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

Michael Shantz; Edlyn Teske

Paper 2013/596

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

Michael Shantz and Edlyn Teske

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. This paper appears in the Festschrift on the occasion of Johannes Buchmann's 60th birthday. The final publication is available at link.springer.com, LNCS vol. 8260.
Keywords: Elliptic curve discrete logarithm problem
Contact author(s): eteske @ uwaterloo ca
History: 2013-09-14: received
Short URL: https://ia.cr/2013/596
License: CC BY

BibTeX

@misc{cryptoeprint:2013/596,
      author = {Michael Shantz and Edlyn Teske},
      title = {Solving the Elliptic Curve Discrete Logarithm Problem Using Semaev Polynomials, Weil Descent and Gröbner Basis Methods -- an Experimental Study},
      howpublished = {Cryptology ePrint Archive, Paper 2013/596},
      year = {2013},
      note = {\url{https://eprint.iacr.org/2013/596}},
      url = {https://eprint.iacr.org/2013/596}
}