Knowing the limits of factoring capabilities is important for various reasons. A favorite example is the security of factoring based cryptosystems, which is based on our inability to solve the factoring problem. There are also cryptosystems, however, which are not only based on this inability, but which also depend on the ability to solve certain instances of the related discrete logarithm problem. Therefore he not only needs to know what we cannot do, but we also need practical and efficient algorithms for what we supposedly can do. In this paper the author considers how some of these issues are affected by a particular type of massively parallel computers, so-called single instruction, multiple data (SIMD) machines