Twisted Edwards curves. (English) Zbl 1142.94332

Bernstein, Daniel J.; Birkner, Peter; Joye, Marc; Lange, Tanja; Peters, Christiane

Vaudenay, Serge (ed.), Progress in cryptology – AFRICACRYPT 2008. First international conference on cryptology in Africa, Casablanca, Morocco, June 11–14, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-68159-5/pbk). Lecture Notes in Computer Science 5023, 389-405 (2008).

Summary: This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves [H. M. Edwards, “A normal form for elliptic curves”, Bull. Am. Math. Soc., New Ser. 44, No. 3, 393–422 (2007; Zbl 1134.14308)], 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.
For the entire collection see [Zbl 1137.94002].

MSC:

11G20	Curves over finite and local fields
11T71	Algebraic coding theory; cryptography (number-theoretic aspects)
14G50	Applications to coding theory and cryptography of arithmetic geometry
14H52	Elliptic curves
11G05	Elliptic curves over global fields
94A60	Cryptography

Keywords:

Elliptic curves; Edwards curves; twisted Edwards curves; Montgomery curves; isogenies

Citations:

Zbl 1134.14308

Software:

SageMath