Part II Numerical Mathematics

BIT Numerical Mathematics

, Volume 20, Issue 2, pp 176-184

First online:

An improved Monte Carlo factorization algorithm

  • Richard P. BrentAffiliated withDepartment of Computer Science, Australian National University

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Pollard's Monte Carlo factorization algorithm usually finds a factor of a composite integerN inO(N 1/4) 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.