction was to either plagiarize or hire someone to write it.
Various speculations flashed through my mind, and the results of the plagiarism check website came out.
The repetition rate is 0.7%.
When this result came out, it at least confirmed that this paper was not plagiarized. Hanhua breathed a sigh of relief.
The next step is to hire someone to write for you.
"Wang Donglai, let me ask you seriously, tell me honestly, did you really write this paper alone? Did no one provide you with an outline or some necessary help? "
Han Hua looked at Wang Donglai and originally wanted to ask more directly, but he still spoke tactfully.
Why couldn’t Wang Donglai understand the meaning of Han Hua’s words?
He saw Han Hua looking at him seriously, waiting for his answer.
Wang Donglai smiled, full of confidence and high spirits.
“I did write it alone. I wrote it in the library. The English version was translated after I returned to the dormitory.”
“Well, since it was you who wrote the paper , then I will ask you about the content of the paper, you should have no problem, right?" Han Hua asked again.
If it were an ordinary student, Hanwha would have ignored it a long time ago, but Wang Donglai is a student of the 'Qian Xuesen Experimental Class'. The school attaches great importance to the students in this experimental class and allocates a lot of resources to cultivate these students. student.
Hanhua also hoped that Wang Donglai was a real genius, and he also had a faint hope in his heart, so he thought of such a way.
If this paper was really written by Wang Donglai, then Wang Donglai must be well aware of the contents of the paper.
On the contrary, if he cannot answer the questions he raised, it proves that there is something wrong with Wang Donglai's paper and it was not written by him at all.
"Teacher, please ask."
Wang Donglai did not think that Hanhua did this because he looked down on himself or had an opinion against him.
Putting himself in his shoes, Wang Donglai can completely understand Hanwha's behavior.
A freshman who had just been in college for a few days said that he wanted to publish a paper, and he also came up with such a professional paper. It was not academic garbage. Naturally, his first reaction was disbelief.
"Okay, can you please explain in detail the symmetric encryption algorithm AES and the asymmetric encryption algorithm RSA you mentioned in the paper?" Although Hanhua is a professor in the Department of Mathematics, he also has a lot of knowledge about computers. understanding, so I asked this question.
Wang Donglai opened his mouth to explain without any hesitation.
“AES is the abbreviation of Advanced Encryption Standard and is the most common symmetric encryption algorithm. AES, also known as Rijndael encryption in cryptography, is a block encryption standard adopted by the Bald Eagle federal government.
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"Its encryption formula is C=E(K,P), where K is the key, P is the plaintext, and C is the ciphertext.
"The encryption process is to first group the plaintext, and the length of each group All are 128 bits, and then encrypted group by group until all plaintext has been encrypted. The length of the key can be 128, 192 or 256 bits.
"In the encryption function E, a round function will be executed. Except for the last execution, the execution of the previous rounds is the same. Taking AES-128 as an example, the recommended number of encryption rounds is 10 rounds. That is, the operations performed in the first 9 rounds are the same, and the operations performed in the 10th round are the same as the previous ones. Different. The recommended number of encryption rounds is different for different key lengths...
"When encrypting, the plaintext is grouped in units of 128 bits, and each group contains 16 bytes, from top to bottom, Arranged from left to right into a 4×4 matrix, called the plaintext matrix. The encryption process of AES is performed in a matrix of the same size of 4×4, called the state matrix. The initial value of the state matrix is the value of the plaintext matrix. After each round of encryption, the value of the state matrix changes once. After the round function is executed, the value of the state matrix is the value of the ciphertext. The ciphertext matrix is obtained from the state matrix, and the value of the ciphertext matrix is sequentially extracted to obtain the 128-bit ciphertext.
“Take a 128-bit key as an example. The key length is 16 bytes and is also represented by a 4×4 matrix. The order is also from top to bottom and from left to right. AES arranges the keys through The function expands the key matrix into a key sequence containing 44 words, the first 4 of which The word is the original key used for initial encryption, and the following 40 words are used for 10 rounds of encryption. Each round uses 4 words. The key recursive generation rule is as follows: "If i is not a multiple of 4, then by equation w. [i]=w[i-4]⊕w[i-1] OK;
“If i is a multiple of 4, then it is determined by the equation w[i]=w[i-4]⊕T(w[i-1]);
“Encrypted The round function from round 1 to round 9 is the same, including 4 operations: byte substitution, row displacement, column mixing and round key addition. The last iteration does not perform column blending. In addition, before the first round of iteration, an XOR encryption operation is performed on the plaintext and the original key.
“The decryption process is still 10 rounds, and the operation of each round is the reverse operation of the encryption operation. Since the four rounds of AES operations are all reversible, one round of the decryption operation is the sequential execution of the retrograde shift. Bit, reverse byte substitution, round key addition and reverse column mixing are similar to the encryption operation. The reverse column mixing is not performed in the last round and is decrypted in the first round. Before, a key addition operation needs to be performed
The round function operation of AES encryption includes byte substitution SubBytes, row displacement ShiftRows, column mixing MixColumns, round key plus AddRoundKey, etc. Each step is They are all closely connected.”
"..."
"As for the asymmetric encryption algorithm RSA, in 1977 three mathematicians Rivest, Shamir and Adleman designed an algorithm that can achieve asymmetric encryption. Using an asymmetric encryption algorithm requires generating The public key and the private key are encrypted using the public key and decrypted using the private key. "
"..."
Wang Donglai was very eloquent, simple, clear and clear. You can tell at a glance. Really understand this stuff.
Hanhua actually gradually began to believe that this paper was written by Wang Donglai himself, but he still picked a few questions and asked, "What is a mutual prime relationship?"
This question is very simple. Anyone who has read the book can know it, but according to the course, Wang Donglai has not learned it yet.
“Primenumber, also known as prime number, has infinite numbers. A natural number greater than 1 cannot be divisible by other natural numbers except 1 and itself. In other words, the number is except for 1 and itself. There are no other factors; otherwise It is called a composite number. If two positive integers have no other common factors except 1, we say that the two numbers are in a mutually prime relationship. The mutually prime relationship does not require that both numbers are prime numbers. The composite number can also be summed by one. Prime numbers form a mutually prime relationship."
Wang Donglai answered quickly.
Hanwha then asked: "Then you can talk about the Euler function."
"The Euler function refers to the positive integer n. The Euler function is the sum of positive integers less than n. The number of numbers that are relatively prime to n is represented by φ(n) ”
"For example, φ(8)=4, because 1357 is relatively prime with 8."
"If n is the k power of prime number p, and except for multiples of p, all other numbers are relatively prime with n, then The mathematical formula is..."
"If m and n are relatively prime, then the mathematical formula is..."
"When n is an odd number, then the mathematical formula is..."
"When n is a prime number, then The mathematical formula is..."
His answers were fluent, unlike a freshman who had just entered college. In Hanwha's opinion, his fluency was no less than that of some juniors.
The three seniors in the office also stopped their movements at this time and listened carefully to Wang Donglai and Ge Hanhua's questions and answers.
"Modulo negation element."
"If two positive integers a and n are relatively prime, then the integer b can be found such that ab-1 is divisible by n, or ab is divisible by n The remainder of division is 1. At this time, b is called the 'modular inverse element' of a. "
"For example, if 3 and 11 are relatively prime, then. The modular inverse element of 3 is 4, because (3×4)-1 can be divided by 11. Obviously, there is more than one modular inverse element, and the integer multiples of 4 plus or minus 11 are all the modular inverse elements of 3 {…, -18, - 7, 4, 15, 26,…}, that is, if b is the modular inverse element of a, then b+kn are all the modular inverse elements of a. ”
"What about Euler's theorem?"
"Euler's theorem is a property about congruence. Euler's theorem shows that if n and a are positive integers, and n and a are relatively prime, then there is a^ φ(n)≡1(modn)”
etc. After Wang Dong finished speaking, Han Hua applauded subconsciously.
"Okay, okay, I really didn't expect you to give me such a big surprise."
"Previously, the quality of your paper was very high. I thought you didn't write it, so I asked you this to see if you understood it. I didn't expect you to give me such a big surprise."
< br>"There is no problem with your paper, and the argumentation process is also perfect. It's just that there is some arrangement. Small problems in the page and errors in citing references are all minor problems and can only be corrected a little bit.”
“But do you know the real value of your paper?”
After Han Hua finished speaking, he looked at Wang Donglai quietly, waiting for his answer.
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(End of this chapter)