Fully Homomorphic Encryption: A Privacy Protection Tool in the AI Era

The recent market has been sluggish, providing us with more time to focus on the development of some emerging technologies. Although the crypto market in 2024 is not as grand as in previous years, there are still some new technologies gradually maturing. Today, we will delve into one of the most notable technologies: fully homomorphic encryption (FHE).

To understand the complex concept of FHE, we need to clarify the meanings of "encryption" and "homomorphic", as well as why the emphasis on the word "fully" is necessary.

Basic Concepts of Encryption

The most basic encryption methods are well known to everyone. For example, if Alice wants to send a secret message "1314 520" to Bob, but has to pass it through a third party C. To ensure the information is secure, Alice can use a simple encryption method: multiplying each number by 2. This way, the message becomes "2628 1040". When Bob receives the message, he just needs to divide each number by 2 to restore the original message "1314 520".

This symmetric encryption method allows Alice and Bob to transmit information while employing C, without letting C know the specific content. This basic encryption concept is applied in many confidential communications.

Homomorphic Encryption Principles

Now, let's look at a more complex situation. Suppose Alice is only 7 years old, and she can only perform the simplest operations of multiplying by 2 and dividing by 2. Alice's family has a monthly electricity bill of 400 yuan and is in arrears for 12 months, but she cannot calculate 400 multiplied by 12.

Alice does not want others to know the specific amount of the electricity bill and the number of months owed, as this is sensitive information. So, she came up with a solution: first, multiply 400 and 12 by 2 for simple encryption, and then ask C to calculate the result of 800 multiplied by 24.

C quickly calculated 19200 and told Alice. Alice then divided this result by 2 and then by 2 again, resulting in the actual electricity bill of 4800.

This is a simple example of homomorphic encryption for multiplication. 800 times 24 is actually a mapping of 400 times 12, and the form remains consistent before and after encryption, hence the term "homomorphic." This method allows Alice to delegate computations to an untrusted third party without revealing sensitive data.

The Necessity of Fully Homomorphic Encryption

However, problems in the real world are often more complex than this. If C can deduce through repeated trials that what Alice originally intended to calculate was 400 and 12, then more advanced "fully homomorphic encryption" technology is required to solve this.

Fully homomorphic encryption allows for an arbitrary number of addition and multiplication operations on encrypted data, not limited to specific operations or a finite number of operations. This ensures the security of the data even in the face of complex polynomial operations, virtually eliminating the possibility of third parties spying on private data.

Fully homomorphic encryption technology did not achieve breakthrough progress until 2009 and is regarded as the "Holy Grail" in the field of cryptography.

The Application Prospects of Fully Homomorphic Encryption

The FHE technology has broad application prospects in the field of artificial intelligence. As we all know, powerful AI systems require massive amounts of data for training, but this data often involves privacy issues. FHE technology can effectively resolve this contradiction:

1. Users can encrypt sensitive data using FHE method.
2. Provide the encrypted data to AI for computation.
3. AI returns a string of encrypted results.
4. The user decrypts the result locally to obtain the required information.

In this way, the AI system can provide services to users without accessing the original sensitive data, truly achieving a win-win situation for data utilization and privacy protection.

FHE technology can also be applied in fields such as facial recognition. For example, during identity verification, it is important to ensure accuracy while also protecting users' facial feature information from being disclosed.

Challenges and Developments of Fully Homomorphic Encryption

Although the prospects for FHE technology are promising, practical applications still face challenges. The main issue is that FHE requires substantial computational resources, and the processes of encryption, decryption, and computation are time-consuming and labor-intensive.

To address this issue, some projects are exploring the establishment of dedicated FHE computing networks. These networks typically employ incentive mechanisms similar to cryptocurrency mining to encourage participants to provide computing power.

With the continuous advancement of technology, FHE is expected to become an important tool for protecting personal privacy in the AI era. From national security to personal daily life, FHE technology may play a significant role, becoming the last line of defense for privacy protection in the digital age.