Volume 83, Number 3, August 2008
Article Number 34008
Number of page(s) 4
Section Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics
Published online 29 July 2008
EPL, 83 (2008) 34008
DOI: 10.1209/0295-5075/83/34008

Factoring numbers with interfering random waves

S. Weber, B. Chatel and B. Girard

Laboratoire Collisions, Agrégats, Réactivité - IRSAMC-(CNRS, Université de Toulouse, UPS) - Toulouse, France, EU

received 16 April 2008; accepted in final form 20 June 2008; published August 2008
published online 29 July 2008

We report on a new implementation of the factorisation of numbers using Gauss sums which improves tremendously the efficiency to eliminate all "ghost" factors. We show that by choosing randomly the terms in the Gauss sum, the required number of terms varies as lnN instead of $\sqrt[4]{N} $. As an illustration, we present experimental results obtained by interfering thirty ultrashort laser pulses where we factorise 1340333404807. This new approach is totally general and can be implemented for all the experiments based on the Gauss sum.

42.65.Re - Ultrafast processes; optical pulse generation and pulse compression.
02.10.De - Algebraic structures and number theory.
42.79.Kr - Display devices, liquid-crystal devices.

© EPLA 2008