Computing endomorphism rings of elliptic curves under the GRH

Details Computing endomorphism rings of elliptic curves under the GRH Computing endomorphism rings of elliptic curves under the GRH

2011-01-22

arxiv.org/abs/1101.4323v2

Mathematics

Number Theory

11 pages, 1 figure

Scientific paper

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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