Phantom: A CUDA-Accelerated Word-Wise Homomorphic Encryption Library

Homomorphic encryption (HE) is a promising technique for privacy-preserving computations, especially the word-wise HE schemes that allow batching. However, the high computational overhead hinders the deployment of HE in real-word applications. GPUs are often used to accelerate execution, but a comprehensive performance comparison of different schemes on the same platform is still missing. In this work, we fill this gap by implementing three word-wise HE schemes BGV, BFV, and CKKS on GPU, with both theoretical and engineering optimizations. We enhance the hybrid key-switching technique, significantly reducing the computational and memory overhead. We explore several kernel fusing strategies to reuse data, resulting in reduced memory access and IO latency, and enhancing the overall performance. By comparing with the state-of-the-art works, we demonstrate the effectiveness of our implementation. Meanwhile, we introduce a unified framework that finely integrates our implementation of the three schemes, covering almost all scheme functions and homomorphic operations. We optimize the management of pre-computation, RNS bases, and memory in the framework, to provide efficient and low-latency data access and transfer. Based on this framework, we provide a thorough benchmark of the three schemes, which can serve as a reference for scheme selection and implementation in constructing privacy-preserving applications.