Fully Homomorphic Encryption ( FHE ) Technology Analysis: Principles, Applications, and Future Prospects

Recently, the cryptocurrency market has seen little volatility, giving us more time to focus on the development of emerging technologies. Although the cryptocurrency market in 2024 may not be as grand as in previous years, there are still some new technologies gradually maturing, including the topic we will discuss today: fully homomorphic encryption (FHE).

To understand the complex concept of FHE, we need to first understand what "encryption" is, what "homomorphic" means, and why it is "fully."

Basic Concepts of Encryption

The most basic encryption method is very familiar to everyone. For example, if Alice wants to send a secret message "1314 520" to Bob. If the message needs to be transmitted through a third party C while ensuring the confidentiality of the information, a simple method is to multiply each number by 2 for encryption, turning it into "2628 1040". When Bob receives it, he just needs to divide each number by 2 to decrypt Alice's original message. This method is the most basic symmetric encryption.

Homomorphic Encryption Concept

Now, suppose Alice is only 7 years old and can only perform the simplest multiplication and division by 2 operations. She needs to calculate the total electricity bill for her home over 12 months, with a monthly bill of 400 yuan. However, multiplying 400 by 12 is too complicated for her, and she cannot compute it. At the same time, she does not want others to know the specific electricity bill information.

In this case, Alice can use a simple Homomorphic Encryption method. She encrypts 400 and 12 by multiplying them by 2, resulting in 800 and 24, and then has C calculate the result of 800 multiplied by 24. After C calculates 19200 and tells Alice, Alice divides the result by 2 and then by 2 again, obtaining the correct total electricity bill of 4800 yuan.

This is a simple example of multiplicative Homomorphic Encryption. 800 multiplied by 24 is actually a mapping of 400 multiplied by 12, and the forms before and after the transformation are the same, hence it is called "homomorphic." This method allows for computation by untrusted entities while protecting sensitive data from being leaked.

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 exhaustive methods, then a more advanced encryption method is required, which is where fully homomorphic encryption comes into play.

Fully homomorphic encryption allows for an arbitrary number of addition and multiplication operations on encrypted data, rather than being limited to a specific number of operations. This greatly increases the difficulty of decryption and virtually eliminates the possibility of third parties spying on private data.

It was not until 2009 that the new ideas proposed by Gentry and other scholars truly opened up the possibility of fully homomorphic encryption. This technology is regarded as one of the holy grails in the field of encryption.

Applications of FHE

The FHE technology has potential application value in multiple fields, particularly in the AI field.

During the AI training process, the privacy protection of large amounts of data has always been a thorny issue. The FHE technology can effectively address this problem:

1. Encrypt sensitive data using fully homomorphic encryption (FHE).
2. Use encrypted data for AI computation
3. AI outputs the encrypted result
4. The user decrypts the result locally.

This approach not only protects data privacy but also fully utilizes the powerful computing power of AI, achieving the goal of "both needs must be met."

Challenges of FHE in Practical Applications

Despite the broad prospects of FHE technology, it still faces huge challenges in practical applications, mainly due to its high computational costs. To address this issue, some projects are attempting to build dedicated computing networks and supporting facilities.

For example, some projects have proposed a network architecture similar to PoW+PoS to solve the computing power problem. They have launched dedicated hardware devices for mining, as well as NFT assets similar to work certificates. These attempts aim to establish a powerful computing power network, paving the way for the large-scale application of FHE.

Future Prospects of FHE

If AI can widely apply FHE technology, it will greatly advance the development of AI, especially in terms of data security and privacy protection. From national security to personal privacy protection, FHE technology has broad application prospects.

In today's rapidly developing AI landscape, data privacy issues have become increasingly important. If FHE technology can truly mature, it will undoubtedly become the last line of defense for humanity in protecting privacy in the digital age. With continuous advancements in technology, we have reason to expect that FHE will play a significant role in more fields in the future, providing strong technical support for data security and privacy protection.