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To achieve efficient and compatible encryption of color-gray multi-image and 3D models, an encryption scheme based on multilevel confusion and hyperchaotic map is proposed in this paper. First, the ISL-HMC hyperchaotic map is employed to generate pseudorandom sequences of the confusing scheme, and its rich dynamical behavior is demonstrated through phase diagrams under different parameters, Lyapunov exponents, and NIST results. Second, the images are subjected to data processing, where multiple color-gray multi-size images are merged into a single image and the 3D model is converted into a 2-dimensional matrix. Multi-level confusion is performed next and consists of three parts: pixel point confusion within a 66-pixel block, inter-block confusion of 33-pixel blocks, and confusion of all pixel points. Finally, bi-directional diffusion is performed, which effectively improves the unpredictability and attack resistance of encrypted data. The simulation results demonstrate that the proposed encryption scheme specifies excellent encryption performance and dependability, and is also able to maintain good decryption results. At the same time, the proposed scheme can flexibly handle different models of data, showing excellent compatibility and adaptability, and providing an innovative solution for the secure transmission of multimedia information.

Initial condition-dominated offset boosting provides a special channel for coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. Typically, the distance between two attractors or two petals of an attractor is fixed. Moreover, any chaotic signal and sequence need to be modified with amplitude and offset for a real application. In this paper, an initially-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. In this case, all the coexisting attractors are arranged in phase space in a direction defined by the initial value and the distance between two petals of any double-scroll orbit is adjusted. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation.

Since the current general image encryption algorithms based on chaotic systems and classical permutation diffusion structures typically suffer from stochastic degradation, simple algorithm structures, and reduced execution efficiency when dealing with images with large data, this paper proposes a new multiprocess image encryption algorithm based on a new hyperchaotic coupled sine map. To begin with, by performing dynamic analyses of the map, including equilibrium points, bifurcation diagrams, Lyapunov exponent diagrams, and phase diagrams, associated performance analyses show high spectral entropy (SE) values and permutation entropy (PE) values. Meanwhile, sequences generated by the proposed map are able to pass the NIST randomness test, which shows its suitability for the design of encryption algorithms. Then, a chaos-based image encryption algorithm is proposed in this paper: In the preprocessing stage, the images are sparsely sampled using a compressed-sensing method; in the permutation stage, the image is decomposed into eight bit-plane images containing only 0s and 1s and a clockwise cyclic shift operation based on a chaotic sequence is applied in each bit-plane image to achieve a bit-level permutation effect; in the diffusion stage, the block DNA random computing is applied to the permuted image to modify the pixel values and the final cipher image is obtained. In addition, the initial value of the map is determined by the preset initial value, user-defined strings, and the Hash value of the plain image, where the Hash value of the plain image is calculated by the SHA-256 algorithm. Finally, the analysis of the algorithm demonstrates that the algorithm exhibits extremely strong plaintext correlation externally and excellent encryption performance in terms of attack resistance and execution efficiency.

This study presents 2D-PECLSM, a novel hyperchaotic map that integrates the 2D Logistic and the Sine map to enhance chaotic behavior. We propose a new image encryption algorithm (IEA) that leverages this map alongside fractal theory and global cross-coupled diffusion techniques. The 2D-PECLSM generates two essential chaotic sequences for secure encryption and based on this map associated with fractal theory processes. Each pixel of the plain image is effectively confused using a fractal matrix and globally diffused, ensuring robust protection of visual data. Experimental results demonstrate that the 2D-PECLSM-based IEA significantly outperforms the existing state-of-the-art IEAs, highlighting its potential as a powerful tool for enhancing image security against digital threats. This work contributes valuable insights to the field of cryptography, emphasizing the need for innovative approaches to safeguard sensitive visual information.

In recent years, some efforts have been devoted to nonlinear dynamics of fractional discrete-time systems. A number of papers have so far discussed results related to the presence of chaos in fractional maps. However, less results have been published to date regarding the presence of hyperchaos in fractional discrete-time systems. This paper aims to bridge the gap by introducing a new three-dimensional fractional map that shows, for the first time, complex hyperchaotic behaviors. A detailed analysis of the map dynamics is conducted via computation of Lyapunov exponents, bifurcation diagrams, phase portraits, approximated entropy and $C_0$ complexity. Simulation results confirm the effectiveness of the approach illustrated herein.