Constructing a non-degeneracy 3D hyperchaotic map and application in image encryption

We designed an image encryption algorithm based on a non-degeneracy 3D chaotic map and a keyed strong S-Box, which is capable of encrypting color image with any size. First, we constructed a non-degeneracy 3D discrete hyperchaotic map (3D-DHCM), and based on it we constructed a keyed strong S-Box without fixed point, reverse fixed point or short period rings. The map is based on modular exponentiation operation, and its inverse function is the discrete logarithm problem. Finally, we applied blurring techniques to the plain image prior to encryption and employed permutation, confusion, and diffusion techniques to shuffle all pixels. Experimental and analytical results demonstrated that the NPCR and UACI are all close to their ideal values 99.6094070% and 33.4635070%, and the pixels of the cipher image are completely confused, which are all close to the ideal value 8. In addition, the chi-square values for encrypted images are significantly lower than before, with a maximum value of 255.1503. It is showed that the algorithm is superior to others in terms of its ability to encrypt images with any size and withstand common attacks.