Submitted:
02 November 2019
Posted:
05 November 2019
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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
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