Difference operators and generalized discrete fractional transforms in signal and image processing

Robust structural similarity index measure for images with non-Gaussian distortions

A variable-order fractional memristor neural network: Secure image encryption and synchronization via a smooth and robust control approach

Generating grid double-scroll attractors from magnetized SC-CNN and its application in image encryption

Memristor is a kind of resistance with a memory function and its special properties decide its broad prospect for application. At present, the focus and difficulty of the research in memristor lie in the establishment of new models and related applications. Therefore, in this paper a new continuous and smooth memristor model is put forward first and the correctness of this new model is proved through the study in the phase trajectory relationship between voltage and current. Then based on Chua’s circuit, a new fifth-order hyper-chaotic circuit including two new memristor models is designed and the dimensionless mathematical model is deduced. By the classical nonlinear method of circuit analysis, the dissipation of the new system is put into study in this paper. It is proved through numerical simulation, bifurcation diagram, Lyapunov spectrum that the new system has its unique dynamical behavior. At last, chaotic sequence of the new system is used to encrypt the image and the encrypted histogram, the correlation and anti-attack capability between adjacent pixels and the key sensitivity are emphatically analyzed. It turns out that when applied to image encryption, the newly proposed memristor chaotic system has relatively high safety performance.

A new method of color image encryption is proposed in this paper, with the combination of a two-dimensional (2D) Henon-like chaotic map and compressed sensing for better performance. A sinusoidal function is introduced into the 2D Henon map for increasing randomness. Image encryption algorithm includes three procedures: compression of a color image through the Bernoulli observation matrix, encryption of the compressed image by 2D-Henon map with sinusoidal factor, and reconstruction of color image based on compressed sensing algorithm of orthogonal matching pursuit (OMP). Numerical simulation shows that the proposed encryption algorithm has some advantages including being hardware-friendly, sufficient keyspace, and higher security.

The widespread adoption of consumer electronics (CE), particularly in smart home ecosystems, has led to the proliferation of intelligent devices such as smart cameras, video doorbells, and smart door locks. While these devices enhance convenience and automation, they generate massive amounts of visual data containing sensitive personal information, thereby increasing the risk of privacy leakage and challenging traditional encryption methods in consumer IoT networks. To address this issue, a cryptanalysis-driven image encryption scheme via a chaos-based 3D S-box and genetic code is proposed, specifically designed to safeguard visual privacy in consumer applications. First, a novel dynamical architecture, formally termed 3D Non-degenerate Hyperchaos (3D-NDHC), is constructed to serve as a robust entropy source. Explicitly defined as a globally bounded volume-expanding hyperchaotic system, 3D-NDHC distinguishes itself from traditional dissipative maps by exhibiting global robust hyperchaos and scalable complexity, where the Lyapunov exponents grow logarithmically with control parameters, ensuring high unpredictability. Next, a dynamically generated three-dimensional S-box driven by these chaotic sequences is introduced to perform efficient image permutation. Subsequently, a genetic code method enhanced by cryptanalysis is applied to confuse the permuted image matrix, specifically addressing the security vulnerabilities often inherent in lightweight encryption algorithms. Finally, under the control of pseudo-chaotic sequences, a lightweight wave diffusion process is employed to spread the pixel values and produce the final ciphertext image. In contrast to conventional algorithms that rely on standard encryption techniques, the proposed approach integrates a chaos-driven 3D S-box with a cryptanalysis-enhanced genetic code scheme. This combination introduces a high level of confusion and diffusion, significantly increasing the difficulty for attackers attempting to illegally decrypt sensitive images from smart devices. Experimental results and security analyses demonstrate that the scheme effectively resists various cryptographic attacks and outperforms several recently proposed image encryption algorithms, offering a robust solution for protecting digital image privacy in smart home environments.

In this article coset diagrams of the action of PSL(2, Z) on a PL(F_p) are obtained, through parametrization, which yields one of the eight finite generalized triangle groups which are homomorphic images or quotients of PSL(2, Z). Other than this we analyzed the coset diagrams for the parameter for three finite generalized triangle groups. One of the most dependable methods for achieving data security has been the block cipher. S-Boxes constructed using algebraic structure have gained popularity recently because of their advantageous cryptographic properties and high non-linearity have been found in these structures, which attract researchers. With the help of these parametrized actions, a novel algebraic method to create 2^8 S-Boxe was established. The S-Box provides strong cryptographic qualities of nonlinearity 112, differential uniformity 6, linear approximation probability of 0.0576 and differential attack probability of 0.0039. To assess the practical applicability of our S-box, we integrate it into an image encryption scheme and present experimental results to showcase its efficacy in real-world scenarios. When used with an image encryption framework, the following results were obtained: NPCR = 0.9959, UACI = 0.3348, and approx. Entropy 7.98. Therefore, GTG based parametrisation has been shown to be an effective and secure alternative to traditional algebraic construction method for S-Boxes.

Based on elementary quadratic chaotic flows with no equilibria, this paper proposes a novel four-dimensional hyperchaotic hidden attractor system. Compared with traditional chaotic systems, this system has more complex dynamic behaviors and higher degrees of freedom. Developing this novel system can further expand the research scope of chaos theory and reveal the intrinsic laws and characteristics of chaotic behaviors in higher dimensions.Through nonlinear dynamical analysis, the system exhibits diverse dynamic behaviors with varying parameters and possesses multiple hidden attractors, demonstrating the property of multistability. Subsequently, an analog circuit is constructed using Multisim 14.0 to further validate the system. Finally, image encryption is performed by employing different DNA encoding rules and corresponding operation rules based on chaotic sequences for diffusion. The cipher images are analyzed in terms of histograms, information entropy, and correlation. Experimental results indicate that the proposed algorithm achieves effective encryption and can withstand common attacks.

Accelerated adventures in computer Science and technology has made digital technology, a need of the day. Academicians, researchers, and technologists are anxious to share their secret data through the communication channel along with its security. The security of data, transmission rate, and error correction capability are the fundamental questions against the data transmission through any algebraic code dependent communication channel. Though, data security is always questioned due to the synchronized encoding and decoding algorithms. In this paper, a novel approach is developed to ensure the data security issues occurred due to synchronized encoding-decoding of a BCH code and for data transmission, a computational technique is designed by which data can be encoded and transmitted by using Field-Linear BCH code or a Ring-Linear BCH code of the same dimension, designed distance and code length. Although the Ring-Linear BCH code is preferable for encoding, on the other hand decoding of data is adept by Field-Linear BCH code. Accordingly, a computational technique of Barlekamp Massey Algorithm is utilized for the purpose. This scheme provides a quick code selection of the desired level of transmission rate and error correction capability during the communication. Thus, it also addresses the dimension issue of primitive BCH code. In addition, for the data security perspective we utilize a BCH code in round key addition and mixed column matrix steps in AES algorithm and then put on this modified AES algorithm to image encryption. The image encryption quality permits to incorporate this alteration in AES.

A 3D chaotic system with multi-transient behavior and its application in image encryption

Nonlinear analysis, circuit implementation, and application in image encryption of a four-dimensional multi-scroll hyper-chaotic system

SummaryIn this paper, a new fifth‐order eight‐wing chaotic system is proposed on the basis of a five‐dimensional four‐wing chaotic system. The resulting new system is used as a basis for introducing a method that can control both the number of wings of the system and the direction of the change in the number of wings. Add a rounding function with a cosine function or a sine function to the system equation. The number of wings of the control system is controlled by changing the parameter values of the rounding function. This method can significantly increase the complexity of the system when applied in multiple directions of the system equations. And this method can achieve the purpose of controlling the wing number of the whole system by changing only one parameter. By observing the phase diagram and bifurcation diagram of the system, it is found that it has more complex chaotic properties and rich dynamical behavior and there are coexisting attractors. The chaotic properties of the system are confirmed by observing the Poincaré cross section and the 0–1 test results of the system. Afterward, the simulation circuit of the fifth‐order system is built in the simulation software Multisim. And the obtained phase diagram is consistent with the results obtained in MATLAB which confirmed the realizability of the system. An FPGA hardware implementation of this fifth‐order eight‐wing system has also been completed at the end of the paper to demonstrate the implementability of the system. And the results are highly consistent with those obtained in the MATLAB software.The fifth‐order chaotic system is combined with the dislocation algorithm and diffusion algorithm to apply to the image encryption system. The encryption system contains a variety of encryption algorithms for secondary encryption of images including Arnold dislocation and repeat‐free scrambling algorithm. The diffusion algorithm includes the addition of the modulus length diffusion and multiplicative operation diffusion based on the GF(257) domain. After a series of performance analysis, the encryption system is proved to have good secrecy effect and great application value in the image encryption neighborhood.

Background: Current work is associated with the deployment of synchronized chaotic Secure Hash Algorithm (SHA256) random number generators along with their application in image encryption. Methods: This study aimed to design a perfect communication system to encrypt and decrypt the images via image processing. We introduced a new sliding mode scheme for master-slave fourdimensional (4D) Lorenz-Stenflo systems to deal with the synchronization problem. Then, a new synchronized dynamic secure hash algorithm (SHA-256) was implemented to generate the dynamic random numbers. Results: An image encryption and decryption mechanism was implemented by using synchronized chaotic master-slave systems corresponding to the generated hash values. Here, the master systems were used for encryption, and the slave systems were responsible for the decryption mechanism. The complete design of this paper was implemented in a Python environment. Conclusion: The demonstration of simulation results includes the state responses, strange attractors, and synchronization error responses of master-slave chaotic systems with appropriate switching functions and control input.

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application

This article is about a criterion based on credibility complex fuzzy set (CCFS) to study the prevailing substitution boxes (S-box) and learn their properties to find out their suitability in image encryption applications. Also these criterion has its own properties which is discussed in detailed and on the basis of these properties we have to find the best optimal results and decide the suitability of an S-box to image encryption applications. S-box is the only components which produces the confusion in the every block cipher in the formation of image encryption. So, for this first we have to convert the matrix having color image using the nonlinear components and also using the proposed algebraic structure of credibility complex fuzzy set to find the best S-box for image encryption based on its criterion. The analyses show that the readings of GRAY S-box is very good for image data.