Fully Homomorphic Encryption on GPUs: Design, Implementation & Performance Evaluation

This invited talk presented my research on accelerating homomorphic encryption (FHE) on Graphical Processing Units (GPUs). Focusing on RLWE-based FHE schemes, I discussed their design, implementation, and performance optimization on GPU platforms. My key contributions include:

• Efficient Polynomial Arithmetic: Utilizing the Discrete Galois Transform (DGT), a novel variant of the Number Theoretic Transform (NTT), significantly optimized polynomial operations within FHE.
• GPU-tailored Mapping: Effectively mapped fundamental FHE primitives to GPUs and memory hierarchy, leveraging inherent parallelism and concurrency for performance gains.
• Real-world Applications: Demonstrated the practical potential of GPU-accelerated FHE through applications in image processing, machine learning, and secure multi-party computation.
• Performance Comparison: Showcased the substantial performance advantage of GPU-based FHE over traditional CPU-based implementations.

Abstract
Over the past decade, lattice cryptography has gained overwhelming attention due to its role in empowering various emerging cryptographic technologies. For instance, lattices have been utilized to construct quantum-safe cryptosystems. Moreover, they have been used to construct Fully Homomorphic Encryption (FHE) schemes that enable computing on encrypted data without access to the decryption key. Despite the attractive properties of these technologies, they face several major challenges in terms of compute efficiency, key/ciphertext sizes, usability, and standardization. In this talk, I will address the computational aspect of RLWE-based FHE schemes and describe a method to accelerate them via Graphics Processing Units (GPUs). I will present both algorithmic and architectural solutions for efficient implementation of these schemes. The main topics covered are 1) a brief introduction to FHE; 2) a variant of the Number Theoretic Transform (NTT) known as the Discrete Galois Transform (DGT); 3) methods for mapping FHE primitives to GPUs; and 4) real-world FHE applications. Besides, I will present some performance evaluation experiments to show the feasibility, benefits and limitations of GPU platforms as a vehicle for accelerating lattice-based cryptography.