A BSP parallel model of the Göttfert algorithm for polynomial factorization over F₂

Abstract

In Niderreiter's factorization algorithm for univariate polynomials over finite fields, the factorization problem is reduced to solving a linear system over the finite field in question, and the solutions are used to produce the complete factorization of the polynomial into irreducibles. For fields of characteristic 2, a polynomial time algorithm for extracting the factors using the solutions of the linear system was developed by Göttfert, who showed that it is sufficient to use only a basis for the solution set. In this paper, we develop a new BSP parallel algorithm based on the approach of Göttfert over the binary field, one that improves upon the complexity and performance of the original algorithm for polynomials over F₂. We report on our implementation of the parallel algorithm and establish how it achieves very good efficiencies for many of the case studies. When combined with our previous for solving large sparse Niederreiter linear systems over the binary field, this provides an efficient alternative to other implementations of the Niederreiter algorithm for the factorization of large sparse polynomials over F₂.