Application of chaotic ergodicity in image encryption and watermarking

In this paper, the chaotic 3D Arnold map is employed to scramble the pixel positions of plain images to get cipher images with a totally differently visual effect. Different from the conventional shuffling schemes, we disorder the pixel positions by orbits of the 3D Arnold map. Setting the initial positions and the control parameters as the encryption keys, one can get an orbit of the map. The orbit will generally fill the unit cube due to the chaotic ergodicity of the map; the points on the orbit have their corresponding order numbers which can be used to shuffle the image pixel positions. The shuffling procedure can be used to disorder the host image in watermarking schemes to enhance the robustness against attacks. Experimental results show that the proposed scheme yields good shuffling effects compared with the conventional ways. The watermarked images are robust against attacks as well.