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.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.inria.fr/inria-00560258
Contributor : Gaetan Bisson <>
Submitted on : Thursday, January 27, 2011 - 6:10:29 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:25 PM

Links full text

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

178