Leveraging Lévy Flight for Efficient Divisor Identification in Odd Composite Integers
Leveraging Lévy Flight for Efficient Divisor Identification in Odd Composite Integers
Xingbo Wang
TLDR
An innovative approach that integrates LF with specific local search techniques (LS) to identify a divisor of N and exhibits minimal space complexity and, in theory, achieves logarithmic time complexity in optimal scenarios is presented.
Abstract
In accordance with the distribution law of composite integers possessing a divisor of the odd semi-prime N = pq with 2 < p < q, and considering the characteristics of Lévy flight (LF), this paper presents an innovative approach that integrates LF with specific local search techniques (LS) to identify a divisor of N. This method exhibits minimal space complexity and, in theory, achieves logarithmic time complexity in optimal scenarios. A comprehensive framework for the approach is outlined, alongside the introduction of a simple-random-walk-blended LF (SRW-blended LF) algorithm. Key issues pertinent to the implementation of the algorithm are thoroughly analyzed and elucidated. Experiments conducted to factorize semi-primes demonstrate that the newly developed approach, implemented using Matlab software, yields highly satisfactory results.