Software Implementation of Elliptic Curve Cryptography over Binary Fields Page 1 Software Implementation of Elliptic Curve Cryptography over Binary Fields Darrel Hankerson1⋆, Julio López Hernandez2, and Alfred Menezes3 1 Dept. of Discrete and Statistical Sciences, Auburn University, USA hankedr@mail.auburn.edu 2 Dept. of Computer Science, University of Valle, Colombia jlopez@borabora.univalle.edu.co 3 Dept. of Combinatorics and Optimization, University of Waterloo, Canada ajmeneze@uwaterloo.ca Abstract. This paper presents an extensive