New Compression Point Reducing Memory Size in Field of Characteristic ≠ 2,3

Abstract

Compression point is a new method to compress the space memory and still have the same data. In this paper, we will present a new method of compression points work well with addition operation in elliptic curve, so instead of storing the value of two points P = (xP,yP ), Q = (xQ,yQ), we will store the addition of the x-coordinates i,e ( α = xP + xQ,yP,yQ) or the y-coordinates i,e (xP,xQ,β = yP + yQ). In this article, we show a new technique for compressing two points in elliptic curve with different coordinate system: Affine, Projective and Jacobian in a field of characteristic ≠ 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.