Designs, Codes and Cryptography

, Volume 86, Issue 12, pp 2807–2823 | Cite as

Speeding up Huff form of elliptic curves

  • Neriman Gamze Orhon
  • Huseyin HisilEmail author


This paper presents faster inversion-free point addition formulas for the curve \(y (1+ax^2) = cx (1+dy^2)\). 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 \(6\mathbf{{M}}+ 5\mathbf{{S}}\) to \(8\mathbf{{M}}\) and mixed addition operation count record from \(10\mathbf{{M}}\) to \(8\mathbf{{M}}\). Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of \(2\mathbf{{M}}\) per either of the group operations.


Elliptic curves 2-Isogeny Efficient Scalar multiplication Huff curves Inversion-free point addition Parallel computation 

Mathematics Subject Classification

94A60 11T71 14G50 68P25 



The authors thank the anonymous reviewers for their suggestions and comments.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Gediz Electric Inc.GedizTurkey
  2. 2.Yasar UniversityIzmirTurkey

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