An Experimental Demonstration of Optical Number Factorization by Gaußian Sums

Factorization of a large integer N is the crucial obstacle on the way to break the modern public-key RSA-encodement based on the trapdoor property of the product of two large prime numbers. We built an illustrative model to demonstrate the mechanism of an optical factor analyzer on the basis of a Gaußian sum by using the interference of laser light at a special grating with a stepwise reduced grating constant. The device produces a two dimensional interference pattern on a screen, which marks the factors of an integer by light speckles. Though the size of the model limits the integer to about 50, and the factors to 12, it is an optical realization of the sieve of Eratosthenes and beautifully demonstrates the power of Gaußian sums in interferometry.