Analysis of S-Box Based on Image Encryption Application Using Complex Fuzzy Credibility Frank Aggregation Operators

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.

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

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.

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.

S-boxes are designed to be computationally efficient, compact and resistant to attacks, making them critical to the overall security of block ciphers. Therefore, a well-designed S-box can significantly increase the strength and robustness of block ciphers against various cryptanalytic attacks. As a result, the researchers continue to explore new and improved S-box designs to enhance the security of block ciphers. In this article the substitution matrix is assembled using the elements of Galois field of order 256 with the help of Mobius transformation. In order to increase its invulnerability an appropriate permutation is used. The proposed S-box is then used to encrypt different images after their security evaluation. At the end the results are compared with the different renowned S-boxes. AMS subject classification: Primary: 94A60; Secondary: 68P25

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.

Compared with integer order chaotic systems, fractional order chaotic systems can reflect natural phenomena more accurately, which are more suitable for chaotic cryptosystems. In order to explore the application of fractional order chaotic system in cryptography, a novel fractional order hyperchaotic system is constructed and implemented on DSP platform. More progressively, based on Adomian decomposition method, the dynamic behavior is studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum and spectral entropy (SE) complexity. It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state. Therefore, the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system have sufficient randomness and are well suited for applications in secure communications. In addition, a color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA dynamic coding. Firstly, the improved Arnold algorithm is used to scramble the original image, then the column cyclic shift method is applied for secondary scrambling, and finally the pixel value is diffused by DNA sequence operation. The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively, but also has high security and can resist various common attacks.

An n-dimensional polynomial modulo chaotic map with controllable range of Lyapunov exponents and its application in color image encryption

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

Construction of new 5D Hamiltonian conservative hyperchaotic system and its application in image encryption