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Paper: Twisted Edwards Curves

Authors:
Daniel J. Bernstein
Peter Birkner
Marc Joye
Tanja Lange
Christiane Peters
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URL: http://eprint.iacr.org/2008/013
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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.
BibTeX
@misc{eprint-2008-17690,
  title={Twisted Edwards Curves},
  booktitle={IACR Eprint archive},
  keywords={Elliptic curves, Edwards curves, twisted Edwards curves, Montgomery curves, isogenies.},
  url={http://eprint.iacr.org/2008/013},
  note={ tanja@hyperelliptic.org 13951 received 8 Jan 2008, last revised 13 Mar 2008},
  author={Daniel J. Bernstein and Peter Birkner and Marc Joye and Tanja Lange and Christiane Peters},
  year=2008
}