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In this paper, we propose a homogenized Chebyshev-Arnold map (HCAM) by homogenizing the linear coupling of Chebyshev map and Arnold map. The proposed HCAM has complex dynamical behaviors and can avoid the problems of the original Chebyshev map when used in image encryption. Based on the HCAM, we present a color image encryption algorithm that contains confusion and diffusion processes. In the confusion stage, we use the random chaotic matrix transform (RCMT) to randomize the shifting steps, which can eliminate the regular pattern of the original CMT and enhance the security level. In the diffusion stage, we use a SHA-512- and SHA-384-based fast pixel substitution scheme to perform the bit-level exclusive-or operation, which can obtain outstanding self-adaptiveness and high efficiency. The experimental results and security analysis demonstrate that the proposed algorithm has high level of security and robust to the potential attacks.

Homogenized Chebyshev-Arnold Map and its Application to Color Image Encryption