Discussing the principles and application prospects of fully homomorphic encryption ( FHE ) technology

Recently, the market trend has slowed down, giving us more time to focus on the development of some emerging technologies. Although the cryptocurrency market in 2024 is not as spectacular as in previous years, there are still some new technologies gradually maturing. The topic we are going to discuss today is the technology of "fully homomorphic encryption(Fully Homomorphic Encryption, FHE)."

To understand the complex concept of FHE, we need to first understand the meanings of "encryption" and "homomorphic", and why we need to achieve the "fully" level.

The Basic Concepts of Encryption

The most basic encryption method is well known to everyone. For example, if Alice wants to send Bob a secret number "1314 520", but does not want the third party C to know the content. They can agree on a simple encryption rule: multiply each number by 2. Thus, the information sent by Alice becomes "2628 1040". After receiving it, Bob only needs to divide each number by 2 to get the original information. This is a simple symmetric encryption method.

The Concept of Homomorphic Encryption

Now let's imagine a more complex scenario: 7-year-old Alice can only perform the simplest operations of multiplying by 2 and dividing by 2. She needs to calculate the total electricity bill for her home over 12 months, with a monthly bill of 400 yuan. But this multiplication operation is too difficult for her.

Alice didn't want others to know the specific electricity bill information, but she needed help with the calculation. So she encrypted the data by multiplying by 2 and asked C to calculate the result of 800 multiplied by 24. C quickly calculated 19200 and told Alice. Alice then divided the result by 2 twice to get the correct total electricity bill of 4800 yuan.

This is a simple example of homomorphic encryption for multiplication. 800 multiplied by 24 is actually a mapping of 400 multiplied by 12, and the form remains the same before and after encryption, hence it is called "homomorphic". This method allows delegating computations to untrusted third parties while protecting sensitive data from being disclosed.

The Necessity of Fully Homomorphic Encryption

However, problems in the real world are often more complex. If C can infer Alice's original data through certain methods, then simple Homomorphic Encryption is not secure enough.

At this point, it is necessary to introduce "fully homomorphic encryption" technology. Alice can add more computational steps on the basis of the original multiplication, such as multiple multiplication and addition operations. This greatly increases the difficulty for C to crack it.

The meaning of "fully" refers to the ability to perform arbitrary additions and multiplications of polynomial operations, no matter how complex, in an encrypted state, and finally decrypt to obtain the correct result. This technology can handle almost all mathematical problems, not just limited to simple calculations.

Fully homomorphic encryption has long been the holy grail in the field of cryptography. It wasn't until 2009 that new ideas proposed by Gentry and other scholars truly opened up the possibilities of fully homomorphic encryption.

Application Scenarios of FHE Technology

One important application area of FHE technology is artificial intelligence. It is well known that powerful AI systems require vast amounts of data for training, but much of the data is highly sensitive. FHE technology can effectively address this contradiction:

1. Encrypt sensitive data using fully homomorphic encryption (FHE)
2. Train AI models with encrypted data
3. AI outputs the results of encryption

In this way, the AI system itself does not access the original data but processes the encrypted vectors. Data owners can securely decrypt the AI's output results locally. This achieves the full utilization of AI's powerful computing power while protecting data privacy.

Challenges of FHE in Practical Applications

Although FHE technology has broad prospects, it still faces some challenges in practical applications. The main issue is that FHE computation requires extremely large computing power, and the processes of encryption, computation, and decryption are very time-consuming.

To address this issue, some projects are attempting to build dedicated FHE computing networks. For example, a certain project proposed a network architecture that combines the characteristics of PoW and PoS, and launched dedicated hardware devices and NFT assets to support the operation of the network.

The Importance of FHE Technology

If AI can widely apply fully homomorphic encryption (FHE) technology, it will greatly promote the development of AI. Currently, many countries focus their regulation of AI on data security and privacy protection, and FHE technology can effectively address these concerns.

From national security to personal privacy protection, the application range of FHE technology is very broad. In the upcoming AI era, FHE technology may become the last line of defense in protecting human privacy. As technology continues to mature, we have reason to expect that FHE will play an increasingly important role in the future.