High-Dimensional Memristive Hyperchaos and RNA Rule Chains for Robust Color Image Encryption

This article presents a novel six-dimensional (6D) ideal flux-controlled memristive hyperchaotic system and its application to secure color image encryption. The proposed system extends a five-dimensional hyperchaotic system by incorporating a cosine-type memductance into its dynamics. Numerical simulations show that the proposed 6D memristive system substantially reduces the severe amplitude disparity present in the original system. Equilibrium and dissipativity analyses establish the system’s mathematical foundation, while phase portraits, Poincaré sections, and Lyapunov exponent spectra confirm its hyperchaotic dynamics. Furthermore, the system exhibits greater dynamical complexity, achieving a Lyapunov dimension of 4.2824, which exceeds that of the base model and other selected comparison systems. Based on these properties, a plaintext-dependent color image encryption scheme is developed using the SHA-512 hash of the full plaintext byte sequence, a 512-bit external secret key, and six secret offset parameters to generate sensitive initial conditions. The algorithm combines a 3D chaotic rule-chain RNA scrambling mechanism with adaptive RNA diffusion incorporating pixel-wise feedback. Evaluations demonstrate near-ideal entropy, near-zero adjacent-pixel correlations, NPCR and UACI values close to theoretical ideals, and exact lossless decryption. The scheme achieves a nominal key space of 2830, passes NIST SP 800-22 tests, and successfully resists chosen-plaintext and known-plaintext attacks. Furthermore, cropping and noise experiments demonstrate robustness against data loss and transmission corruption. Ultimately, the proposed memristive hyperchaotic system and its associated encryption scheme offer a promising solution for secure color image communication.