We describe the quadratic sieve factoring algorithm and a pipeline architecture on which it could be efficiently implemented. Such a device would be of moderate cost to build and would be able to factor 100-digit numbers in less than a month. This represents an order of magnitude speed-up over current implementations on supercomputers. Using a distributed network ofmany such devices, it is predicted much larger numbers could be practically factored. 1. Introduction. The problem of efficiently factoring large composite numbers has been of interest for centuries. It shares with many other basic problems in the sciences the twin attributes of being easy to state, yet (so far) difficult to solve. In recent years, it has also become an applied science. In fact, several new public-key cryptosystems and signature schemes, including the RSA public-key cryptosystem (10), base their security on the supposed intractability of the factoring problem. Although there is no known polynomial time algorithm for factoring, we do have subexponential algorithms. Over the last few years there has developed a remarkable six-way tie for the asymptotically fastest factoring algorithms. These methods all have the common running time