Multiplication with Fourier Optics Simulating 16-Bit Modular Multiplication

Though optical computing has been unable to compete with CMOS technology in mainstream computing, its natural capacity for computing Fourier transforms gives it an advantage in convolution-type problems. This may make optics a viable approach in post-Moore‘s era computing. This paper presents an optical approach to one suitable yet nontrivial problem: modular multiplication. We first explore the mathematical details of performing a basic optical convolution using lenses and masks. Then we discuss a simulation tool developed by the authors to explore some design considerations for an optical convolution circuit. Finally, we layout an algorithm for performing Montgomery modular multiplication in an optical system along with simulation results for an all-optical implementation. The proposed approach presents an extremely energy efficient solution to computing 16-bit modular multiplication without the need for analog-digital conversions in intermediate steps.