Efficient Hardware Implementation of Finite Field Arithmetic AB+C for Binary Ring-LWE Based Post-Quantum Cryptography
Jiafeng Xie, Pengzhou He, Xiaofang Maggie Wang, José Luis Imaña · IEEE Transactions on Emerging Topics in Computing · 2021
Post-quantum cryptography (PQC) has gained significant attention from the community recently as it is proven that the existing public-key cryptosystems are vulnerable to the attacks launched from the well-developed quantum computers. The finite field arithmetic$AB+C$, where A and C are integer polynomials and$B$is a binary polynomial, is the key component for the binary Ring-learning-with-errors (BRLWE)-based encryption scheme (a low-complexity PQC suitable for emerging lightweight applications). In this paper, we propose a novel hardware implementation of the finite field arithmetic$AB+C$through three stages of interdependent efforts: (i) a rigorous mathematical formulation process is presented first; (ii) an efficient hardware architecture is then presented with detailed description; (iii) a thorough implementation has also been given along with the comparison. Overall, (i) the proposed basic structure ($u=1$) outperforms the existing designs, e.g., it involves 46.3\% less area-delay product (ADP) than \cite{b14b} for$n=512$; (ii) the proposed design also offers very efficient performance in time-complexity and can be used in many future applications.