Image Encryption based on Chaotic Map and Fractal Sorting Matrix

Since high-dimensional chaotic maps exhibit greater randomness, improved unpredictability, and successful resistance to repeated attacks, we introduce a novel 3D hyperchaotic Non-Linear Sine map (3D-NLS). We analyze this map through phase diagrams, bifurcation diagrams, and the NIST randomness test. The experimental findings indicate that the map exhibits potential ergodic behavior and a vast range of hyperchaotic phenomena. The sequence obtained from the proposed chaotic map is treated with a novel “Bit separation” procedure to double the size of the sequence. Further, the NIST test on the modified sequences passes all the pseudo-random properties. The modified chaotic sequences, in conjunction with the Fractal Sorting Matrix, are utilised to develop an Image Cryptography Scheme (ICS). The security analysis of the developed ICS method is performed on many images and compared with available state-of-the-art (SOTA) methods using several performance measures. The experimental findings exhibit the efficacy of the proposed ICS method in securely encrypting images, effectively safeguarding them against a broad range of attacks, such as brute force, differential, noise, and data loss.