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1
Content available Double-image encryption scheme based on the phase-truncated multiple-parameter Fresnel transform
Zhou Ling, Zhou Hang, Ma Yan, Zhou Nan-Run
Optica Applicata
|
2022
|
Vol. 52, nr 2
163--177
EN
A double-image encryption algorithm is proposed with the phase-truncated multiple-parameter Fresnel transform. Firstly, the pixel positions of two plaintext images are scrambled and then the results are merged into one image with the scrambling operation. Subsequently, the resulting image is encrypted by phase truncation and phase reservation in the multiple-parameter Fresnel transform domain. The phase information is scrambled by the affine transform and then recombined with the amplitude information. The final encryption image is obtained with the pixel scrambling and diffusion methods to further enhance the security of the image encryption system, where the scrambling and diffusion operations are based on logistic map, logistic-sine system and 2D logistic-adjusted-sine map. The image encryption scheme is robust against the common attacks due to the nonlinear properties of diffusion and phase truncation. Numerical simulation results verify the performance and the security of the proposed double-image algorithm based on the phase-truncated multiple-parameter Fresnel transform.
2
Content available Double-image encryption algorithm based on discrete fractional angular transform and fractional Fourier transform
Qiu Tian, Dai Wei-Hua, Chen Su-Hua, Zhou Hang, Gong Li-Hua
Optica Applicata
|
2022
|
Vol. 52, nr 4
669--684
EN
By combining fractional Fourier transform with discrete fractional angular transform, a double-image encryption algorithm is designed. The discrete cosine transform is performed on two grayscale images to generate a spectrum image, and then the generated spectrum image is compressed into an image with Zigzag scanning. The compressed image is processed with the discrete fractional angular transform, and then fractional Fourier transform and double random phase coding are executed on the image. The DNA operation controlled by chaotic system is introduced to change the pixel values. Finally, the ciphertext image is obtained through bit-level permutation and pixel adaptive diffusion. The statistical information of the plaintext images is employed as the input of the SHA-256 to calculate the initial conditions of the chaotic map. Simulation experiments demonstrate that the double-image encryption algorithm can effectively reduce the correlation among adjacent pixels of the plaintext images.
3
Content available remote A Novel Chaotic System and its Modified Compound Synchronization
Sun Junwei, Li Nan, Wang Yanfeng, Wang Wei
Fundamenta Informaticae
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2019
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Vol. 164, nr 2-3
259--275
EN
In this paper, a new chaotic system is proposed, whose dynamical behaviors are discussed with the change of the parameters in detail. The specific effects of different parameters on the system are also discussed. By adjusting these parameters of the proposed circuit, this nonlinear circuit can produce the different dynamical behaviors, such as, hyper chaotic behavior, periodic behavior, transient behavior, etc. Furthermore, a novel kind of modified compound synchronization has been investigated, where the multiple chaotic systems have been considered for different combination modes: the compound system of four scaling drive systems and one response system. The corresponding controllers are designed to realize the modified compound synchronization. The theoretical proofs and numerical simulations are given to demonstrate the validity and applicability of the proposed chaotic system and the modified compound synchronization.
4
Content available Finite-time adaptive modified function projective multi-lag generalized compound synchronization for multiple uncertain chaotic systems
Li Q., Liu S., Chen Y.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 4
613--624
EN
In this paper, for multiple different chaotic systems with fully unknown parameters, a novel synchronization scheme called ‘modified function projective multi-lag generalized compound synchronization’ is put forward. As an advantage of the new method, not only the addition and subtraction, but also the multiplication of multiple chaotic systems are taken into consideration. This makes the signal hidden channels more abundant and the signal hidden methods more flexible. By virtue of finite-time stability theory and an adaptive control technique, a finite-time adaptive control scheme is established to realize the finite-time synchronization and to properly evaluate the unknown parameters. A detailed theoretical derivation and a specific numerical simulation demonstrate the feasibility and validity of the advanced scheme.
5
Content available Hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems
Serrano F., Rossell J. M.
Acta Mechanica et Automatica
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2017
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Vol. 11, no. 2
96--103
EN
In this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyperchaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropria.
6
Content available A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control
Vaidyanathan S.
Archives of Control Sciences
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2016
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Vol. 26, no. 1
19--47
EN
This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.20572, L2 = 0 and L3 = −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as DKY = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.
7
Content available Pipelined architecture of a chaotic pseudo-random number generator in a Cyclone V SoC device
Dąbal P., Pełka R.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 7
287--289
EN
In this paper, we present a novel, optimized microarchitecture of a pseudo-random number generator (PRNG) based on the chaotic model with frequency dependent negative resistances (FDNR). The project was focused on optimization of the PRNG architecture to achieve the highest possible output throughput of the generated pseudo-random sequences. As a result we got a model of the pipelined PRNG that was implemented in Cyclone V SoC from Altera and verified experimentally. All versions of the PRNG were tested by standard statistical tests NIST SP800-22. In addition, we also provide a brief comparison with the PRNG implementation in SoC from Xilinx.
8
Content available remote Multi-model identification system properties near extremum: simulations and analysis
Guda A., Mikhalyov A.
Journal of Applied Computer Science
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2015
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Vol. 23, nr 2
21--28
EN
This article concerns the question about properties and behavior of the multi-model adaptive-searching identification methods near extremum point. The model of the relation between criterion and parameters is proposed. Numerous simulations of identification process was held under different parameters of this model and identification system. Advantages and drawbacks of the two extremum point estimation are studied. Recommendations and rough calculations to determine correct parameters of identification system itself is given.
9
Content available Pipelined pseudo-random number generator with the efficient post-processing method
Dąbal P.
International Journal of Microelectronics and Computer Science
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2015
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Vol. 6, nr 2
43--48
EN
This brief proposes a novel architecture of the chaotic pseudo-random bit generators (PRBGs) based on the chaotic nonlinear model and pipelined data processing. We investigated PRBG built on the chaotic logistic map and frequency dependent negative resistances (FDNR). A significant enhancement in terms of output throughput has been achieved by combining the advantages of pipelining with post-processing based on fast logical operations like bit shifting and XOR. The proposed method has been implemented using programmable SoC Zynq device from Xilinx. We verified output pseudo-random bit stream by standard statistical tests NIST SP800-22. We also present detailed comparison of the proposed post-processing method with the methods reported previously by the other authors. In particular, we compared the maximum output throughput and amount of total logical resources required by PRBG implementation in the programmable SoC device. For PRBGs based on the logistic chaotic map and frequency dependent negative resistance (FDNR) we obtained speed-up factors equal to 33% and 14%, respectively. By composing the output stream of 3 data channels in PRBG with FDNR element, we get the maximum throughput equal to 38.43 Gbps. That is significantly greater comparing to the chaotic PRBGs described so far.
10
Content available Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system
Vaidyanathan S., Volos C.
Archives of Control Sciences
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2015
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Vol. 25, no. 3
333--353
EN
First, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1 = 0.0395, L2 = 0 and L3 = −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY =3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.
11
Content available remote A Novel Image Encryption Scheme Based on Generalized Multi-sawtooth Maps
Ye R.
Fundamenta Informaticae
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2014
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Vol. 133, nr 1
87--104
EN
In this paper, a generalized multi-sawtooth map based image encryption scheme with an efficient permutation-diffusion mechanism is proposed. In the permutation process, a generalized multi-sawtooth map is utilized to generate one chaotic orbit used to get one index order sequence for the permutation of image pixel positions, while in the diffusion process, two generalized multi-sawtooth maps are employed to yield two pseudo-random grey value sequences for a twoway diffusion of pixel grey values. The yielded grey value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can effectively resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results show that the new image encryption scheme has satisfactory security thanks to its large key space and robust permutation-diffusion mechanism, which makes it a potential candidate for designing image encryption schemes.
12
Content available Periodic signal detection with using duffing system poincare map analysis
Martynyuk V, Fedula M, Balov O
Advances in Science and Technology. Research Journal
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2014
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Vol. 8, nr 22
26--30
EN
In this article the periodic signal detection method on the base of Duffing system chaotic oscillations analysis is presented. This work is a development of the chaos-based signal detection technique. Generally, chaos-based signal detection is the detection of chaotic-to-periodic state transition under input periodic component influence. If the in¬put periodic component reaches certain threshold value, the system transforms from chaotic state to periodic state. The Duffing-type chaotic systems are often used for such a signal detection purpose because of their ability to work in chaotic state for a long time and relatively simple realization. The main advantage of chaos-based signal detection methods is the utilization of chaotic system sensitivity to weak signals. But such methods are not used in practice because of the chaotic system state control problems. The method presented does not require an exact system state control. The Duffing system works continuously in chaotic state and the periodic signal detection process is based on the analysis of Duffing system Poincare map fractal structure. This structure does not depend on noise, and therefore the minimum input signal-to-noise ratio required for periodic signal detection is not limited by chaotic system state control tolerance.
13
Content available Different synchronization schemes for chaotic Rikitake systems
Ali Khan M.
International Journal of Applied Mechanics and Engineering
|
2013
|
Vol. 18, no. 2
383--393
EN
This paper presents the chaos synchronization by designing a different type of controllers. Firstly, we propose the synchronization of bi-directional coupled chaotic Rikitake systems via hybrid feedback control. Secondly, we study the synchronization of unidirectionally coupled Rikitake systems using hybrid feedback control. Lastly, we investigate the synchronization of unidirectionally coupled Rikitake chaotic systems using tracking control. Comparing all the results, finally, we conclude that tracking control is more effective than feedback control. Simulation results are presented to show the efficiency of synchronization schemes.
14
Content available remote Controlling Chaotic Systems Using Aggregated Linear Quadratic Regulator
Wang D., Ha P.
Przegląd Elektrotechniczny
|
2012
|
R. 88, nr 7b
336--340
EN
A systematic design method for controlling chaotic systems is presented in this paper. The aggregated multiple local models are adopted to express chaotic systems. The Linear Quadratic Regulator (LQR) theory is proposed to design state feedback control system for each local model. Multi-model control strategy has come into being by combining of T-S fuzzy model and LQR. The global stability of closed loop control system can guarantee and it is illustrated with several chaotic systems as examples.
PL
Zaproponowano projekt sterowania systemem chaotycznym. Zaadaptowano wypadkowe (aggregated) połączenie wielu lokalnych modeli do opisu system chaotycznego. Każdy lokalny model jest sterowany z wykorzystaniem teorii LQR – linear quadratic regulator.
15
Content available remote Generalized anti-synchronization of different chaotic systems
Khan M. A., Pal S. N., Poria S.
International Journal of Applied Mechanics and Engineering
|
2012
|
Vol. 17, no. 1
83-99
EN
In this paper, we propose the theory of generalized anti-synchronization of two chaotic systems via linear transformations. We also propose the theory for generalized anti-synchronization of two non-autonomous chaotic systems. The functional relationship between the driving system and driven system after generalized anti-synchronization can be predicted by our theory. We discuss our theory taking a chaotic dynamo model and a four dimensional hyper-chaotic Chen and Lu system as examples. Finally, simulation results are presented to show the efficiency of our method.
16
Odwrotne problemy dynamiki nieliniowej algorytmy i zastosowania dla układów chaotycznych
Berczyński S., Kravtsov Y.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
2004
|
z. 23
33-38
PL
Przedstawione zostały algorytmy rozwiązywania odwrotnych problemów dynamiki nieliniowej tj. algorytmy ustalania struktury i parametrów modeli układów nieliniowych na podstawie przebiegów czasowych wyznaczonych doświadczalnie. Algorytmy te polegają na dopasowaniu modelu (równań różniczkowych) określonej struktury do doświadczalnie wyznaczonych sygnałów na podstawie kryterium najmniejszej sumy kwadratów. Przedstawiono wyniki rozwiązania tego problemu na przykładzie układu Rosslera, który ma trzy stopnie swobody i wykazuje chaotyczne zachowanie się przy pewnych wartościach parametrów. Przedstawiono przykłady identyfikacji parametrów układu Rosslera na podstawie informacji uzyskanych z przebiegów czasowych na podstawie pomiarów trzech i dwóch zmiennych stanu. Wykazano, że krytyczny poziom szumu, uniemożliwiający rekonstrukcję układu nieliniowego, znacznie maleje w warunkach niepełnej informacji.
EN
Algorithms for the solution of inverse problems of nonlinear dynamics (IPND) have been described, and in particular the ones used for a reconstruction of nonlinear systems motion equations on the basis of empirical time-series. The algorithms for the IPND solution are based on fitting differential equations' model of a defined structure to experimental signals in frame of certain criteria, most often - on the basis of the least squares. The efficiency of IPND procedures is illustrated with the example of Rossier's system, which demonstrates chaotic behavior in some area of parameter's space. It has been shown that in absence of noise or in the conditions of weak noise Rossler's system's parameters can be determined with satisfactory accuracy, whereas for larger noise the behavior of the reconstructed system may drastically differ from the original one.
17
Content available remote Applications of QR-based algorithm to determination of fractal dimension of chaotic system
Stręk T.
Vibrations in Physical Systems
|
2002
|
Vol. 20
274--275
18
Content available remote Antyfazowa synchronizacja chaosu przez nieciągłe połączenie: dwa uderzające oscylatory
Błażejczyk-Okolewska B., Brindley J., Czołczyński K., Kapitaniak T.
Vibrations in Physical Systems
|
2000
|
Vol. 19
62--63
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