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

Gaetan Bisson; Andrew V.  Sutherland

Paper 2009/100

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

Gaetan Bisson and Andrew V. Sutherland

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.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): gaetan bisson @ loria fr
History: 2009-03-17: last of 2 revisions; 2009-03-02: received; See all versions
Short URL: https://ia.cr/2009/100
License: CC BY

BibTeX

@misc{cryptoeprint:2009/100,
      author = {Gaetan Bisson and Andrew V.  Sutherland},
      title = {Computing the endomorphism ring of an ordinary elliptic curve over a finite field},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/100},
      year = {2009},
      url = {https://eprint.iacr.org/2009/100}
}