Accelerating Stencil Computation with Fully Homomorphic Encryption Using GPU

Stencil computations with fully homomorphic encryption (FHE) is an emerging area with significant potential to address the challenges of protecting sensitive data of HPC applications in outsourcing computing environment. However, the computational overhead introduced by FHE can drastically reduce the performance of stencil computations compared to unencrypted implementations. This paper proposes two optimized algorithms for stencil computation with FHE tailored to GPU platforms: Matrix Overlap Processing (MOP) and Matrix Fixed-point Processing(MFP). MOP divides the input matrix into multiple slices, encrypts elements at the same positions across slices into a single ciphertext, and processes them with a uniform computing pattern. MFP directly encrypts neighbouring elements into ciphertexts, stores them in a table, and processes them in parallel on the GPU. The experimental results show that our proposed methods achieve significant speedups compared to the corresponding OpenMP implementations on CPU. Specifically, the MOP implementation achieves a speedup of 8.7 \(\times \) , while the MFP implementation achieves a speedup of 10.3 \(\times \) on GPU.