Field Of Secure Communication Research Articles

Dynamic analysis based on a memristive hyperchaotic system with stable unfixed point and its synchronization application

A novel two-memristor hyperchaotic system is obtained by introducing a cubic magnetic-controlled memristor and a hyperbolic sine function memristor. The dynamics of the new system are analyzed by various techniques such as Lyapunov exponents, complexity, 0–1 test, bifurcation diagram and phase diagram. The results demonstrate that the new system exhibits complex dynamic behaviors, including transient chaos, transient transition, intermittent chaos, and offset-boosting. Notably, a rare phenomenon with stable unfixed point has been discovered in this newly proposed system. The largest Lyapunov exponent of the stable unfixed point fluctuates around 0 and remains predominantly less than or equal to 0. Despite this, the new system still partially exhibits chaotic characteristics, indicating that the stable unfixed point can be regarded as a local chaotic attractor. Furthermore, there are four types of coexisting attractors with period-period, chaos-chaos, chaos-stable unfixed point and stable unfixed point-stable unfixed point in the new system. The circuit design is implemented to validate the accuracy of the memristive chaotic system, and the consistency between numerical calculations and simulation results is confirmed. Finally, the coupling synchronization and tracking synchronization methods are designed, which hold practical applications in the field of secure communication, control systems and signal processing.

Effects of impulse on prescribed-time synchronization of switching complex networks

The specified convergence time, designated by the user, is highly attractive for many high-demand applications such as industrial robot control, missile guidance, and autonomous vehicles. For the application of neural networks in the field of secure communication and power systems, the importance of prescribed-time synchronization(PTs) and stable performance of the system is more prominent. This paper introduces a prescribed-time controller without the fractional power function and sign function, which can reach synchronization at a prescribed time and greatly reduce the chattering phenomenon of neural networks. Additionally, by constructing synchronizing/desynchronizing impulse sequences, the PTs of switching complex networks(SCN) is achieved with impulse effects, where the time sequences of switching and impulse occurrences in the networks are constrained by the average dwell time. This approach effectively reduces the impact of frequent mode switching on network synchronization, and the synchronization time can be flexibly adjusted within any physically allowable range to accommodate different application requirements. Finally, the effectiveness of the proposed control strategy is demonstrated by two examples.

Designing an Image Encryption Algorithm Based on Hyperchaotic System and DCT

In the field of secure communications, the robustness of cipher images transmitted in various channels is becoming increasingly important. In this paper, a robust image encryption algorithm combining a new chaotic system and discrete cosine transform is proposed, which is interlinked with plain information and is resistant to high-intensity noise attacks. First, a 5D continuous hyperchaotic system is proposed, leading to an interrelated sequence of five chaotic sequences. Second, the plain image is subjected to discrete cosine transform. Then the transform domain image is quantized, and some high-frequency components are removed, and then the high-frequency components are filled with chaotic sequences. Next, the transform domain image is scrambled, and inverse discrete cosine transform is performed, and its gray value is mapped to obtain a spatial domain image. Finally, the spatial image is scrambled by the spiral transformation, and then the diffusion operation is performed to obtain the encrypted image. Through the simulation experiment, the histogram, correlation, differential attack, and robustness are analyzed. The experimental results show that the proposed encryption algorithm can resist high-intensity noise attacks and has good encryption performance.

Hopf Bifurcation and Stability of the Double-Delay Lorenz System

Based on the nonlinear dynamics theory, the stability of the double-delay Lorenz system is investigated at the equilibrium points, and the conditions of the occurrence of Hopf bifurcation are analyzed. The double-delay Lorenz system has more complex dynamic behaviors, and it is applicable to many fields. Firstly, the equilibrium points of the system are calculated. Subsequently, the local stability of the system at the equilibrium points is determined by analyzing the distribution of the roots of the characteristic equation of the system, and the critical values of the time delays for generating Hopf bifurcation are yielded. With the time delays as the bifurcation parameter, the conditions of the existence of Hopf bifurcation in the system under the same and different time delays are analyzed. Lastly, it is confirmed numerically that the conclusions are drawn complying with the theoretical analysis and applied in the field of secure communication to make the encrypted information more secure and difficult to decipher during transmission.

Dynamic Exploration of a Controllable Thermosensitive Neuron Model and Its Applications

A specific functional electric component is connected to any branch of the neural circuit, which can enhance the corresponding biological function as a smart sensor, whereas the temperature has a significant effect on the firing rhythm of neurons by regulating channel conductance and excitability. So for this paper, a controllable thermosensitive neuron model is established by paralleling two thermistors in the FitzHugh–Nagumo neural circuit. Especially, the thermistors are controlled by two switches, where three working modes can be selected, for which bifurcation diagrams, time response diagrams and spectral entropy (SE) complexity are used to analyze the dynamic behaviors in different operating modes. It is found that any modulation of thermistor can regulate the branch current and output voltage completely under the three working modes. More importantly, the neuronal activities show different mode transitions from periodic to bursts or chaos. The superior dynamic characteristics and rich firing behavior make the new model more suitable for images encryption. For this purpose, we consider switching the three thermosensitive neuron models continuously to obtain more complex chaotic sequences. Next, based on the feature of high pixel correlation among color image components, a 3D projection scrambling algorithm is designed, and then employed in combination with the universal gravitational diffusion method to propose a color image encryption scheme. In addition, the designed algorithm is executed by encrypting and decrypting some color images. The experimental results show that the algorithm cannot only encrypt the color image effectively, but also has no limitation on the size of the test image. It is worth mentioning that the designed encrypted algorithm has satisfactory security performance and considerable robustness against noise attacks and shearing attacks. The exploration of this paper about the thermosensitive neuron model and its application may provide some theoretical guidance and experimental basis in the field of secure communication.

Multi-scroll fractional-order chaotic system and finite-time synchronization

The definition of fractional calculus is introduced into the 5D chaotic system, and the 5D fractional-order chaotic system is obtained. The new 5D fractional-order chaotic system has no equilibrium, multi-scroll hidden attractor and multi-stability. By analyzing the time-domain waveform, phase diagram, bifurcation diagram and complexity, it is found that the system has no equilibrium but is very sensitive to parameters and initial values. With the variation of different parameters, the system can produce attractors of different scroll types accompanied by bursting oscillation. Secondly, the multi-stability of the hidden attractor is studied. Different initial values lead to the coexistence of attractors of different scroll number, which shows the advantages of the system. The correctness and realizability of the fractional-order chaotic system are proved by analog circuit and physical implement. Finally, because of the high security of multi-scroll attractor and hidden attractor, finite-time synchronization based on the fractional-order chaotic system is studied, which has a good application prospect in the field of secure communication.

Chaos Synchronization Based on Hybrid Entropy Sources and Applications to Secure Communication

We experimentally demonstrate a chaotic synchronization scheme based on the electro-optic hybrid entropy sources. The chaos synchronization method is experimentally validated that 200 km high-level chaos synchronization can be attained and the distance can be further extended. The digital signal induced chaos synchronization signal has good robustness against the potential distortions in long-haul optical transmission. On the basis of the digital signal induced chaos synchronization strategy, a correlated random bit generation (CRBG) scheme with bit rate of 1.25 Gb/s and distance of 200 km is proposed. The generated correlated random bit sequences (CRBSs) pass all the NIST tests. Meanwhile, a data encryption scheme based on the robust chaos synchronization method is proposed with low computation complexity. The synchronization signal, in which the encrypted data is embedded, maintains the strength in long-haul transmission. The strong robustness of the scheme under parameter mismatch is numerically analyzed. These propositions show great potential in the field of secure communication, especially the long-haul scenario.

The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

Studying the Chaotic Dynamics Using Rossler-Chua Systems Combined with A Semiconductor Laser

In this paper, two different chaotic dynamic systems are coupled using a semiconductor laser to produce a new chaotic system. These two chaotic systems are Rossler and Chua systems. X-dynamic of Rossler system was coupled optically using optical fiber as a carrier of signal with x, y, and z-dynamics of Chua system. The results were analyzed and the behavior of Chua system was found to be changing in time series which, in turn, changed the attractor. The Chua attractor was converted from double scroll to single scroll. The results obtained from connecting two different systems in chaotic behavior showed a remarkable increase in the bandwidth of Chua system. This increase in bandwidth opens up a wide field for many applications, the most important of which is in the field of secure communications.

Synchronization between Integer and Fractional Chaotic Systems Via. Tracking Control and Non Linear Control With Application

In this paper the synchronization between complex fractional order chaotic system and integer order hyper chaotic system has been investigated. Due to increased complexity and presence of additional variables, it seems to be very interesting and can be associated with real life problems. Based on the idea of tracking control and non linear control, we have designed the controllers to obtain the synchronization between the chaotic systems. To establish the efficacy of the methods computations have been carried out. Excellent agreement between the analytical and computational studies has been observed. The achieved synchronization is illustrated in field of secure communication. The results have been compared with published literature.

Design of 9-D global chaotic system and its application in secure communication

PurposeIn this paper, a nine-dimensional chaotic system is designed and applied to secure communication.Design/methodology/approachFirstly, the equilibrium characteristics, dissipativity, bifurcation diagram and Lyapunov exponent spectrum are used to analyze the relevant characteristics of the proposed nine-dimensional chaotic system. In the analysis of Lyapunov exponential spectrum, when changing the linear parameters, the system shows two states, hyperchaos and chaos. For secure communication, there is a large secret key space. Secondly, C0 complexity and SEcomplexity of the system are analyzed, which shows that the system has sequences closer to random sequences.FindingsThe proposed nine-dimensional system has a large key space and more complex dynamic characteristicsOriginality/valueThe results show that the proposed nine-dimensional hyperchaotic system has excellent encryption capabilities and can play an important role in the field of secure communication.

Changing Dynamics of the First, Second and Third Approximations of the Exponential Chaotic System and Their Application in Secure Communication Using Synchronization

In this manuscript a chaotic system with exponential term has been considered and studied. Its basic dynamical properties such as time series, phase plots, Lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare section etc. have been discussed and compared with its first, second and third approximate systems. The main aim of this study is to explore the dynamics of the approximations of the exponential chaotic systems. Also, the controllers have been designed to synchronize the chaotic system and its approximations using a technique “compound combination synchronization” and show its application in the field of secure communication. Simulations have been provided to show the efficacy of the used method.

Dynamical Analysis of a Novel 4-D Hyper-Chaotic System With One Non-Hyperbolic Equilibrium Point and Application in Secure Communication

In this article, a novel hyper-chaotic system has been introduced and its dynamical properties (i.e., phase plots, time series, lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare sections, etc.) have been studied. Also, the novel chaotic systems have been synchronized using novel synchronization technique multi-switching compound difference synchronization and its application have been shown in the field of secure communication. Numerical simulations have been undertaken to validate the efficacy of the synchronization in secure communication.

Hybrid synchronization of high-dimensional chaos with self-excited attractors

The phenomena of Hybrid Synchronization (HS)-based has widely been utilized to provide higher security and privacy in the field of secure communication by integrating the nonlinear control strategy with the Lyapunov stability theory. To address the dynamic information resulted from sending picture and messages, this paper present another approach which called a Linearization technique to replace traditional Lyapunov stability theory. The Linearization approach can achieve convergence according to the hybrid synchronization attitude. The proposed method is verified using two non-identical 6-D hyperchaotic systems with a self-excited attractor. Experimental results indicate that the proposed tool can significant improvement in results precision under the conditions of hybrid synchronization and specific Lyapunov function unavailability. Numerical simulations are carried out by using MATLAB to validate the effectiveness of the analytical technique.

Secure Communication: Using Parallel Synchronization Technique On Novel Fractional Order Chaotic System

In this paper a novel 4-D fractional order chaotic system has been introduced. It has been synchronized in dislocated phase and anti-phase synchronization with its parallel systems by constructing non linear control inputs. The synchronization technique has been illustrated with help of an example in the field of secure communication.

Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy.

The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, a multi-scale entropy theory analysis and statistical analysis are carried out on the chaotic sequences produced by different parameters and different initial values of logistic systems. According to the simulation results, the complexity of the chaotic system represented by the logistic system is mainly decided by parameter μ. Not all characteristic parameters of the chaotic system depend on the initial values. It is possible to make a reasonable estimation and prediction of the chaotic system from a macroscopic level. A variance estimation method for the parameter μ is proposed and applied to a logistic system and to another chaotic system, which is equally effective.

Enhancement of network synchronizability via two oscillatory system

Network’s synchronization destabilizes at large coupling strength when its nodes exchange information by scalar coupling (few coordinates) instead of using vector coupling (all coordinates). This issue is commonly tackled by modifying the network topology like a ring network to Small World or Scale Free networks which increases the coupling cost and decreases the robustness. In the present work, we show that without any structural alteration even a large ring network in the nearest neighborhood configuration using only a single coordinate in the coupling, could be made synchronizable. The primary condition is that the node dynamics should be given by a pair of oscillators (say, two oscillatory system TOS) rather than by a conventional way of single oscillator (say, single oscillatory system). It has been found that TOS not only stabilizes the chaotic synchronization but also the hyperchaotic synchronization manifold (a major challenge in the field of secure communication wherein multi parameter BK method is needed). The frameworks of drive-response system and master stability function have been used to study the TOS effect by varying TOS parameters with and without feedback (feedback means quorum sensing conditions). The TOS effect has been found numerically both in the chaotic (Rössler, Chua and Lorenz) and hyperchaotic (electrical circuit) systems. However, since threshold also increases as a side effect of TOS, the extent of β enhancement depends on the choice of oscillator model like larger for Rössler, intermediate for Chua and smaller for Lorenz.

Synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive neural network control

Time delay frequently appears in many phenomena of real life and the presence of time delay in a chaotic system leads to its complexity. It is of great practical significance to study the synchronization control of fractional-order chaotic systems with time delay. This is because it is closer to the real life and its dynamical behavior is more complex. However, the chaotic system is usually uncertain or unknown, and may also be affected by external disturbances, which cannot make the ideal model accurately describe the actual system. Moreover, in most of existing researches, they are difficult to realize the synchronization control of fractional-order time delay chaotic systems with unknown terms. In this paper, for the synchronization problems of the different structural fractional-order time delay chaotic systems with completely unknown nonlinear uncertain terms and external disturbances, based on Lyapunov stability theory, an adaptive radial basis function (RBF) neural network controller, which is accompanied by integer-order adaptive laws of parameters, is established. The controller combines RBF neural network and adaptive control technology, the RBF neural network is employed to approximate the unknown nonlinear functions, and the adaptive laws are used to adjust corresponding parameters of the controller. The system stability is analyzed by constructing a quadratic Lyapunov function. This method not only avoids the fractional derivative of the quadratic Lyapunov function, but also ensures that the adaptive laws are integer-order. Based on Barbalat lemma, it is proved that the synchronization error tends to zero asymptotically. In the numerical simulation, the uncertain fractional-order Liu chaotic system with time delay is chosen as the driving system, and the uncertain fractional-order Chen chaotic system with time delay is used as the response system. The simulation results show that the controller can realize the synchronization control of the different structural fractional-order chaotic systems with time delay, and has the advantages of fast response speed, good control effect, and strong anti-interference ability. From the perspective of long-term application, the synchronization of different structures has greater research significance and more development prospect than self synchronization. Therefore, the results of this study have great theoretical significance, and have a great application value in the field of secure communication.

Online real-time 7 Gbit/s physical random number generation utilizing chaotic laser pulses

Random numbers are used to encrypt the information in the field of secure communications. According to one-time pad theory found by Shannon, the absolute security of the high-speed communication requires the ultrafast reliable random numbers to be generated in real-time. Using complex algorithms can generate pseudorandom numbers, but they can be predicted due to their periodicity. Random numbers based on physical stochastic phenomena (such as electronic noise, frequency jitter of oscillator) can provide reliable random numbers. However, their generation rates are at a level of Mbit/s typically, limited by the bandwidth of traditional physical sources. In recent years, high-speed physical random number generation based on chaotic laser has attracted much attention. Common methods of extracting random numbers are to sample and quantitate the chaotic signal in electronic domain with a 1-bit or multi-bit analog-to-digital converter (ADC) triggered by an RF clock and then post-process the original binary sequences into random numbers. However, the large jitter of the RF clock severely restricts the speed of ADC. Moreover, the existence of the subsequent post-processing process put a huge challenge to how the synchronization is kept among all the devices (e.g., XOR gates, memory buffers, parallel serial converters) by using an RF clock. Thus, to our knowledge, the fastest real-time speed of the reported physical random number generator is less than 5 Gbit/s. In this paper, we propose a novel method of generating the real-time physical random numbers by utilizing chaotic laser pulses. Through sampling the chaotic laser in all-optical domain by using a mode-locked pulsed laser, chaotic laser pulse sequences can be obtained. Then, real-time physical random numbers are obtained directly by self-delay comparing the chaotic pulse sequences with no need of RF clock nor any post-processing. Furthermore, a proof-of-principle experiment is carried out, in which an optical feedback chaotic semiconductor laser is employed as an entropy source. Experimental results show that the real-time random number sequences at rates of up to 7 Gbit/s can be achieved. The real-time speed is mainly limited by the bandwidth of the applied chaotic signal. If the chaotic laser with a higher bandwidth is adopted, the real-time generation rate can be further enhanced.

A memristor-based chaotic system and its field programmable gate array implementation

A nanoscale memristor can replace the nonlinear part of a chaotic system, which can greatly reduce the physical size of the chaotic system. More importantly, it can enhance the complexity of the chaotic system and the randomness of signals. In this paper, a new memristor-based chaotic system is designed based on a new three-dimensional autonomous chaotic system. In order to study the complex dynamic characteristics of the memristive system, the chaotic system is investigated by the theoretical derivation, numerical simulation, stabilization of equilibrium points, and Lyapunov exponent spectrum. The influences of different parameters on the phase diagram and the stability of equilibrium point of this system are also discussed in detail. It is interesting that when system parameters a and c take different values, the location and stability of the equilibrium point of the system will be changed, then two scrolls of the system will be overturned at a different angle, and it will produce a different degree of aliasing between the two scrolls. Parameter b has a large variable range, when it is changed, and the system will transform into three kinds of classical chaotic systems defined by Vaněček and Celikovsk. These indicate that the memristor-based chaotic system has a lot of valuable dynamic behaviors, so it has applications in the field of secure communication, information processing etc. Field programmable gate array (FPGA) technology has a large capacity and high reliability, which is widely used in modern digital signal processing. And with the development of FPGA technology, applying FPGA technology to realizing the chaotic systems has gradually become a hot topic. Moreover, the improved Newton iteration method is used to design a square root operator of memristor in this paper by using verilog hardware description language (verilog HDL) which only needs three times iteration to reach the required accuracy. The results of FPGA hardware are consistent with the numerical simulation results. It breaks through the previous bottleneck that the chaotic system based on titanium dioxide memristor can only be simulated in computer, which is of great significance for further studing of memristor, and provides a reference for further research on the memristor-based chaotic system and applications in secure communication and information processing.