Image encryption is an effective way to protect image data. However, existing image encryption algorithms are still unable to strike a good balance between security and efficiency. To overcome the shortcomings of these algorithms, an image encryption algorithm based on plane-level image filtering and discrete logarithmic transformation (IEA-IF-DLT) is proposed. By utilizing the hash value more rationally, our proposed IEA-IF-DLT avoids the overhead caused by repeated generations of chaotic sequences and further improves the encryption efficiency through plane-level and three-dimensional (3D) encryption operations. Aiming at the problem that common modular addition and XOR operations are subject to differential attacks, IEA-IF-DLT additionally includes discrete logarithmic transformation to boost security. In IEA-IF-DLT, the plain image is first transformed into a 3D image, and then three rounds of plane-level permutation, plane-level pixel filtering, and 3D chaotic image superposition are performed. Next, after a discrete logarithmic transformation, a random pixel swapping is conducted to obtain the cipher image. To demonstrate the superiority of IEA-IF-DLT, we compared it with some state-of-the-art algorithms. The test and analysis results show that IEA-IF-DLT not only has better security performance, but also exhibits significant efficiency advantages.

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.

Medical images demand robust privacy protection, driving research into advanced image encryption (IE) schemes. However, current IE schemes still encounter certain challenges in both security and efficiency. Fractional-order Hopfield neural networks (HNNs) demonstrate unique advantages in IE. The introduction of fractional-order calculus operators enables them to possess more complex dynamical behaviors, creating more random and unpredictable keystreams. To enhance privacy protection, this paper introduces a high-performance medical IE scheme that integrates a novel 4D fractional-order HNN with a differentiated encryption strategy (MIES-FHNN-DE). Specifically, MIES-FHNN-DE leverages this 4D fractional-order HNN alongside a 2D hyperchaotic map to generate keystreams collaboratively. This design not only capitalizes on the 4D fractional-order HNN’s intricate dynamics but also sidesteps the efficiency constraints of recent IE schemes. Moreover, MIES-FHNN-DE boosts encryption efficiency through pixel bit splitting and weighted accumulation, ensuring robust security. Rigorous evaluations confirm that MIES-FHNN-DE delivers cutting-edge security performance. It features a large key space ($2^{383}$), exceptional key sensitivity, extremely low ciphertext pixel correlations (7.999 bits), uniform ciphertext pixel distributions, outstanding resistance to differential attacks (with average NPCR and UACI values of $99.6096\%$ and $33.4638\%$, respectively), and remarkable robustness against data loss. Most importantly, MIES-FHNN-DE achieves an average encryption rate as high as 102.5623 Mbps. Compared with recent leading counterparts, MIES-FHNN-DE better meets the privacy protection demands for medical images in emerging fields like medical intelligent analysis and medical cloud services.

Amid growing threats of image data leakage and misuse, image encryption has become a critical safeguard for protecting visual information. However, many recent image encryption algorithms remain constrained by trade-offs between security, efficiency, and practicability. To address these challenges, this paper first proposes a novel two-dimensional variable fractional-order coupled quadratic hyperchaotic map (2D-VFCQHM), which incorporates a state-dependent dynamic memory effect, wherein the fractional-order is adaptively determined at each iteration by the mean of the system’s current state. This mechanism substantially enhances the complexity and unpredictability of the underlying chaotic dynamics. Building upon the superior hyperchaotic properties of the 2D-VFCQHM, we further develop a high-performance image encryption algorithm that integrates a novel fusion strategy within a dynamic vector-level diffusion-scrambling framework (IEA-VMFD). Comprehensive security analyses and experimental results demonstrate that the proposed algorithm achieves robust cryptographic performance, including a key space of $2^{298}$, inter-pixel correlation coefficients below 0.0018, ciphertext entropy greater than 7.999, and near-ideal plaintext sensitivity. Crucially, the algorithm attains an encryption speed of up to 126.2963 Mbps. The exceptional balance between security strength and computational efficiency underscores the practical viability of our algorithm, rendering it well-suited for modern applications such as telemedicine, instant messaging, and cloud computing.

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.

The magnetization mechanism of Co-doped BaTiO₃ ultrathin films is a subject of debate, which results in difficulties with the design of new multiferroics based on BaTiO₃ matrixes. With the aid of a first-principles approach, it was observed that when the interstitial site and Ti vacancy were filled with Co, the configuration behaved in a nonmagnetic manner, indicating the significance of the Co content. Moreover, in the case of Co substituting two neighboring Ti atoms, when a direct current field was applied in the [100] direction, the magnetic domains excluding those in the [100], [010], and [001] directions were directed away. Further, the magnetoelectric constant was evaluated at ~449.3 mV/cmOe, showing strong magnetoelectric coupling at room temperature. Clearly, our study indicates that strict control of Ba, Ti, O, and Co stoichiometry can induce an electric and magnetic field conversion in two-dimensional BaTiO₃ and may provide a new candidate for single-phase multiferroics for application in next-generation multifunctional devices.