A novel data hiding method by using a chaotic system without equilibrium points

Abstract

In this paper, we investigate how special is the choice of parameter values in the three-dimensional nonlinear system, proposed by Akgul and Pehlivan (2016), in producing a system, which exhibits chaos but has no real equilibrium states. Also, a data hiding method with a three-dimensional chaotic system without equilibrium point, developed by Akgul and Pehlivan, is realized. Numerous encryption studies have recently been made based on chaos. Encryption processes that are used with chaos bring about some security deficiencies in some cases. Steganography, unlike encryption studies, helps communicate the secret data by hiding it in an innocent-looking cover in order to avoid detection by third parties at first glance. In this work, a novel chaos-based data hiding method that hides an image with a different color into color images is proposed. Via the proposed method, data are hidden in bit spaces with the help of the chaotic random number generator (RNG). The generated random numbers are found with a chaotic system without equilibrium point, which is new in the literature. Shilnikov method cannot be applied to find whether the system is chaotic or not because they cannot have homoclinic or heteroclinic orbits. Thus, it can be useful in several engineering applications, especially in chaos-based cryptology and coding information. In the study, bits are hidden in pixels indicated by numbers generated by RNG. As the order of the hiding process is made randomly on a chaotic level, it has made data hiding algorithm stronger. The proposed method hides the data in cover image in such a way that it cannot be easily detected. Furthermore, the proposed method has been evaluated with steganalysis methods and image distortion measurement method PSNR. The chaos-based steganography method realized here has produced more best results in image distortion measurement method PSNR than other studies in the literature.