Tools for designing chaotic systems for secure random number generation

It is well known that the output of chaotic systems can be completely predicted from the exert knowledge of the initial conditions. However, their extreme sensitivity to initial conditions lends itself to being exploited for generation of random numbers. This work explores this possibility and gives a simple circuit arrangement, together with the tools necessary to assess the random characteristics of its output. The fact that the statistical characteristics of a chaotic system can be determined through spectral analysis of an evolution operator is shown. Numerical techniques for practical estimation of this operator are presented. Special attention is paid to robustness both with respect to numerical approximation and circuit tolerances. Error bounds of practical significance are given. One example of the proposed method and results is given. The results presented are valid for generic sampled chaotic systems and can also be used for applications other than random number generation, e.g., chaotic communications.