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 have the same data. In this paper, we will present a new method of compression points work well with addition opera- tion 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.

Keywords: Elliptic curve, Affine coordinate, Projective coordinate, Jacobian coordinate, compression point.

Received Date: April 10, 2024                  Accepted Date: May 11, 2024            

Published Date: June 01, 2024

Available Online at: https://www.ijsrisjournal.com/index.php/ojsfiles/article/view/156

DOI: https://doi.org/10.5281/zenodo.11244720