## 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.

Short URL: ia.cr/2008/013

[ Cryptology ePrint archive ]