In the office, when Han Hua asked this question, 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 spoke 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 what about 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.
Even if he calculated everything he could, the classes he took at Tangdu Jiaotong University would 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 a ghostwriter.
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.
"It was indeed written by me alone, in the library. The English version was translated after I returned to my dormitory."
"Well, since you wrote the paper, 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, Hanhua would have ignored it a long time ago, but Wang Donglai is a student of Qian Xuesen's experimental class. The school attaches great importance to the students in this experimental class and allocates a lot of resources to train these students.
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 didn't think that Hanhua did this because he looked down on him 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 highly professional paper. It was not academic garbage. The first reaction was naturally 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, so he asked Something went wrong.
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.
"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 into groups, each group is 128 bits long, and then encrypt group by group until all the 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 execution of the first 9 rounds The operations are the same, but the operations performed in the 10th round are different from the previous ones. The recommended number of encryption rounds is different for different key lengths...
"When encrypting, the plaintext is grouped in units of 128 bits. Each group contains 16 bytes, which are arranged from top to bottom and from left to right into a 4×4 matrix, called the plaintext matrix. AES encryption process It is carried out in a matrix with 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 execution of the round function, the state The value of the matrix is the value of the ciphertext. The ciphertext matrix is obtained from the state matrix, and the values of the ciphertext matrix are extracted in sequence 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 expands the key matrix through the key arrangement function into a key sequence containing 44 words, the first 4 words of which are the original keys used for initial encryption, the next 40 words are used for 10 rounds of encryption, and 4 words are used in each round. The key is generated recursively The rules are as follows:
"If i is not a multiple of 4, then it is determined by the equation w[i]= w[i-4]⊕ w[i-1];
"If i is a multiple of 4, then it is determined by the equation w[i]= w[i-4]⊕ T(w[i-1]);
"The round function from the 1st to the 9th round of encryption is the same, including 4 operations: byte substitution, row displacement, column mixing and round key addition. The last round of iteration does not perform column mixing. In addition, in the first Before each round of iteration, the plaintext and the original key are first subjected to an XOR encryption operation.
"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 to sequentially perform retrograde shift and reverse byte generation. Switching, round key addition and reverse column mixing. Similar to the encryption operation, the reverse column mixing is not performed in the last round. Before the first round of decryption, a key addition operation is performed.
The round function operations of AES encryption include byte substitution SubBytes, row displacement ShiftRows, column mixing MixColumns, round key plus AddRoundKey, etc. Each step is 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 the asymmetric encryption algorithm requires generating a public key and a private key, and using the public key for encryption , decrypt using the private key."
"..."
Wang Donglai's talk was eloquent, simple, clear and clear. You can tell at a glance that he really understands the content.
Han Hua 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.
"Prime numbers, also known as prime numbers, have infinite numbers. A natural number greater than 1 cannot be divisible by other natural numbers except 1 and itself. In other words, the number has no other numbers except 1 and itself. Factor; 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, and the composite number is also It can form a coprime relationship with a prime number."
Wang Donglai answered quickly.
Han Hua then asked: "Then you can talk about the Euler function."
"The Euler function refers to the positive integer n. The Euler function is the number of numbers that are relatively prime to n among the positive integers less than n, represented by φ(n)."
"For example, φ(8) = 4, because 1 3 5 7 are all relatively prime to 8."
"If n is the kth power of a prime number p, and except for multiples of p, all other numbers are relatively prime to n, then the mathematical formula is..."
"If m and n are mutually prime, the mathematical formula is..."
"When n is an odd number, the mathematical formula is..."
"When n is a prime number, 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.
"An anti-element."
"If two positive integers a and n are relatively prime, then you can definitely find an integer b such that ab - 1 is divisible by n, or the remainder of ab divided by n is 1. At this time, b is called the 'modulo inverse element of a '."
"For example, 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 modulo 3 Anti-elements {…, -18, -7, 4, 15, 26,…}, that is, if b is the modular anti-element of a, then b + k n are all modular anti-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 a^φ(n)≡ 1 (mod n)."
"Assuming that the positive integer a and the prime number p are relatively prime, because φ(p)= p-1, then Euler's theorem can be written as a^(p-1)≡ 1 (mod p)."
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."
"There are no problems with your paper, and the argumentation process is also perfect. There are just some minor typographical problems and errors in citing references. These are minor problems. Just make some corrections."
"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.
