Designing digital image encryption using 2D and 3D reversible modular chaotic maps.

This paper presents a gray level image encryption method based on permutation operation and diffusion operation on image pixels. In diffusion operation, the image is subdivided into equal size sub-images, and the pixels of each sub-image are changed with the help of logical operators and circular shifts. In the permutation operation, the image is first divided into four bit-plate images, and the pixels of each bit-plate image are permuted in parallel by chaotic maps. In this research, reversible two-dimensional and three-dimensional chaotic maps based on modular mathematics are proposed to increase the key space, improve speed and period. The key space exponentially is increased as compared to standard chaotic maps through defining the reversibility in residue matrices, chaotic map in 3D space and changing the key in each round. In the proposed modular 3D chaotic map, the 2D image is first converted into 3D space, and then mapping operations are carried out for permuting the pixels into 3D space. The proposed encryption method for images improves the standard parameters of evaluation such as entropy, adjacent pixel correlations, histogram, and expanded key space. [ABSTRACT FROM AUTHOR]