Parallel processing for multiplication modulo by means of phase modulation

We apply optical parallel processing to operations for multiplication modulo, which is one of the key components of a factorization algorithm. With this method, optical phase modulation provides the results of modulo operations. We construct a prototype system based on a Michelson interferometer with a photodetector array. Mirrors are set at both object and reference arms to generate interference fringes. A mirror in the object arm is tilted slightly, whereas the reference arm is set perpendicular to the optical axis. The tilt angle is determined by parameters for the target modulo operations. The presented system can achieve massive data processing in parallel with only simple implementation. We present our experimental results to verify the usefulness of our method.