An Improved Monte Carlo Factorization Algorithm
نویسنده
چکیده
Pollard’s Monte Carlo factorization algorithm usually finds a factor of a composite integer N in O(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. CommentsOnly the Abstract is given here. A preliminary version appeared as [2] and the full paperappeared as [1]. The result improved the efficiency of Pollard’s “rho” method [4]. A furthermodification was used to factor the eighth Fermat number [3]. References[1] R. P. Brent, “An improved Monte Carlo factorization algorithm”, BIT 20 (1980), 176-184. MR 82a:10007,Zbl 439.65001. rpb051[2] R. P. Brent, Analysis of some new cycle finding and factorization algorithms, Technical Report TR-CS-79-11,DCS, ANU (November 1979), 10 pp.[3] R. P. Brent and J. M. Pollard, “Factorization of the eighth Fermat number”, Math. Comp. 36 (1981), 627-630.MR 83h:10014. rpb061[4] J. M. Pollard, “A Monte Carlo method for factorization”, BIT 15 (1975), 331–334. MR 52 #13611.Department of Computer Science, Australian National University, Canberra, ACT 260
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