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 ringsGRH
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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2011/042}},
      url = {https://eprint.iacr.org/2011/042}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.