Neriman Gamze OrhonHuseyin HisilOrhon, Neriman GamzeHisil, Huseyin2025-10-0620180925-10221573-758610.1007/s10623-018-0475-42-s2.0-85044595477http://dx.doi.org/10.1007/s10623-018-0475-4https://gcris.yasar.edu.tr/handle/123456789/6471https://doi.org/10.1007/s10623-018-0475-4This 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 6M + 5S to 8M and mixed addition operation count record from 10M to 8M. Both sets of formulas are shown to be 4-way parallel leading to an effective cost of 2M per either of the group operations.Englishinfo:eu-repo/semantics/closedAccessElliptic curves, 2-Isogeny, Efficient, Scalar multiplication, Huff curves, Inversion-free point addition, Parallel computationTWISTED EDWARDS CURVES, MODELParallel ComputationEfficientHuff CurvesInversion-Free Point Addition2-isogenyScalar MultiplicationElliptic CurvesArticle