Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Elliptic curve discrete logarithm problem

Original Publication (with minor differences): This paper appears in the Festschrift on the occasion of Johannes Buchmann's 60th birthday. The final publication is available at, LNCS vol. 8260.

Date: received 13 Sep 2013

Contact author: eteske at uwaterloo ca

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Version: 20130914:224740 (All versions of this report)

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