Article
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Analysis of Pollard's Rho Factoring Method
Version 1
: Received: 2 November 2019 / Approved: 5 November 2019 / Online: 5 November 2019 (05:20:33 CET)
How to cite: Mohamed, S.K. Analysis of Pollard's Rho Factoring Method. Preprints 2019, 2019110044. https://doi.org/10.20944/preprints201911.0044.v1 Mohamed, S.K. Analysis of Pollard's Rho Factoring Method. Preprints 2019, 2019110044. https://doi.org/10.20944/preprints201911.0044.v1
Abstract
A comprehensive heuristic analysis of the Pollard's Rho Method (PRM) is given. The analysis is based on ultimate periods and tails distribution of sequences. If $n$ is the composite number to be factored, then an improved version of PRM is developed which has an expected run time of $O(\sqrt[8]{n}\ln n)$ on a multi-core architecture which utilized a clever way of evaluating polynomials.
Keywords
ultimate period distribution; parallelization; tail distribution
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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