### 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 language | English |
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Publisher | s.n. |

Number of pages | 16 |

Publication status | Published - 2009 |

### Publication series

Name | Cryptology ePrint Archive |
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Volume | 2009/100 |

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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.