Chaos-driven design of highly nonlinear S-boxes for secure and efficient lightweight image encryption

Substitution boxes (S-boxes) are a type of nonlinear component which provides confusion and robustness to cryptanalysis in modern symmetric ciphers. Due to the requirements of lightweight encryption (LWE) systems to achieve a high degree of security while minimizing computational overhead, we propose chaos-driven constructions of highly nonlinear S-boxes using permutations of the logistic map to create bijective and statistically randomized substitution patterns. We have extensively evaluated the cryptographic strength of our proposed S-box using standard metrics, including Nonlinearity (NL), Strict Avalanche Criteria (SAC), Bit Independence Criteria (BIC), Balancedness, Differential Approximation Probability (DAP), and Linear Approximation Probability (LAP). Our proposed S-box has demonstrated competitive performance with existing S-boxes by achieving average nonlinearity values of 112.75 and SAC/BIC values very close to ideal thresholds. To demonstrate practical applicability, we have integrated the proposed S-box into an image encryption scheme, where statistical analyses confirm near ideal entropy and negligible pixel correlation, demonstrating strong resistance to both statistical and differential attacks. Additionally, our proposed scheme has achieved comparable levels of security within a smaller number of rounds than traditional methods, thus enhancing both computational efficiency and throughput, making it suitable for real-time and resource-constrained multimedia security applications.