—Acceleration of cryptographic applications on Graphical Processing Units (GPUs) platforms is a research topic with practical interest, because these platforms provide huge computational power for this type of applications. In this paper, we propose a parallel algorithm for Elliptic Curve (EC) point multiplication in order to compute EC cryptography on GPUs. The proposed approach relies in using the Residue Number System (RNS) to extract parallelism on high precision integer arithmetic. Results suggest a maximum throughput of 9990 EC multiplications per second and minimum latency of 24.3 ms for a 224-bit underlying field, for an Nvidia 285 GTX GPU. We present performances up to an order of magnitude better in latency and 122 % in throughput regarding other approaches reported in the related art.