Speeding up Huff form of elliptic curves

Abstract

This paper presents faster inversion-free point addition formulas for the curve y(1 + ax2) = cx(1 + dy2). The proposed formulas improve the point doubling operation count record (I M S D a are arithmetic operations over a field. I: inversion M: multiplication S: squaring D: multiplication by a curve constant a: addition/subtraction) from 6 M+ 5 S to 8 M and mixed addition operation count record from 10 M to 8 M. Both sets of formulas are shown to be 4-way parallel leading to an effective cost of 2 M per either of the group operations. © 2018 Elsevier B.V. All rights reserved.