The 3D modular chaotic map to digital color image encryption

The cryptography is one of the important security mechanisms for the confidentiality, integrity and authentication of text and multimedia data. This study proposes a five-step color images encryption method in 3D space based on substitution and permutation operations for diffusion and confusion properties. To transform the image to a 3D space, in the first step, the red, green, and blue spectra of the color image are subdivided into the sub-images, in this case the rows, columns, and the number of sub-images are specified in 3D axis coordinates for carrying out 3D substitution and permutation operations. In the second and fifth steps of encryption, 3D substitution operations are performed by using logical exclusive OR and circular shift operators on the sub-images pixels. In the middle steps, the permutation operations of sub-images pixels are accomplished with the help of 3D permutation and 3D modular chaotic map. The 3D modular chaotic presented in this research is multiplicative reversible based on modular arithmetic, which improves speed, period, and space of the key. The proposed method, with the help of permutations and substitutions in 3D space, improves the performance parameters and increases the key space in comparison to other image cryptography researches. (C) 2019 Elsevier B.V. All rights reserved.