Fully Homomorphic Encryption: Principles and Application Scenarios

Traditional encryption methods mainly include static encryption and transmission encryption. Static encryption encrypts data and stores it in hardware devices, allowing only authorized personnel to decrypt and view it. Transmission encryption ensures that data transmitted over the network can only be interpreted by the designated recipient. Both methods rely on encryption algorithms and guarantee data integrity through authenticated encryption.

However, certain multi-party collaborative scenarios require complex processing of ciphertext, which involves privacy protection technologies, among which fully homomorphic encryption ( FHE ) is an important solution. Taking online voting as an example, traditional encryption methods struggle to achieve accurate vote counting while protecting voters' privacy. FHE technology allows for function computation directly on ciphertext without decryption, thereby protecting privacy.

The FHE system typically includes the following types of keys:

1. Decryption Key: System Master Key, used to decrypt FHE ciphertext, kept solely by the holder.

2. Encryption Key: Used to convert plaintext into ciphertext, which can be made public in public key encryption mode.

3. Calculation key: used for homomorphic operations on ciphertext, can be made public but cannot be used to decrypt the ciphertext.

Typical application scenarios of FHE include:

1. Outsourcing model: Outsourcing computing tasks to cloud service providers to protect data privacy.

2. Both parties calculation model: Both parties conduct joint calculations without disclosing their private data.

3. Aggregation Mode: Aggregates multiple parties' data in a compact and verifiable manner, suitable for scenarios such as federated learning.

4. Client-Server Model: The server provides private computing services for multiple independent clients, such as private AI model computations.

The security of FHE is based on cryptographic algorithms and does not rely on hardware security. To ensure the validity of computation results, methods such as redundant computation and digital signatures can be employed. In scenarios involving multiple parties, techniques such as secret sharing are typically used to manage decryption keys, enhancing the overall security of the system.

FHE is currently the only solution that guarantees the resource consumption of homomorphic computation is proportional to the original task. However, FHE also faces the technical challenge of noise accumulation, which needs to be controlled through bootstrapping operations. With in-depth research and the development of dedicated hardware, FHE is expected to be applied in more privacy computing scenarios.