Image Encryption Scheme Based on Non-autonomous Chaotic Systems

Abstract

In this chapter, the great sensitivity of nonlinear systems, and especially of chaotic systems, on the initial conditions and on the variation of their parameters, was used to design a novel image encryption scheme. Until now, a great number of chaotic autonomous continuous systems or discrete dynamical systems, have been used in various image encryption processes, as a source of random numbers. However, in this work, a Chaotic Random Bit Generator (CRBG), which is based on a non-autonomous dynamical system, is used. For ridding from the system the influence of the external source and increasing the security of the proposed generator, the Poincar\(\acute{e}\) section for sampling the signal has been used. As a dynamical system, the very well-known Duffing–van der Pol system has been chosen, presenting very good statistical results. The aforementioned CRBG is the “heart” of the proposed image encryption scheme. Finally, the security analysis of the proposed encryption scheme, based on histogram analysis, correlation of two adjacent pixels, differential analysis and information entropy, demonstrate the robustness of the proposed chaotic encryption scheme against all kinds of statistical, cryptanalytic, and brute-force attacks.