Abstract. This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formula...
Daniel J. Bernstein, Tanja Lange, Reza Rezaeian Fa...
Abstract. This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over...
Daniel J. Bernstein, Peter Birkner, Marc Joye, Tan...
Abstract. This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields GF(p). We use this processor to compare a new algorit...
Brian Baldwin, Richard Moloney, Andrew Byrne, Gary...
This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a ...
We use two parametrizations of points on elliptic curves in generalized Edwards form x2 + y2 = c2 (1 + dx2 y2 ) that omit the xcoordinate. The first parametrization leads to a diff...