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On Edwards curves and ZVP-attacks

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Elliptic curve cryptography on smart cards is vulnerable under a particular Side Channel Attack: the existence of zero-value points (ZVP). One approach to face this drawback relies on changing the curve for an isogenous one, until a resistant curve is found. This paper focuses on an alternative strategy: exploiting the properties of a recently introduced form of elliptic curves, Edwards curves. We show that these curves achieve conditions for being resistant to ZVP-attacks. Hence, using Edwards curves is a good countermeasure to avoid these attacks.

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Acknowledgments

This work has been partially supported by grants MTM2010-21580-C02-01/02 and MTM2010-16051 from Spanish Ministerio de Economía y Competitividad.

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Authors and Affiliations

  1. Universitat de Lleida, Lleida, Spain

    S. Martínez, R. Tomàs & M. Valls

  2. Universidad de Cantabria, Cantabria, Spain

    D. Sadornil

  3. IMUVA, Universidad de Valladolid, Valladolid, Spain

    J. Tena

Authors
  1. S. Martínez
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  2. D. Sadornil
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  3. J. Tena
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  4. R. Tomàs
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  5. M. Valls
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Correspondence to D. Sadornil.

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Martínez, S., Sadornil, D., Tena, J. et al. On Edwards curves and ZVP-attacks. AAECC 24, 507–517 (2013). https://doi.org/10.1007/s00200-013-0211-2

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  • DOI: https://doi.org/10.1007/s00200-013-0211-2

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