Parallelized Pollard's Rho algorithm for ECDLP on Graphic Cards

The recent introduction by NVidia of Compute Unified Device Architecture (CUDA) libraries for High Performance Computing on Graphic Processing Units has started the trend of video cards for resolution of many computationally hard problems in different areas like fluid dynamics, molecular dynamics, computer vi- sion and astrophysics. In this paper we show how CUDA libraries and hardware can be introduced in cryptography as a cryptoanalytic tool.We describe an implementation of a parallelized Pollard’s rho attack on ECDLP, based upon recent results about the optimization of Pollard’s rho method and enhanced by some ”ad-hoc” choices for CUDA