Multi-composition-exponential-modulo chaotification model

This work explores a chaotification technique that consists of the composition of exponential functions with offset boosting, in which the exponential term includes a seed function in its exponent. This architecture offers a high degree of design freedom, as several different map families can be designed, considering the number of compositions, the values of the control parameters, and the type of seed function. Based on this general family of maps, three different map examples are designed. Several analytical results are provided regarding the Lyapunov exponent expression and the existence of fixed points. The maps are then also studied numerically, through computation of cobweb, fixed point, bifurcation, and Lyapunov exponent diagrams. Interesting behaviors are observed, like the absence of fixed points and thus hidden attractors, as well as robust chaos. The maps are then successfully applied to the problem of pseudorandom bit generation. Overall, this family of maps gives very promising results for further studies.