A novel hyperchaotic four-dimensional memristive log-logistic sine map with histogram equalisation for image encryption

Existing chaotic maps for image encryption often exhibit limited dynamic complexity, which can potentially compromise security. To address this limitation, this work introduces a novel four-dimensional Hyperchaotic Memristive Log-Logistic Sine Map (4D-HMLLSM). Its architecture integrates memristive dynamics with coupled logarithmic and sinusoidal nonlinearities, a design that generates complex hyperchaotic behaviour, supports a large key space, and promotes high unpredictability. An encryption scheme is presented that couples the 4D-HMLLSM with histogram equalisation of its chaotic sequences. In this approach, the 4D-HMLLSM drives permutation and diffusion, while histogram equalisation flattens the statistical signature of the key stream. The resulting encrypted images exhibit high information entropy, with average values for 1024×1024 images 7.9998. The scheme’s parameters provide a key space 2278 for effective resistance to brute-force attempts, while the average encryption time for a 1024×1024 image is approximately 0.7612 s. Security evaluations confirm the algorithm’s robust performance, achieving a number of pixels change rate value of an average 99.6083% and a unified average changing intensity value of an average 33.4683, indicating a strong diffusion characteristic. The system also demonstrates near-zero inter-pixel correlation, 1-bit change key sensitivity, and resilience to noise and cropping attacks.