An Accelerated GPU Library for Homomorphic Encryption Operations of BFV Scheme

This paper presents an accelerated and parallelized GPU implementation for homomorphic encryption operations of the Brakerski-Fan-Vercauteren (BFV) scheme. We improved the run-time performance by optimizing homomorphic multiplication, relinearization, rotation, and addition using Number Theoretic Transform (NTT) and Barrett Reduction and utilizing a Compute Unified Device Architecture (CUDA). To the best of our knowledge, this implementation performs the fastest homomorphic operations in the literature. We used the Simple Encrypted Arithmetic Library (SEAL) version 3.6.6 BFV scheme for implementation on a GPU. Our implementation achieved 13.39x, 47.01x, 39.6x, and 33.71x speedup compared to SEAL running on CPU for addition, multiplication, relinearization, and rotation, respectively for a modulus size of 438-bits and ring degree of 16,384. For the same modulus size and ring degree, this implementation performed one homomorphic multiplication in 1 ms, a relinearization operation in 0.4 ms, a rotation in 0.5 ms, and an addition in 0.017 ms, which demonstrates significant performance improvement over state-of-the-art.