Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson

Paper 2011/042

Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson

Abstract

We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: endomorphism rings GRH
Contact author(s): gaetan bisson @ loria fr
History: 2011-02-14: revised; 2011-01-25: received; See all versions
Short URL: https://ia.cr/2011/042
License: CC BY

BibTeX

@misc{cryptoeprint:2011/042,
      author = {Gaetan Bisson},
      title = {Computing endomorphism rings of elliptic curves under the {GRH}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/042},
      year = {2011},
      url = {https://eprint.iacr.org/2011/042}
}