New compression point reducing memory size in field of characteristic different from 2 and 3

Abstract

Compression point is a new method to compress the space memory and still havethe same data. In this paper, we will present a new method of compression points workwell with addition operation in elliptic curve, so instead of storing the value of two pointsP = (xP;yP), Q = (xQ;yQ), we will store the addition of the x-coordinates i,e(a = xP+xQ;yP;yQ) or the y-coordinates i,e (xP;xQ;b = yP+yQ).In this article, we show a new technique for compressing two points in elliptic curve withdifferent coordinate system: Affine, Projective and Jacobian in a field of characteristic different from 2& 3 , and show the cost of theses operations. This method can save if we work with affine,Projective or Jacobian coordinates, at least 25%, 17%, 17% of memory size respectively,and also see what happens in case if we take Edwards curve and Montgomery curve cases.