Preprint Article Version 1 This version is not peer-reviewed

# 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 (doi: 10.20944/preprints201911.0044.v1). Mohamed, S.K. Analysis of Pollard's Rho Factoring Method. Preprints 2019, 2019110044 (doi: 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.

## Subject Areas

ultimate period distribution; parallelization; tail distribution