Accelerating Finite Field Arithmetic for Homomorphic Encryption on GPUs

Fully homomorphic encryption (FHE) is a rapidly developing technology that enables computation directly on encrypted data, making it a compelling solution for security in cloud-based systems. In addition, modern FHE schemes are believed to be resistant to quantum attacks. Although FHE offers unprecedented potential for security, current implementations suffer from prohibitively high latency. Finite field arithmetic operations, particularly the multiplication of high-degree polynomials, are key computational bottlenecks. The parallel processing capabilities provided by modern GPUs make them compelling candidates to target these highly parallelizable workloads. In this article, we discuss methods to accelerate polynomial multiplication with GPUs, with the goal of making FHE practical.