Extremely-Large Key-Space Color Image Encryption Scheme using Combined Memristive Chaotic System

The security level and robustness of memristive image encryption techniques depend on the order and dynamics complexity of the memristive system. The grid multi-double-scroll (GMDS) chaotic system (CS) offers extremely rich dynamics but the implementation of high-order chaos needs large computation time. To overcome this limitation, researchers have proposed the use of muti-lower-order CSs to assist the encryption process individually. This scenario may reduce the security level since the non-friendly user may attack each involved CS independently. This paper proposes an effective six-dimensional (6D) memristive chaotic system constructed by combining 5D, 5D, and 7D GMDS chaotic systems. Each of the six chaotic sequences is generated from three sequences corresponding to two or three of the basic CSs. The combined CS shares the same total key parameters (initial values and design parameters associated with the three basic CSs) and this leads to a key space of 22392, the highest among the reported image encryption techniques. The combined CS is used to assist the operation of a proposed color image encryption scheme consisting of four sequential stages that perform compressive sensing, scrambling, DNA encoding, and diffusion, respectively. Simulation results validate the feasibility and robust security of the proposed encryption scheme.