Topological horseshoe analysis for a three-dimensional anti-control system and its application

Abstract

This paper designs a new three-dimensional dynamical system to be chaotic by the anti-control method. Then, by the theory of topological horseshoe, we prove that there exists a invariant compact set in the Poincare mapping section of the new anti-control system such that it is semi-conjugate to a 2-shift dynamics with computer-assisted, so the new anti-controlled system is chaotic. Furthermore, an image encryption scheme is designed based on the chaotic system. First, the image pixel positions are scrambled by the pseudo-random sequences generated from the chaotic system. Second, the pixel values are encrypted for multiple rounds by the chaotic stream cipher, so it achieves the double chaotic encryption. Finally, the statistical analyses are given to show the feasibility and security of the proposed encryption scheme.