From Continuous-time Chaotic Systems to Pseudo Random Number Generators: Analysis and Generalized Methodology

L. DE MICCO; M. ANTONELLI; O. A. ROSSO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Lugar: Basel; Año: 2021

1099-4300

Chaotic systems are very attractive to be used in electronics as Pseudo-Random Number Generators (PRNGs). Among them, continuous-time ones are less used because, in addition to having strong temporal correlations, they require further computations to obtain the discrete solutions. Here, the time step and discretization method selection are first studied by conducting a detailed analysis of their effect on the systems´ statistical and chaotic behaviour. We employ an approach based on interpreting the time step as a parameter of the new "maps". From our analysis, it follows that to use them as PRNG two actions should be achieved (i) to keep the chaotic oscillation and (ii) to destroy the inner and temporal correlations. We then propose a simple methodology to achieve chaos-based PRNGs with good statistical characteristics and high throughput, that can be applied to any continuous-time chaotic system. We analyse the generated sequences by means of quantifiers based on Information Theory (Permutation Entropy, Permutation Complexity, and Causal Entropy $imes$ Complexity plane). We show that the proposed PRNG generates sequences that successfully pass Marsaglia Diehard and NIST (National Institute of Standards and Technology) tests. Finally, we show that its hardware implementation requires very few resources.