Hexadecimal permutation and 2D cumulative diffusion image encryption using hyperchaotic sinusoidal exponential memristive system

The performance of chaos-based image encryption (IE) highly depends upon chaotic system's complexity and diversity; and IE algorithm's permutation and diffusion strategies. Existing chaotic systems often face limitations in achieving sufficient complexity and dynamical richness, limiting their effectiveness in high unpredictability. To overcome these limitations, a novel hyperchaotic 2D sinusoidal exponential memristive system (2D-SEMS) is designed and validated through a hardware circuit. Additionally, a novel hexadecimal permutation and two dimensional (2D) cumulative diffusion IE (Hp2DCd-IE) is contrived using the 2D-SEMS. The 2D-SEMS is built upon two introduced designs of simplified exponential discrete memristors (SEDMs), forming the basis of its dynamic and chaotic framework. The 2D-SEMS validated by comparison with existing maps through an evaluation in terms of Lyapunov exponents (LE1, LE2), sample entropy (SE), correlation dimension (CD), and Kolmogorov entropy, and (KE), which are measured on average as 4.2889, 0.0250, 1.3204, 1.7599, and 1.6428. The Hp2DCd-IE is corroborated across wide range of cryptanalysis by comparing with the existing IE algorithms. The results demonstrate that the Hp2DCd-IE has high shuffling and manipulating performance thanks to complexity and diversity of the 2D-SEMS.