Twisted Edwards Curves
- Cite this paper as:
- Bernstein D.J., Birkner P., Joye M., Lange T., Peters C. (2008) Twisted Edwards Curves. In: Vaudenay S. (eds) Progress in Cryptology – AFRICACRYPT 2008. AFRICACRYPT 2008. Lecture Notes in Computer Science, vol 5023. Springer, Berlin, Heidelberg
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.
KeywordsElliptic curves Edwards curves twisted Edwards curves Montgomery curves isogenies
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