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In this paper, the problem of chaos control in discrete-time chaotic systems with unknown governing equations and limited measurable states is investigated. Using the time-series of only one measurable state, an algorithm is proposed to stabilize unstable fixed points. The approach consists of three steps: first, using Takens embedding theory, a delayed phase space preserving the topological characteristics of the unknown system is reconstructed. Second, a dynamic model is identified by recursive least squares method to estimate the time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate linear delayed feedback controller is obtained for stabilizing unstable fixed points of the system. Controller gains are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to the generalized hyperchaotic Henon system, prey-predator population map, and the discrete-time Lorenz system. [ABSTRACT FROM AUTHOR]

Abstract: In recent years, a variety of chaos-based image encryption algorithms have been proposed. Most of them employ the confusion-diffusion architecture and operate at the pixel level. In this paper, we analyze the intrinsic features of the bit distributions, the high correlation among bit planes and other issues related to the bit information of an image. Due to the superior characteristics of bit-level operations and the intrinsic bit features of the image, an expand-and-shrink strategy is employed to shuffle the image with reconstructed permuting plane. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed scheme. [Copyright &y& Elsevier]

Abstract: Based on elementary cellular automata, a new image encryption algorithm is proposed in this paper. In this algorithm, a special kind of periodic boundary cellular automata with unity attractors is used. From the viewpoint of security, the number of cellular automata attractor states are changed with respect to the encrypted image, and different key streams are used to encrypt different plain images. The cellular neural network with chaotic properties is used as the generator of a pseudo-random key stream. Theoretical analysis and experimental results have both confirmed that the proposed algorithm possesses high security level and good performances against differential and statistical attacks. The comparison with other existing schemes is given, which shows the superiority of the proposal scheme. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest a new steganographic spatial domain algorithm based on a single chaotic map. Unlike most existing steganographic algorithms, the proposed algorithm uses one chaotic map to determine the pixel position of the host color image, the channel (red, green or blue) and the bit position of the targeted value in which a sensitive information bit can be hidden. Furthermore, this algorithm can be regarded as a variable-sized embedding algorithm. Experimental results demonstrate that this algorithm can defeat many existing steganalytic attacks. In comparison with existing steganographic spatial domain based algorithms, the suggested algorithm is shown to have some advantages over existing ones, namely, larger key space and a higher level of security against some existing attacks. [Copyright &y& Elsevier]

Abstract: Recently [Solak E, Çokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405–1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259–1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749–761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications. [Copyright &y& Elsevier]

Abstract: The pseudo-randomness and complexity of binary sequences generated by chaotic systems are investigated in this paper. These chaotic binary sequences can have the same pseudo-randomness and complexity as the chaotic real sequences that are transformed into them by the use of Kohda’s quantification algorithm. The statistical test, correlation function, spectral analysis, Lempel–Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudo-randomness and complexity of these binary sequences. The experimental results show the finite binary sequences generated by the chaotic systems have good properties with the pseudo-randomness and complexity of sequences. However, the pseudo-randomness and complexity of sequence are not added with the increase of sequence length. On the contrary, they steadily decrease with the increase of sequence length in the criterion of approximate entropy and statistical test. The constraint of computational precision is a fundamental reason resulting in the problem. So only the shorter binary sequences generated by the chaotic systems are suitable for modern cryptography without other way of adding sequence complexity in the existing computer system. [Copyright &y& Elsevier]

Abstract: Recently, many scholars have proposed chaotic cryptosystems in order to promote communication security. However, there are a number of major problems detected in some of those schemes such as weakness against differential attack, slow performance speed, and unacceptable data expansion. In this paper, we introduce a new chaotic block cipher scheme for image cryptosystems that encrypts block of bits rather than block of pixels. It encrypts 256-bits of plainimage to 256-bits of cipherimage within eight 32-bit registers. The scheme employs the cryptographic primitive operations and a non-linear transformation function within encryption operation, and adopts round keys for encryption using a chaotic system. The new scheme is able to encrypt large size of images with superior performance speed than other schemes. The security analysis of the new scheme confirms a high security level and fairly uniform distribution. [Copyright &y& Elsevier]

Abstract: A block encryption for image using combination of confusion and diffusion is proposed in this paper. In this encryption, a new compound mode is proposed. Baker map is used to generate a pseudo-random sequence, and several one-dimension chaotic maps are dynamically selected to encrypt blocks of image, in the order of the pseudo-random sequence generated by Baker map. Different with other combined encryptions, the algorithm of this encryption does not confusion original image directly, but generate a pseudo-random, which is used as a route for diffusion, combines pixels to block randomly and arrays them. When diffusion is executing, for mutual diffusion of pixels, the confusion is working by the pseudo-random order of route, the combination is deep-seated. [Copyright &y& Elsevier]

Abstract: Recently, a variety of chaos-based hash functions have been proposed. Nevertheless, none of them can realize modification localization. In this paper, a hash function with both modification detection and localization capabilities is proposed, which can also support the parallel processing mode. By using the mechanism of changeable-parameter and self-synchronization, the keystream can establish a close relation with the algorithm key, the content, and the order of each message unit. Theoretical analysis and computer simulation indicate that the proposed algorithm can satisfy the performance requirements of hash functions. [Copyright &y& Elsevier]

Abstract: In this paper, nonlinear time series modeling techniques are applied to analyze building energy consumption data. The time series were obtained for the benchmark data set Proben 1, and comes from the first energy prediction contest, the Great Building Energy Predictor Shootout I, organized by ASHRAE. The phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem suggested by TAKENS. The embedding parameters, e.g. the delay time and the embedding dimension are estimated using the average mutual information (AMI) of the data and the false nearest neighbor (FNN) algorithm, respectively. Nonlinearity was detected, by applying the surrogate data sets method. Numerically estimated non-integral fractal dimension and a positive Lyapunov exponent are not necessarily sufficient indication of chaos; therefore we apply a more stringent criterion, developed by Gao and Zheng, which is based on the logarithmic displacement of time-dependent exponent curves, and show that these data are chaotic. Based on this analysis and proof, we then calculate the correlation dimension of the resulting attractor and the largest Lyapunov exponent. The correlation dimension 3.47 and largest Lyapunov exponent 0.047 are estimated. These results indicate that chaotic characteristics obviously exist in the specific energy consumption data set, and thus techniques based on phase space dynamics can be used to analyze and predict buildings energy use. [Copyright &y& Elsevier]

Abstract: The construction of a new Hash function attracts much attention recently. In Kwok and Tang (2005) [Kwok HS, Tang WKS. A chaos-based cryptographic Hash function for message authentication. Int J Bifurcat Chaos 2005;15:4043–50], a chaos-based Hash function has been proposed. In this paper, the potential flaws in the original algorithm are analyzed in detail, and then the corresponding improving measures are proposed. We enhance the influence that each bit of the final Hash value is closely related to all the bits of the message or key and a single bit change in message or key results in great changes in the final Hash value. Simulation results show that the proposed improving algorithm has strong diffusion and confusion capability, good collision resistance, extreme sensitivity to message and secret key. [Copyright &y& Elsevier]

Abstract: Chaos is undesirable in many engineering applications since it causes a serious degradation of the system performance and restricts the system’s operating range. Therefore, the problem of controlling chaos has attracted intense interest in recent years. This paper proposes an approach for optimizing the control of chaotic systems with input saturation using an input-state linearization scheme. In the proposed approach, the optimal system gains are identified using the Nelder–Mead simplex algorithm. This algorithm does not require the derivatives of the cost function (or the performance index) to be optimized, and is therefore particularly applicable to problems with undifferentiable elements or discontinuities. Two numerical simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper proposes an approach for detecting unstable periodic orbits embedded in chaotic systems by using the simplex method. The simplex algorithm is easily implemented and does not require the derivatives of the function to be optimized. As a result, it is also applicable to chaotic systems with discontinuities or in which functions contain noise. [Copyright &y& Elsevier]

Abstract: A block encryption algorithm using dynamic sequences generated by multiple chaotic systems is proposed in this paper. In this algorithm, several one-dimension chaotic maps generate pseudo-random sequences, which are independent and approximately uniform. After a series of transformations, the sequences constitute a new pseudo-random sequence uniformly distributing in the value space, which covers the plaintext by executing Exclusive-OR and shifting operations some rounds to form the cipher. This algorithm makes the pseudo-random sequence possess more concealment and noise like characteristic, and overcomes the periodic malpractice caused by the computer precision and single chaotic system. Simulation results show that the algorithm is efficient and useable for the security of communication system. [Copyright &y& Elsevier]

• A novel technique for the analysis of dynamical systems is presented. The proposed method is based on the relative error of a pair of discrete maps obtained through semi-implicit methods of the same accuracy order but with different commutation matrices. • The proposed analysis method does not require the choice of initial divergence or the normalization procedure contrary to the traditional LLE estimation algorithms and allows distinguishing chaotic and periodic dynamics. • The minimum simulation time required for the convergence of investigated quantitative metrics is studied with the developed experimental testbench and methodology. • The proposed method appears to be the most numerically efficient algorithm among the tested analysis techniques. Many novel chaotic systems have recently been identified and numerically studied. Parametric chaotic sets are a valuable tool for determining and classifying oscillation regimes observed in nonlinear systems. Thus, efficient algorithms for the construction of parametric chaotic sets are of interest. This paper discusses the performance of algorithms used for plotting parametric chaotic sets, considering the chaotic Rossler, Newton-Leipnik and Marioka-Shimizu systems as examples. In this study, we compared four different approaches: calculation of largest Lyapunov exponents, statistical analysis of bifurcation diagrams, recurrence plots estimation and introduced the new analysis method based on differences between a couple of numerical models obtained by semi-implicit methods. The proposed technique allows one to distinguish the chaotic and periodic motion in nonlinear systems and does not require any additional procedures such as solutions normalization or the choice of initial divergence value which is certainly its advantage. We evaluated the performance of the algorithms with the two-stage approach. At the first stage, the required simulation time was estimated using the perceptual hash calculation. At the second stage, we examined the performance of the algorithms for plotting parametric chaotic sets with various resolutions. We explicitly demonstrated that the proposed algorithm has the best performance among all considered methods. Its implementation in the simulation and analysis software can speed up the calculations when obtaining high-resolution multi-parametric chaotic sets for complex nonlinear systems. [ABSTRACT FROM AUTHOR]