Fully Homomorphic Encryption: Concept Introduction and Application Scenarios

Encryption technology is generally divided into two types: static encryption and encryption in transit. Static encryption protects data stored on devices or in the cloud, allowing only authorized personnel to access the decrypted content. Encryption in transit ensures that data transmitted over the network can only be interpreted by designated recipients, and it will not be leaked even when passing through public channels.

Both of these encryption methods rely on encryption algorithms and ensure data integrity through authenticated encryption. However, certain multi-party collaboration 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 schemes struggle to achieve vote counting while protecting privacy. The FHE technology allows for direct function computation on ciphertext without decryption, thereby protecting privacy while achieving the required functionality.

FHE is a compact encryption scheme where the size of the ciphertext of the output result and the complexity of decryption are only related to the original input, unaffected by the intermediate computation process. It is typically regarded as an alternative to secure execution environments such as TEE, with security based on cryptographic algorithms rather than hardware devices.

The FHE system typically consists of several components, including the decryption key, encryption key, and computation key. Among them, the decryption key is the most sensitive, and it is essential to ensure the effectiveness and security of the entire homomorphic operation chain.

Application Modes of FHE

Outsourcing Model

This model transforms ordinary cloud computing into private computation similar to SGX and TEE. Data owners send encrypted inputs to the cloud service provider, which performs homomorphic encryption and returns the encrypted results.

Currently, the FHE outsourcing model is mainly used for private information retrieval ( PIR ) scenarios, such as when a client queries information from a large public database without exposing the query content.

Two-party computation model

In this mode, the computing party will also incorporate its own private data during the process. FHE provides an ideal solution for two-party computation with minimal communication complexity.

Potential applications include the "Millionaire's Problem" in cryptography, where two parties compare their wealth without disclosing the exact amounts.

Aggregation Mode

Improvement of the outsourcing model to aggregate data from multiple participants in a compact and verifiable manner. Typical use cases include federated learning and online voting systems.

Client-Server Model

The extension of two-party computation model allows the server to provide FHE computation services for multiple independent key clients. This can be used for private AI model computation services, where client data is encrypted and processed by the AI model on the server side.

Other Technical Details of FHE

• Ensure the validity of external computation results through redundancy calculations or digital signatures.
• Control the decryption scope by restricting access to intermediate ciphertext or secret sharing of decryption keys.
• Compared to partial homomorphic encryption and leveled homomorphic encryption, FHE supports arbitrary computational tasks and its parameters do not increase with complexity.
• FHE needs to perform periodic bootstrapping operations to control noise.

Fully Homomorphic Encryption, as a powerful privacy protection technology, shows broad application prospects in multiple fields. With the continuous optimization of algorithms and hardware, it is believed that FHE will play a greater role in the future.