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}
}
  • R. Brent
  • Published 1 June 1980
  • Computer Science
  • BIT Numerical Mathematics
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. 
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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.
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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
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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
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TLDR
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.
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Toward A Theory of Pollard's Rho Method
  • E. Bach
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  • 1991
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