A log-log speedup for exponent one-fifth deterministic integer factorisation

TL;DR

This paper presents a deterministic integer factorization algorithm that achieves a significant speedup, reducing the complexity to roughly N^{1/5} with a log-log factor improvement over previous methods.

Contribution

The authors introduce a new deterministic factorization method that improves the complexity bound by a factor of (log log N)^{3/5}, advancing the state of the art.

Findings

Achieves a complexity of O(N^{1/5} log^{16/5} N / (log log N)^{3/5})

Improves previous factorization bounds by a (log log N)^{3/5} factor

Demonstrates the effectiveness of recent techniques in deterministic factorization

Abstract

Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer $N$ may be rigorously and deterministically factored into primes in at most \[ O\left( \frac{N^{1/5} \log^{16/5} N}{(\log\log N)^{3/5}}\right) \] bit operations. This improves on the previous best known result by a factor of $(\log \log N)^{3/5}$.