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Computing the endomorphism ring of an ordinary elliptic curve over a finite field

Computing the endomorphism ring of an ordinary elliptic curve over a finite field,10.1016/j.jnt.2009.11.003,Journal of Number Theory,Gaetan Bisson,And

Computing the endomorphism ring of an ordinary elliptic curve over a finite field   (Citations: 6)
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We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of logq, while our bound for the second algorithm depends primarily on log|DE|, where DE is the discriminant of the order isomorphic to End(E). As a byproduct, our method yields a short certificate that may be used to verify that the endomorphism ring is as claimed.
Journal: Journal of Number Theory - J NUMBER THEOR , vol. 131, no. 5, pp. 815-831, 2011
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