Factoring Polynomials and the Knapsack Problem

Although a polynomial time algorithm exists, the most commonly used algorithm for factoring a univariate polynomial f with integer coeecients is the Berlekamp-Zassenhaus algorithm which has a complexity that depends exponentially on n where n is the number of modular factors of f. This exponential time complexity is due to a combinatorial problem; the problem of choosing the right subset of these n factors. In this paper we reduce this combinatorial problem to a knapsack problem of a kind that can be solved with polynomial time algorithms such LLL or PSLQ. The result is a practical algorithm that can factor large polynomials even when n is large as well.