Discrete chaotic systems based on memristors exhibit excellent dynamical properties and are more straightforward to implement in hardware, making them highly suitable for generating cryptographic keystreams. However, most existing memristor-based chaotic systems rely on a single memristor. This paper introduces a novel discrete chaotic system employing dual memristors, named the 3D memristive cubic map with dual discrete memristors (3D-MCM). The 3D-MCM system demonstrates richer and more intricate dynamical behaviors compared to its single-memristor counterparts, as verified through bifurcation diagrams, Lyapunov exponent spectra, and complexity analyses. Notably, the system exhibits coexisting attractors, substantially enhancing its dynamical complexity. Hardware implementation of the 3D-MCM attractors confirms its feasibility for industrial applications. To illustrate the system’s potential in encryption tasks, this study integrates the quaternary-based permutation and dynamic emanating diffusion (QPDED-IE) scheme for image encryption with the 3D-MCM.Experimental results demonstrate that the QPDED-IE scheme based on the 3D-MCM exhibits strong diffusion and confusion properties, effectively resisting cryptanalytic attacks.

Images are widely used in social networks, necessitating efficient and secure transmission, especially in bandwidth-constrained environments. This paper aims to develop a color image encryption algorithm that enhances security while optimizing computational efficiency. A novel parallel color image encryption algorithm based on the 2D Logistic-Rulkov neuron map (2D-LRNM) is proposed. In this approach, the three channels of the color image are first separated. Cross-channel information interaction is introduced to form three new channels, which are then processed in parallel. During the encryption process of each channel, a block-wise parallel encryption mechanism is applied, ensuring simultaneous encryption of each block. This block-wise strategy effectively leverages parallel computing resources and balances the task load. To meet the demand for a large number of keystreams during encryption, the 2D-LRNM is introduced. It combines the simplicity and chaotic properties of the Logistic map with the multi-timescale dynamics and neurodynamic behaviors of the Rulkov map. By overcoming the dimensional limitations inherent in the single Logistic map, this approach extends the system to a two-dimensional framework, significantly increasing the complexity of chaotic behavior and improving its unpredictability. Experimental results demonstrate that the proposed encryption algorithm achieves high security and reduces computation time by approximately 83.3%.

We propose an Iterative Mean Filter (IMF) to eliminate the salt-and-pepper noise. IMF uses the mean of gray values of noise-free pixels in a fixed-size window. Unlike other nonlinear filters, IMF does not enlarge the window size. A large size reduces the accuracy of noise removal. Therefore, IMF only uses a window with a size of 3×3. This feature is helpful for IMF to be able to more precisely evaluate a new gray value for the center pixel. To process high-density noise effectively, we propose an iterative procedure for IMF. In the experiments, we operationalize Peak Signal-to-Noise Ratio (PSNR), Visual Information Fidelity, Image Enhancement Factor, Structural Similarity (SSIM), and Multiscale Structure Similarity to assess image quality. Furthermore, we compare denoising results of IMF with ones of the other state-of-the-art methods. A comprehensive comparison of execution time is also provided. The qualitative results by PSNR and SSIM showed that IMF outperforms the other methods such as Based-on Pixel Density Filter (BPDF), Decision-Based Algorithm (DBA), Modified Decision-Based Untrimmed Median Filter (MDBUTMF), Noise Adaptive Fuzzy Switching Median Filter (NAFSMF), Adaptive Weighted Mean Filter (AWMF), Different Applied Median Filter (DAMF), Adaptive Type-2 Fuzzy Filter (FDS): for the IMAGESTEST dataset – BPDF (25.36/0.756), DBA (28.72/0.8426), MDBUTMF (25.93/0.8426), NAFSMF (29.32/0.8735), AWMF (32.25/0.9177), DAMF (31.65/0.9154), FDS (27.98/0.8338), and IMF (33.67/0.9252); and for the BSDS dataset – BPDF (24.95/0.7469), DBA (26.84/0.8061), MDBUTMF (26.25/0.7732), NAFSMF (27.26/0.8191), AWMF (28.89/0.8672), DAMF (29.11/0.8667), FDS (26.85/0.8095), and IMF (30.04/0.8753).