Neriman Gamze OrhonHüseyin Hişil2025-10-06201809251022, 157375860925-10221573-758610.1007/s10623-018-0475-4https://www.scopus.com/inward/record.uri?eid=2-s2.0-85044595477&doi=10.1007%2Fs10623-018-0475-4&partnerID=40&md5=b7ca05cfaffee2ac7d035edfc094f2b4https://gcris.yasar.edu.tr/handle/123456789/9506This 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.English2-isogeny, Efficient, Elliptic Curves, Huff Curves, Inversion-free Point Addition, Parallel Computation, Scalar Multiplication, Computer Applications, Mathematical Techniques, 2-isogeny, Efficient, Elliptic Curve, Huff Curves, Parallel Computation, Point Additions, Scalar Multiplication, GeometryComputer applications, Mathematical techniques, 2-Isogeny, Efficient, Elliptic curve, Huff curves, Parallel Computation, Point additions, Scalar multiplication, GeometryArticle