Homomorphic Encryption (HE) is an emerging encryption scheme that allows computations to be performed directly on encrypted messages. This property provides promising applications such as privacy-preserving deep learning and cloud computing. Prior works have been proposed to enable practical privacy-preserving applications with architectural-aware optimizations on CPUs, GPUs and FPGAs. However, there is no systematic optimization for the whole HE pipeline on Intel GPUs. In this paper, we present the first-ever SYCL-based GPU backend for Microsoft SEAL APIs. We perform optimizations from instruction level, algorithmic level and application level to accelerate our HE library based on the Cheon, Kim, Kimand Song (CKKS) scheme on Intel GPUs. The performance is validated on two latest Intel GPUs. Experimental results show that our staged optimizations together with optimizations including low-level optimizations and kernel fusion accelerate the Number Theoretic Transform (NTT), a key algorithm for HE, by up to 9.93X compared with the na\"ive GPU baseline. The roofline analysis confirms that our optimized NTT reaches 79.8% and85.7% of the peak performance on two GPU devices. Through the highly optimized NTT and the assembly-level optimization, we obtain 2.32X - 3.05X acceleration for HE evaluation routines. In addition, our all-together systematic optimizations improve the performance of encrypted element-wise polynomial matrix multiplication application by up to 3.10X.
Accelerating Encrypted Computing on Intel GPUs