Paper 2004/015

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

Trond Stølen Gustavsen and 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
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystemspoint counting
Contact author(s)
stolen @ math uio no
History
2004-01-27: received
Short URL
https://ia.cr/2004/015
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2004/015}},
      url = {https://eprint.iacr.org/2004/015}
}
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