Package de.tilman_neumann.jml.factor.pollardRho

Class PollardRho

  • public class PollardRho
extends FactorAlgorithm
    From: http://www.cs.princeton.edu/introcs/79crypto/PollardRho.java (INTRODUCTION TO COMPUTER SCIENCE by Robert Sedgewick and Kevin Wayne) Pollards Rho method. Pollard's rho method is a randomized factoring algorithm that can factor 128 bit numbers in a reasonable amount of time, especially if the numbers have some small factors. It is based on the following fact: if d is the smallest nontrivial factor of N and x - y is a nontrivial multiple of d then gcd(x-y, N) = d. A naive method would be to generate a bunch of random values x[1], x[2], ..., x[m] and compute gcd(x[i]-x[j], N) for all pairs i and j. Pollard's rho method is an ingenious method way to find x and y without doing all of the pairwise computations. It works as follows: choose a and b at random between 1 and N-1, and initialize x = y = a. Repeatedly update x = f(x), y = f(f(y)), where f(x) = x^2 + b as long as gcd(x-y, N) = 1. The gcd is a factor of N, but if you get unlucky, it could be equal to N. By randomly choosing a and b each time, we ensure that we never get too unlucky.
    Author:
    Tilman Neumann