This paper proposes an image compression and encryption algorithm based on 3D Logistic-Sine-Memristor coupled map (3D-LSMCM), compressed sensing (CS) and the Game of Life scrambling with Semi-Tensor Product (STP-GoL) to solve the problems of computational redundancy and security vulnerability in image transmission. First, the 3D-LSMCM is initialized by using a hash function to generate a random chaotic sequence iteratively and it improves key unpredictability. Second, The Semi-Tensor Product (STP) measurement matrix constructed from these sequences significantly reduces storage requirements in CS whilst supporting lossless compression through arithmetic coding. STP technology enables flexible matrix dimension design, effectively lowering computational costs. Finally, STP is used to convert logical operations into matrix operations in the entire encryption process. The cryptographic technique consists of the STP-GoL scrambling, chaotic global scrambling with STP (STP-CG) and the chain XOR diffusion based on STP (STP-CXOR). Furthermore, theoretical analysis indicates that the computational complexity of this algorithm is expected to be reduced by approximately 28% compared with recent studies, while the average information entropy of the ciphertext reaches 7.9987. Overall, this study proposes a novel, secure and efficient image compression and encryption method, with its source code publicly available at https://github.com/Ssshou7/STP-GoL.

This paper studies the partial synchronization problem of multi-layer mixed valued logical networks (MMVLNs) under state-circulated control (SCC). In the proposed method, first, MMVLNs are transformed into multi-layer k-valued logical networks (MKVLNs) using two methods, dimension expansion and state constraint, and the state transition matrix is constructed using the algebraic state space representation (ASSR) method. Then, various synchronization scenarios in the multi-layer network are integrated, and the necessary and sufficient conditions for the partial synchronization of the MKVLNs under SCC are proposed. Subsequently, based on the SCC, the necessary and sufficient conditions for partial synchronization of the MKVLNs under different complex conditions (disturbances and asynchronous update) are investigated. Meanwhile, multiple graph-based algorithms for the largest control invariant set (LCIS) are developed during the partial synchronization research. Finally, several numerical examples verify the results of partial synchronization.

This study investigates the asynchronous controllability of non-homogeneous Markov switch generalized asynchronous Boolean control networks (NMHGABCNs) and random switching signals in these networks, aiming to follow a non-homogeneous Markov process. The controllability of the proposed networks is achieved using the discrepancy between the Markov chain mode and the control mode. Assisted by the semi-tensor product (STP), the algebraic forms of the NMHGABCNs are obtained, and the sufficient and necessary criteria for their asynchronous controllability are derived. The effectiveness of controllability is demonstrated through two examples, which validate the theoretical results.

To conquer the limitations of traditional watermarking algorithms in adaptively embedding watermarks and to address the constrained feature representation capability of convolution-based methods, this paper introduces a robust deep learning watermarking model named FreqTransNet. This model effectively integrates convolutional modules, Transformer structures, and frequency-domain transformations to enhance its ability in both capturing multi-scale image features and improving robustness. Specifically, the self-attention mechanism inherent in the Transformer effectively models long-range dependencies and global context, thereby improving the model's representation of complex structures. The integration of frequency-domain transformations also mitigates spatial distortions, further amplifying resistance to interference. The extensive experimental results reveal that FreqTransNet surpasses existing state-of-the-art deep learning watermarking approaches in both visual quality and robustness. Compared to the best-performing baseline, FreqTransNet achieves a notable 3.09 dB enhancement in PSNR (from 47.46 dB to 50.55 dB). Additionally, it consistently maintains extraction accuracy exceeding 97% in the presence of various attack scenarios, highlighting its practical applicability and stability in real-world applications.

This article introduces a memristor-based neural network with bidirectional cyclic constructed from square wave pulse functions. Additionally, we design an image encryption and compression network framework incorporating a self-attention mechanism based on this memristor neural network. Specifically, this study introduces a novel model of a high-dimensional multiscroll memristor neural network (MMNN) that incorporates three neurons and a synapse made from memristive elements. Its complex dynamic behavior is analyzed in depth. Theoretical analysis and numerical simulations demonstrate that the proposed MMNN can generate an unlimited number of hyperchaotic multiscroll attractors and various other types of dynamics, which can be fine-tuned by modifying the system’s parameters or initial conditions. Additionally, a simulated equivalent circuit for MMNN proves the validity and practicality of the multiscroll attractor behavior. Finally, an image encryption and compression network framework based on end-to-end and MMNN and the self-attention mechanism is proposed, called SAECNet. Extensive performance evaluation highlights the system’s high accuracy in compression and reconstruction, strong encryption capabilities, and solid defense against potential attacks.

Abstract This paper proposes a Boolean network model with high dimensional chaos driving and investigates the synchronization of the chaos‐driven Boolean network with a semi‐tensor product. In order to protect the privacy and ensure the security of image transmission, the synchronization results are utilized in the image cryptosystem to achieve compression and encryption. First, the driving chaos system is coupled with multiple local systems and synchronized with the transmitted encrypted signals. Second, the Boolean network is driven and synchronized with derived chaos signals. Finally, images are encrypted and compressed with chaos‐driven Boolean network signals in the transmitter, and then decrypted and recovered with synchronized chaos and Boolean network signals in the recipient. Because of the complexities of high dimensional chaos and Boolean network, the proposed cryptosystem has good security in the secure communication and image process.

Abstract This paper models a networked coupling chaotic system with a fractional‐like local map based on network topology and fractional theory. The proposed model contains more system parameters and a more relaxed coupling relationship. The entropy analysis also shows that the proposed model is more sensitive to the changes in the coupling parameter. Based on this model, an effective image cipher system is designed using universal scrambling and diffusion based on DNA encoding. The proposed method utilizes the generated pseudo‐random signals from the networked chaotic map. The secret keys can be generated in parallel and the security is also improved due to the rise of complexity of the new chaotic map. Analysis and simulations confirm that the new chaotic map as well as the DNA encoding technology improves the effectiveness and robustness of the proposed encryption algorithm.

In this study, the authors advance a novel multiple images encryption algorithm using the coupled map lattices (CML) system and DNA encoding. The algorithm adopts a permutation‐diffusion structure. First, the initial values and parameters of the CML system are determined by given values and SHA hash key of original images. Secondly, several plain images are grouped and permuted among groups. Next, different groups are combined into eight blocks of the same size, each of which is independently coded and scrambled. Thirdly, in the diffusion process, a DNA‐level multiplication operation is redefined, and required key matrices are resulted from a small key connected with original images. Finally, dynamic DNA coding/decoding is adopted, and the coding and decoding rules are determined by original images. The evaluation of the simulation experiment shows that the proposed algorithm is safe and feasible, and has good encryption effect.

This paper presents the module-phase synchronization for a class of neural networks with weights identification and time delays. In module-phase synchronization, complex-valued node states are taken into consideration. The topology weights considered here are uncertain and the time delays are bounded. By constructing a Lyapunov-Krasovskii functional and employing adaptive feedback control, sufficient conditions for module-phase synchronization are derived. After the general synchronization theory, the synchronization with topology identification is discussed. Finally, pertinent examples are given to demonstrate the effectiveness of the obtained results.

In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.

In this paper, the synchronizations of Boolean networks with different update schemes (synchronized Boolean networks and asynchronous Boolean networks) are investigated. All nodes in Boolean network are represented in terms of semi-tensor product. First, we give the concept of inner synchronization and observe that all nodes in a Boolean network are synchronized with each other. Second, we investigate the outer synchronization between a driving Boolean network and a corresponding response Boolean network. We provide not only the concept of traditional complete synchronization, but also the anti-synchronization and get the anti-synchronization in simulation. Third, we extend the outer synchronization to asynchronous Boolean network and get the complete synchronization between an asynchronous Boolean network and a response Boolean network. Consequently, theorems for synchronization of Boolean networks and asynchronous Boolean networks are derived. Examples are provided to show the correctness of our theorems.