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The Jacobi Model of an Elliptic Curve and Side-Channel Analysis

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2643))

Abstract

A way for preventing SPA-like attacks on elliptic curve systems is to use the same formula for the doubling and the general addition of points on the curve. Various proposals have been made in this direction with different results. This paper re-investigates the Jacobi form suggested by Liardet and Smart (CHES 2001). Rather than considering the Jacobi form as the intersection of two quadrics, the addition law is directly derived from the underlying quartic. As a result, this leads to substantial memory savings and produces the fastest unified addition formula for curves of order a multiple of 2, as those required for OK-ECDH or OK-ECDSA.

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Author information

Authors and Affiliations

  1. Card Security Group, Gemplus Card International, La Vigie, Av. du Jujubier, ZI Athélia IV, 13705, La Ciotat Cedex, France

    Olivier Billet & Marc Joye

  2. Télécom Paris (ENST), 46 rue Barrault, 75634, Paris Cedex 13, France

    Olivier Billet

  3. Laboratoire Dieudonné, UNSA, Parc Valrose, 06108, Nice Cedex 02, France

    Olivier Billet

Authors
  1. Olivier Billet
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  2. Marc Joye
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole Street, Holmes Hall 455, Honolulu, HI, 96822, USA

    Marc Fossorier

  2. Department of Mathematics, The Technical University of Denmark, Bldg. 303, DK-2800, Lyngby, Denmark

    Tom Høholdt

  3. IRIT - Université Paul Sabatier, 31602, Toulouse cédex, France

    Alain Poli

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© 2003 Springer-Verlag Berlin Heidelberg

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Billet, O., Joye, M. (2003). The Jacobi Model of an Elliptic Curve and Side-Channel Analysis. In: Fossorier, M., Høholdt, T., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2003. Lecture Notes in Computer Science, vol 2643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44828-4_5

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  • DOI: https://doi.org/10.1007/3-540-44828-4_5

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40111-7

  • Online ISBN: 978-3-540-44828-0

  • eBook Packages: Springer Book Archive

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