An Adaptive and Fragile Image Watermarking Algorithm Based on Composite Chaotic Iterative Dynamic System

This paper proposes a color image encryption algorithm based on a cloud model Fibonacci chaotic system, as well as a matrix convolution operation that can protect image content effectively and safely. The algorithm combines the cloud model with the generalized Fibonacci, creating a new complex chaotic system that realizes the dynamic random variation of chaotic sequences. The chaotic sequence is used to scramble the pixel coordinates of the mosaic images of the R, G, and B components of the color image. Then, the chaotic sequence value is used as a matrix convolution cloud algorithm that alternately updates the input value of the matrix convolution operation and the pixel value to obtain the permutation transformation of the original pixel value. Finally, the pixel values of the replacement and cloud model Fibonacci chaotic sequence and the pixel values of the front (rear) adjacent pixel points are subjected to a two-way exclusive XOR operation. Realizing the change of the arbitrary pixel value causes a chain transformation of the pixel values of all of the pixel points, and sequentially generates an encrypted image. Experiments show that the histogram of the encrypted image is smoother and adjacent pixels of the image have low correlation. In addition, this algorithm can resist attack experiments such as differential attack, select plaintext attack and noise attack and provides high encryption security, high anti-interference, and strong robustness. The dynamic chaotic system is used to realize the color image encryption of the dynamic key, and the encryption algorithm has higher security and the validity of the algorithm.

Back to table of contents Previous article Next article LETTERFull AccessGlobal Versus Local Perspectives on SchizophreniaSareh ZendehrouhFatemeh BakouieShahriar Gharibzadeh,Sareh ZendehrouhSearch for more papers by this authorFatemeh BakouieSearch for more papers by this authorShahriar GharibzadehSearch for more papers by this author,Published Online:1 Apr 2009AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail To the Editor: Recent neurobiological studies indicate that schizophrenia may be a neurodevelopmental and progressive disorder with multiple biochemical abnormalities involving dopamine, serotonin, glutamate, and gamma-aminobutyric acid secretion. In postmortem tissue studies, structural abnormalities and alterations in synaptic connectivity have been observed in the intracortical circuitry of the prefrontal dorsal cortex of schizophrenia patients. These morphological changes could be the sequelae of earlier environmental insults and genetic processes. There are probably multiple susceptibility genes, each of small effect, which act in conjunction with environmental factors as obstetric abnormalities, intrauterine infection, and abnormal nutrition. Candidate identified genes could influence neurodevelopment, synaptic plasticity, and neurotransmission. 1 The recent findings are consistent with notions that epigenetic factors play a major role in the disease process and epigenetic factors may continue to influence the expression of the affected genes in adulthood. 2 It is also demonstrated that schizophrenia is a dynamical disease—i.e., that important aspects of schizophrenia can be understood on the basis of concepts of the theory of nonlinear dynamical systems. 3 Chaotic dynamical systems are characterized by a lawful but delicate sensitivity to initial conditions. This leads to the observation that initially similar behaviors evolve into a striking divergence of behavioral patterns over time. Therefore, small differences in the input can result in an entirely different sequence of outputs. 4 We believe that genes act as initial conditions and environmental factors are the control parameters of a chaotic human brain system, which can force the system to special states with particular characteristics (e.g., schizophrenia). Since in chaotic dynamical systems, control parameters can direct the system to special states, environmental factors play a key role in aggravation or decline of schizophrenia symptoms. This complies with some reports that showed high relapse rate of schizophrenia in families that expressed high emotion, 5 which can be considered as a positive control factor. Based on our hypothesis, we propose that schizophrenia could be considered a chaotic model and the global features of the disease could be extracted instead of paying attention to local detailed features. In such a perspective, the manner of managing the disease will be changed. For example, we think that it is not necessary to include the effects of each part of the brain circuits and to correct any change in the amount of neurotransmitters; instead it is better to model the disease state as a chaotic system and recognize the interaction of different environmental factors, such as maternal health, birth complications, emotional states, familial relationships, etc., on it and try to minimize the pathological effects of them. We stress that it is not the compartments but the global interactions of different elements that play major roles in the disease and deserve attention. Modeling the behavior of schizophrenia on the basis of chaos theory to control the disease seems to be a good place to start.Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran

In recent years, there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle, butterfly, heart and apple. This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve. The proposed chaotic system has two quadratic, two cubic and two quartic nonlinear terms. It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points. It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states. A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve. We have shown MATLAB plots to illustrate the capsule equilibrium curve, phase orbits of the new chaotic system, bifurcation diagrams and multi-stability. As an engineering application, we have proposed a speech cryptosystem with a numerical algorithm, which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve. The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array (FPGA) platform. Experimental results show that the proposed encryption system utilizes 33% of the FPGA, while the maximum clock frequency is 178.28 MHz.

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

To build safe and reliable distributed decentralized systems using blockchain technology, a continuous chain of blocks is created, the unauthorized modification of which is not allowed by the applied cryptographic mechanisms. This is achieved by using unidirectional, collision resistant and search prototypes of cryptographic functions whose hash values from previous blocks are included in subsequent blocks. As a result, an unauthorized change in at least one bit of data in the previous blocks will be immediately detected. However, in the case of distributed storage of information, there is an additional requirement of synchronization of individual chains of blocks that are stored by various nodes. These and other issues are resolved by applying consensus building mechanisms, through which, after a certain sequence of actions, a continuous sequence of blocks (blockchain chain) becomes the same on all nodes of a decentralized network. This work examines one of the main vulnerabilities of blockchain systems built by consensus with probabilistic completion, namely, a double-spend attack. Based on the model of “independent players”, an analytical expression is obtained for calculating the probability of an attacker's successful double-spending attack. The quantitative values of the probability of a successful attack are given for various abilities of an attacker, a different number of generated blocks and a different race duration. Using computer simulation, the calculated values are experimentally verified. All empirical estimates were obtained with high accuracy (relative error not higher than 1%) and reliability (confidence level of at least 99%). To confirm the adequacy of the results obtained, a comparison of empirical results with theoretical calculations is given.

Finding synchronization between the signals of a neural system such as the brain (as a dynamic chaotic system) has a critical role in characterizing the system activities and integration of information within and across a disorder. Therefore, applying a synchronization measure, which is able to capture the important features of the system, has a great effect on the results. In this paper, we propose the horizontal visibility graph (HVG) method as a new, straightforward and fast method to measure synchronization between brain signals. By using the HVG method, a signal is mapped into a graph network and the signals properties are captured well. Our analysis shows that the proposed method is a robust and reliable measure for finding synchronization between signals of a dynamic chaotic (non-)noisy system. As examples for real life applications, the HVG method is used to observe Multiple Sclerosis (MS) brain network by using brain EEG signals. The results are in line with previous neurophysiology studies. Therefore, the proposed method could be a promising choice for analyzing real neural signals to characterize the system connectivity.

Chaotic sequences and chaotic dynamical systems are attractive candidates for use in signal synthesis and analysis as well as in communications applications. In previous works, various methods for the estimation of chaotic sequences under noise were developed. However, although the methods were different, their qualitative performance was the same: for high signal-to-noise ratio (SNR) the performance was good, but below some threshold SNR, a sharp degradation in performance occurred. We prove and quantify the existence of this threshold effect and derive lower bounds on the value of the threshold SNR. Using information-theoretic tools, we prove that for any ergodic chaotic system, there is a certain threshold SNR level below which the ratio between the mean-square error obtained by any estimator of the system's initial state at the output of additive white Gaussian noise (AWGN) channel and the Cramer-Rao bound increases exponentially fast as the number of observations N grows without bound. We explain the connection between the existence of a threshold effect in the estimation of chaotic sequences and the converse to the joint source-channel coding theorem. We derive lower bounds on SNR/sub th/, the value of the threshold SNR, as a function of the system's Lyapunov exponent. Our bounds have two versions, one for a finite number of observations, and one for the asymptotic regime as N/spl rarr//spl infin/. For the asymptotic regime, the bound we develop on the threshold SNR incorporates the key parameters of chaotic systems, the Lyapunov exponent, and the chaotic sequence power spectrum into a simple formula. We demonstrate our results on the chaotic system governed by the r-diadic map.

Blockchain technology is being studied in many innovative applications, such as: cryptocurrencies, smart contracts, communication systems, healthcare, Internet of Things, financial systems, software development, electronic voting and many others. Using a transparent and fully distributed peer-to-peer blockchain architecture, applications benefit from a data-only model, in which “transactions” are accepted into the blockchain ledger and, if the system is functioning properly, cannot be modified or deleted. The transparency of blockchain systems makes it possible to store publicly available and irrefutable records. A peer-to-peer blockchain system provides verifiable ledger maintenance without centralized management, which solves the problems of a single point of failure and a single point of trust. The article deals with the issue of the security of application of accounting systems built on decentralized principles using blockchain technology. Particular attention is paid to the problem of the possibility of double spending in such accounting systems. The article exemplifies the reorganization of records in blockchain ledgers, performed by successfully carrying out a 51% attack on consensus algorithms based on proof of work. Given refinement of analytical expressions of 51% attack probability obtained in the works of S. Nakamoto and M. Rosenfeld using a more general model, namely, the model of independent players, where the probability of block formation by attackers and an honest network are independent events. The results of comparing of the success probability of a double-spending attack on the blockchain systems calculated according to different models are presented.

Modeling, stabilization, and identification processes are significant stages in the process of developing knowledge about chaotic dynamical systems which entail the effective prediction depending on the degree of uncertainty toleration in the forecast, accuracy of the current state to be measured as well as a time scale resting on the dynamics of the system. Control of under-activated dynamical systems has been considered substantially, and it is for periods and is currently developing in various domains such as biology, data analysis, computing systems, and so forth. Dynamic systems of growing population signifies a model describing the way a population evolves over time during which population goes through major life events, split into discrete time periods. The size of the population at a given time period is determined by the rate of growth as well as other related factors. Most progress has been made in model-based control theory, which has drawbacks when the system under consideration is exceedingly complicated, and no model can be constructed. Accordingly, a 3D-discrete and dynamic human population growth system with many controllers is proposed by examining the stability and symmetry of controller system clarifications. The symmetric stability control results are presented by considering a special parametric dynamic system in its coefficients besides suggesting periodic functional coefficients in terms of sin and cos functions. The controllers have the ability to reduce population growth rate unpredictability or enhance system stability under various external conditions. The unique and very effective strategies in relevant domains could provide a deeper understanding of their impact as well as the theoretical or technological innovations thereof. These controllers are capable of reducing population growth rate unpredictability or improving system stability under various external conditions, and applicable strategies in the relevant domains can provide profound comprehension over the impact along with the theoretical as well as technological advancements.

The ultimate semiclassical wave packet propagation technique is a complex, time-dependent Wentzel-Kramers-Brillouin method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out fully in practice. In its place roughly twenty years ago, linearized wave packet dynamics was generalized to methods that include sets of off-center, real trajectories for both classically integrable and chaotic dynamical systems that completely capture the dynamical transport. The connections between those methods and GGWPD are developed in a way that enables a far more practical implementation of GGWPD. The generally complex saddle-point trajectories at its foundation are found using a multidimensional Newton-Raphson root search method that begins with the set of off-center, real trajectories. This is possible because there is a one-to-one correspondence. The neighboring trajectories associated with each off-center, real trajectory form a path that crosses a unique saddle; there are exceptions that are straightforward to identify. The method is applied to the kicked rotor to demonstrate the accuracy improvement as a function of ℏ that comes with using the saddle-point trajectories.

This paper proposes a user-biometric-based image encryption using chaotic dynamical systems, SHA-256 hash function, and zigzag transformation. Three chaotic systems, namely, the Henon map, logistic map, and Lorenz system, are used to apply the chaotic properties to the encryption system. The hash value of the user biometric image is used to generate the initial value of the Henon map. The initial values for the logistic map and Lorenz system are generated from the hash value of the plain image. SHA-256 hash algorithm generates the hash values of the biometric and plain images. The plain image is scrambled using the two-dimensional chaotic values generated by the Henon map first. Next, the first scrambled image’s pixels are XORed with the one-dimensional chaotic values generated from the logistic map and produce the second scrambled image. Finally, take the second scrambled image’s pixels, and XOR them with the three-dimensional chaotic values generated from the Lorenz system and create the final encrypted image. The robustness and flexibility of the encryption system are analyzed using various security and performance analyses. The experiment results are compared with the existing algorithms to prove the efficiency of the proposed algorithm.

The master stability function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the master stability function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability. Published by the American Physical Society 2024

In this paper, we study communication systems, modulators, and demodulators using chaotic systems from the perspective of reconstruction of attractors. We consider a two-step approach to the recovery of information signals from chaotic modulation. To recover the information signal modulated by a chaotic dynamical system, the first step is to reconstruct the chaotic attractor given a subset of the state variables. The second step is to reconstruct the information signal from the chaotic attractors. Two main techniques to accomplish this are the Takens reconstruction theorem and the chaotic synchronization theorem. In general, a combination of these two techniques are needed to recover the information signal. We show a systematic way to reconstruct an attractor and the injected signal exactly from a scalar observable for a subclass of Lur'e systems. We illustrate this approach using several examples. Extensions to discrete-time systems are also presented.

Chaos synchronization between two different chaotic dynamical systems

The helicity of adjacent phase trajectories in chaotic dynamic systems may be characterized by the distribution of local angular-rotation velocities of the infinitesimal displacement vector whose evolution is determined by linearized equations of motion. This distribution is close to the distribution of local Lyapunov exponents. The simplest models show that the whirl velocity of adjacent trajectories affects the rate of mixing of dynamical variables and sensitivity of the phase trajectories to perturbations.