Dynamical Analysis of a new statistically highly performant deterministic function for chaotic signals generation

Sebastien Hénaff (1) , Ina Taralova (1) , René Lozi (2)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 JAD - Laboratoire Jean Alexandre Dieudonné

In some engineering applications, such as chaotic encryption, chaotic maps have to exhibit required spectral and statistical properties close to those of random signals. In order to evaluate the latter features, statistical tests developed for random number generators (RNG) can also be applied to chaotic maps, in order to gather evidence that the map generates ”good” chaotic signals, i.e. having a considerable degree of randomness. To address this particular problem, different statistical tests for the systematic evaluation of the randomness of cryptographic random number generators can be applied, among which the most popular NIST (National Institute of Standards and Technology) tests. In this paper we present the analysis of a new ultra weakly coupled maps system introduced by Lozi (its statistical properties and its evolution with parameter variation.

Mots clés: chaos; identifiability; observer; synchronisation

Domaines: Systèmes dynamiques [math.DS]

Sebastien Hénaff, Ina Taralova, René Lozi. Dynamical Analysis of a new statistically highly performant deterministic function for chaotic signals generation. 2009. ⟨hal-00368844⟩