A image encryption scheme based on dynamical perturbation and linear feedback shift register

Because low-dimensional chaotic precision degradation has seriously affected the security of encryption, compound chaotic function is designed. It is based on two new one-dimensional chaotic functions. By the definition of Devaney chaotic, the properties of compound chaotic functions are rigidly proved. Based on the compound chaotic function and linear feedback shift register (LFSR), a new pseudo-random sequence generator is designed to generate a more random sequence and expand the key space. The properties of compound chaotic functions and LFSR are also established. In the scheme, a dynamic block division of the 3D baker and dynamical perturbation are illustrated using the compound chaotic map to derive the confusion image. The new pseudo-random sequence generator expands the key space and improves the security of image encryption scheme. The results of entropy analysis, difference analysis, weak-key analysis, statistical analysis, cipher random analysis, and cipher sensitivity analysis show that the encryption scheme has a better security. Compared with traditional encryption scheme and one-dimensional logistic chaotic map, the new image encryption scheme has a better performance in speed, complexity, and security. This paper illustrates how to solve the problem of short periods and low precision of one-dimensional chaotic function by perturbation and LFSR together.     

Hardware implementation of pseudo-random number generators based on chaotic maps

We show the usefulness of bifurcation diagrams to implement a pseudo-random number generator (PRNG) based on chaotic maps. We provide details on the selection of the best parameter values to obtain high entropy and positive Lyapunov exponent from the bifurcation diagram of four chaotic maps, namely: Bernoulli shift map, tent, zigzag, and Borujeni maps. The binary sequences obtained from these maps are analyzed to implement a PRNG both in software and in hardware. The software implementation is realized using 32 and 64 bits microprocessor architectures, and with floating point and fixed point computer arithmetic. The hardware implementation is done by using a field-programmable gate array (FPGA) architecture. We developed a serial communication interface between the PRNG on the FPGA and a personal computer to obtain the generated sequences. We validate the randomness of the generated binary sequences with the NIST test suite 800-22-a both in floating point and fixed point arithmetic. At the end, we show that those chaotic maps are suitable to implement a PRNG but according to the hardware resources, the one based on the Bernoulli shift map is better. In addition, another advantage is that the required initial value for the sequences can be within the whole interval \([-1,1]\), including its bounds.     

Separation of isochromatics and isopachics using a Faraday rotator in dynamic-holographic photoelasticity

A method is presented that allows the simultaneous separation of isochromatic- and isopachic-fringe patterns for transient-plane stress problems. Isopachic fringes are obtained by means of holography with a Faraday cell and a pulsed ruby laser flashing dual pulses. As usual isochromatic whole-order fringes are recorded in a circular-light polariscope. The shock generator (air-gun) and its synchronizing system with the ruby laser is described. The procedure is applied to the recording of the isochromatic- and isopachic-fringe patterns in a disk under radial dynamic loads.     

Dynamical randomicity and predictive analysis in cubic chaotic system

The dynamical randomicity and grey prediction in cubic chaotic system will be studied in this paper. These stochastic symbolic sequences bear three features. The distribution of frequency, inter-occurrence times, the first passage time, the rth passage time and the ordinal passage time are discussed separately. By using transfer probability of Markov chain (MC), one obtains analytic expressions of generating functions in three-probabilities stochastic wander model, which can be applied to all three symbolic systems. The visitation density function of cubic map will also be resolved. Especially, after introducing grey system theory, one is mainly using GM(1,1) model to forecast data sequences, and the usual forecast precision is approximately 90%. In the symbolic prediction of cubic chaotic dynamical system, the precision of grey prediction certainly will decrease as the length of symbolic sequence is increasing. But in this place we have found a generating rule that may realize chaotic synchronization at least in short and medium terms, and we can analyze and forecast in this way.     

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.

     

Partial synchronization in a system of globally coupled maps

We study the appearance of a chaotic partial synchronization in a system of globally coupled maps. We analyze the structure of cluster zones for small values of the coupling parameter and conditions for the formation of chaotic attractors on cluster manifolds. We find a formula that describes the relationship between the transversal and longitudinal Lyapunov numbers for trajectories on the manifold and necessary conditions for the transversal stability of these trajectories.Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 229–240, April–June, 2004.     

Application of two-dimensional photoelasticity to the study of acceleration stresses under quasi-static conditions

A laboratory method has been developed to simulate the state of stress in various structures under rapid-acceleration loading conditions. This method subjects a two-dimensional photoelastic model to impact loading, using a commercially purchased drop tester. The particular approach selected for studying this dynamic situation was a static technique utilizing a 4×5 studio camera and a high-intensity Xenon-light source. The light was flashed by the maximum pulse from an accelerator mounted on the model. This static treatment provided a significant improvement in the optical quality of the fringe patterns over that obtained by dynamic high-speed photographic methods used in earlier impact studies. It permitted evaluation of the reproducibility of the loading system and associated photographic synchronization and triggering circuits, since double exposures could be taken of separate individual tests of the same loading condition with little degradation of the optical fringe data. A composite picture made of four separate photographs of a series of individual tests, with the camera viewing a different portion of the sample in each picture, showed continuity of fringe pattern and highlighted the regions of critical stress within the model.     

Provably secure three-party key agreement protocol using Chebyshev chaotic maps in the standard model

Recently, several key agreement protocols based on Chebyshev chaotic maps have been proposed in the literature. However, they can normally achieve “heuristic” security, that is, once drawbacks are found in these protocols, they are either modified to resist the new attacks, or are discarded. Under these circumstances, it is necessary and significant to define standard security models that can precisely characterize the capabilities of the participants and a potent adversary. Hence, we propose to use public key encryption based on enhanced Chebyshev chaotic maps and pseudo-random function ensembles to construct an efficient three-party key agreement protocol under the standard model, in which the adversary is able to make a wider range of queries and have more freedom than the other proposed schemes. In the design of our protocol, we follow the ideas in the recent key agreement protocol of Yang and Cao’s. The proposed protocol is shown to be provably secure if decisional Diffie–Hellman problem, which is based on Chebyshev chaotic maps, is computationally infeasible. To the best of our knowledge, our protocol is the first provably secure 3PAKE protocol using Chebyshev chaotic maps under the standard model.     

Application of faraday's effect in static and dynamic holographic photoelasticity

The basic principle of applying Faraday's effect to achieve the separation of fringes in static and dynamic holographic photoelasticity, and a study and application of Faraday's light rotator are described in this paper. It is proposed that Faraday's light rotator be used for automating photoelastic instrumentation for measuring isoclinics and the decimal orders of isochromatic fringes.     

A practical synchronization approach for fractional-order chaotic systems

A practical synchronization approach is proposed for a class of fractional-order chaotic systems to realize perfect \(\delta \)-synchronization, and the nonlinear functions in the fractional-order chaotic systems are all polynomials. The \(\delta \)-synchronization scheme in this paper means that the origin in synchronization error system is stable. The reliability of \(\delta \)-synchronization has been confirmed on a class of fractional-order chaotic systems with detailed theoretical proof and discussion. Furthermore, the \(\delta \)-synchronization scheme for the fractional-order Lorenz chaotic system and the fractional-order Chua circuit is presented to demonstrate the effectiveness of the proposed method.     

Parameter identification of bidirectional IPT system using chaotic asexual reproduction optimization

Bidirectional inductive power transfer (IPT) system facilitates contactless power transfer between two sides and across an air gap, through weak magnetic coupling. Typically, this system constitutes a high-order resonant circuit and, as such, is difficult to design and control. In this study, a novel technique for parameter identification of bidirectional IPT system is presented by using chaotic asexual reproduction optimization (CARO). The asexual reproduction optimization (ARO) is a novel kind of evolutionary-based algorithm that mathematically models the budding mechanism of asexual reproduction. The CARO employs chaotic sequence to enhance ARO’s global searching ability. The parameter identification of a bidirectional IPT system is posed as an optimization process with an objective function minimizing the errors between the estimated and measured value. The implementation of the CARO-based parameter identification technique is analyzed in detail. Simulations are used to test the robustness and generalization ability of the proposed technique.     

A novel pseudo-random number generator from coupled map lattice with time-varying delay

Chaos has been widely combined with cryptography in the field of information security, especially, a considerable amount of studies of generating pseudo-random numbers based on chaotic systems have been proposed in recent decades. However, many of them are easy to be attacked via utilizing the nonlinear prediction method based on phase space reconstruction and other analysis. Furthermore, under the finite precision environment of computer simulation, there does not exist a random sequence which is truly non-periodic. Unfortunately, few researches had made a related analysis on the above two discussions. This paper is devoted to designing a pseudo-random number generator based on coupled map lattice with time-varying delay, analyzing the random properties of the generated pseudo-random numbers and discussing the dynamical degradation of the system under finite precision of computer simulation. The proposed scheme merely depends on the determining equation; thus, the algorithm itself is not complex, which does not impose high demand on computer hardware and its efficiency is excellent. In order to meet the requirements of using the proposed pseudo-random number generator in cryptography and other practical engineering applications, the proposed pseudo-random number generator is subjected to statistical tests utilizing the well-known test suites, such as NIST SP800-22 and TestU01. Moreover, other related properties, such as permutation entropy, invariant distribution, degradation of dynamical characteristics and parameter test, are also investigated. All results illustrate that the new pseudo-random number generator can generate a high percentage of available pseudo-random numbers for scientific computer simulation and practical applications in the field of information security.     

Measurement of strain fields near coldworked holes

Residual strains near coldworked holes were measured for several degrees of radial expansion. Moiré-grating photography created magnified replicas of deformed gratings. Fringe patterns with sensitivity multiplication and S/N improvement were obtained by optical data processing and by using slotted apertures for photography. Computer data reduction and plotting provided the required strain maps.     

Robust \mathcal{H}_{\infty} decentralized dynamic control for synchronization of a complex dynamical network with randomly occurring uncertainties

This paper considers synchronization problem of an uncertain complex dynamical network. The norm-bounded uncertainties enter into the complex dynamical network in randomly ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under the circumstances, a robust $\mathcal{H}_{\infty}$ decentralized dynamic feedback controller is designed to achieve asymptotic synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality (LMI) framework, the existence condition for feasible controllers is derived in terms of LMIs. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our result.     

The dependence of crack velocity on the critical stress in fracture

The constant velocity of crack propagation in PMMA is investigated in terms of the fracture stress for both continuously increasing loading (strain rate ?=0.59×10^?4 s^?1) and dynamic loading (strain rate ?=0.35 s^?1). It was found that the constant crack velocity increases with increasing fracture stress and that it depends on the loading conditions (continuously increasing or dynamic loading). In particular, it was found that the increase of the constant velocity for the static loading case is higher than for the dynamic one. However, in both cases, the constant velocity reaches a limiting value for stresses higher than a certain level.     

The grid-shift technique for moiré analysis of strain in solid propellants

Moiré principles and procedures were surveyed with a view toward adaptation to measurement of complex strain distribution in solid propellants. Compliant coating and photosensitive materials were selected for grid reproduction. The most flexible of the several possible procedures for recording moiré data was found to be grid photography. A novel “grid-shift” technique employing coarse grids was developed for point-by-point determination of surface displacement derivatives, and the grid-shift relations for large strain and large rotation were derived. The technique is extremely versatile, permitting the analysis of strain of dynamically deformed specimens in nonambient environmental conditions of temperature, pressure or atmosphere. The utility of the technique was demonstrated by application to static and dynamic problems.     

Adaptive dynamic surface control for MEMS triaxial gyroscope with nonlinear inputs

An adaptive dynamic surface control algorithm that incorporates adaptive control and fuzzy logic system into the implementation of dynamic surface control for regulating problem of MEMS triaxial gyroscope subject to external disturbance, uncertainty and input uncertainty is developed in this work. To relax the requirement of exact model and obtain fully adaptive property, a fuzzy logic system is introduced to approximate the uncertainty. With adaptive control structure, the proposed controller can obtain the properties of fast dynamic response and high tracking-accuracy, even the existence of disturbance, uncertainty and control input nonlinearity. All parameters adjustment rules for the proposed control scheme are derived from Lyapunov theory such that the trajectory of tracking-error converges to the small neighborhood of equilibrium point. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.     

Dynamic fracture toughness of Homalite-100

Dynamic fracture toughness of Homalite-100 determined by T. Kobayashi and Dally are compared with those previously obtained by the authors where similarities in the two results for single-edged-notch specimens of various configurations are noted. Dynamic fracture toughness of Araldite B obtained by Kalthoff, Beinert and Winkler and those of Homalite-100 obtained by the authors are then compared and, again, similarities in the two results and, in particular, the scatters in experimental data for wedge-loaded DCB specimens of different sizes are found. All three teams of investigators used static near-field solution to compute the dynamic stress-intensity factors from recored dynamic isochromatics or dynamic caustics. Errors generated through this use of static near-field solutions, as well as through the use of larger isochromatic lobes, are thus discussed.     

Calculation of the rotational transition probabilities of diatomic molecules when they collide with heavy particles

The collisional rotational transition probabilities for molecule-molecule and molecule-atom interactions in three-dimensional space are calculated. The quasiclassical approach developed in [1] is used. Expressions are obtained that are suitable for practical calculations of single-quantum and double-quantum rotational transitions in diatomic molecules. The collisional rotational transition probabilities are averaged over the Maxwell velocity distribution and their dependence on the gas temperature is obtained. To illustrate the method the results of a calculation of the probabilities for HCl-HCl, HCl-He, CO-CO interaction are presented.     

Synchronization of stochastic reaction–diffusion systems via boundary control

This paper studies the problem of mean square asymptotical synchronization and \(H_\infty \) synchronization for coupled stochastic reaction–diffusion systems (SRDSs) via boundary control. Based on the deduced synchronization error dynamic, we design boundary controllers to achieve mean square asymptotical synchronization. By virtue of Lyapunov functional method and Wirtinger’s inequality, sufficient conditions are obtained for ensuring mean square asymptotical synchronization. When coupled SRDSs are subject to external disturbance, mean square \(H_\infty \) synchronization is investigated and corresponding criterion is presented under a designed boundary controller. In addition to focusing on systems with Neumann boundary conditions, we also briefly study coupled SRDSs with mixed boundary conditions and sufficient conditions are provided to achieve the desired performance. Numerical examples are used to verify the effectiveness of our theoretical results.