The Development and Application of Fully Homomorphic Encryption ( FHE )

The concept of fully homomorphic encryption ( FHE ) can be traced back to the 1970s, but it has been difficult to achieve for a long time. The core idea of FHE is to perform computations on encrypted data without the need for decryption beforehand. Initially, only simple operations such as addition, subtraction, multiplication, and division could be performed on encrypted data, which is known as partial homomorphic encryption. In 2009, Craig Gentry made a significant breakthrough by demonstrating the possibility of performing arbitrary computations on encrypted data, thus advancing the development of FHE.

FHE is an advanced encryption technology that allows computation directly on encrypted data without the need for decryption. This means that operations can be performed on ciphertext and generate encrypted results, with the decrypted results being consistent with those obtained by performing the same operations on the original plaintext.

The key features of FHE include:

1. Homomorphic property: The addition or multiplication operations on ciphertext are equivalent to performing the same operations on plaintext.

2. Noise Management: FHE encryption introduces noise to ensure security, but the noise increases after each operation. Controlling and minimizing noise is crucial for ensuring the accuracy of computations.

3. Unlimited Operations: Unlike certain Homomorphic Encryption ( PHE ) and some type of Homomorphic Encryption ( SHE ), FHE supports unlimited additions and multiplications, allowing any type of computation to be performed on encrypted data.

The main challenge facing FHE is computational efficiency. The overhead of computing on ciphertext can be 10,000 to 1,000,000 times higher than that of plaintext computation. True fully homomorphic encryption is achieved only when unlimited additions and multiplications can be performed on ciphertext.

Homomorphic Encryption can be divided into the following categories based on the level of implementation:

• Partial Homomorphic Encryption ( PHE ): Supports unlimited operations of either addition or multiplication (.
• A certain type of Homomorphic Encryption ) SHE (: Supports a limited number of addition and multiplication operations.
• fully homomorphic encryption)FHE(: supports unlimited addition and multiplication operations, allowing arbitrary calculations on encrypted data.

The main advantage of FHE is its ability to perform any type of computation on encrypted data while ensuring the privacy and security of the entire process.

In the blockchain field, FHE is expected to become a key technology for solving scalability and privacy protection issues. Current blockchain systems are generally transparent, with all transactions and smart contract variables being public. FHE can transform a fully transparent blockchain into a partially encrypted form while maintaining the control capabilities of smart contracts.

For example, a company is developing an FHE virtual machine that allows developers to write smart contract code that operates on FHE primitives. This approach can address the current privacy issues on the blockchain, enabling applications such as encrypted payments and online gambling, while preserving the transaction graph, making it more regulatory-friendly compared to other privacy solutions.

FHE can also improve the user experience of privacy projects through private message retrieval )OMR(, allowing wallet clients to synchronize data without exposing the content accessed.

However, FHE cannot directly solve the scalability issues of blockchain. Combining FHE with zero-knowledge proofs )ZKP( may address some scalability challenges. Verifiable FHE can ensure that computations are executed correctly, providing a trustworthy computing mechanism for the blockchain environment.

FHE and ZKP are complementary technologies, but serve different purposes. ZKP allows for verifiable computation and zero-knowledge properties, providing privacy protection for private states. However, ZKP cannot provide privacy for shared states, which is crucial for many decentralized application platforms. FHE and multiparty computation )MPC( can fill this gap, allowing computation on encrypted data without exposing the data itself.

The development of FHE is currently about three to four years behind ZKP, but it is catching up quickly. The first generation of FHE projects has begun testing, and the mainnet is expected to launch later this year. Although the computational overhead of FHE is still higher than that of ZKP, its potential for large-scale application has already become apparent. Once FHE enters production and achieves scalability, it is expected to develop rapidly like ZK Rollups.

The application of FHE faces some challenges, including computational efficiency and key management. The bootstrapping operation in FHE is computation-intensive, but algorithm improvements and engineering optimizations are continuously enhancing its efficiency. For certain specific applications, such as machine learning, alternatives that do not use bootstrapping may be more efficient.

Key management is also an important challenge. Some FHE projects require threshold key management, involving a group of validators with decryption capabilities. This approach needs further development to overcome single point of failure issues.

The FHE market is attracting the attention of many investors. Some encryption venture capital firms are actively investing in the FHE field, recognizing its potential. Certain projects are developing applications based on FHE, such as online gambling, commercial payments, and gaming.

Threshold FHE) TFHE( combines FHE with MPC and blockchain technology, showing particularly promising potential and opening up new application scenarios. The developer friendliness of FHE allows for programming using common smart contract languages, enhancing its practicality in application development.

The regulatory environment for FHE varies across different regions. Although data privacy is generally supported, financial privacy remains a contentious area. FHE has the potential to enhance data privacy protection, allowing users to retain data ownership and possibly benefit from it, while still maintaining social benefits such as targeted advertising.

Looking to the future, theoretical research, software development, hardware optimization, and algorithm improvements are expected to make FHE increasingly practical. The development of FHE is transitioning from theoretical research to practical application, and significant progress is expected in the next three to five years.

![Progress and Applications of Fully Homomorphic Encryption (FHE)])https://img-cdn.gateio.im/webp-social/moments-97e1ef48e90d438cfe636a91f4eff522.webp(

Overall, FHE is at the forefront of revolutionizing the encryption field, providing new possibilities for privacy and security solutions. With continuous technological advancements and sustained interest from venture capital, FHE is expected to achieve widespread applications, addressing key issues of blockchain scalability and privacy protection. As the technology matures, FHE is anticipated to open up new possibilities for various innovative applications within the encryption ecosystem.