Fully Homomorphic Encryption FHE: A Revolutionary Technology in the World of Encryption

The recent 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, including the topic we will discuss today: fully homomorphic encryption (FHE).

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

The Basic Concepts of Encryption

Encryption is a well-known concept. For a simple example, if Alice wants to send a secret message "1314 520" to Bob through a third party C, and she does not want C to know the content, she can use a simple encryption method: multiply each number by 2. In this way, the transmitted message becomes "2628 1040". When Bob receives the message, he just needs to divide each number by 2 to decrypt the original content. This symmetric encryption method allows the two to exchange information without trusting the intermediary.

Homomorphic Encryption Advancement

Now, let's complicate the situation a bit. Suppose Alice is only 7 years old and can only perform the most basic operations of multiplying by 2 and dividing by 2. She needs to calculate the electricity bill for 12 months, which is 400 yuan per month, but this exceeds her calculation ability. At the same time, she doesn't want others to know the specific electricity bill information.

In this case, Alice can use simple Homomorphic Encryption. She multiplies 400 and 12 by 2 to get 800 and 24, and then lets C calculate 800×24. After C calculates the result of 19200, Alice divides it by 2 twice to obtain the correct total electricity bill of 4800 yuan.

This process demonstrates the core idea of Homomorphic Encryption: performing operations on encrypted data, the result obtained after decryption is equivalent to the result of directly performing operations on the original data.

The Necessity of Fully Homomorphic Encryption

However, the simple homomorphic encryption methods mentioned above are at risk of being cracked. For example, C may deduce the original data through brute force methods. This necessitates the introduction of more complex encryption methods, namely fully homomorphic encryption.

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

It wasn't until 2009 that the new ideas proposed by Gentry and other scholars truly opened up the possibility of fully homomorphic encryption.

The Application Prospects of FHE

FHE technology has potential application value in multiple fields, especially in artificial intelligence (AI).

The development of AI requires a large amount of data, but much of that data is highly sensitive. FHE allows AI to process encrypted data without exposing the original data. This way, users can utilize the powerful computing capabilities of AI while protecting their privacy.

For example, in facial recognition technology, FHE enables machines to determine whether it is a real person without accessing any sensitive facial information. This addresses the dilemma of "utilizing data while protecting privacy."

Challenges and Developments of FHE

Despite the promising prospects of FHE, its practical applications still face significant challenges, mainly because it requires substantial computational resources. To address this issue, some projects are developing specialized hardware and network architectures to support FHE computations.

With the popularity of AI technology, data privacy and security issues are becoming increasingly important. From facial unlocking on personal devices to national-level information security, FHE technology may play a significant role. If FHE technology can truly mature, it will become the last line of defense for protecting human privacy in the AI era.