Achieving Efficient BGV Scheme with Semi-Honest TEE Assistance

Fully Homomorphic Encryption (FHE) allows computations on encrypted data. However, FHE faces significant performance overhead due to the time-consuming homomorphic multiplications and bootstrapping operations, which limits its practical applications. Meanwhile, many FHE optimization schemes have been proposed based on a Trusted Execution Environment (TEE), but they heavily rely on the trustworthiness of the TEE. In outsourcing scenarios, the TEE owner might be a third-party service provider, posing a risk of data leakage for users. To address these issues, we propose an efficient BGV scheme with semi-honest TEE assistance. We consider the TEE to be honest-but-curious, meaning the TEE owner might eavesdrop on the user's data during computation. Based on this assumption, we design a new BGV homomorphic multiplication protocol that operates in a smaller ciphertext space without compromising the original security level and substantially improves computational efficiency. With the assistance of a semi-honest TEE, our multiplication protocol eliminates the need for the switch key, reducing initialization time and supporting an unlimited number of homomorphic multiplication operations without bootstrapping. Furthermore, we provide a security proof using a simulationbased real/ideal world model. Extensive experiments show that our scheme outperforms mainstream libraries such as SEAL, OpenFHE, and Helib.