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

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

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

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.

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.

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

Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic 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.

This paper proposes a new five-dimensional memristive conservative chaotic system (5D MCCS) by introducing a flux-controlled memristor into a conservative chaotic system. Dynamic characteristics of the 5D MCCS are validated through spectral entropy(SE), bifurcation diagrams, Lyapunov exponents (LEs), and Poincaré mappings. Compared with other conservative chaotic systems, the 5D MCCS contains only three nonlinear terms yet can generate complex dynamic characteristics. Additionally, under fixed initial values, parameter variations lead the 5D MCCS to switch between chaotic states and quasi-periodic states. The 5D MCCS exhibits chaotic states over wide parameter and initial value range. Afterwards, the 5D MCCS is realized on Field Programmable Gate Array (FPGA) platform. Finally, the pseudorandom sequences generated by the 5D MCCS have been certified through the National Institute of Standards and Technology (NIST) and are utilized for image encryption.

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.

Optimal algorithm for color medical encryption and compression images based on DNA coding and a hyperchaotic system in the moments

With the advancement of multimedia technology and coming of big data era, the size of image data is significantly increased. However, the traditional image encryption methods cannot solve the emerging problems of efficient compression. To settle with this challenge, an effective content-adaptive image compression and encryption method based on compressive sensing and double random phase encoding (DRPE) is proposed in this paper. The original image is converted to one low-frequency part and three high-frequency parts by DWT and then permutated by sorting-based chaotic sequences. Afterward, a novel measurement matrix optimization algorithm based on adaptive step size is presented to measure the high-frequency components. To enhance the security of the scheme, the DRPE, quantization, and diffusion are successively performed on the complex matrix composed of the shuffled low-frequency component and three measurement value matrices to obtain the cipher image. Logistic-Sine chaotic system is utilized to produce the chaotic keystreams for the encryption process, and its system parameter and initial value are determined by the information entropy of the plain image and external key parameters, so that the proposed cipher can withstand known-plaintext and chosen-plaintext attacks effectively. Numerical experiments demonstrate the effectiveness of the proposed image compression and encryption algorithm.

A novel image encryption algorithm based on a hybrid model of deoxyribonucleic acid (DNA), cellular automata (CA) and chaotic system is proposed. CA due to its complex behavior has several applications such as generating random numbers and cryptography. DNA rules, DNA sequence XOR operator and CA rules are used simultaneously to encrypt the plain-image pixels. To determine rule number in DNA sequence and also CA, a 2-dimension logistic map is employed. Experimental results show that the proposed image encryption scheme has a lot of characteristics, including large key space, low correlation of adjacent cipher pixels, and high security, which can effectively protect the security of the encrypted image.

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

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.