An Efficient Hardware Implementation of Improved Plantard Mod-Multiplication for Lattice-Based Cryptography

The modular multiplication (mod-multiplication) algorithm is an essential operation in lattice-based cryptography (LBC) that utilizes the Number Theoretical Transform (NTT) for polynomial multiplication. An efficient mod-multiplication algorithm determines the computational efficiency and performance of the entire polynomial multiplier/NTT computation unit. In this manuscript, we propose an improved Plantard modmultiplication algorithm for the NTT in Kyber and Dilithium, which not only reduces one multiplication but also eliminates the post-processing operations compared with the original Plantard algorithm. Additionally, we design an optimized hardware implementation for the improved Plantard mod-multiplication algorithm. Based on the Xilinx Artix-7 platform, when compared with state-of-the-art designs, our improved Plantard algorithm reduces the number of slices by 22.2%∼53.3% for Kyber and 18.4%∼35.4% for Dilithium, while boosting hardware efficiency by 43.9%∼55.9% for Kyber and 33.7%∼54.4% for Dilithium. Overall, our improved Plantard algorithm shows significant advantages in resource consumption and computational speed.