An exponent one-fifth algorithm for deterministic integer factorisation

TL;DR

This paper improves the deterministic integer factorization algorithm's complexity from approximately N^{1/4} to N^{1/5} using advanced techniques, marking a significant theoretical advancement in computational number theory.

Contribution

The paper introduces a new deterministic algorithm for integer factorization with complexity N^{1/5+o(1)}, improving upon previous bounds and extending Hittmeir's recent methods.

Findings

Deterministic factorization complexity reduced to N^{1/5+o(1)}.

Builds upon and extends Hittmeir's recent techniques.

Achieves a new theoretical bound for integer factorization.

Abstract

Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, the best known complexity bound for this problem was $N^{1/4+o(1)}$, a result going back to the 1970s. In this paper we push Hittmeir's techniques further, obtaining a rigorous, deterministic factoring algorithm with complexity $N^{1/5+o(1)}$.