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)


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.


Deterministic Algorithm Irreducible Factor Factorization Algorithm Polynomial Factorization Permutation Polynomial 


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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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