Cryptology ePrint Archive: Report 2008/013
Twisted Edwards Curves
Daniel J. Bernstein and Peter Birkner and Marc Joye and 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.
Category / Keywords: Elliptic curves, Edwards curves, twisted Edwards curves, Montgomery curves, isogenies.
Date: received 8 Jan 2008, last revised 13 Mar 2008
Contact author: tanja at hyperelliptic org
Available format(s): PDF | BibTeX Citation
Note: Included material on isogenies.
Version: 20080313:155312 (All versions of this report)
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