A New Approach to Elliptic Curve Cryptography: an RNS Architecture

Abstract

An elliptic curve point multiplier (ECPM) is the main part of all elliptic curve cryptography (ECC) systems and its performance is decisive for the performance of the overall cryptosystem. A VLSI residue number system (RNS) architecture of an ECPM is presented in this paper. In the proposed approach, the necessary mathematical conditions that need to be satisfied, in order to replace typical finite field circuits with RNS ones, are investigated. It is shown that such an application is feasible and that it leads to a significant improvement in the execution time of a scalar point multiplication.