  This paper will describe a simulator developed by the authors to explore the
design of Fourier transform based multiplication using optics. Then it will
demonstrate an application to the problem of constructing an all-optical
modular multiplication circuit. That circuit implements a novel approximate
version of the Montgomery multiplication algorithm that enables the calculation
to be performed entirely in the analog domain. The results will be used to
corroborate the feasibility of scaling the design up to 16-bits without the
need for analog to digital conversions at intermediate steps.
