Exploring Energy Efficient Architectures for RLWE Lattice-Based Cryptography

Abstract

Quantum computers are imminent threat to secure signal processing because they can break the contemporary public-key cryptography schemes in polynomial time. Ring learning with error (RLWE) lattice-based cryptography (LBC) is considered as the most versatile and efficient family of post-quantum cryptography (PQC). Polynomial multiplication is the most compute-intensive routine in the RLWE schemes. Convolutions and Number Theoretic Transform (NTT) are two common methods to perform the polynomial multiplication. In this paper, we explore the energy efficiency of different polynomial multipliers, NTT-based and convolution-based, on GPU and FPGA. When synthesized on a Zynq UltraScale+ FPGA, our NTT-based and convolution-based designs achieve on average 5.1x and 22.5x speedup over state-of-the-art. Our convolution-based design, on a Zynq UltraScale+ FPGA, can generate more than 2x signatures per second by CRYSTALS-Dilithium. The designed NTT-based multiplier on NVIDIA Jetson TX2 is 1.2x and 2x faster than our baseline NTT-based multiplier on FPGA for polynomial degrees of 512 and 1024, respectively. Our explorations and guidelines can help designers choose proper implementations to realize quantum-resistant signal processing.