Exploring the Connotation and Application Prospects of Fully Homomorphic Encryption Technology

Recently, the market has been sluggish, 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. Today, we will focus on a remarkable technology: fully homomorphic encryption (FHE).

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

Basic Concepts of Encryption

Encryption is a common means of protecting information security. For example, if Alice wants to send a secret number, like "1314 520", to Bob through a third party C, she can use a simple encryption method: multiply each number by 2. This way, the transmitted information becomes "2628 1040". When Bob receives this string of numbers, he only needs to divide each number by 2 to restore the original information. This method allows information transmission through a third party without leaking the real content.

The Concept of Homomorphic Encryption

Homomorphic Encryption goes a step further as it allows specific computational operations to be performed on encrypted data without needing to decrypt it first. Suppose Alice is only 7 years old and can only perform the most basic operations of multiplying by 2 and dividing by 2. Now she needs to calculate the total electricity bill for 12 months, with a monthly bill of 400 yuan. Since 400 multiplied by 12 exceeds her computational ability, she decides to seek help from others but does not want to disclose the exact amount.

Thus, Alice adopted the idea of Homomorphic Encryption. She multiplied 400 and 12 by 2 respectively, obtaining 800 and 24, and then asked C to help calculate 800 multiplied by 24. After C calculated the result of 19200, he told Alice, who then divided this result by 4 (equivalent to dividing by 2 twice), thus obtaining the correct total amount of 4800 yuan. In this process, C did not know what the actual computation was, but Alice obtained the correct result through simple decryption.

The Necessity of Fully Homomorphic Encryption

However, the simple homomorphic encryption method mentioned above has the risk of being cracked. If C is smart enough, they might guess the original data through brute force. This requires a more complex encryption method, namely fully homomorphic encryption.

Fully homomorphic encryption allows for arbitrary numbers of addition and multiplication operations to be performed on encrypted data, rather than being limited to a specific number of operations. This greatly increases the difficulty of decryption, enabling even complex mathematical problems to be computed while preserving privacy.

It is worth mentioning that fully homomorphic encryption did not achieve breakthrough progress until 2009. Prior to this, only partial homomorphic encryption could be realized.

Applications of Fully Homomorphic Encryption

The application prospects of fully homomorphic encryption technology are very broad, especially in the field of artificial intelligence. It is well known that powerful AI systems require massive amounts of data for training, but much of this data involves privacy issues. Fully homomorphic encryption provides a possible solution to this contradiction:

1. Encrypt sensitive data using FHE.
2. Train AI models with encrypted data
3. AI outputs the encrypted result
4. The data owner securely decrypts the results locally.

This approach not only ensures data privacy but also fully utilizes the powerful computing capabilities of AI, achieving the best of both worlds.

In addition to the AI field, FHE also has important applications in scenarios such as facial recognition. For example, it can determine whether a person is real without accessing the original facial data.

Challenges and Solutions of Fully Homomorphic Encryption

Despite the broad prospects of FHE, it still faces enormous challenges in practical applications, primarily due to the huge computational load. To address this issue, some projects have proposed innovative solutions, such as building dedicated computational networks and supporting infrastructure.

For example, some projects have designed network architectures that resemble a mix of PoW (Proof of Work) and PoS (Proof of Stake), and have launched supporting products such as dedicated hardware devices and NFTs (Non-Fungible Tokens) to support large-scale FHE computation.

Conclusion

With the popularization of AI technology, data privacy issues are becoming increasingly prominent. From national security to personal privacy protection, FHE technology may become an important technological defense line. Although FHE is still in the development stage, its potential should not be ignored. In the future, if FHE technology can truly mature, it will provide strong support for privacy protection in the AI era and become an important tool for humanity to face digital challenges.