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International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2003: Advances in Cryptology — EUROCRYPT 2003 pp 374–387Cite as

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The GHS Attack Revisited

The GHS Attack Revisited

  • Florian Hess5 
  • Conference paper
  • First Online: 01 January 2003
  • 3443 Accesses

  • 11 Citations

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2656)

Abstract

We generalize the Weil descent construction of the GHS attack to arbitrary Artin-Schreier extensions. We give a formula for the characteristic polynomial of Frobenius of the obtained curves and prove that the large cyclic factor of the input elliptic curve is not contained in the kernel of the composition of the conorm and norm maps. As an application we almost square the number of elliptic curves which succumb to the basic GHS attack, thereby weakening curves over \( \mathbb{F}_{2^{155} } \) further. We also discuss other possible extensions or variations of the GHS attack and conclude that they are not likely to yield further improvements.

Keywords

  • Elliptic Curve
  • Elliptic Curf
  • Discrete Logarithm
  • Hyperelliptic Curve
  • Discrete Logarithm Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Author information

Authors and Affiliations

  1. Computer Science Department, University of Bristol, Woodland Road, BS8 1UB, UK

    Florian Hess

Authors
  1. Florian Hess
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Eli Biham

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© 2003 International Association for Cryptologic Research

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Cite this paper

Hess, F. (2003). The GHS Attack Revisited. In: Biham, E. (eds) Advances in Cryptology — EUROCRYPT 2003. EUROCRYPT 2003. Lecture Notes in Computer Science, vol 2656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39200-9_23

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  • DOI: https://doi.org/10.1007/3-540-39200-9_23

  • Published: 13 May 2003

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14039-9

  • Online ISBN: 978-3-540-39200-2

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