A new encryption scheme for RGB color images by coupling 4D chaotic laser systems and the Heisenberg group

This research focuses on introducing a novel algorithm for RGB image encryption. The proposed approach is a hybrid fusion of mathematical principles, namely group theory and chaos theory. It leverages the favorable characteristics of the Heisenberg subgroup of G L 2 n + 1 ( Z ) and a 4D chaotic laser system derived from the Lorenz-Haken equations. The algorithm aims to provide robust encryption by truncating four sequences from the 4D chaotic map. The initial Heisenberg matrix is generated using two input parameters, while the second matrix is constructed using two additional parameters.To enhance encryption efficiency, four square boxes of dimensions 16 × 16 are designed specifically for the 4D laser system. Each box contains cells that represent the rank of values relative to similar values in the same stream. Furthermore, the source image is divided into three monochromatic components. The foreground of the Heisenberg matrix is multiplied by each channel extracted from the source image. The encryption process proceeds with digram substitution, wherein two-pixel couples are replaced using the values stored in the four box squares. The first value is selected from box 1, followed by the second value from box 4. The remaining values needed to complete the rectangle are retrieved from boxes 2 and 3. For the subsequent digram, a circular rotation of the boxes is performed. The first value is obtained from box 2, the second value from box 3, and so forth, ensuring a continuous circular pattern. Finally, a second multiplication is applied, involving the second plane of the Heisenberg matrix and the result obtained in the previous stage. Experimental results demonstrate the algorithm’s effectiveness, exhibiting resistance to differential attacks, statistical attacks, and superior performance compared to existing encryption techniques.