A deterministic algorithm for integer factorization

TL;DR

This paper introduces a deterministic algorithm for integer factorization that operates in subexponential time, testing divisibility over short intervals simultaneously, and includes an implementation demonstrating its practicality.

Contribution

The paper presents a novel deterministic factorization algorithm that improves efficiency by testing multiple divisors simultaneously within short intervals.

Findings

Algorithm runs in $n^{1/3+o(1)}$ bit operations

Implemented the algorithm to demonstrate practical feasibility

Offers a new approach to deterministic integer factorization

Abstract

A deterministic algorithm for factoring $n$ using $n^{1/3+o(1)}$ bit operations is presented. The algorithm tests the divisibility of $n$ by all the integers in a short interval at once, rather than integer by integer as in trial division. The algorithm is implemented.