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Title:
Computing endomorphism rings of elliptic curves under the GRH
Authors: Gaetan Bisson
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.
ePrint: https://eprint.iacr.org/2011/042
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