The Development and Application of Fully Homomorphic Encryption (FHE)

Fully Homomorphic Encryption (FHE) has undergone a long development process since it was first proposed in the 1970s. Its core idea is to perform computations directly on encrypted data without the need for decryption. Early implementations could only achieve simple addition or multiplication operations, known as partially homomorphic encryption. In 2009, Craig Gentry's groundbreaking research enabled arbitrary computations on encrypted data, marking the arrival of the era of fully homomorphic encryption.

FHE, as an advanced encryption technology, allows computation on ciphertext without the need for prior decryption. This means that operations can be performed on encrypted data, generating encrypted results that, when decrypted, are consistent with the results of operating directly on the original data.

The core features of FHE include homomorphism, noise management, and unlimited operational capability. Homomorphism ensures that operations such as addition and multiplication on ciphertext are equivalent to the corresponding operations on plaintext. Noise management is crucial because each operation increases the noise in the ciphertext, and excessive noise can lead to computation failure. Unlike partially homomorphic encryption and some homomorphic encryption, FHE supports unlimited addition and multiplication operations, allowing it to perform any type of computation on encrypted data.

However, FHE faces challenges in computational efficiency. Computation on ciphertext can be 10,000 to 1,000,000 times slower than computation on plaintext. Fully homomorphic encryption is only truly achieved when unlimited addition and multiplication can be performed on ciphertext.

FHE shows great potential in the blockchain field. It may become a key technology for solving scalability and privacy protection issues in blockchain. By transforming a fully transparent blockchain into a partially encrypted form, FHE can enhance privacy protection while maintaining control over smart contracts. This approach is expected to enable applications such as encrypted payments and privacy games, while preserving transaction graphs to meet regulatory requirements.

FHE can also improve the user experience of existing privacy projects. Through the privacy message retrieval (OMR) technology, FHE allows wallet clients to synchronize without exposing the accessed content, addressing issues such as balance information retrieval delays faced by some projects.

Although FHE itself cannot directly solve the blockchain scalability issue, combining it with Zero-Knowledge Proofs (ZKP) may provide new solutions for scalability. Verifiable FHE can ensure that computations are executed correctly, providing a trustworthy computing mechanism for the blockchain environment.

FHE and ZKP are complementary technologies, each serving different purposes. ZKP focuses on verifiable computation and zero-knowledge properties, while FHE allows computation on encrypted data without exposing the data. Combining the two, although it significantly increases computational complexity, may bring unique advantages in specific use cases.

Currently, the development progress of FHE is approximately three to four years behind that of ZKP, but it is rapidly catching up. The first generation of FHE projects has begun testing and is expected to launch the mainnet later this year. Although the computational overhead of FHE is still higher than that of ZKP, its potential for large-scale applications is gradually becoming apparent.

The application of FHE faces several challenges, including computational efficiency and key management. The computational intensity of bootstrapping operations is a major bottleneck, but the situation is gradually improving with algorithmic advancements and engineering optimizations. For specific applications like machine learning, alternatives that do not use bootstrapping operations may be more efficient. Key management is also an issue that needs to be addressed, particularly in the context of threshold key management involving a group of validators.

Encryption venture capital firms have shown a strong interest in the field of FHE. Threshold FHE (TFHE) combines FHE with multi-party computation and blockchain technology, creating new application scenarios. The developer-friendliness of FHE, especially with support for programming in Solidity, makes it both practical and feasible in application development.

The regulatory environment for FHE technology varies by region. While data privacy is generally supported, financial privacy remains in a gray area. FHE has the potential to enhance data privacy protection, allowing users to retain data ownership and possibly benefit from it, while maintaining social benefits such as targeted advertising.

With the continuous advancement of theoretical research, software development, hardware optimization, and algorithm improvement, FHE is expected to achieve significant progress in the next three to five years, transitioning from the theoretical research stage to the practical application stage.

Fully homomorphic encryption technology is at the forefront of revolutionizing the encryption field, providing advanced privacy and security solutions. With the continuous advancement of technology and ongoing interest from venture capital, FHE is expected to achieve large-scale applications, addressing key issues of blockchain scalability and privacy protection. As the technology matures, FHE is poised to unlock new possibilities, driving innovative development of various applications in the encryption ecosystem.