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(Virtually) Free Randomization Techniques for Elliptic Curve Cryptography

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Information and Communications Security (ICICS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2836))

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Abstract

Randomization techniques play an important role in the protection of cryptosystems against implementation attacks. This paper studies the case of elliptic curve cryptography and propose three novel randomization methods, for the elliptic curve point multiplication, which do not impact the overall performance.

Our first method, dedicated to elliptic curves over prime fields, combines the advantages of two previously known solutions: randomized projective coordinates and randomized isomorphisms. It is a generic point randomization and can be related to a certain multiplier randomization technique. Our second method introduces new elliptic curve models that are valid for all (non-supersingular) elliptic curves over binary fields. This allows to use randomized elliptic curve isomorphisms, which in turn allows to randomly compute on elliptic curves with affine coordinates. Our third method adapts a double ladder attributed to Shamir. We insist that all our randomization methods share the common feature to be free: the cost of our randomized implementations is virtually the same as the cost of the corresponding non-randomized implementations.

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Author information

Authors and Affiliations

  1. UCL Crypto Group, Place du Levant 3, 1348, Louvain-la-Neuve, Belgium

    Mathieu Ciet

  2. Gemplus, Card Security Group, La Vigie, Avenue du Jujubier, ZI Athélia IV, 13705, La Ciotat Cedex, France

    Marc Joye

Authors
  1. Mathieu Ciet
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  2. Marc Joye
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Editor information

Editors and Affiliations

  1. Institute of Softwear, Chinese Academy of Sciences, 100080, Beijing, China

    Sihan Qing

  2. Institute for Security in Distributed Applications, Hamburg University of Technology, 21071, Hamburg, Germany

    Dieter Gollmann

  3. Cryptography and Security Department Institute for Infocomm Research, Singapore

    Jianying Zhou

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© 2003 Springer-Verlag Berlin Heidelberg

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Ciet, M., Joye, M. (2003). (Virtually) Free Randomization Techniques for Elliptic Curve Cryptography. In: Qing, S., Gollmann, D., Zhou, J. (eds) Information and Communications Security. ICICS 2003. Lecture Notes in Computer Science, vol 2836. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39927-8_32

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  • DOI: https://doi.org/10.1007/978-3-540-39927-8_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20150-2

  • Online ISBN: 978-3-540-39927-8

  • eBook Packages: Springer Book Archive

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