Integer factorization algorithms

Abstract

Integer Factorization is an old problem in Number Theory, which has long been regarded as a fundamentally difficult problem. Since 1970, there have been substantial advances in integer factorization. A number of algorithms have been developed for the factorization of moderate to large-sized integers with exponential and sub-exponential run times. This report describes the principles and implementation of a few of these recent algorithms on a general-purpose time-shared minicomputer, and some results obtained using the implementation.