my scientific age

Chapter 453 20 days!
"According to intelligence from the Military Intelligence Bureau, the Purple Code has completely replaced the old code system of the Japanese General Headquarters, the Japanese Army, and the Japanese Navy, becoming a new generation code system used by the three. According to our previous speculation, the Purple Code was compiled about a month ago. Obviously, the Japanese mathematicians who participated in compiling the Purple Code have not fully mastered asymmetric cryptography, and the loopholes are obvious."

"Purple key large prime numbers are usually 128 bits and 256 bits. No 516-bit large prime numbers were found in the 3958 public key plaintexts involving Purple key from various parties in Japan. My approach is to use factorization, the remainder theorem, and low encryption exponent small plaintext attacks, as well as brute force attacks. Except for brute force attacks which are not feasible for the time being, the other three attack methods have achieved certain results. In terms of time, it would take me about 268 days, 270 days, and 271 days to complete the cracking by myself."

"If Japan were to develop a more comprehensive and secure asymmetric cryptography system to replace the Purple Code, I estimate it would take another year to a year and a half. Therefore, the time available for deciphering the Purple Code is relatively ample."

"Of course, we cannot rule out another possibility: that the Japanese believe their Purple Cryptosystem is already perfect, with impeccable security and overall performance, and therefore have not immediately begun developing the next generation of asymmetric cryptography."

After handing over the documents, Hua Luogeng smoked a cigarette while explaining his thoughts.

After receiving the document detailing the results of the Purple Code decryption, Yu Hua immersed himself in it, studying it carefully. After a while, he nodded in approval of the entire document. As a top mathematician and one of the few cryptography experts in China, his mentor's decryption direction was indeed correct. All four attack methods could successfully break through the Purple Code's defense layer and achieve decryption.

Being on the right track is the most fundamental and important condition in the field of cryptography.

If the direction is wrong, then all the efforts and resources invested in the process will be meaningless.

As the master said, judging from the number of prime numbers in Purple Code, the Japanese coder did not fully understand the theory of asymmetric cryptography. This 'Purple Code' is like a product rushed into production, with obvious vulnerabilities. The most serious vulnerability is that the 128-bit and 256-bit values ​​are too small, making it easy to crack by brute force.

Of course, this 'obvious vulnerability' situation is limited to Hua Luogeng and Yu Hua. For the current cryptography community, 128-bit and 256-bit asymmetric cryptography is already very secure, with its security performance almost ten times that of the Enigma machine. If the number of bits for large prime numbers reaches 516 bits and 1024 bits, the timeliness of the ciphertext will be greatly reduced.

The difficulty and computational complexity of factoring large prime numbers with high digits increase exponentially with the number of digits, and there are no efficient algorithms. If the mathematical computational abilities of the communicating parties are not high, it will greatly reduce the efficiency of private key decryption of public key.

In this era, mathematical calculations relied entirely on pen and paper, and there were no highly efficient computers for encryption and decryption processing.

Between security and timeliness, militaries around the world have unanimously chosen the latter.

"Xiao Hua, what are your thoughts?" After Yu Hua carefully reviewed all the information about the deciphering results of the Purple Code, Hua Luogeng extinguished his cigarette, adjusted his glasses, and asked seriously.

Yu Hua responded, "The vulnerability in Purple Mine is obvious. I think we can first use the factorization attack method."

"How long do you think it will take to complete the decryption?" Hua Luogeng nodded. Yu Hua's choice did not surprise him. The factorization attack method was very effective against low-digit purple codes.

"If it's just the two of us, it will take about 20 days. The gap between Purple Secret and our first-generation asymmetric cryptography is too big." Yu Hua pondered for a few seconds before giving a precise timeframe.

"Only 20 days?! Xiao Hua, this isn't a secret."

Upon hearing this, Hua Luogeng looked shocked; this reply greatly surprised him.

Hua Luogeng was already a man at the very top of the Chinese mathematics community. Even with his mathematical calculation ability, it would take him 268 days to use the factorization attack method, let alone others.

However, now that Yu Hua only needs twenty days, Hua Luogeng suddenly had a strange feeling. Why was he, as the master, somewhat powerless in front of this disciple?

The two young men standing beside him were inwardly in tears. Good heavens, they finally understood what the two were talking about. Their eyes turned to Yu Hua. The information and mathematical jargon that had seemed like gibberish before had disappeared, replaced by 20 days.

Professor Hua would have needed 268 days to decipher the code, but this young man only needed 20 days after joining the team.

I understand now, I finally understand.

This classmate surnamed Yu is very capable; he can help them end their days of reading gibberish early.

As members of the Purple Code decryption team, their role was to serve as a tool, providing Professor Hua Luogeng and every decryption expert to the greatest extent possible, including shielding them from gunfire with their bodies after an attack.

As for the actual decoding work, sorry, they're only good at killing.

Which Kuomintang intelligence agent is good at math?

"Master, have you forgotten that I'm very good at mathematical calculations? I'm especially skilled at calculating discrete logarithms and factoring large prime numbers." Yu Hua didn't reveal anything about himself, joking with a smile. Suddenly remembering something, he asked, "By the way, Master, has the school announced when the entrance exam for students going to study in the US will begin?"

Mathematics is the subject that is most tolerant of geniuses and prodigies. No matter how incredible your mathematical talent is, others can recognize and admire it.

"You lad, I always feel your mathematical talent is getting higher and higher... As for the exams for studying in the US, if nothing unexpected happens, it should be in mid-November. After all, American universities are about to have their final break, and most American universities start in late January. The exams here must be in time for the start of the American university semester." Hua Luogeng realized that his favorite disciple was best at all kinds of repetitive calculations and factoring large prime numbers, and replied with a soft sigh.

“Okay, Master, let’s begin. The sooner we decipher the Purple Code, the greater the help in the war against the enemy.” Yu Hua nodded in satisfaction after receiving a definite answer from his master, and then said solemnly.

After initial contact, Yu Hua has learned about the current progress of the Purple Code deciphering and now he must go all out to complete the deciphering work as soon as possible.

If the Purple Code could be deciphered in about 20 days, it would be of great help to the defense of Nanjing and the national battlefield, since Japan had already listed the Purple Code as a shared code among the army, navy and political parties.

"it is good."

Hua Luogeng nodded upon hearing this, took out the documents, and began working.

With the addition of Yu Hua, who possesses an astonishing computing power of 500 million calculations per second, the progress of deciphering the Purple Code increased at a visible speed. Just like when they were deciphering the Red Code, the master and apprentice worked closely together, one taking the lead and the other performing efficient calculations.

……

Nanjing area.

As the capital of the Republic of China, Nanjing held an extraordinary influence and status. The Yangtze River flows through the city, connecting Nanjing and Shanghai like a silk thread, making them two shining pearls in the southern region.

Nanjing's politics and Shanghai's economy were the two major arteries of the Republic of China.

The massive battle that erupted in the Songhu area determined the fate of the entire city of Nanjing. While the political and business circles of Nanjing were focused on the Songhu area, a headline article from major newspapers circulated among the common people and played its role quietly.

(End of this chapter)