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

G. Bisson, A.V. Sutherland

Research output: Book/ReportReportAcademic

Abstract

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 log q, while our bound for the second algorithm depends primarily on log IDEI, 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.
Original languageEnglish
Publishers.n.
Number of pages16
Publication statusPublished - 2009

Publication series

NameCryptology ePrint Archive
Volume2009/100

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  • Cite this

    Bisson, G., & Sutherland, A. V. (2009). Computing the endomorphism ring of an ordinary elliptic curve over a finite field. (Cryptology ePrint Archive; Vol. 2009/100). s.n.