Related to the lattice encryption algorithm, the most popular one derived from it today is the fully homomorphic encryption algorithm.

If f(a)+f(b)=f(a+b), then this cryptographic function is called additive homomorphism.

If f(a)*f(b) = f(a*b), then this cryptographic function is called multiplicative homomorphism.

If the cryptographic function f satisfies only the addition homomorphism, then only addition and subtraction can be performed, and if only the multiplicative homomorphism is satisfied, then only multiplication and division can be performed.

Only when both additive homomorphism and multiplicative homomorphism are satisfied can it become fully homomorphic encryption.

Today's RSA algorithms are homomorphic for multiplication.

The concept of fully homomorphic encryption was proposed on the Blue Dome from the 80s of the last century, and it was not until 2009 that the first fully homomorphic encryption that satisfies both additive and multiplicative homomorphism-Gentry algorithm was born.

Because it can be added, subtracted, multiplied and divided, fully homomorphic encryption has an amazing ability that other algorithms do not have: it can calculate ciphertext data without decryption, which makes it possible to process the data without destroying sensitive source data.

A simple example, 1 is encrypted to A, and 26 is encrypted to Z. The fully homomorphic text can be mathematically calculated on the encrypted ciphertext, such as A+Z=AA, so the correct decryption of AA is 27.

This kind of processing is simply nonsense on other encryption algorithms, but it can only be called basic operation for fully homomorphic encryption.

In this way, it is possible to avoid the appearance of the data being made available in clear text at the time of data processing.

In other words, the demander can completely encrypt the data and transmit it to the data processor.

Because most of the current data analysis methods of Edomus are mathematical statistical methods, the data processor can still perform homomorphic ciphertext calculation on ciphertext data.

The processed ciphertext is then returned to the demander, who decrypts it through its own key.

In this way, it will not affect the accuracy of data calculation, but also protect data privacy and security, and the data processor can only process ciphertext and not private data.

Yan An picks and chooses, and what he ultimately values is the fully homomorphic encryption algorithm.

However, this thing is not without its drawbacks, first of all, it requires very high computing performance, which means that it takes a certain amount of time and performance to execute.

Secondly, the current fully homomorphic encryption algorithm of Blue Dome can only support addition, subtraction, multiplication and division, but many mathematical statistical methods will have operations such as opening the root number.

Here, the approximation theory in information theory and mathematics can only be used to achieve the same or similar computational purpose through approximation algorithms.

As a result, there is usually a loss of accuracy and a large calculation error.

These are all problems that Yan An wants to solve, and it is impossible to have both fish and bear's paws, and the expansion of the fully homomorphic encryption algorithm will inevitably increase the demand for computing performance.

Algorithms that reduce the demand for computing performance will inevitably have the second problem.

Yan An searched all over BT's database, but he couldn't find an algorithm that met both of these conditions.

Perhaps hidden, there are algorithms that meet the conditions in the technology after the first-level civilization, but BT will never be open to him.

Even if he is open, he will probably not need it, and he will have to raise the theory and equipment of the Blue Dome Star first.

"Then you'll have to do it yourself." Yan An was full of interest and turned out all the fully homomorphic encryption algorithms in the database that could be read.

Not all of these algorithms meet the requirements of "encryption, signature, and authentication in one", and there are some shortcomings that cannot be ignored for Yan An in all aspects.

There are a total of seven well-established fully homomorphic encryption algorithms, and Yan An plans to learn them all in one go, and then design a set of encryption algorithms that are excellent in all aspects.

It's just that it's not easy to learn, and he didn't advance much for a whole day on the 23rd, and it is estimated that it will take nearly a month to learn these seven algorithms.

On the twenty-fourth Chinese New Year's Eve, there was a sound of a rope at the door, and Yan An asked BT to turn the camera and saw Gao Shenghan's family who were busy pasting couplets.

The couplet was written by himself, and the pen looked a little strange, not like Gao Shenghan's words.

Yan An looked at it for a while, and two more people came up from downstairs, a man and a woman were about the same age as Yan An, and when they saw Gao Shenghan, they shouted, "Hello uncle."

Gao Shenghan was originally happy, but when he heard this name, he put his face up, and the darkness was not scary.

The man and woman grinned and didn't care, and entered the door to say hello to Gao Shenghan's father.

Can't look any further...... Yan An forced himself to turn off the surveillance, repeating in his heart that this was nothing to look at.

He tried to turn his attention back to the algorithm in front of him to continue learning, but the sound of frolicking outside made him unable to calm down.

Really unqualified, Yan An found an excuse and scolded in his heart, completely forgetting that he could easily enter the state of learning in a noisy environment before.

Since he had no intention of studying and it was a holiday, Yan An rarely gave himself a vacation, and used the members of the ACM Zhu Chi Council to find some papers in the digital library to read.

I didn't read it for long, I just opened the paper and read the beginning, and I couldn't stand the excitement outside and turned it off, and then I changed the paper to see the beginning, and the whole morning was consumed like this.

At noon, the dumplings filled with pork and cabbage are cooked, and the quick-frozen dumplings have the advantage of being stable and will not show the filling like hand-wrapped.

After checking the quick-frozen pot under warm water on the Internet, Yan An threw it in when there were small bubbles in the pot, and successfully got a bowl of white and tender dumplings.

Before starting, he looked at the hot air rising from the dumplings and was stunned, "Twelve years." ”

I don't know how many years will be in the future.

It's the same at night, he replaced the pork and cabbage stuffing with Orleans chicken dumplings, this flavor is the first time he eats, the filling is red, and it looks very festive.

Just as he was about to move, there was a knock on the door.

On Chinese New Year's Eve, someone will knock on the door?

Yan An got up in surprise, and when he opened the door, he saw the one-armed old man, and Gao Shenghan was one position behind.

When the old man saw him open the door, he quickly glanced into the room, and there was no one in the living room, dining room, or kitchen, and there was only a steaming bowl on the dining table.

He asked with a smile, "Haven't you eaten yet?" ”

"Just about to eat." Yan An replied a little timidly, he couldn't understand the old man's intention, but that smiling face made him let down his guard.

"It's good that you haven't eaten it yet!" The old man had only his left arm left, and the sleeve of his right arm was empty, and it was amputated from the shoulder.

He stretched out a hand as shriveled as old tree bark and grabbed Yan An, "If you haven't eaten, you will come to our house to eat."

Gao Shenghan, this little cub, didn't say anything to me, I still wonder, why haven't I seen your family these days, I only found out when I asked at noon today, it turned out that you were alone here.

During the Chinese New Year, how lonely it is to stay in the house alone, there is no fireworks, take a walk, come to our house to eat, many people are lively. ”

The old man enthusiastically pulled him towards the opposite door, although he only had one hand and was amazingly thin, his strength was surprisingly great, and Yan An was almost dragged out by him.

was scolded by his father, Gao Shenghan looked sneered, the impression that Yan An left him in the past was that he was an unruly genius, a quirk and not close to people, no one could know the real thoughts in his head.

But he forgot that Yan An was alone in this world.

"Don't do it." Yan An subconsciously refused, and hurriedly retracted his hand, resisting and unwilling to move forward.

"I have a lot of quirks, and they all say that I am not educated, and it is not good to sweep away your interest in this New Year. And I also cooked dumplings, and it was good to eat dumplings, so it didn't bother. ”