A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period

In this paper, a very low complexity method is proposed to achieve a guaranteed substantial extension in the period of a popular class of chaos-based digital pseudo-random number generators (PRNGs). To this end, the relation between the chaotic PRNG and multiple recursive generators is investigated and some theorems are provided to show that how a simple recursive structure and an additive piecewise-constant perturbation inhibit unpredictable short period trajectories and ensure an a priori known long period for the chaotic PRNG. The statistical performance of the proposed PRNG is evaluated, and the results show that it is a good candidate for applications in which long-period secure pseudo-random sequence generators at a low complexity level are required.