Skip to main content
Article thumbnail
Location of Repository

Solving Large Sparse Linear Systems Over Finite Fields

By B. A. Lamacchia and A. M. Odlyzko

Abstract

Many of the fast methods for factoring integers and computing discrete logarithms require the solution of large sparse linear systems of equations over finite fields. This paper presents the results of implementations of several linear algebra algorithms. It shows that very large sparse systems can be solved efficiently by using combinations of structured Gaussian elimination and the conjugate gradient, Lanczos, and Wiedemann methods. 1. Introduction Factoring integers and computing discrete logarithms often requires solving large systems of linear equations over finite fields. General surveys of these areas are presented in [14, 17, 19]. So far there have been few implementations of discrete logarithm algorithms, but many of integer factoring methods. Some of the published results have involved solving systems of over 6 \Theta 10 4 equations in more than 6 \Theta 10 4 variables [12]. In factoring, equations have had to be solved over the field GF (2). In that situation, ordinary..

Publisher: Springer
Year: 1991
OAI identifier: oai:CiteSeerX.psu:10.1.1.36.9222
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.farcaster.com/paper... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.