An Area Efficient With Serial-In Parallel-Out By Using Rb Multiplier

Abstract

Redundant Based Multiplier Over Gaulois Field (GF (2 m)) has gained huge popularity in elliptic curve cryptography (ECC) mainly because of their negligible hardware cost for squaring and modular reduction. In this paper, we have proposed a novel recursive decomposition algorithm for RB multiplication to obtain high throughput digit-serial implementation. Based on a specific feature of redundant representation in a class of finite fields, two new multiplication algorithms along with their pertaining architectures are proposed to alleviate this problem. Considering area-delay product as a measure of evaluation, it has been shown that both the proposed architectures considerably outperform existing digit-level multipliers using the same basis. It is also shown that for a subset of the fields, the proposed multipliers are of higher performance in terms of area-delay complexities among several recently proposed optimal normal basis multipliers. The main characteristics of the post place & route application specific integrated circuit implementation of the proposed multipliers for three practical digit sizes are also reported.