Low-complexity bit-serial sequential polynomial basis finite field GF(2[formula omitted]) Montgomery multipliers

Abstract

GF(2m) multiplication is a complex and performance-critical operation in Elliptic curve cryptography algorithms. Many techniques have been proposed in the literature for efficient implementation of GF(2m) multipliers. Montgomery multiplication is a technique used for fast GF(2m) multiplications, which is more efficient when there is a need for computation of many consecutive multiplications. In this paper, we present two modified bit-serial algorithms namely most significant bit (MSB) first algorithm and least significant bit (LSB) first algorithm for Montgomery multiplication where the modification involves employing more efficient logical relations in the formulation of the algorithms. Furthermore, the hardware structures developed for the proposed modified algorithms using bit-serial sequential architectures are also presented in this paper. Comparison of the analytical as well as implementation results of the proposed multipliers with the existing multipliers shows that the proposed multipliers require low area and time complexities. The proposed MSB-first multiplier and the proposed LSB-first multiplier achieve around 17% and 13% reduction in area-delay-product (ADP) complexities for m=409, respectively, when compared with the respective best multipliers available in the literature. The proposed bit-serial sequential multipliers can be used in low-hardware and low-cost applications such as IoT edge devices.