Recent Advances in the design and implementation of Large Integer Factorization Algorithms

The latest and possibly fastest of the general factoring methods for large composite numbers is the quadratic sieve of Carl Pomerance. A variation of the algorithm is described and an implementation is suggested which combines the forces of a fast pipeline computer such as the Cray I, and a high speed highly parallel array processor such as the Goodyear MPP. A running time analysis, which is based on empirical data rather than asymptotic estimates, suggests that this method could be capable of factoring a 60 digit number in as little as 10 minutes and a 100 digit number is as little as 60 days of continuous computer time.