Image Encryption Using Chaotic 3-D Arnold’s Cat Map and Logistic Map

Abstract

Image encryption is different from that of traditional texts or binary data because of some inherent properties of images such as large data capacity, i.e., enormous size and high redundancy (statistical and psycho-visual), making them difficult to handle by traditional methods. In recent years, chaos theory has been explored to find efficient ways to develop secure image cryptosystems. Due to the desirable properties of mixing and sensitivity to initial conditions and parameters (butterfly effect), chaotic systems have found great deal in the domain of image encryption. In this paper, the 2-D chaotic cat map is generalized to its 3-D map counterpart for designing a real-time secure and reliable symmetric encryption design. This new scheme deploys the 3-D Arnold’s cat map to shuffle the positions of image pixels and uses the other chaotic logistic map to perplex the relationship between the plain-image and the cipher-image, thereby significantly enhancing the robustness to differential and statistical attacks. Experimental tests are carried out with comprehensive analysis, demonstrating the high security of the scheme.