Fully Homomorphic Encryption FHE: A New Chapter 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 encryption market in 2024 is not as dramatic as in previous years, there are still some new technologies gradually maturing. The topic we will discuss today is "FHE / fully homomorphic encryption."

To understand the complex concept of fully homomorphic encryption, we first need to grasp the meanings of "encryption" and "homomorphic," as well as why it is "fully."

Encryption Basics

The simplest encryption method is the one everyone is most familiar with. For example, if Alice wants to send a secret message "1314 520" to Bob through a third party C, and does not want C to know the content, she can use a simple encryption method: multiply each number by 2. Thus, the transmitted message becomes "2628 1040". When Bob receives it, he just needs to divide each number by 2 to decrypt the original message. This is a basic symmetric encryption process.

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. If she needs to calculate the total electricity bill for 12 months at 400 yuan per month, but doesn't want others to know the exact amount, what should she do?

Alice can use a simple Homomorphic Encryption method. She tells C to compute the result of 800x24, which is actually (400x2) multiplied by (12x2). After C computes 19200, he tells Alice, and then Alice divides the result by 4 to get the actual outstanding amount of 4800 yuan.

This process demonstrates the simplest form of Homomorphic Encryption for multiplication. 800x24 is simply a mapping of 400x12, and it essentially maintains the same form before and after encryption, hence the term "homomorphic." This method allows for computations to be delegated to untrusted third parties while protecting sensitive data from being disclosed.

The Necessity of Fully Homomorphic Encryption

However, the problems in the real world are much more complicated. If C is smart enough, it might crack Alice's original data through brute force. At this point, "fully homomorphic encryption" is needed to solve the issue.

Fully homomorphic encryption allows for arbitrary numbers of addition and multiplication operations on encrypted data, not just limited to specific operations. This greatly increases the difficulty of cracking, making it possible to perform even complex polynomial operations while in an encrypted state, and still obtain the correct result after decryption.

Fully homomorphic encryption technology did not achieve breakthrough progress until 2009 and is regarded as the holy grail of the field of cryptography.

The Application Prospects of Fully Homomorphic Encryption

Fully homomorphic encryption technology has broad application prospects in the field of artificial intelligence. For example, it can address data privacy issues during the AI training process:

1. Encrypt sensitive data using fully homomorphic encryption (FHE)
2. Train AI with encrypted data
3. AI outputs the encrypted result
4. Users securely decrypt results locally

This method allows AI to perform computational tasks without accessing the original sensitive data, greatly protecting user privacy.

Challenges of Fully Homomorphic Encryption in Practical Applications

Although fully homomorphic encryption technology has great potential, it still faces challenges in practical applications, primarily due to its massive computational demands. To address this issue, some projects are developing specialized computing networks and hardware devices.

For example, a certain project proposed a network architecture that combines PoW-like and PoS-like mechanisms, and launched dedicated mining hardware and NFT "work certificates". These innovations aim to provide the necessary computational power support for fully homomorphic encryption.

Conclusion

Fully Homomorphic Encryption technology has the potential to become a key tool for protecting data privacy in the AI era. From international conflicts to facial recognition in daily life, data privacy issues are everywhere. As AI technology continues to develop, if FHE technology can truly mature, it will become the last line of defense for protecting human privacy.