Twisted Edwards Curves

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

Paper 2008/013 Original: eprint.iacr.org/2008/013 ↗

Twisted Edwards Curves

Daniel J. Bernstein

Peter Birkner

Marc Joye

Tanja Lange

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.

Metadata

Available format(s): PDF
Publication info: Preprint.
History: 2008-03-13: last updated; 2008-01-14: published
Short URL: https://ia.cr/2008/013
License: https://creativecommons.org/licenses/by/4.0/

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}
}