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Journal Articles Journal of Number Theory Year : 2011

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

Abstract

We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field F_q. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of log q, while our bound for the second algorithm depends primarily on log |D_E|, where D_E 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.

Dates and versions

inria-00383155 , version 1 (12-05-2009)

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Cite

Gaetan Bisson, Andrew V. Sutherland. Computing the endomorphism ring of an ordinary elliptic curve over a finite field. Journal of Number Theory, 2011, Elliptic Curve Cryptography, 131 (5), pp.815--831. ⟨10.1016/j.jnt.2009.11.003⟩. ⟨inria-00383155⟩
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