Faster deterministic integer factorization

TL;DR

This paper improves the deterministic complexity bound for integer factorization, reducing the time complexity by a factor of the square root of log log N, advancing the efficiency of prime factorization algorithms.

Contribution

The authors present a novel method that improves the deterministic complexity bound for integer factorization by a factor of (log log N)^(1/2).

Findings

Complexity bound improved by a factor of (log log N)^(1/2)

Advances deterministic integer factorization efficiency

Builds on prior Pollard–Strassen approach

Abstract

The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of multiplying k-bit integers. This result is due to Bostan--Gaudry--Schost, following the Pollard--Strassen approach. We show that this bound can be improved by a factor of (log log N)^(1/2).