Iterative sparse matrix-vector multiplication for integer factorization on GPUs

Abstract

The Block Wiedemann (BW) and the Block Lanczos (BL) algorithms are frequently used to solve sparse linear systems over GF(2). Iterative sparse matrix-vector multiplication is the most time consuming operation of these approaches. The necessity to accelerate this step is motivated by the application of these algorithms to very large matrices used in the linear algebra step of the Number Field Sieve (NFS) for integer factorization. In this paper we derive an efficient CUDA implementation of this operation using a newly designed hybrid sparse matrix format. This leads to speedups between 4 and 8 on a single GPU for a number of tested NFS matrices compared to an optimized multi-core implementation. © 2011 Springer-Verlag.