Number Theory Algorithms on GPU Clusters

Many algorithms from Number Theory and their implementation in software are of high practical importance, since they are the building primitives of many protocols for data encryption and authentication of Internet connections. Number theory algorithms are also the basic part of cryptanalytic procedures. Many of these algorithms can be parallelized in a natural way. In this paper we describe our efforts to develop a software package that implements various Number Theory algorithms on GPU clusters and in partial our implementations of integer factorization using NVIDIA CUDA on clusters equipped with NVIDIA GPUs. Also we report results of our experiments regarding the performance of our implementation.