A Parallel Strategy for Solving Sparse Linear Systems Over Finite Fields

Authors

  • Luis Rivera-Zamarripa Tampere University, Tampere, Finland
  • Gora Adj Department de Matemàtiea, Universitat de Lleida, Spain
  • Nareli Cruz-Cortés Centro de Investigación en Computación, Instituto Politécnico Nacional
  • Carlos Aguilar-Ibañez Centro de Investigación en Computación, Instituto Politécnico Nacional
  • Francisco Rodríguez-Henríquez

DOI:

https://doi.org/10.13053/cys-26-1-3494

Keywords:

Linear Algebra, Finite Field, Parallel Computing

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.

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Published

2022-03-28

Issue

Vol. 26 No. 1 (2022): Recent Advances in Language & Knowledge Engineering (Guest editors: D. Pinto, B. Beltrán, A. Vázquez, D. Vilariño)

Section

Articles

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