The Magic Words are Squeamish Ossifrage

We describe the computation which resulted in the title of this paper Furthermore we give an analysis of the data collected during this computation From these data we derive the important observation that in the nal stages the progress of the double large prime variation of the quadratic sieve integer factoring algorithm can more e ectively be approximated by a quartic function of the time spent than by the more familiar quadratic function We also present as an update to some of our experiences with the management of a large computation distributed over the Internet Based on this experience we give some realistic estimates of the current readily available computational power of the Internet We conclude that commonly used bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars and to wait a few months