Journal Articles Journal of Mathematical Cryptology Year : 2011

Computing endomorphism rings of elliptic curves under the GRH

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.

Dates and versions

inria-00560258 , version 1 (27-01-2011)

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Cite

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