Factorization in the Cloud: Integer Factorization Using F# and Windows Azure

Implementations are presented of two common algorithms for integer factorization, Pollard’s “p – 1” method and the SQUFOF method. The algorithms are implemented in the F# language, a functional programming language developed by Microsoft and officially released for the first time in 2010. The algorithms are thoroughly tested on a set of large integers (up to 64 bits in size), running both on a physical machine and a Windows Azure machine instance. Analysis of the relative performance between the two environments indicates comparable performance when taking into account the difference in computing power. Further analysis reveals that the relative performance of the Azure implementation tends to improve as the magnitudes of the integers increase, indicating that such an approach may be suitable for larger, more complex factorization tasks. Finally, several questions are presented for future research, including the performance of F# and related languages for more efficient, parallelizable algorithms, and the relative cost and performance of factorization algorithms in various environments, including physical hardware and commercial cloud computing offerings from the various vendors in the industry.