Extracting sparse factors from multivariate integral polynomials

Abstract

In this paper we present a new algorithm for extracting sparse factors from multivariate integral polynomials. The method hinges on a new type of substitution, which reduces multivariate integral polynomials to bivariate polynomials over finite fields and keeps the sparsity of the polynomial. We retrieve the multivariate sparse factors, term by term, using discrete logarithms. We show that our method is really effective when used for factoring multivariate polynomials that have only sparse factors and when used to extract sparse factors of multivariate polynomials that may also have dense factors.