Date: 01 Dec 2000

The Quadratic Sieve Factoring Algorithm

Abstract

The quadratic sieve algorithm is currently the method of choice to factor very large composite numbers with no small factors. In the hands of the Sandia National Laboratories team of James Davis and Diane Holdridge, it has held the record for the largest hard number factore since mid-1983. As of this writing, the largest number it has crackd is the 71 digit number (1071−1)/9, taking 9.5 hours on the Cray XMP computer at Los Alamos, New Mexico. In this paper I shall give some of the history of the algorithm and also describe some of the improvements that habe been suggested for it

supported in part by a grant from the National Science Foundation.