The Development and Application of Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE), as an advanced encryption technology, has undergone a long development process since it was first proposed in the 1970s. Its core idea is to perform computations on encrypted data without decrypting it. In 2009, Craig Gentry's groundbreaking work paved the way for the practical application of FHE.

FHE allows operations on ciphertext and generates encrypted results, with the decrypted results being consistent with the results of operations on plaintext. This technology has homomorphic properties, supporting unlimited additions and multiplications, enabling arbitrary computations on encrypted data.

However, FHE also faces some challenges. Noise management is a key issue, as each operation increases the noise in the ciphertext. In addition, the computational overhead of FHE is thousands to millions of times higher than that of plaintext computation, which limits its use in certain application scenarios.

In the field of blockchain, FHE is expected to become a key technology for addressing scalability and privacy protection issues. It can transform a transparent blockchain into a partially encrypted form while retaining the control capabilities of smart contracts. Some projects are developing FHE virtual machines that allow programmers to write smart contract code that operates FHE primitives.

FHE can also improve the usability of privacy projects, such as solving wallet synchronization issues through Obfuscated Message Retrieval (OMR). Although FHE itself cannot directly address blockchain scalability issues, combining it with Zero-Knowledge Proofs (ZKP) may offer some solutions.

FHE and ZKP are complementary technologies, each with different application scenarios. ZKP provides verifiable computation and zero-knowledge properties, while FHE allows computations on encrypted data without exposing the data itself. Combining the two may significantly increase computational complexity, thus requiring a trade-off based on specific use cases.

Currently, the development of FHE is about three to four years behind ZKP, but it is rapidly catching up. Some FHE projects have already begun testing networks, and the mainnet is expected to be launched later this year. Although the computational overhead of FHE is still relatively high, its potential for large-scale adoption is becoming apparent.

The applications of FHE face some challenges, including computational efficiency and key management. Bootstrapping operations are computationally intensive, but algorithmic advancements and engineering optimizations are improving this issue. Key management also needs further development to overcome single points of failure.

In the market, multiple companies are developing technologies and applications related to fully homomorphic encryption (FHE). These companies include Zama, Sunscreen, Octra, Fhenix, Mind Network, and Inco, among others. They focus on different FHE application scenarios, such as developing FHE tools, building FHE blockchain networks, and providing FHE computing services.

The regulatory environment also has a significant impact on the development of FHE. While data privacy is generally supported, financial privacy remains a gray area. FHE has the potential to enhance data privacy while maintaining social benefits.

Looking ahead, FHE technology is expected to make significant progress in the next three to five years. With continuous improvements in theory, software, hardware, and algorithms, FHE is poised to trigger revolutionary changes in the field of encryption, providing new solutions for blockchain scalability and privacy protection, and driving innovation in various applications within the encryption ecosystem.