Spatiotemporal chaos in a recursively permuted lattice with dual maps on odd and even sites and its application in image encryption

Abstract This paper proposes a new spatiotemporal chaotic system called the recursively permuted cross coupled map lattice (RPCCML) and applies it to image encryption. The system extends the conventional cross coupled map lattice. It introduces a one dimensional sinusoidal power modulated logistic remainder map (1DSPLR map) as the local map. It uses a recursive permutation matrix constructed by Latin square based block substitution as a time varying index table. It also adopts an odd–even split dual map structure at the lattice level. Odd and even sites use different local maps and are updated in a time interleaved manner. The joint design of the local dynamics and the coupling topology yields stronger chaotic behavior, more uniform state coverage and lower spatial mutual information over a wide parameter range. This improves the suitability of the RPCCML for secure communication. Based on this system, an image encryption algorithm is developed. Chaos driven nonlinear table lookup and rank based mapping first achieve simultaneous permutation of pixel positions and gray levels and provide initial diffusion. A three branch multi phase reordering and chained diffusion process is then performed in the integer domain. This rapidly propagates a single pixel disturbance over the entire ciphertext. Simulation results demonstrate the advantages of the proposed algorithm in terms of security, robustness and computational efficiency.