Hua Luogeng carefully explained the situation about the Hill password. Yu Hua paid full attention and did not miss any details. With Hua Luogeng's explanation, Yu Hua finally understood what the Hill password was.
The so-called Hill cipher refers to a new cryptographic algorithm born in 1929 using the mathematical matrix principle. It is one of the mainstream algorithms of cryptosystems in various countries around the world. The basic idea of the encryption algorithm is to convert n plaintext letters into n letters through mathematical linear transformation.
To decrypt the ciphertext letters, only one inverse transformation is needed, and the key is the matrix itself. The entire cryptographic system is extremely confidential and is almost difficult to be cracked by the outside world.
Coders only need to develop different types of encryption matrices and replace them regularly.
Matrix, domestically translated as rectangular matrix, is one of the basic contents of mathematical analysis and the soul of Hill cipher.
The password itself has functional characteristics. The relationship between plaintext and ciphertext is one-to-one and one-to-many. From a mathematical point of view, plaintext is a function of ciphertext. In the past, shift ciphers and single-letter substitution ciphers had poor confidentiality. This is why
The reason is that the codebreaker only needs to know a little bit of elementary mathematics to crack the code.
In order to improve the complexity and confidentiality of passwords, cryptographers immediately proposed multi-alphabetic substitution ciphers that contained the idea of matryoshka dolls, layered within one layer, one layer within another, and the level of complexity was simply outrageous.
Due to the complexity and confidentiality of multi-letter substitution ciphers, which are much higher than shift ciphers and single-letter ciphers, once it came out, it immediately became a sought-after object in various countries, making the decipherers who tried to obtain the information content look up to the sky and sigh.
However, the multi-letter substitution password does not mean invincibility, because mathematicians who symbolize the pinnacle of human wisdom invented the frequency analysis attack method of the era. By studying the frequency of occurrence of letters and letter combinations in the original plaintext and filtering records, they can crack it
password.
Under the frequency analysis attack method, any type of multi-letter replacement cipher would not survive for more than a month. The reason for Germany's defeat in World War I was inseparable from the fact that the cipher was deciphered and intelligence information was leaked. This situation lasted for a long time, until suddenly one day
, the Hill cipher based on the matrix principle appeared.
Other multi-letter substitution ciphers cannot survive for a month, but the Hill cipher can survive for three months or even more than half a year in the face of frequency analysis attacks. The main reason is that the core algorithm of the Hill cipher uses matrices in linear algebra.
Multiplication operations and inverse operations can resist frequency analysis well and are difficult to break, thereby filling the shortcomings of various previous passwords.
The Hill cryptosystem has a total of three keys, vector dimension, letter arrangement table and encryption matrix. If you want to decipher it, you must have profound mathematical attainments and logical thinking, and reversely deduce the encryption matrix through frequency analysis.
The entire deciphering process requires a huge amount of work. If it exceeds a certain time, the other party can replace it with a new encryption matrix, thus making the decipherer's efforts in vain.
Of course, the Hill cipher is not invincible. As the saying goes, bricks can fly with great force. As long as the engine is strong enough, bricks can fly into the sky. The decipherer only needs to have sufficient manpower and resources, plus mathematics that can be called the soul.
Home, you can decipher it.
"After my identification, the Japanese red cipher system is based on the Hill cipher algorithm. The alphabet arrangement is Japanese Hiroshima dialect words, and our first main goal is to crack the encryption matrix." Hua Luogeng finished talking about the Hill cipher and frequency analysis.
, with a serious face, said the first goal of cracking the red secret: "What you have to do is to use the frequency analysis attack method to find Japanese words that appear frequently, formulate them into alphabetical tables, and finally crack the encryption matrix.
I hope we can solve it within 50 days and crack the red code as much as possible."
50 days!
This is Hua Luogeng's goal.
Reverse decryption of the Hill code is the most difficult, but this does not stump Hua Luogeng, a mathematical genius. He knows the idea of cracking the red secret system very well and is extremely clear. He does not need any machine, just a pen and paper.
The biggest problem has always been the lack of manpower.
"So, professor, our goal is not to crack a single ciphertext, but the entire ciphertext system mechanism?" Yu Hua finally came back to his senses after listening to it for the first time. He was surprised and shocked, and couldn't help but ask aloud.
Hua Luogeng nodded and said with a smile: "Why, are you scared?"
"I'm not afraid, I just feel... shocked. I didn't expect that our goal would be to crack the entire Japanese encryption system." Yu Hua shook his head. He had no fear or fear. He took a deep breath and said.
Fear?
This word does not exist in his dictionary.
"No, the red secret is not the only cryptographic system in Japan. It is the cryptographic system used by the Japanese Army and Foreign Affairs Department. As far as I know, the cryptographic system used by the Japanese Navy and internally, if nothing else, should be another cryptosystem based on
The cryptographic system of the German Enigma prototype." Hua Luogeng pointed out Yu Hua's mistake and corrected it.
Eggs cannot be put in one basket. Japan adopts two sets of cryptographic systems, one internal and one external, to prevent information security and intelligence leakage from causing major losses.
"Two systems...students understand."
After hearing this explanation, Yu Hua thought thoughtfully and basically understood the Japanese cryptographic mechanism: "Then do we need to crack another Japanese cryptographic system?"
"This is one of the goals in the future. Of course, if the authorities need it, cracking the Enigma machine will require a huge amount of resources and manpower. Most countries cannot afford it. Let's solve the red secret system first and then talk about other things." Hua Luogeng responded.
He had heard of this kind of cipher machine in the UK and understood its working principle. The Enigma machine belongs to Germany and is the strongest cipher machine in the world today. Theoretically, the number of password combinations possible is as high as one billion.
It can't be broken by force at all.
It is basically impossible to decipher it.
Yu Hua nodded and did not continue to ask questions. Then he followed Hua Luogeng to learn more about cryptography and tackle frequency analysis attack methods and Hill cipher theory matrix types. Although he studied cryptography to break the red secret, Hua Luogeng still spoke very seriously.
In one morning, with a solid foundation in advanced mathematics, Yu Hua made very fast learning progress. It didn't take long for him to get started with cryptography. By the end of the course, his overall level was comparable to that of a student who has studied cryptography for about a year.
At noon, Yu Hua stayed in the room to study real variable function theory and cryptography by himself, striving to meet the standards of his master Hua Luogeng as soon as possible. Hua Luogeng left with Yu Hua's calculus final mathematics thesis and went to Tsinghua University for classes.
Office of the Department of Mathematics, Tsinghua University.
"Squeak." The office door opened gently.
"Luo Geng is back?" The person who spoke was Yang Wuzhi.
"Hello, Uncle Hua."
"Hello, Uncle Hua."
Immediately afterwards, two other young voices came out.
PS: I have been taking traditional Chinese medicine recently to take care of my body. Sorry, I will update when my body recovers a little.