# An improved Monte Carlo factorization algorithm

@article{Brent1980AnIM, title={An improved Monte Carlo factorization algorithm}, author={Richard P. Brent}, journal={BIT Numerical Mathematics}, year={1980}, volume={20}, pages={176-184} }

Pollard's Monte Carlo factorization algorithm usually finds a factor of a composite integerN inO(N1/4) arithmetic operations. The algorithm is based on a cycle-finding algorithm of Floyd. We describe a cycle-finding algorithm which is about 36 percent faster than Floyd's (on the average), and apply it to give a Monte Carlo factorization algorithm which is similar to Pollard's but about 24 percent faster.

## 206 Citations

Some integer factorization algorithms using elliptic curves

- Computer Science, MathematicsArXiv
- 2010

A way in which Lenstra's integer factorization algorithm can be speeded up by the addition of a second phase is suggested, and some refinements which give greater speedup are mentioned.

An Experimental Study of Monte Carlo Factoring Techniques

- Physics
- 1982

Different polynomials are tested in the Monte Carlo factoring algorithm to see if a more efficient factoring can be obtained, and the results are inconclusive.

Speeding the Pollard and elliptic curve methods of factorization

- Mathematics
- 1987

Since 1974, several algorithms have been developed that attempt to factor a large number N by doing extensive computations module N and occasionally taking GCDs with N. These began with Pollard's p 1…

Random Walks Revisited: Extensions of Pollard's Rho Algorithm for Computing Multiple Discrete Logarithms

- Computer Science, MathematicsSelected Areas in Cryptography
- 2001

This paper extends the analysis of Pollard's rho algorithm for solving a single instance of the discrete logarithm problem in a finite cyclic group G to the case of solving more than one instance of…

A quantum version of Pollard's Rho of which Shor's Algorithm is a particular case

- Mathematics
- 2020

Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable…

Speeding the Pollard and Elliptic Curve Methods

- Mathematics
- 2010

Since 1974, several algorithms have been developed that attempt to factor a large number N by doing extensive computations modulo N and occasionally taking GCDs with N. These began with Pollard's p 1…

On the Efficiency of Pollard's Rho Method for Discrete Logarithms

- Computer ScienceCATS
- 2008

An empirical performance analysis of several widely applied algorithms is described to provide a better combination of algorithms and a good choice of parameters for Pollard's rho method.

Accelerating Pollard’s Rho Algorithm on Finite Fields

- Computer Science, MathematicsJournal of Cryptology
- 2010

A technique for traveling through the random graph without fully computing each node is developed and an extension to the distinguished point collision detection method that is suitable for this new situation is provided.

Analysis of Pollard's Rho Factoring Method

- Mathematics
- 2019

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…

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