Application
The algorithm is very fast for numbers with small factors. For example, on a 3 GHz workstation, the original rho algorithm found the factor 274177 of the sixth Fermat number (18446744073709551617) in 26 milliseconds; the Richard Brent variant found the same factor in 5 milliseconds. However, for a semiprime of the same size (10023859281455311421), the same workstation using the original rho algorithm took 109 milliseconds to find a factor; the Richard Brent variant took 31 milliseconds.
For f, we choose a polynomial with integer coefficients. The most common ones are of the form:
The rho algorithm's most remarkable success has been the factorization of the eighth Fermat number by Pollard and Brent. They used Brent's variant of the algorithm, which found a previously unknown prime factor. The complete factorization of F8 took, in total, 2 hours on a UNIVAC 1100/42.
Read more about this topic: Pollard's Rho Algorithm
Famous quotes containing the word application:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“The human mind is capable of excitement without the application of gross and violent stimulants; and he must have a very faint perception of its beauty and dignity who does not know this.”
—William Wordsworth (1770–1850)
“The main object of a revolution is the liberation of man ... not the interpretation and application of some transcendental ideology.”
—Jean Genet (1910–1986)