An improved Monte Carlo factorization algorithm

@article{Brent1980AnIM,
  title={An improved Monte Carlo factorization algorithm},
  author={R. Brent},
  journal={BIT Numerical Mathematics},
  year={1980},
  volume={20},
  pages={176-184}
}
  • R. Brent
  • Published 1980
  • Mathematics
  • 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. 
    194 Citations
    Some integer factorization algorithms using elliptic curves
    • R. Brent
    • Mathematics, Computer Science
    • ArXiv
    • 2010
    • 41
    • PDF
    An Experimental Study of Monte Carlo Factoring Techniques
    Speeding the Pollard and elliptic curve methods of factorization
    • 1,118
    • Highly Influenced
    • PDF
    On the Efficiency of Pollard's Rho Method for Discrete Logarithms
    • 19
    • PDF
    Accelerating Pollard’s Rho Algorithm on Finite Fields
    • 8
    • PDF
    Toward A Theory of Pollard's Rho Method
    • E. Bach
    • Mathematics, Computer Science
    • Inf. Comput.
    • 1991
    • 47
    • PDF
    Factorization of large integers on some vector and parallel computers
    • 5
    • PDF

    References

    SHOWING 1-10 OF 15 REFERENCES
    A Fast Monte-Carlo Test for Primality
    • 621
    Factorization of the eighth Fermat number
    • 99
    • PDF
    Monte Carlo methods for index computation ()
    • 756
    • PDF
    Theorems on factorization and primality testing
    • 367
    Riemann's Hypothesis and tests for primality
    • G. Miller
    • Mathematics, Computer Science
    • STOC '75
    • 1975
    • 369
    A design for a number theory package with an optimized trial division routine
    • 30
    A monte carlo method for factorization
    • 377
    The complexity of finding periods
    • 12
    New directions in cryptography
    • 13,549
    • PDF