Multidirectional chaos-based encryption scheme using the ABC fractional derivative for secure multimedia data transmission

In this work, we studied a non-equilibrium point chaotic system with single signum function nonlinearity and multidirectional parameters under the Atangana-Baleanu-Caputo (ABC) fractional derivative. The control parameters were used to generate chaotic signals in multiple directions, such as a 1D line, 2D lattice, and 3D grid. The dynamical properties of the system were analyzed by graphical results, phase plots, and bifurcation plots. The ABC fractional analog circuit was designed using resistors, capacitors, operational amplifiers, and frequency domain approximations in the sense of ABC to ensure the system's feasibility. Random numbers were generated to evaluate the randomness of the system. These numbers were verified by the NIST test suite, and the test results established the strong unpredictability of the system. Text, video, and image files were the components that made up multimedia data, and as the usage of multimedia data sent over the internet continues to grow, so does the need for secure multimedia data. A significant topic in information security is the merging of chaos theory with encryption. For this purpose, we suggested a nonlinear 3D multidirectional chaos-based simple encryption scheme, in which a 3D multidirectional chaotic system was employed for position and value transformation. The proposed image encryption scheme employs a multidirectional chaotic system to enhance randomness and security, beginning with histogram equalization to uniformly distribute pixel intensities. This is followed by sequential row and column rotations and a final exclusive OR (XOR) operation, effectively achieving strong confusion and diffusion in the encrypted image. We computed several metrics to assess the quality of an image, including mean square error (MSE), peak signal-to-noise ratio (PSNR), entropy, the correlation coefficient, and image distance. NPCR (number of pixels change rate) and UACI (unified average change intensity) are standard statistical measures used to evaluate the effectiveness of image encryption, particularly in resisting differential attacks.