A Parallel Strategy for Solving Sparse Linear Systems over Finite Fields

In this paper we describe a number of parallel techniques that were applied to the problem of finding the null-spaces of thousands of large sparse matrices. This collection of matrices were derived from the discrete logarithm problem attack over the finite field F-36.509 recently carried out by Adj et al. in [2]. Our software library was mainly executed in the supercomputer ABACUS [7], where in total 21,870 large sparse linear algebra systems were processed. Solving those linear algebra problems involved a computational effort of over 138 core-years, requiring a memory space of over 645 gigabytes to store the corresponding vector solutions.