Paper 2001/054
Extending the GHS Weil Descent Attack
S. D. Galbraith, F. Hess, and N. P. Smart
Abstract
In this paper we extend the Weil descent attack due to Gaudry, Hess and Smart (GHS) to a much larger class of elliptic curves. This extended attack still only works for fields of composite degree over $\F_2$. The principle behind the extended attack is to use isogenies to find a new elliptic curve for which the GHS attack is effective. The discrete logarithm problem on the target curve can be transformed into a discrete logarithm problem on the new isogenous curve. One contribution of the paper is to give an improvement to an algorithm of Galbraith for constructing isogenies between elliptic curves, and this is of independent interest in elliptic curve cryptography. We conclude that fields of the form $\F_{q^7}$ should be considered weaker from a cryptographic standpoint than other fields. In addition we show that a larger proportion than previously thought of elliptic curves over $\F_{2^{155}}$ should be considered weak.
Metadata
- Available format(s)
- PS
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curve cryptosystems
- Contact author(s)
- nigel @ cs bris ac uk
- History
- 2001-07-06: received
- Short URL
- https://ia.cr/2001/054
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2001/054,
author = {S. D. Galbraith and F. Hess and N. P. Smart},
title = {Extending the GHS Weil Descent Attack},
howpublished = {Cryptology ePrint Archive, Paper 2001/054},
year = {2001},
note = {\url{https://eprint.iacr.org/2001/054}},
url = {https://eprint.iacr.org/2001/054}
}
