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arXiv · 2506.12844

Choosing iteration maps for the parallel Pollard rho method

Finn Rudolph
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Abstract

Pollard's rho method finds a prime factor $p$ of an integer $N$ by searching for a collision in a map of the form $x \mapsto x^{2k} + c$ modulo $N$. This search can be parallelized to multiple machines, which may use distinct parameters $k$ and $c$. In this paper, we give an asymptotic estimate for the expected running time of the parallel rho method depending on the choice of $k$ for each machine. We also prove that $k = 1$ is the best choice for one machine, if nothing about $p$ is known in advance.

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Finn Rudolph. 2025-06-15. Choosing iteration maps for the parallel Pollard rho method. https://arxiv.org/abs/2506.12844

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