An AGM-type elliptic curve point counting algorithm in characteristic three

Trond Stølen Gustavsen; Kristian Ranestad

Paper 2004/015 Original: eprint.iacr.org/2004/015 ↗

An AGM-type elliptic curve point counting algorithm in characteristic three

Trond Stølen Gustavsen

Kristian Ranestad

Abstract

Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for computing the number of points. Our methods are based on the study of an explicitly and naturally given $3$-isogeny between elliptic curves on Hesse form.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2004-01-27: last updated; 2004-01-27: published
Short URL: https://ia.cr/2004/015
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2004/015,
      author = {Trond Stølen Gustavsen and Kristian Ranestad},
      title = {An AGM-type elliptic curve point counting algorithm in characteristic three},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/015},
      year = {2004},
      url = {https://eprint.iacr.org/2004/015}
}