Constructing a non-degeneracy nD chaotic map model and counteracting dynamic degradation through adaptive impulsive perturbation

Abstract

The characteristics of state point trajectory in phase space of a chaotic map, such as ergodicity, aperiodicity, broadband and noise-like, have been proved to be suitable for cryptography. However, some weaknesses, such as small key space, multiple bifurcations and dense windows that exist in some classic 1D and 2D chaotic maps, effect their practical application. To solve these problems, we constructed a non-degeneracy nD chaotic model, and instantiated it to obtain a 3D chaotic map (3D-NDCM), the dynamics analysis results demonstrated that the 3D-NDCM has a sufficiently large chaotic range, its state point trajectories has ergodicity in phase space. To counteract dynamic degradation and extend the aperiodic length of state time sequences, we further constructed a 6D-NDCM based on the model. Experimental analysis results demonstrated that, a state time sequence with longer aperiodicity can be obtained, through both dimension expansion and adaptive impulsive perturbation.