Computing Endomorphism Rings Of Elliptic Curves Under The Grh
JOURNAL OF MATHEMATICAL CRYPTOLOGY(2011)
摘要
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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关键词
Elliptic curves, endomorphism rings, subexponential algorithm, generalized Riemann hypothesis
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