Analysis of Finite Field in Elliptic Curve Cryptography for Software Implementation

Abstract

Finite field is the field with finite number of elements. In Elliptic Curve Cryptography finite field can be prime field or extensive field. In this paper we will study the finite fields those are suggested and analyze that how general prime field are used and are much more compatible with software implementation then other existing. Existing study suggests to use binary fields as they have low cost of implementation but we are suggesting to use general prime field though their implementation cost is little high then those of binary but they desire less computational power as compared to them. In this paper we are suggesting the prime field that would be future of finite field in elliptic curve cryptography.

Keywords: Elliptic Curve Cryptography, Extensive Fields, Finite Field, Prime Field.