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Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Gröbner Basis Methods – An Experimental Study

  • Michael Shantz
  • Edlyn Teske
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8260)

Abstract

At ASIACRYPT 2012, Petit and Quisquater suggested that there may be a subexponential-time index-calculus type algorithm for the Elliptic Curve Discrete Logarithm Problem (ECDLP) in characteristic two fields. This algorithm uses Semaev polynomials and Weil Descent to create a system of polynomial equations that subsequently is to be solved with Gröbner basis methods. Its analysis is based on heuristic assumptions on the performance of Gröbner basis methods in this particular setting. While the subexponential behaviour would manifest itself only far beyond the cryptographically interesting range, this result, if correct, would still be extremely remarkable. We examined some aspects of the work by Petit and Quisquater experimentally.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael Shantz
    • 1
  • Edlyn Teske
    • 1
  1. 1.University of WaterlooCanada

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