Deterministic Integer Factorization Algorithms
N. A. Carella

TL;DR
This paper introduces a new deterministic integer factorization algorithm with improved complexity, capable of factoring integers more efficiently than previous methods, especially when partial information about factors is available.
Contribution
The paper presents a novel deterministic factorization algorithm with complexity $O(N^{1/6+ ext{ε}})$, improving upon the previous $O(N^{1/5+ ext{ε}})$ algorithm.
Findings
Achieves factorization in $O(N^{1/6+ ext{ε}})$ arithmetic operations.
Can factor integers in polynomial time given partial bits of a factor.
Provides a more efficient deterministic approach compared to prior algorithms.
Abstract
A new integer deterministic factorization algorithm, rated at arithmetic operations to arithmetic operations, is presented in this note. Equivalently, given the least bits of a factor of the balanced integer , where and are primes, the algorithm factors the integer in polynomial time , with constant, and an arbitrarily small number. It improves the current deterministic factorization algorithm, rated at arithmetic operations to arithmetic operations.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cryptography and Residue Arithmetic
