The coupled Kaplan–Yorke-Logistic map for the image encryption applications

Chaos has practical significance in various domains, including the stock market, quantum physics, communication networks, disease diagnosis, cosmic events, and digital data security. Chaotic maps are widely utilised for encrypting multimedia data for secure communication due to their sensitivity to initial conditions and unpredictability. However, some chaotic maps suffer from weak chaotic dynamics that can make them vulnerable to certain types of attacks, limiting their effectiveness in sensitive applications such as encryption or secure communication in military operations and personal data. This research study proposes a novel nonlinear discrete chaotic map termed a coupled Kaplan–Yorke-Logistic map. By coupling chaotic maps, the Kaplan–Yorke map and the Logistic map, we have significantly enhanced key features such as the length of chaotic orbits, output distribution, and the security of chaotic sequences. An empirical assessment of the proposed coupled Kaplan–Yorke-Logistic map in terms of several measures such as bifurcation diagrams, phase diagrams, Lyapunov exponent analysis, permutation entropy, and sample entropy shows promising ergodicity and a diverse range of hyperchaotic behaviours compared to several recent chaotic maps. Consequently, the proposed map is utilised to develop an efficient image encryption algorithm. The encryption algorithm employs a methodology that utilises simultaneous confusion and diffusion processes aiming to significantly reduce the computation time for encryption and decryption processes for real-time applications without compromising the security parameters. A thorough assessment of the proposed image encryption algorithm is performed on a variety of image datasets by utilising multiple cryptanalysis methods, including key space analysis, information entropy, correlation coefficient evaluation, differential attack, key sensitivity testing, histogram analysis, computational time analysis, and occlusion and noise attacks. Comparative analysis with the state-of-the-art methods indicates the superiority of the proposed algorithm.