[Resource Topic] 2001/054: Extending the GHS Weil Descent Attack

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Extending the GHS Weil Descent Attack

Authors: S. D. Galbraith, F. Hess, N. P. Smart


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
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.

ePrint: https://eprint.iacr.org/2001/054

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