A GPU implementation of the Montgomery multiplication algorithm for elliptic curve cryptography

This work presents a GPU implementation of the Montgomery multiplication algorithm that is heavily optimized for the GPU's SEVID architecture, as well as the field sizes and constraints required for elliptic curve cryptography. We present and compare the throughput results of our proposed algorithm for 10 commonly used field sizes from 112 to 521 bits. When executed by our NVIDIA GTX-480 GPU device, the proposed algorithm's measured throughput in multiplication operations per second is 1.24 to 1.72 times greater than the next fastest GPU-based algorithm running on the same device, and is significantly greater than all other published CPU and GPU-based implementations. The proposed work could be used as a component of an elliptic curve cryptography acceleration appliance, or for cryptanalysis.