Construction of a non-degeneracy 3D chaotic map and application to image encryption with keyed S-box

In recent years, chaotic maps have been widely used in image encryption. In order to solve the common problems in chaotic encryption schemes, we designed a novel image encryption scheme based on chaotic map and S-Box. (1) To solve the weaknesses in some 1D chaotic maps, we constructed a non-degenerate 3D hyper chaotic map (3D-HCM), and its dynamic analysis results demonstrated that, compared with 1D seed maps, the 3D-HCM has ergodicity, better randomness and a larger chaotic range. (2) To counteract dynamic degradation, we adjusted the exponent in real time in each iteration. (3) Based on 3D-HCM, we constructed a keyed S-Box without fixed point, reverse fixed point or short period ring. (4) To enhance the ability of the image encryption scheme for resisting common attacks, we blurred the plain image tinily before encryption and applied cross-plane permutation and diffusion to shuffle all the pixels. Experimental and security analysis results demonstrated that the proposed image encryption scheme has higher security, and it can resist to common attacks.