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TitleSolving the elliptic curve discrete logarithm problem using semaev polynomials, Weil descent and Gr\"obner basis methods -- an experimental study.
Author(s) Schweinfurter Michael, Edlyn Teske
TypeBook, Chapter in Book, Conference Proceeding
AbstractAt 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.
URL http://link.springer.com/chapter/10.1007%2F978-3-642-42001-6_7
PublisherBerlin: Springer
Translation No
Refereed No