Twisted Edwards Curves

Daniel J.  Bernstein; Peter Birkner; Marc Joye; Tanja Lange; Christiane Peters

Paper 2008/013

Twisted Edwards Curves

Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange, and Christiane Peters

Abstract

This paper introduces ``twisted Edwards curves,'' a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.

Note: Included material on isogenies.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curves Edwards curves twisted Edwards curves Montgomery curves isogenies.
Contact author(s): tanja @ hyperelliptic org
History: 2008-03-13: last of 2 revisions; 2008-01-14: received; See all versions
Short URL: https://ia.cr/2008/013
License: CC BY

BibTeX

@misc{cryptoeprint:2008/013,
      author = {Daniel J.  Bernstein and Peter Birkner and Marc Joye and Tanja Lange and Christiane Peters},
      title = {Twisted Edwards Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/013},
      year = {2008},
      url = {https://eprint.iacr.org/2008/013}
}