Dynamical Analysis and Homogenization Process of Unimodal Chaotic Mapping Utilized for Pseudo-Random Sequences

In this paper, a novel unimodal chaotic system is presented which has stable Lyapunov exponents, a wider range of parameters and a larger phase space. In order to generate evenly distributed chaotic sequences, a general homogenization scheme is proposed with a rigorous mathematical proof. To generate high-quality pseudo-random number sequences, a PRNG scheme based on cross-coupling is designed. Theoretical derivation and experimental analysis fully demonstrate that the proposed PRNG has the ability to produce high-security random numbers with excellent random characteristics.