Deterministic Integer Factorization Algorithms

Abstract

A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced integer $N = pq$, where $p$ and $q$ are primes, the algorithm factors the integer in polynomial time $O(\log(N)^c)$, with $c \geq 0$ constant, and $\varepsilon > 0$ an arbitrarily small number. It improves the current deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/5+\varepsilon})$ arithmetic operations.