A coupled chaotic four-block dual-prime framework for secure RGB image encryption

RGB images contain strong spatial and interchannel correlations, which make them unsuitable for direct protection through simple permutation or substitution alone. Many existing image-encryption methods rely on fixed S-boxes, directly quantized chaotic sequences, or complicated hybrid operations whose reversibility and key-stream separation are not always clearly established. This paper presents a coupled chaotic four-block dual-prime framework for RGB image encryption. The byte space is partitioned according to 61 + 61 + 67 + 67 = 256, and extended cyclic residue systems over Z₆₁ and Z₆₇ are used to construct dynamic substitution maps, a separate map being generated for each colour channel and encryption round. The substitution core keys two affine layers around inversion in F_2⁸ , fixing nonlinearity $$112$$ , differential uniformity 4 and algebraic degree $$7$$ by affine-equivalence invariance. The chaotic controller is combined with HMAC-SHA- $$256$$ -based domain separation and AES-256-CTR expansion to generate independent control material for whitening, cyclic shifts, global permutation, substitution, channel mixing, and diffusion. Each encryption round applies row and column shifts, a global byte permutation obtained as the rank vector of L independent $$64$$ -bit variates drawn from the permutation stream, channel-wise substitution, reversible cross-channel modular mixing, and forward-backward diffusion; an optional tiled diffusion mode bounds the causal horizon of every ciphertext byte, exchanging avalanche for tolerance of noise and data loss, and an encrypt-then-MAC wrapper supplies ciphertext authentication. Theoretical analysis establishes the bijectivity of the substitution maps and the exact reversibility of the complete encryption process. The construction is further supported by an ablation of the control-stream generator, the NIST SP 800-22 battery applied to the six domain-separated streams, an ensemble Lyapunov validation over key-derived initial conditions, and a same-hardware AES-256-CTR baseline. Experiments on six colour images, the 512 × 512 House, Baboon and F-16 benchmarks together with two aerial and satellite scenes and a dermoscopic melanoma photograph, one of them non-square, produced exact recovery, with MSE=0 , PSNR=∞ , and SSIM=1 . The cipher images achieved a mean entropy of 7.9994 and a mean absolute adjacent-pixel correlation of 0.001145. The mean plaintext-sensitivity NPCR and UACI were 99.610 and 33.466%, while the corresponding key-sensitivity values over the thirty-key ensemble were 99.608 and 33.465%. These results show strong statistical behaviour, effective diffusion, and sensitivity to small plaintext and key changes.