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Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

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Progress in Cryptology — INDOCRYPT 2001 (INDOCRYPT 2001)

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Abstract

We analyze the Gaudry-Hess-Smart (GHS) Weil descent attack on the elliptic curve discrete logarithm problem (ECDLP)for elliptic curves defined over characteristic two finite fields of composite extension degree. For each such field F2 N, N ∈ [160, 600], we identify elliptic curve parameters such that (i)there should exist a cryptographically interesting elliptic curve E over F2 N with these parameters; and (ii)the GHS attack is more efficient for solving the ECDLP in E(F N2 )than for any other cryptographically interesting elliptic curve over F2 N.

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Author information

Authors and Affiliations

  1. Dept. of C&O, University of Waterloo, Canada

    Markus Maurer, Alfred Menezes & Edlyn Teske

Authors
  1. Markus Maurer
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  2. Alfred Menezes
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  3. Edlyn Teske
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai, India

    C. Pandu Rangan

  2. Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong

    Cunsheng Ding

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© 2001 Springer-Verlag Berlin Heidelberg

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Maurer, M., Menezes, A., Teske, E. (2001). Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree. In: Rangan, C.P., Ding, C. (eds) Progress in Cryptology — INDOCRYPT 2001. INDOCRYPT 2001. Lecture Notes in Computer Science, vol 2247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45311-3_19

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  • DOI: https://doi.org/10.1007/3-540-45311-3_19

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  • Print ISBN: 978-3-540-43010-0

  • Online ISBN: 978-3-540-45311-6

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