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

Recently, the cryptocurrency market has become relatively calm, giving us more time to explore some emerging technologies. Although the crypto market in 2024 is not as dramatic as in previous years, there are still some new technologies maturing. One of the topics we will discuss today is: fully homomorphic encryption (FHE).

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

Basic Concepts of Encryption

The simplest encryption method is something we are all familiar with. For example, if Alice wants to send a secret message "1314 520" to Bob, but needs to pass it through a third party C. To keep it confidential, Alice can multiply each number by 2, turning it into "2628 1040". When Bob receives it, he divides each number by 2 to decrypt the original message. This is a simple symmetric encryption method.

Homomorphic Encryption Advanced

Now let's assume 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 her home for 12 months, with a monthly cost of 400 yuan, but this exceeds her calculation ability. She doesn't want others to know the specific electricity bill information, so she encrypted the data by multiplying by 2, allowing C to calculate the result of 800 multiplied by 24. After C calculates 19200, Alice then divides by 4 to get the actual debt 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 the term "homomorphic". This method allows delegating computations to untrusted third parties while protecting sensitive data from being disclosed.

Why is "fully" homomorphic encryption needed

However, problems in the real world are often more complex. If C can break Alice's original data through brute force, then a more advanced encryption method is needed.

The goal of fully homomorphic encryption is to allow arbitrary numbers of addition and multiplication operations on encrypted data, rather than being limited to specific simple operations. This enables the handling of more complex mathematical problems while virtually eliminating the possibility of third-party inspection of the raw data through multiple encryptions.

It was not until 2009 that homomorphic encryption technology broke the limitation of only supporting "partial homomorphic encryption." The new ideas proposed by Gentry and other scholars paved the way for fully homomorphic encryption.

Applications of FHE

One important application scenario of FHE technology is in the field of artificial intelligence. AI requires a large amount of data for training, but much of the data is highly sensitive. FHE allows AI to process encrypted data while protecting data privacy.

Specifically, users can:

1. Encrypt sensitive data using FHE.
2. Provide the encrypted data to AI for computation
3. AI returns the encrypted result

Users can then securely decrypt the results locally, utilizing the powerful computing power of AI without revealing the original data.

This method is particularly suitable for unsupervised AI systems, as they essentially deal with vector data and do not need to understand the specific meaning of the input.

The Importance of FHE in the AI Era

With the popularization of AI technology, data privacy and security issues have become increasingly important. From facial unlocking on personal mobile phones to national-level intelligence protection, FHE technology could become a crucial tool for privacy protection.

However, the practical application of FHE still faces challenges, mainly because it requires enormous computational resources. Some projects are trying to address this issue by establishing dedicated computing networks.

If FHE technology can be widely applied in the AI field, it will greatly promote the development of AI while alleviating people's concerns about data privacy. In this information age, FHE may become the last line of defense in protecting personal and organizational data privacy.