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Designs, Codes and Cryptography

, Volume 49, Issue 1–3, pp 47–60 | Cite as

On solving sparse algebraic equations over finite fields

  • Igor Semaev
Article

Abstract

A system of algebraic equations over a finite field is called sparse if each equation depends on a small number of variables. In this paper new deterministic algorithms for solving such equations are presented. The mathematical expectation of their running time is estimated. These estimates are at present the best theoretical bounds on the complexity of solving average instances of the above problem. In characteristic 2 the estimates are significantly lower the worst case bounds provided by SAT solvers.

Keywords

Sparse algebraic equations over finite fields Constraint satisfaction problem Gluing Random allocations 

AMS Classifications

11T71 68Q25 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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