International Association
for Cryptologic Research

This paper presents a fast implementation to compute the scalar multiplication of elliptic curve points based on a ``General-Purpose computing on Graphics Processing Units\'\' (GPGPU) approach. A GPU implementation using Dan Bernstein\'s Curve25519, an elliptic curve over a 255-bit prime field complying with the new 128-bit security level, computes the scalar multiplication in less than a microsecond on AMD\'s R9 290X GPU. The presented methods and implementation considerations can be applied to any parallel architecture.