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Huff’s Model for Elliptic Curves

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Algorithmic Number Theory (ANTS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6197))

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Abstract

This paper revisits a model for elliptic curves over ℚ introduced by Huff in 1948 to study a diophantine problem. Huff’s model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of ℤ/4ℤ ×ℤ/2ℤ is birationally equivalent to a Huff curve over the original field.

This paper extends and generalizes Huff’s model. It presents fast explicit formulæ for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the so-obtained formulæ feature some useful properties, including completeness and independence of the curve parameters.

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Author information

Authors and Affiliations

  1. Technicolor, Security & Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. École Normale Supérieure – C.N.R.S. – I.N.R.I.A., 45, Rue d’Ulm, 75230, Paris CEDEX 05, France

    Mehdi Tibouchi & Damien Vergnaud

Authors
  1. Marc Joye
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  2. Mehdi Tibouchi
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  3. Damien Vergnaud
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Editor information

Editors and Affiliations

  1. LIP/ENS-Lyon, 46, allée d’Italie, 69364, Lyon, Cedex 07, France

    Guillaume Hanrot

  2. Laboratoire d’Informatique (CNRS/UMR 7650), École polytechnique, 91128, Palaiseau Cedex, France

    François Morain

  3. INRIA Nancy, project CARAMEL, 615 rue du jardin botanique, 54602, Villers-lès-Nancy Cedex,, France

    Emmanuel Thomé

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Joye, M., Tibouchi, M., Vergnaud, D. (2010). Huff’s Model for Elliptic Curves. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_20

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  • DOI: https://doi.org/10.1007/978-3-642-14518-6_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14517-9

  • Online ISBN: 978-3-642-14518-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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