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Solvability of a System of Bivariate Polynomial Equations over a Finite Field

(Extended Abstract)
  • Neeraj Kayal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)

Abstract

We investigate the complexity of the following polynomial solvability problem: Given a finite field \({\mathbb F}_{q}\) and a set of polynomials

$$f_{1}(x,y),f_{2}(x,y),...,f_{n}(x,y),g(x,y) \ \epsilon \ {\mathbb F}_{q} [x,y]$$

determine the \({\mathbb F}_{q}\)-solvability of the system

$$f_{1}(x,y)=f_{2}(x,y)=...=f_{n}(x,y)=0 \ {\rm and} \ {\it g}(x,y) \neq 0$$

We give a deterministic polynomial-time algorithm for this problem.

Keywords

Deterministic Algorithm Irreducible Factor Factorization Algorithm Polynomial Factorization Permutation Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Neeraj Kayal
    • 1
    • 2
  1. 1.Indian Institute of TechnologyKanpur
  2. 2.National University of Singapore 

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