Leveraging GPU in Homomorphic Encryption: Framework Design and Analysis of BFV Variants

Homomorphic Encryption (HE) enhances data security by enabling computations on encrypted data, advancing privacy-focused computations. The BFV scheme, a promising HE scheme, raises considerable performance challenges. Graphics Processing Units (GPUs), with considerable parallel processing abilities, offer an effective solution. In this work, we present an in-depth study on accelerating and comparing BFV variants on GPUs, including Bajard-Eynard-Hasan-Zucca (BEHZ), Halevi-Polyakov-Shoup (HPS), and recent variants. We introduce a universal framework for all variants, propose optimized BEHZ implementation, and first support HPS variants with large parameter sets on GPUs. We also optimize low-level arithmetic and high-level operations, minimizing instructions for modular operations, enhancing hardware utilization for base conversion, and implementing efficient reuse strategies and fusion methods to reduce computational and memory consumption. Leveraging our framework, we offer comprehensive comparative analyses. Performance evaluation shows a 31.9 $\times$ speedup over OpenFHE running on a multi-threaded CPU and 39.7% and 29.9% improvement for tensoring and relinearization over the state-of-the-art GPU BEHZ implementation. The leveled HPS variant records up to 4 $\times$ speedup over other variants, positioning it as a highly promising alternative for specific applications.