Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson 1, 2
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.
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Article dans une revue
Journal of Mathematical Cryptology, De Gruyter, 2011, 5 (2), pp.101-113. 〈10.1515/JMC.2011.008〉
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https://hal.inria.fr/inria-00560258
Contributeur : Gaetan Bisson <>
Soumis le : jeudi 27 janvier 2011 - 18:10:29
Dernière modification le : jeudi 22 septembre 2016 - 14:31:29

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Gaetan Bisson. Computing endomorphism rings of elliptic curves under the GRH. Journal of Mathematical Cryptology, De Gruyter, 2011, 5 (2), pp.101-113. 〈10.1515/JMC.2011.008〉. 〈inria-00560258〉

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