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Generalising the GHS Attack on the Elliptic Curve Discrete Logarithm Problem

Published online by Cambridge University Press:  01 February 2010

F. Hess
F. Hess
Affiliation:
Technical University of Berlin, Faculty II- Institute of Mathematics, MA8-1 Straße des 17. Juni 136, 10623 Berlin, Germany, hess@math.tu-berlin.de, http://www.math.tu-berlin.de/~hess

Abstract

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The Weil descent construction of the GHS attack on the elliptic curve discrete logarithm problem (ECDLP) is generalised in this paper, to arbitrary Artin-Schreier extensions. A formula is given for the characteristic polynomial of Frobenius for the curves thus obtained, as well as a proof that the large cyclic factor of the input elliptic curve is not contained in the kernel of the composition of the conorm and norm maps. As an application, the number of elliptic curves that succumb to the basic GHS attack is considerably increased, thereby further weakening curves over GF2155.

Other possible extensions or variations of the GHS attack are discussed, leading to the conclusion that they are unlikely to yield further improvements.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 167 - 192
Copyright
Copyright © London Mathematical Society 2004

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