Narrow Results

In this paper, we develop a novel n-dimensional discrete chaotic map. First, the chaotic behaviors of the proposed map are studied. Next, to illustrate the effectiveness of our map, the 4D hyperchaotic map as an example is analyzed using the phase diagram, Lyapunov exponents, bifurcation diagrams and different types of entropy, etc. Moreover, the chaotic signals generated by the proposed map passed the NIST test and were implemented on the hardware DSP. Finally, we apply our chaotic map in image encryption using true numbers and extended XOR. The experimental results express that the presented encryption algorithm has a higher level of security than same other sophisticated methods.

This paper introduces a novel three-neuron memristive synaptic coupling Piecewise-Linear Hopfield Neural Network (PWL-HNN) and extends it to fractional order. This study delves into studying the dynamical behaviors of the fractional-order memristive PWL-HNN using bifurcation diagrams, largest Lyapunov exponential spectra, Poincaré cross-sections, attraction basins, and two-parameter bifurcation diagram, and exploring variations in PWL activation function parameters, memristive coupling strengths, and initial conditions. Subsequently, an equivalent circuit model of the fractional-order memristive PWL-HNN on the Cadence/PSpice platform is developed, verifying its dynamic behavior through circuit simulation experiments. Additionally, a digital circuit of the fractional-order memristive HNN model is implemented on the LabVIEW platform, with NI PXIe equipment utilized for hardware circuit realization. The experimental results align closely with numerical and circuit simulation results, affirming the theoretical analysis’s accuracy. Lastly, this paper investigates the generation of a pseudo-random sequence using fractional-order memristive HNN and explores an image encryption algorithm in conjunction with the DNA algorithm, assessing the encryption algorithm’s reliability through security analysis.

Since the advent of networked systems, fuzzy graph theory has surfaced as a fertile paradigm for handling uncertainties and ambiguities. Among the different modes of handling challenges created by the uncertainties and ambiguities of current networked systems, integrating fuzzy graph theory with cryptography has emerged as the most promising approach. In this regard, this review paper elaborates on potentially studying fuzzy graph-based cryptographic techniques, application perspectives, and future research directions. Since the expressive power of fuzzy graphs allows the cryptographic schemes to handle imprecise information and to enhance security in many domains, several domains have benefited, such as image encryption, key management, and attribute-based encryption. The paper analyzes in depth the research landscape, mainly by focusing on the varied techniques used, such as fuzzy logic for key generation and fuzzy attribute representation for access control policies. A comparison with performance metrics unveils the trade-offs and advantages of different fuzzy graph-based approaches in efficiency, security strength, and computational overhead. Additionally, the survey explores the security applications of fuzzy graph-based cryptography and underpins potential development for secure communication in wireless sensor networks, privacy-preserving data mining, fine-grained access control in cloud computing, and blockchain security. Some challenges and research directions, such as the standardization of fuzzy logic operators, algorithmic optimization, integration with emerging technologies, and exploitation of post-quantum cryptography applications, are also brought out. This review will thus bring insight into this interdisciplinary domain and stimulate further research for the design of more robust, adaptive, and secure cryptographic systems in the wake of rising complexities and uncertainties.

Cellular automaton (CA) has a lot of inherent features, such as simple regular structure, local interaction, random-like behavior and massive parallelism, which make it a good candidate to design cryptosystems. Therefore, a number of CA-based image encryption systems have been proposed, though the drawbacks of small key space and weak security in one-dimensional (1D) CA cryptosystems are obvious. In this paper, a novel image encryption scheme is presented using a two-dimensional (2D) CA with nonlinear balanced rules. During the whole process of encryption, the confusion operation is performed by the nonlinear rule of CA, while the diffusion operation is achieved by the local interactions among cells. So confusion and diffusion are well integrated in our proposed scheme. The corresponding simulations and analyses illustrate that the scheme has quite prominent cryptographic properties as well as high security.

A novel encryption algorithm to cipher digital images is presented in this work. The digital image is rendering into a three-dimensional (3D) lattice and the protocol consists of two phases: the confusion phase where 24 chaotic Cat maps are applied and the diffusion phase where a 3D cellular automata is evolved. The encryption method is shown to be secure against the most important cryptanalytic attacks.

The study of the reversibility of elementary cellular automata with rule number 150 over the finite state set 𝔽_p and endowed with periodic boundary conditions is done. The dynamic of such discrete dynamical systems is characterized by means of characteristic circulant matrices, and their analysis allows us to state that the reversibility depends on the number of cells of the cellular space and to explicitly compute the corresponding inverse cellular automata.

A novel image encryption algorithm using the chaotic system and deoxyribonucleic acid (DNA) computing is presented. Different from the traditional encryption methods, the permutation and diffusion of our method are manipulated on the 3D DNA matrix. Firstly, a 3D DNA matrix is obtained through bit plane splitting, bit plane recombination, DNA encoding of the plain image. Secondly, 3D DNA level permutation based on position sequence group (3DDNALPBPSG) is introduced, and chaotic sequences generated from the chaotic system are employed to permutate the positions of the elements of the 3D DNA matrix. Thirdly, 3D DNA level diffusion (3DDNALD) is given, the confused 3D DNA matrix is split into sub-blocks, and XOR operation by block is manipulated to the sub-DNA matrix and the key DNA matrix from the chaotic system. At last, by decoding the diffused DNA matrix, we get the cipher image. SHA 256 hash of the plain image is employed to calculate the initial values of the chaotic system to avoid chosen plaintext attack. Experimental results and security analyses show that our scheme is secure against several known attacks, and it can effectively protect the security of the images.

This study aims to solve the problem of small key space in image cryptosystems based on logistic mapping. First, a new one-dimensional (1D) chaotic system, with a wide continuous chaotic interval, a large Lyapunov exponent and obvious chaotic characteristics are presented. Subsequently, a novel image encryption algorithm based on the new 1D chaotic system and dynamic DNA encoding is designed. Compared with other DNA coding methods, the proposed image encryption algorithm encodes chaotic sequences and ensures that the sequence elements at different positions correspond to different DNA coding schemes. This will help to overcome the fixity of DNA coding and make the proposed dynamic DNA coding easy to operate and implement. Finally, the cipher image is obtained by scrambling and bit XOR operation based on the chaotic sequences. The fixed DNA coding method is compared with other chaotic image encryption schemes, and the experimental results indicate that the image encryption algorithm has higher security and can resist common attacks.

This paper puts forward a novel image encryption algorithm that is based on permutation-diffusion architecture. In pixels' permutation stage, algorithm takes full advantage of the idea of magic cube's scrambling. There is only simple cyclic shift operation in each sub-block's permutation, but when the algorithm has disposed the current sub-block, the adjacent sub-blocks will be dealt with, too. In the cyclic shift of each row, stable points will help to decrease the correlation of adjacent pixels. To make encryption procedure uncertain, this paper brings in a parameter named delay-time that is generated by chaotic map. In the diffusion stage, by combining multiple operations and dynamic look-up table together, the proposed algorithm highly increases the uncertainty of the encryption procedure. At last, the experiment results of key space analysis, information entropy analysis, histogram analysis and etc. show that the encryption algorithm has well performance and it can be used in image encryption and transmission.

In this paper, an image encryption algorithm based on couple multiple chaotic systems is presented. It made the one-dimensional Coupled Map Lattice (CML) formed by Skew Tent map as spatiotemporal chaotic system and made its output sequence as the initial value of logistic and meanwhile did iterative of specific times to get the final key sequence, and then did XOR operations with corresponding pixels to finish the encryption. Numerical analysis expresses that this algorithm has large enough space and high security.

This paper offers two different attacks on a freshly proposed image encryption based on chaotic logistic map. The cryptosystem under study first uses a secret key of 80-bit and employed two chaotic logistic maps. We derived the initial conditions of the logistic maps from using the secret key by providing different weights to all its bits. Additionally, in this paper eight different types of procedures are used to encrypt the pixels of an image in the proposed encryption process of which one of them will be used for a certain pixel which is determined by the product of the logistic map. The secret key is revised after encrypting each block which consisted of 16 pixels of the image. The encrypting process have weakness, worst of which is that every byte of plaintext is independent when substituted, so the cipher text of the byte will not change even the other bytes have changed. As a result of weakness, a chosen plaintext attack and a chosen cipher text attack can be completed without any knowledge of the key value to recuperate the ciphered image.

The high-dimensional chaotic systems (HDCS) have a lot of advantages as more multifarious mechanism, greater the key space, more ruleless for the time series of the system variable than with the low-dimensional chaotic systems (LDCS), etc. Thus, a novel encryption scheme using Lorenz system is suggested. Moreover, we use substitution–diffusion architecture to advance the security of the scheme. The theoretical and experimental results show that the suggested cryptosystem has higher security.

In this paper, a color image encryption method using the memristive hyperchaotic system and deoxyribonucleic acid (DNA) encryption is proposed. First, the pseudo-random sequences are generated by a keystream generation mechanism based on a memristive hyperchaotic system and the plain image. Due to this, the memristive hyperchaotic system has a complex dynamical behavior and is highly sensitive to initial conditions, the proposed keystream generation mechanism is highly random which is also dependent on the plain images. Second, a permutation based on the cycle-shift operation is designed to eliminate the correlations between adjacent pixels in the plain images. Then, the scrambled sequences are processed by DNA encryption to increase the system ability to defense the brute force attacks. Finally, the cipher image is obtained after the diffusion and interaction among red, green and blue components. Experimental analysis and performance comparisons show that the proposed method has high security, good efficiency and strong robustness under different attacks.

Chaotic systems can be used for secure communication and image encryption by applying a variety of encryption algorithms. While most of the low-dimensional chaotic systems and maps can be estimated by using phase reconstruction and thus the safety in signal processing and propagation is attacked. In this paper, an initial-dependent dynamical system, which is developed from the Rössler system by adding memristive function and disturbance function on the memristive variable $z$, is presented for realizing image encryption and bifurcation analysis is supplied in detail. Time-varying disturbance from sampled variables is applied to control the memristive variable and the dependence of mode oscillation on initial values is enhanced. As a result, the dynamics of this memristive system is switched between different oscillation modes (e.g., periodical to chaotic, chaotic to chaotic) by activating the initial value, memristive gain and disturbance gain, respectively. From a dynamical viewpoint, the involvement of stochastic adjustment on the memristive variable can reset the initial value and then induce time-varying parameter regulation or switch on certain parameter embedded in the memristive nonlinearity and function, and thus the dynamics dependence on the initial setting is enhanced. Standard bifurcation analysis is carried out on this memristive system and then the sampled time series are used for image encryption, furthermore, the reliability for this scheme is discussed and suggestions for further study are supplied in the end.

In this paper, a new memristive chaotic system with a relatively simple structure and complex dynamic behavior is proposed by introducing an absolute memristor into the VB19 chaotic system as a positive feedback term. The analysis shows that the new system is a fractional dimensional dissipative system and is unstable at the line equilibrium point. The system’s dynamic characteristics are studied using a bifurcation diagram and Lyapunov exponent’s spectrum. The numerical simulation shows that the period-doubling bifurcation phenomenon occurs when changing the parameters and system change from period to chaos. When the initial condition changes, the dynamic evolution of the system indicates that the coexistence of multiple attractors and chaotic signals can be controlled by local amplitude. In addition, a new image encryption algorithm based on the system is designed and the performance of this algorithm is tested through numerical analyses. The system’s analog circuit is built using electronic components and also realized by the microprocessor. The circuit realization results consistent with the numerical simulation results are obtained to verify the physical existence of the system.

In this paper, a robust image encryption technique that utilizes Fourier–Mellin moments and intertwining logistic map is proposed. Fourier–Mellin moment-based intertwining logistic map has been designed to overcome the issue of low sensitivity of an input image. Multi-objective Non-Dominated Sorting Genetic Algorithm (NSGA-II) based on Reinforcement Learning (MNSGA-RL) has been used to optimize the required parameters of intertwining logistic map. Fourier–Mellin moments are used to make the secret keys more secure. Thereafter, permutation and diffusion operations are carried out on input image using secret keys. The performance of proposed image encryption technique has been evaluated on five well-known benchmark images and also compared with seven well-known existing encryption techniques. The experimental results reveal that the proposed technique outperforms others in terms of entropy, correlation analysis, a unified average changing intensity and the number of changing pixel rate. The simulation results reveal that the proposed technique provides high level of security and robustness against various types of attacks.

Most of the existing image encryption algorithms had two basic properties: confusion and diffusion in a pixel-level plane based on various chaotic systems. Actually, permutation in a pixel-level plane could not change the statistical characteristics of an image, and many of the existing color image encryption schemes utilized the same method to encrypt R, G and B components, which means that the three color components of a color image are processed three times independently. Additionally, dynamical performance of a single chaotic system degrades greatly with finite precisions in computer simulations. In this paper, a novel coupled map lattice with time-varying delay therefore is applied in color images bit-level plane encryption to solve the above issues. Spatiotemporal chaotic system with both much longer period in digitalization and much excellent performances in cryptography is recommended. Time-varying delay embedded in coupled map lattice enhances dynamical behaviors of the system. Bit-level plane image encryption algorithm has greatly reduced the statistical characteristics of an image through the scrambling processing. The R, G and B components cross and mix with one another, which reduces the correlation among the three components. Finally, simulations are carried out and all the experimental results illustrate that the proposed image encryption algorithm is highly secure, and at the same time, also demonstrates superior performance.

In this paper, a new chaotic image encryption algorithm based on pseudo-random bit sequence and DNA plane is proposed. The coupled map lattice (CML) is applied to design a pseudo-random bit sequence generation (PBSG) system and use the system to generate the random sequence needed in the encryption process. The initial values and parameters of the system are generated by the SHA-256 hash algorithm combined with given keys. Firstly, the plane image is decomposed into four DNA planes in combination with the DNA encoding rules, and then the four DNA planes are subjected to row circular permutation and column circular permutation. After that, the diffusion operation on each DNA plane is performed. Finally, the four DNA planes are decoded and then combined into a pixel matrix, that is, the final cipher image is obtained. Throughout the encryption process, the choice of DNA encoding and decoding rules is determined by the PBSG system. Simulation results and security analysis show that the algorithm not only has good encryption effect, but also can resist various classic attacks, and has excellent security performance.

Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

This paper presents dynamic behavior of a fractional-order memristive time-delay system and its application in image encryption. First, a fractional-order memristive time-delay system is proposed, and the stability and bifurcation behaviors of the system are theoretically analyzed. Some limited conditions for describing the stability interval and switching between different dynamic behaviors are derived. Second, the dynamic characteristics of the system are analyzed through the coexisting attractors, coexisting bifurcation diagrams, the Largest Lyapunov exponents (LLE), the 0-1 test. When parameters change, such as time delay and fractional order, the system transits from steady state to periodic state, single scroll chaotic state, double scroll chaotic state. Furthermore, an image encryption scheme based on the fractional-order memristive time-delay system is introduced, and some statistical features are analyzed. Finally, numerical simulations verify the validity of the theoretical analysis and safety of the image encryption scheme based on the fractional-order delayed memristive chaotic system.