Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaotic system and a 2D sinusoidally constrained polynomial hyper-chaotic map (2D-SCPM). Then, we elaborately developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM (MIEA-FCSM). The introduction of the fractional-order 3D Lorenz chaotic system with the fourth parameter not only enables MIEA-FCSM to have a significantly large key space but also enhances its overall security. Compared with recent alternatives, the structure of 2D-SCPM is simpler and more conducive to application implementation. In our proposed MIEA-FCSM, multi-channel fusion initially reduces the number of pixels to one-sixth of the original. Next, after two rounds of plaintext-related chaotic random substitution, dynamic diffusion, and fast scrambling, the fused 2D pixel matrix is eventually encrypted into the ciphertext one. According to numerous experiments and analyses, MIEA-FCSM obtained excellent scores for key space ($2^{541}$), correlation coefficients (<0.004), information entropy (7.9994), NPCR (99.6098%), and UACI (33.4659%). Significantly, MIEA-FCSM also attained an average encryption rate as high as 168.5608 Mbps. Due to the superiority of the new fractional-order chaotic system, 2D-SCPM, and targeted designs, MIEA-FCSM outperforms many recently reported leading image encryption algorithms.

Chaos-based encryption is promising for safeguarding digital images. Nonetheless, existing chaos-based encryption algorithms still exhibit certain shortcomings. Given this, we propose a novel multi-channel image encryption algorithm that leverages pixel reorganization and hyperchaotic maps (MIEA-PRHM). Our MIEA-PRHM algorithm employs two hyperchaotic maps to jointly generate chaotic sequences, ensuring a larger key space and better randomness. During the encryption process, we first convert input images into two fused matrices through pixel reorganization. Then, we apply two rounds of scrambling and diffusion operations, coupled with one round of substitution operations, to the high 4-bit matrix. For the low 4-bit matrix, we conduct one round of substitution and diffusion operations. Extensive experiments and comparisons demonstrate that MIEA-PRHM outperforms many recent encryption algorithms in various aspects, especially in encryption efficiency.

Nowadays, the utilization of memristors to enhance the dynamical properties of chaotic systems has become a popular research topic. In this paper, we present the design of a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM) by utilizing the cross-coupling of two TiO${}_2$ memristors. The dynamical properties of the 2D-MPHM were investigated using Lyapunov exponents, bifurcation diagrams, and trajectory diagrams. Additionally, Kolmogorov entropy and sample entropy were also employed to evaluate the complexity of the 2D-MPHM. Numerical analysis has demonstrated the superiority of the 2D-MPHM. Subsequently, the proposed 2D-MPHM was applied to a multi-channel image encryption algorithm (MIEA-MPHM) whose excellent security was demonstrated by key space, key sensitivity, plaintext sensitivity, information entropy, pixel distribution, correlation analysis, and robustness analysis. Finally, the encryption efficiency of the MIEA-MPHM was evaluated via numerous encryption efficiency tests. These tests demonstrate that the MIEA-MPHM not only possesses excellent security but also offers significant efficiency advantages, boasting an average encryption rate of up to 87.2798 Mbps.

As digital images proliferate across open networks, securing them against unauthorized access has become imperative. However, many recent image encryption algorithms are limited by weak chaotic dynamics and inadequate cryptographic design. To overcome these, we propose a new 2D coupling-enhanced cubic hyperchaotic map with exponential parameters (2D-CCHM-EP). By incorporating exponential terms and strengthening interdependence among state variables, the 2D-CCHM-EP exhibits strict local expansiveness, effectively suppresses periodic windows, and achieves robust hyperchaotic behavior, validated both theoretically and numerically. It outperforms several recent chaotic maps in key metrics, yielding significantly higher Lyapunov exponents and Kolmogorov–Sinai entropy, and passes all NIST SP 800-22 randomness tests. Leveraging the 2D-CCHM-EP, we further develop a hierarchical significance-aware multi-image encryption algorithm (MIEA-CPHS). The core of MIEA-CPHS is a hierarchical significance-aware encryption strategy that decomposes input images into high-, medium-, and low-significance layers, which undergo three, two, and one round of vector-level adaptive encryption operations. An SHA-384-based hash of the fused data dynamically generates a 48-bit adaptive control parameter, enhancing plaintext sensitivity and enabling integrity verification. Comprehensive security analyses confirm the exceptional performance of MIEA-CPHS: near-zero inter-pixel correlation (7.999), and superior plaintext sensitivity (NPCR $\approx 99.61\%$, UACI $\approx 33.46\%$). Remarkably, the hierarchical design and vectorized operations achieve an average encryption throughput of 87.6152 Mbps, striking an outstanding balance between high security and computational efficiency. This makes MIEA-CPHS highly suitable for modern high-throughput applications such as secure cloud storage and real-time media transmission.