A New Image Encryption Algorithm Using Homogenized Chebyshev-Arnold Map

In this paper, a Homogenized Chebyshev-Arnold Map (HCAM) is firstly proposed by homogenizing the linear coupling of Chebyshev map and Arnold map. The proposed HCAM can avoid two problems of origin Chebyshev map which lead to potential safety hazard in image encryption algorithm: one is discontinuous choices of initial values for chaotic property, the other is nonuniform value distribution of generated sequences. Next, based on the HCAM, we propose a novel image encryption algorithm that consists of two parts: confusion and diffusion. For the confusion part, we enhance the chaotic magic transform (CMT) to adjust the shifting times of selected pixels with respect to different plaintext images for higher security level without extra time cost. For the diffusion part, to maintain the low runtime of our algorithm, a bit-operation based pixel substitution scheme is presented. Thereinto, the selection of pixels and certain values for substitution in these two parts are both decided by the HCAM. Simulation results and security analysis have been carried out and demonstrate the security and efficiency of our proposed algorithm in comparison with previous schemes.