Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves

Benjamin Smith 1
1 TANC - Algorithmic number theory for cryptology
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians of hyperelliptic curves of genus three to Jacobians of non-hyperelliptic curves of genus three, which are vulnerable to faster index calculus attacks. We provide algorithms which compute an isogeny with kernel isomorphic to $(Z/2Z)^3$ for any hyperelliptic genus three curve. These algorithms provide a rational isogeny for a positive fraction of all hyperelliptic genus three curves defined over a finite field of characteristic p > 3. Subject to reasonable assumptions, our algorithms provide an explicit and efficient reduction from hyperelliptic DLPs to non-hyperelliptic DLPs for around $18.57\%$ of all hyperelliptic genus three curves over a given finite field.
Type de document :
Communication dans un congrès
Nigel Smart. Eurocrypt 2008, Apr 2008, Istanbul, Turkey. 4965, pp.163-180, 2008, Lecture Notes in Computer Science. 〈10.1007/978-3-540-78967-3_10〉
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https://hal.inria.fr/inria-00537860
Contributeur : Benjamin Smith <>
Soumis le : vendredi 19 novembre 2010 - 15:30:40
Dernière modification le : jeudi 12 avril 2018 - 01:47:21

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Benjamin Smith. Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves. Nigel Smart. Eurocrypt 2008, Apr 2008, Istanbul, Turkey. 4965, pp.163-180, 2008, Lecture Notes in Computer Science. 〈10.1007/978-3-540-78967-3_10〉. 〈inria-00537860〉

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