Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent

Michael Jacobson; Alfred Menezes; Andreas Stein

Paper 2001/041 Original: eprint.iacr.org/2001/041 ↗

Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent

Michael Jacobson

Alfred Menezes

Andreas Stein

Abstract

We provide a concrete instance of the discrete logarithm problem on an elliptic curve over F_{2^{155}} which resists all previously known attacks, but which can be solved with modest computer resources using the Weil descent attack methodology of Frey. We report on our implementation of index-calculus methods for hyperelliptic curves over characteristic two finite fields, and discuss the cryptographic implications of our results.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2001-05-20: last updated; 2001-05-20: published
Short URL: https://ia.cr/2001/041
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2001/041,
      author = {Michael Jacobson and Alfred Menezes and Andreas Stein},
      title = {Solving Elliptic Curve Discrete Logarithm Problems Using Weil Descent},
      howpublished = {Cryptology {ePrint} Archive, Paper 2001/041},
      year = {2001},
      url = {https://eprint.iacr.org/2001/041}
}