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arXiv · 1101.4323

Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson
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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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Gaetan Bisson. 2011-02-14. Computing endomorphism rings of elliptic curves under the GRH. https://doi.org/10.1515/jmc.2011.008

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