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arXiv · 1308.2891

Deterministic Integer Factorization Algorithms

N. A. Carella
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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.

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N. A. Carella. 2013-08-05. Deterministic Integer Factorization Algorithms. https://arxiv.org/abs/1308.2891

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