A group action on multivariate polynomials over finite fields

Factoring Multivariate Polynomials over Finite Fields

We consider the deterministic complexity of the problem of polynomial factorization over finite fields given a finite field Fq and a polynomial h(x, y) ∈ Fq[x, y] compute the unique factorization of h(x, y) as a product of irreducible polynomials. This problem admits a randomized polynomial-time algorithm and no deterministic polynomial-time algorithm is known. In this chapter, we give a determ...

Factoring Multivariate Polynomials over Large Finite Fields

A simple probabilistic algorithm is presented to find the irreducible factors of a bivariate polynomial over a large finite field. For a polynomial f(x, y) over F of total degree n , our algorithm takes at most 4.89, 2 , n log n log q operations in F to factor f(x , y) completely. This improves a probabilistic factorization algorithm of von zur Gathen and Kaltofen, which takes 0(n log n log q) ...

Factorizing Multivariate Polynomials Over Finite Fields

On the evaluation of multivariate polynomials over finite fields

We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.

Polynomial-Time Factorization of Multivariate Polynomials over Finite Fields

We present a probabilistic algorithm that finds the irreducible factors of a bivariate polynomial with coefficients from a finite field in time polynomial in the input size, i.e. in the degree of the polynomial and log (cardinality of field). The algorithm generalizes to multivariate polynomials and has polynomial running time for densely encoded inputs. Also a deterministic version of the algo...