The expectation of success using a Monte Carlo factoring method—some statistics on quadratic class numbers

Abstract

A method has been proposed for factoring an integer N by using the structure of the class groups of quadratic fields of radicand − k N - kN for various small multipliers k. We discuss the method and an implementation of the method, and various theoretical questions which have an impact on the practical use of the method in factoring. Some of the theoretical questions relate to the nature of class numbers and class groups; we present extensive statistical results on the class numbers and class groups of imaginary quadratic fields.