Algorithms for Modular Counting of Roots of Multivariate Polynomials

@article{Gopalan2006AlgorithmsFM,
  title={Algorithms for Modular Counting of Roots of Multivariate Polynomials},
  author={Parikshit Gopalan and Venkatesan Guruswami and Richard J. Lipton},
  journal={Algorithmica},
  year={2006},
  volume={50},
  pages={479-496}
}
Given a multivariate polynomial P(X 1,…,X n ) over a finite field $\ensuremath {\mathbb {F}_{q}}$ , let N(P) denote the number of roots over $\ensuremath {\mathbb {F}_{q}}^{n}$ . The modular root counting problem is given a modulus r, to determine N r (P)=N(P)mod r. We study the complexity of computing N r (P), when the polynomial is given as a sum of monomials. We give an efficient algorithm to compute N r (P) when the modulus r is a power of the characteristic of the field. We show that for… CONTINUE READING