High Efficient Architecture of Polynomial Multiplier with Variable Parameter Based on 2KNTT

Abstract

In July 2022, among the finalists for the fourth round of NIST's post-quantum public key cryptography, lattice-based algorithms using NTT to implement polynomial multiplication are CRYSTALS-KYBER and CRYSTALS-Dilithium. Therefore, in this paper, we design an efficient structure for polynomial multiplication based on the 2KNTT method for the purpose of improving the practical performance and satisfying variable parameters for these two algorithms. According to the existing 2KNTT algorithm, an eight-way parallel practical model that adapts to the requirements of the algorithm is designed under the premise of determining the storage granularity in advance. Specifically, the modulo multiplication unit can meet the operation of different moduli at the same time, and the control unit can meet the requirements of different number of terms. Experimental results show that this design can meet the polynomial multiplication with modulus 12~32 bits, term number 128, 256, 512, 1024, and modulus polynomial number $x^{n}+1$, in which it takes 2052 cycles to perform a polynomial multiplication operation with the maximum parameter (n=1024, q=8380417).