Dynamical analysis of a new statistically highly performant
deterministic function for chaotic signals generation
In some engineering applications, such as chaotic encryption, chaotic maps have to exhibit required spectral properties close to those of random signals.
In this paper, we present the analysis of a new ultra weakly coupled maps system introduced by Lozi . The model is a deterministic one, but exibits spectral properties (spectrum, correlation and autocorrelation)
close to those of random signals, and successfully passed all the statistical tests for closeness to random signals (NIST).
Moreover, if a particular sampling is applied, the Lyapunov exponent is shown to increase by a power of ten.
In the context of chaotic encryption, the space of all possible keys is explored using statistical tests but also dynamiacl systems thery
(sensitivity to the initial conditions, parameter sensitivity, ...)
All performed tests demonstrate the very satisfactory properties of proposed function.