my scientific age

Chapter 111 Two systems!

Hua Luogeng explained the situation about the Hill cipher in detail. Yu Hua was attentive and did not miss any details. With Hua Luogeng's explanation, Yu Hua understood what the Hill cipher was.

The so-called Hill cipher refers to a new cryptographic algorithm born in 1929 using the principle of mathematical matrix. It is one of the mainstream algorithms in the current cryptosystems around the world. The basic idea of ​​the encryption algorithm is to convert n plaintext letters into n letters through mathematical linear transformation. The ciphertext letters can be decrypted by only one inverse transformation. The key is the matrix itself. The confidentiality of the entire cryptosystem is extremely high, and it is almost difficult to be cracked by the outside world.

Coders only need to formulate different types of encryption matrices and replace them regularly.

Matrix, which is translated into rectangular matrix in China, 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 replacement ciphers had poor confidentiality. It is that the decipherer only needs a little knowledge of elementary mathematics to crack the code.

In order to improve the complexity and confidentiality of passwords, cryptographers immediately proposed a multi-letter replacement cipher containing the idea of ​​​​dolls.

Due to the complexity and confidentiality of multi-letter replacement ciphers, it is far higher than that of shift ciphers and single-letter ciphers. Once it came out, it immediately became a sought-after object in various countries, causing decipherers trying to obtain information content to sigh in admiration.

However, multi-letter replacement ciphers do not mean invincibility, because mathematicians who symbolize the peak of human wisdom have invented the frequency analysis attack method of the era. password.

Under the frequency analysis attack method, any type of multi-letter replacement password will not survive for a month. The reason for Germany's defeat in World War I is inseparable from the fact that the password was deciphered and the 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 replacement ciphers can only survive for a month, but the Hill cipher can survive for three months or even more than half a year in the face of the frequency analysis attack method. The main reason is that the core algorithm of the Hill cipher uses the matrix in linear algebra. Multiplication and inverse operations can better resist frequency analysis and are difficult to break, thereby filling the shortcomings of various previous ciphers.

The Hill cipher system has a total of three keys, the vector dimension, the alphabetical arrangement table and the encryption matrix. In order to decipher it, one must have deep mathematical attainments and logical thinking, and reversely deduce the encryption matrix through frequency analysis.

The whole deciphering process requires a lot of work. If it exceeds a certain time, the other party can replace a new set of encryption matrix, so that the decipherer's efforts will be in vain.

Of course, the Hill cipher is not invincible. There is a saying, a big brick can fly. As long as the engine is strong enough, a brick can fly into the sky. As long as the decipherer has sufficient manpower and resources, plus mathematics that can be called the soul home, you can decipher it.

"After my identification, the Japanese red secret system is based on the Hill cipher algorithm, and the alphabetical list is the Japanese Hiroshima dialect words, and our first main goal is to crack the encryption matrix." After Hua Luogeng finished talking about the Hill cipher and frequency analysis , with a serious face, and said the first goal of cracking the red secret: "What you have to do is to use the frequency analysis attack method to find out the Japanese words that appear frequently, formulate them as an alphabetical list, and finally realize the cracking of the encryption matrix, I hope we can resolve it within 50 days and crack the red secret as much as possible."

50 days!
This is Hua Luogeng's goal.

Reverse cracking the Hill code is the most difficult, but this does not deter Hua Luogeng, who is a mathematical genius. He knows the way of cracking the red secret system very well. The biggest problem has always been the lack of manpower.

"So, Professor, isn't our goal to crack a single ciphertext, but the entire ciphertext system mechanism?" Yu Hua finally recalled it after hearing it initially. He was surprised and shocked, and couldn't help asking aloud.

Hua Luogeng nodded and said with a smile, "Why, are you afraid?"

"I'm not afraid, I just feel... Shocked, I didn't expect our goal to be to crack the entire Japanese code system." Yu Hua shook his head, he didn't have any fear or fear, took a deep breath and said.

Scared?
The word does not exist in his dictionary.

"No, the red secret is not the only encryption system in Japan. It is the encryption system used by the Japanese army and foreign affairs department. As far as I know, the encryption system used by the Japanese navy and internal use, if nothing else, should be another system based on The encryption system of the German Enigma prototype." Hua Luogeng pointed out Yu Hua's mistake and corrected him.

Eggs cannot be put in one basket. Japan adopts two sets of cryptographic system mechanisms, one inside and one outside, to prevent major losses from information security and intelligence leakage.

"Two systems... the students understand."

After hearing this explanation, Yu Hua thought about it and basically clarified the Japanese password mechanism: "Then do we need to crack another Japanese password system?"

"This is one of the goals in the future. Of course, if the authorities need it, cracking the Enigma code machine requires a huge amount of resources and manpower, which ordinary countries cannot afford. Let's solve the red secret system first and then talk about other things." Hua Luogeng responded.

He had heard of this cipher machine in the UK and understood its working principle. The Enigma code machine belongs to Germany and is the strongest cipher machine in the world today. Theoretically, the number of cipher combinations may be as high as [-] billion The force cannot be broken at all.

Deciphering it is basically impossible.

Yu Hua nodded and did not continue to ask questions, and then followed Hua Luogeng to learn about cryptography in depth, attacking the frequency analysis attack method and the type of Hill cipher theory matrix. Although learning cryptography was to break the red secret, Hua Luogeng still spoke very seriously.

In one morning, with a solid foundation in advanced mathematics, Yu Hua's learning progress was very fast, and it didn't take long for him to get started with cryptography.

At noon, Yu Hua stayed in the room to teach himself the theory of real variables and cryptography, trying to reach the standard of Master Hua Luogeng as soon as possible. Hua Luogeng took Yu Hua's calculus graduation mathematics paper and left to go to Tsinghua Garden for class.

Office of the Department of Mathematics, Tsinghua Park.

"Squeak." The office door opened gently.

"Luogeng 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'm taking traditional Chinese medicine recently to recuperate my body. I'm sorry to wait for my body to recover a little.

(End of this chapter)