Factoring: Algorithms,computations, and computers

This article discusses the computational structure of the most effective methods for factoring integers and the computer architectures—existing and used, proposed, and under construction—which efficiently perform the computations of these various methods. New developments in technology and in pricing of computers are making it possible to build powerful parallel machines, at relatively low cost, which can substantially outperform standard computers on specific types of computations. The intent of this article is to use factoring and computers for factoring to provoke general thought about this matching of computer architectures to algorithms and computations.The author's research at Louisiana State University was supported in part by the National Science Foundation and the National Security Agency under grants NSF DCR 83-115-80 and NSA MDA904-85-H-0006.