A Proposed Implementation of Elliptic Curve Exponentiation over Prime Field (Fp) in the Global Smart Cards

Abstract

Abstract-this paper is explained about elliptic curve exponentiation over prime field ( ) which are Affine, projective, Jacobian, Chunnovsky-Jacobian and the modified Jacobian coordinate systems that how to implement elliptic curve exponentiation over prime field ( ) into Elliptic Curve (EC) encryption and digital signature in the global smart cards. These coordinate systems are explained the underlying arithmetic operations with formulae and geometrical diagrams. Point addition and doubling of coordinate systems over prime field are mentioned for every coordinate system. Thus, we proposed mixed coordinate systems over prime field ( ) in the EC encryption and digital signature of the global smart cards.Index Terms-Elliptic curve, finite field, exponentiation, coordinate system, DLP, global smart card.