Digit Polynomials and their application to integer factorization

TL;DR

This paper introduces digit polynomials, a new approach for integer factorization that achieves a deterministic, unconditional algorithm with a runtime of approximately N^{1/4+ε}, extending and generalizing Strassen's method.

Contribution

The paper proposes digit polynomials as a novel tool for integer factorization, providing a new deterministic algorithm with potential for improved complexity.

Findings

Achieves a deterministic, unconditional factorization algorithm with runtime ~N^{1/4+ε}

Generalizes Strassen's factoring approach using digit polynomials

Discusses potential improvements to the complexity bound

Abstract

This paper presents the concept of digit polynomials, which leads to a deterministic and unconditional integer factorization algorithm with the runtime complexity $\mathcal{O}(N^{1/4+\epsilon})$. Strassen's well known factoring approach is a special case of our method. We will also consider a possibility to improve upon the complexity bound.