Twisted Edwards Curves

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.

• Type: Conference
• Year: 2008
• Where: AFRICACRYPT
• Authors: Daniel J. Bernstein, Peter Birkner, Marc Joye, Tanja Lange, Christiane Peters
• Keywords: AFRICACRYPT 2008, Cryptology, Curves Save Time, Edwards Curves, Twisted Edwards Curves