A Parallel Strategy for Solving Sparse Linear Systems Over Finite Fields

Abstract

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 $\F_{3^{6\cdot 509}}$ recently carried out by Adj et al. in~\cite{Adj2017}. Our software library was mainly executed in the supercomputer ABACUS~\cite{abacus}, 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.