An RGB Image Encryption Algorithm Based on Clifford Attractors with a Bilinear Transformation

Abstract

This work represents a new contribution in the field of encryption of RGB images, using Clifford attractors, which are the basic constituents of chaos theory, considering the dynamic behavior and random appearance, we generated three substitution boxes $K^{(1)}, K^{(2)},$ $K^{(3)}$ are enerated, each of them helps us to successively encrypt the channels of the original RGB image (red, green, blue). This random permutation is done by digram (sequence of two digits), which means that each pixel of the image to be encrypted with the red color will be replaced by the cell of position (i, j). In fact, the value of i is extracted from the channel $K^{(1)}$ with an increasing step and j is obtained from the channel $K^{(2)}$ of decreasing step. While the modification of the green matrix is done by the choice of the channels $K^{(2)}$ and $K^{(3)}$, on the other side, the blue color uses the channels $K^{(3)}$ and $K^{(1)}$ while following the same principle. On the purpose of making the present approach more efficient in the unreadable and fuzzy image while increasing the decryption time, we resort to the application of an XOR mask between each substituted matrix and each examined matrix with a bilinear transformation of different steps. Based on several criteria such as histogram, differential attacks, entropy, and correlation analysis, this approach has yielded experimental results that justify its performance and reliability in protecting data against any malicious attack. In addition, it marks its competence in front of other existing methods in the literature.