High-Speed VLSI Architectures for Modular Polynomial Multiplication via Fast Filtering and Applications to Lattice-Based Cryptography

Abstract

This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the fast finite impulse response (FIR) filter architecture to reduce the computational complexity of the schoolbook modular polynomial multiplication. We also extend this structure to fast $M$-parallel architectures while achieving low-latency, high-speed, and full hardware utilization. We comprehensively evaluate the performance of the proposed architectures under various polynomial settings as well as in the Saber scheme for post-quantum cryptography as a case study. The experimental results show that our proposed modular polynomial multiplier reduces the computation time and area-time product, respectively, compared to the state-of-the-art designs.

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• The Equivalence of Fast Algorithms for Convolution, Parallel FIR Filters, Polynomial Modular Multiplication, and Pointwise Multiplication in DFT/NTT Domain
• An Iterated Hybrid Fast Parallel FIR Filter