On the Complexity of Integer Factorization

This note presents a deterministic integer factorization algorithm based on a system of polynomials equations. This technique exploits a new idea in the construction of irreducible polynomials with parametized roots, and recent advances in polynomial lattices reduction methods. The main result establishes a new deterministic time complexity bench mark. 1 Introduction This note presents a deterministic integer factorization algorithm based on a system of polynomials equations. This technique combines a new irreducible polynomials construction technique and recent advances in lattice reduction methods to obtain a new result. The main result establishes a new deterministic time complexity bench mark. Background materials in the theory of integer factorization are given in [