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Twisted Edwards Curves
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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 }