An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption

In chaos-based image encryption, better performance of the chaotic system represents higher security of the encryption algorithm, and the Lyapunov exponent (LE) is an important measure to evaluate the chaotic performance. In this paper, an n-dimensional(n-D) polynomial modulo chaotic map (nD-PMCM) is proposed as a general model, whose range of Lyapunov exponent is controlled by the system parameters and the robust chaotic behavior with the desired complexity can be obtained. And an instantiated 2D-PMCM is constructed by setting the corresponding parameters in nD-PMCM, which exhibits superior chaotic performance compared to other chaotic maps. Then a novel color image encryption scheme based on the 2D-PMCM is also constructed, which mainly uses cross-plane cyclic shift permutation and cross-plane XOR diffusion. Different from the traditional encryption scheme with separate processing of color planes, the cross-plane operation disrupts the correlation between color image planes and has higher encryption efficiency due to the ability to disrupt the pixel position while also changing the pixel value. The experimental simulation results show that this encryption scheme has better security and encryption effects.