A digital pseudo-random number generator based on sawtooth chaotic map with a guaranteed enhanced period

Nonlinear Dynamics - We investigate tunneling behavior between two bright solitons in a Bose–Einstein condensate with attractive contact interactions between atoms. The explicit tunneling...     

A novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Nonlinear Dynamics - In last years, low-dimensional and high-dimensional chaotic systems have been implemented in cryptography. The efficiency and performance of these nonlinear systems play an...     

A novel block cryptosystem based on the coupled chaotic map lattice

In this paper, the authors propose a novel block cryptographic scheme based on the coupled chaotic map lattice. A pseudorandom number generator is constructed with the coupled spatiotemporal chaotic map lattice, which depends on the plaintext. The plaintext block is then encrypted by the classical chaotic masking technique. The pseudorandom sequences produced by the generator have excellent statistical properties; therefore, they are suitable for encrypting messages. Moreover, it can be easily implemented in parallel by hardware. Both theoretical analysis and numerical simulation prove the block cryptographic scheme secure and practical.     

A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption

Nonlinear Dynamics - In this work, we propose a novel 3D chaotic map obtained by coupling the piecewise and logistic maps. Showing excellent properties, like a high randomness, a high complexity...     

A new pseudo-random number generator based on CML and chaotic iteration

In this paper, we propose a new algorithm of generating pseudorandom number generator (PRNG), which we call (couple map lattice based on discrete chaotic iteration (CMLDCI)) that combine the couple map lattice (CML) and chaotic iteration. And we can prove that this method can be written in a form of chaos map, which is under the sense of Devaney chaos. In addition, we test the new algorithm in NIST 800-22 statistical test suits and we use it in image encryption.     

Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Nonlinear Dynamics - Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period...     

Pseudo-random number generator based on discrete-space chaotic map

This paper describes an efficient method to predict the nonlinear steady-state response of a complex structure with multi-scattered friction contacts. The contact friction force is equivalent to additional stiffness and damping based on optimal approximation theory, and as a consequence, the computation is simplified greatly by the linearization for a nonlinear system. In order to obtain accurate pressure distribution on the contact interfaces, the dynamic contact normal pressure is obtained by the equivalent static analysis which is validated for most engineering cases. Considering the complex procedure to determine the transformation between two different contact states, the differential forms of friction force are given to solve the tangential force accurately under the complex movement of interfaces. The approaches developed in this paper are particularly suitable to solve the dynamic response of large-scale structures with local contact nonlinearities. The entire procedure to calculate the steady-state response of a finite element model with a large number of degrees of freedom is demonstrated taking the blades with underplatform dampers as an example. The method is proved to be accurate and efficient; in particular, it does not suffer convergence problem in the allowable range of precision error, which exhibits remarkable potential engineering application values.     

Image encryption based on fractional chaotic pseudo-random number generator and DNA encryption method

Nonlinear Dynamics - Nonlinear dynamic systems and chaotic systems have been quite exhaustively researched in the domain of cryptography. However, the possibility of using fractional chaotic...     

Spatiotemporal and synchronous chaos in accumulated coupled map lattice

The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.     

Construction of a novel nth-order polynomial chaotic map and its application in the pseudorandom number generator

Chaotic maps with good chaotic performance have been extensively designed in cryptography recently. This paper gives an nth-order polynomial chaotic map by using topological conjugation with piecewise linear chaos map. The range of chaotic parameters of this nth-order polynomial chaotic map is large and continuous. And the larger n is, the greater the Lyapunov exponent is and the more complex the dynamic characteristic of the nth-order polynomial chaotic map. The above characteristics of the nth-order polynomial chaotic map avoid the disadvantages of one-dimensional chaotic systems in secure application to some extent. Furthermore, the nth-order polynomial chaotic map is proved to be an extension of the Chebyshev polynomial map, which enriches chaotic map. The numerical simulation of dynamic behaviors for an 8th-order polynomial map satisfying the chaotic condition is carried out, and the numerical simulation results show the correctness of the related conclusion. This paper proposed the pseudorandom number generator according to the 8th-order polynomial chaotic map constructed in this paper. Using the performance analysis of the proposed pseudorandom number generator, the analysis result shows that the pseudorandom number generator according to the 8th-order polynomial chaotic map can efficiently generate pseudorandom sequences with higher performance through the randomness analysis with NIST SP800-22 and TestU01, security analysis and efficiency analysis. Compared with the other pseudorandom number generators based on chaotic systems in recent references, this paper performs a comprehensive performance analysis of the pseudorandom number generator according to the 8th-order polynomial chaotic map, which indicates the potential of its application in cryptography.

     

A fast image encryption algorithm based on non-adjacent dynamically coupled map lattice model

Nonlinear Dynamics - This paper proposes a new logistic-dynamic Arnold coupled logistic map lattice model (LDACLML), where coupling coefficient is logistics map. According to the analysis of...     

Control and synchronization of Mandelbrot sets in coupled map lattice

This paper gives the definition of Mandelbrot set in a coupled map lattice (CML Mandelbrot set), and studies its control and synchronization. A proper mathematical transform is used to achieve the scaling, with regards to size, of the CML Mandelbrot set without changing its structure properties. Furthermore, two different methods, gradient control and optimal control, are separately applied to realize the synchronization of different CML Mandelbrot sets, that making one CML Mandelbrot set change into another. Numerical simulations show the effectiveness of these controls and the feasibility of achieving synchronization using the two different methods.     

3-periodic traveling wave solutions for a dynamical coupled map lattice

In this paper, the existence of periodic traveling wave solutions with a priori unknown velocity is considered for a coupled map lattice dynamical system. By trasforming our problem into one that involves polynomials, explicit 2- and 3-periodic traveling wave solutions are found, while the other solutions can be computed numerically. Since there does not seem to be any reports on explicit traveling wave solutions, we hope that our results will lead to the discovery of many others.     

A stream cipher algorithm based on 2D coupled map lattice and partitioned cellular automata

Nonlinear Dynamics - The two-dimensional coupled map lattice (2D CML) is a spatiotemporal chaotic model with complex dynamic behavior and has high potential for designing stream cipher. We...     

Projective-dual synchronization in delay dynamical systems with time-varying coupling delay

The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projective-dual-anticipating to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable coupling delay τ _p (t) is discussed. Using Krasovskii–Lyapunov stability theory, a general condition for projective-dual synchronization is derived. Numerical simulations on the chaotic Ikeda and Mackey–Glass systems are given to demonstrate the effectiveness of the theoretical results.     

Passivity of uncertain neural networks with both leakage delay and time-varying delay

In this paper, the passivity problem is investigated for a class of uncertain neural networks with leakage delay and time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov–Krasovskii functionals, and employing Newton–Leibniz formulation and the free-weighting matrix method, several delay-dependent criteria for checking the passivity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Two examples with simulations are given to show the effectiveness and less conservatism of the proposed criteria.