A Review of Mathematical Foundations and Performance Comparison of Mainstream RLWE-based Homomorphic Encryption Schemes

Abstract

Fully homomorphic encryption (FHE), a core primitive for privacy-preserving computing in cloud storage, medical data sharing and financial secure computing, supports arbitrary arithmetic operations directly on ciphertexts without decryption. Aiming at the research gap that existing studies lack a fair quantitative comparison of three mainstream ring-learning with errors (RLWE)-based FHE schemes (BGV, BFV and CKKS) under unified security parameters, this paper systematically elaborates the mathematical foundations of the three schemes and clarifies their core differences in noise management, plaintext space design and homomorphic operation rules. For the first time, this paper conducts a quantitative performance comparison of the three schemes under a unified 128-bit security parameter based on test data from mainstream open-source libraries, and finally establishes a systematic comparison framework and explicit application selection criteria for the three schemes, providing a comprehensive reference for entry-level research and engineering implementation of homomorphic encryption.