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FPGA realization of spherical chaotic system with application in image transmission. (English) Zbl 1512.37108

Summary: This paper considers a three-dimensional nonlinear dynamical system capable of generating spherical attractors. The main activity is the realization of a spherical chaotic attractor on Intel and Xilinx FPGA boards, with a focus on implementation of a secure communication system. The first major contribution is the successful synchronization of two chaotic spherical systems, in VHDL program, in a master-slave topology using Hamiltonian forms. The synchronization errors show that the two spherical chaotic systems synchronize in a very short time after which the error signals become zero. The second major contribution is the FPGA realization of a spherical chaotic attractor-based secure communication system, which involves encrypting both grayscale and RGB images with chaos and diffusion key at the transmitting system, sending the encrypted image via the state variables, and reconstructing the encrypted image at the receiving system. The Intel Stratix III and Xilinx Artix-7 AC701 results are the same as those of MATLAB. The statistical analyses of the encrypted and received images show that the implemented system is very effective, as it reveals high degree of randomness in the encrypted images with the entropy test, and the obtained correlation coefficient, which is zero, removes relativity between the original and encrypted images. Finally, the transmission system fully recovers the original grayscale and RGB images without loss of information.

MSC:

37N99 Applications of dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
68M10 Network design and communication in computer systems
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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[1] Belmiloudi, A., Dynamical behavior of nonlinear impulsive abstract partial differential equations on networks with multiple time-varying delays and mixed boundary conditions involving time-varying delays, Journal of Dynamical and Control Systems, 21, 1, 95-146 (2015) · Zbl 1319.35292 · doi:10.1007/s10883-014-9230-y
[2] Demina, M. V.; Kuznetsov, N. S., Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces, Journal of Dynamical and Control Systems, 27, 403-415 (2021) · Zbl 1482.34003 · doi:10.1007/s10883-020-09513-2,2021
[3] Dawidowicz, A. L.; Poskrobko, A., On chaos behaviour of nonlinear Lasota equation in Lebesgue space, Journal of Dynamical and Control Systems, 27, 371-378 (2021) · Zbl 1461.35048 · doi:10.1007/s10883-020-09505-2
[4] Nicolis, G.; Peletier, M. A.; van Santen, R. A.; Steur, E., Chapter 1 -the many facets of complexity, Complexity Science: An Introduction, 3-30 (2019), Singapore: World Scientific Publishing Co., Singapore, ISBN: 978-981323960-9
[5] Iqbal, J.; Ullah, M.; Khan, S.; Khelifa, B.; Ćuković, S., Nonlinear control systems - a brief overview of historical and recent advances, Nonlinear Engineering, 6, 4, 301-312 (2017) · doi:10.1515/nleng-2016-0077
[6] Mellodge, P.; Mellodge, P., Chapter 4 - characteristics of nonlinear systems, A Practical Approach to Dynamical Systems for Engineers, 215-250 (2016), Sawston, England: Woodhead Publishing, Sawston, England, ISBN 9780081002025
[7] Ling, W. K., Nonlinear Digital Filters: Analysis and Applications (2010), Cambridge, MA, USA: Academic Press, Cambridge, MA, USA, ISBN 9780080550015
[8] Moysis, L.; Gupta, M. K.; Mishra, V.; Marwan, M.; Volos, C., Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs: application to secure communications, International Journal of Robust and Nonlinear Control, 30, 18, 8139-8158 (2020) · Zbl 1525.93132 · doi:10.1002/rnc.5233
[9] Tian, Y.; Wang, Z., Stability analysis and generalised memory controller design for delayed T-S fuzzy systems via flexible polynomial-based functions, IEEE Transactions on Fuzzy Systems (Early Access), 1 (2020) · doi:10.1109/TFUZZ.2020.3046338.2020
[10] Tian, Y.; Wang, Z., Finite-time extended dissipative filtering for singular T-S fuzzy systems with nonhomogeneous markov jumps, IEEE Transactions on Cybernetics (Early Access), 1-11 (2020) · doi:10.1109/TCYB.2020.3030503.2020
[11] Tian, Y.; Wang, Z., Extended dissipativity analysis for markovian jump neural networks via double-integral-based delay-product-type Lyapunov functional, IEEE Transactions on Nueral Networks and Learning Systems (Early Access), 1-7 (2020) · doi:10.1109/TNNLS.2020.3008691.2020
[12] Chowdhury, D.; Khalil, H. K., Practical synchronization in networks of nonlinear heterogeneous agents with application to power systems, IEEE Transactions on Automatic Control, 66, 1, 184-198 (2021) · Zbl 07320140 · doi:10.1109/tac.2020.2981084
[13] Ozcan, S.; Salamci, M. U.; Nalbantoglu, V., Nonlinear sliding sector design for multi‐input systems with application to helicopter control, International Journal of Robust and Nonlinear Control, 30, 6, 2248-2291 (2020) · Zbl 1465.93031 · doi:10.1002/rnc.4877
[14] Zhang, T.; Kratz, F.; Hou, Y.; Idasiak, V., A continuous-discrete finite memory observer design for a class of nonlinear systems: application to fault diagnosis, Mathematical Problems in Engineering, 2020 (2020) · Zbl 1459.93059 · doi:10.1155/2020/7312521
[15] Min, H.; Xu, S.; Fei, S.; Cui, G.; Tan, Y., Observer‐based tracking control for constrained nonlinear systems with mismatching disturbances and its application, International Journal of Robust and Nonlinear Control, 30, 18, 8485-8502 (2020) · Zbl 1525.93130 · doi:10.1002/rnc.5251
[16] Yao, X.; Yang, Y., Adaptive fault compensation and disturbance suppression design for nonlinear systems with an aircraft control application, International Journal of Aerospace Engineering, 2020 (2020) · doi:10.1155/2020/4531302
[17] Wang, W.; Postoyan, R.; Nešić, D.; Heemels, W. P. M. H., Periodic event-triggered control for nonlinear networked control systems, IEEE Transactions on Automatic Control, 65, 2, 620-635 (2020) · Zbl 07256189 · doi:10.1109/tac.2019.2914255
[18] Dai, L.; Jazar, R. N., Nonlinear Approaches in Engineering Applications (2012), Berlin, Germany: Springer, Berlin, Germany, ISBN 978-1-4614-1468-1
[19] Lorenz, E. N., Deterministic nonperiodic flow, Journal of the Atmospheric Sciences, 20, 2, 130-141 (1963) · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2
[20] Chen, G., The Chen system revisited, Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Applications & Algorithms, 20, 691-696 (2013) · Zbl 1279.93064
[21] Rössler, O. E., Different types of chaos in two simple differential equations, Zeitschrift Fur Naturforschung A, 31, 12, 1976-1231 (1976) · doi:10.1515/zna-1976-1231
[22] Rössler, O. E., Continuous chaos-four prototype equations, Annals of the New York Academy of Sciences, 316, 1, 376-392 (1979) · Zbl 0437.76055 · doi:10.1111/j.1749-6632.1979.tb29482.x
[23] Sprott, J. C., Some simple chaotic flows, Physical Review E, 50, 2, R647-R650 (1994) · doi:10.1103/physreve.50.r647
[24] Chen, G.; Yu, X., Chaos Control: Theory and Applications (2003), Berlin, Germany: Springer Science & Business Media, Berlin, Germany · Zbl 1029.00015
[25] Li, G.; Chen, X., Constructing piecewise linear chaotic system based on the heteroclinic Shil’nikov theorem, Communications in Nonlinear Science and Numerical Simulation, 14, 1, 194-203 (2009) · Zbl 1221.37063 · doi:10.1016/j.cnsns.2007.07.007
[26] Grandner, S.; Heidenreich, S.; Hess, S.; Klapp, S. H. L., Polar nano-rods under shear: from equilibrium to chaos, The European Physical Journal E, 24, 4, 353-365 (2007) · doi:10.1140/epje/i2007-10246-8
[27] Khapko, T.; Duguet, Y.; Kreilos, T.; Schlatter, P.; Eckhardt, B.; Henningson, D. S., Complexity of localised coherent structures in a boundary-layer Flow, European Physical Journal E, 37, 4, 32 (2014) · doi:10.1140/epje/i2014-14032-3
[28] Eisencraft, M.; Attux, R.; Suyama, R., Chaotic Signals in Digital Communications (2018), Boca Raton, FL, USA: CRC Press, Boca Raton, FL, USA
[29] Liao, T.-L.; Chen, C.-Y.; Chen, H.-C.; Chen, Y.-Y.; Hou, Y.-Y., Realization of a secure visible light communication system via chaos synchronization, Mathematical Problems in Engineering, 2021 (2021) · doi:10.1155/2021/6661550
[30] Huang, L.; Shi, D.; Gao, J., The design and its application in secure communication and image encryption of a new lorenz-like system with varying parameter, Mathematical Problems in Engineering, 2016 (2016) · Zbl 1400.94021 · doi:10.1155/2016/8973583
[31] Pang, S.; Feng, Y.; Liu, Y., Finite-time synchronization of chaotic systems with different dimension and secure communication, Mathematical Problems in Engineering, 2016 (2016) · Zbl 1400.93260
[32] Cuomo, K. M.; Oppenheim, A. V., Circuit implementation of synchronized chaos with applications to communications, Physical Review Letters, 71, 1, 65-68 (1993) · doi:10.1103/physrevlett.71.65
[33] Lü, J.; Chen, G., Generating multiscroll chaotic attractors: theories, methods and applications, International Journal of Bifurcation and Chaos, 16, 4, 775-858 (2006) · Zbl 1097.94038 · doi:10.1142/s0218127406015179
[34] Lu, J.; Yu, S.; Leung, H.; Chen, G., Experimental verification of multidirectional multiscroll chaotic attractors, IEEE Transactions on Circuits and Systems I: Regular Papers, 53, 1, 149-165 (2006) · doi:10.1109/TCSI.2005.854412
[35] Gao, T.; Chen, G.; Chen, Z.; Cang, S., The generation and circuit implementation of a new hyper-chaos based upon Lorenz system, Physics Letters A, 361, 1-2, 78-86 (2007) · Zbl 1170.37308 · doi:10.1016/j.physleta.2006.09.042
[36] Qi, G.; Chen, G., Analysis and circuit implementation of a new 4D chaotic system, Physics Letters A, 352, 4-5, 386-397 (2006) · Zbl 1187.37050 · doi:10.1016/j.physleta.2005.12.030
[37] Muñoz-Pacheco, J. M.; Tlelo-Cuautle, E.; Toxqui-Toxqui, I.; Sánchez-López, C.; Trejo-Guerra, R., Frequency limitations in generating multi-scroll chaotic attractors using CFOAs, International Journal of Electronics, 101, 11, 1559-1569 (2014) · doi:10.1080/00207217.2014.880999
[38] Tlelo-Cuautle, E.; Quintas-Valles, A. J.; de la Fraga, L. G.; Rangel-Magdaleno, J. J., VHDL descriptions for the FPGA implementation of PWL-function-based multiscroll chaotic oscillators, PLoS One, 11, 2, e0168300 (2019)
[39] Tuna, M.; Alçın, M.; Koyuncu, İ.; Fidan, C. B.; Pehlivan, İ., High speed FPGA-based chaotic oscillator design, Microprocessors and Microsystems, 66, 72-80 (2019) · doi:10.1016/j.micpro.2019.02.012
[40] Cheng-Hsiung, Y.; Sih-Jie, H., Secure color image encryption algorithm based on chaotic signals and its FPGA realization, International Journal of Circuit Theory and Applications, 46, 12, 2444-2461 (2018) · doi:10.1002/cta.2572
[41] Alcin, M.; Koyuncu, I.; Tuna, M.; Varan, M.; Pehlivan, I., A novel high speed artificial neural network-based chaotic true random number generator on field programmable gate array, International Journal of Circuit Theory and Applications, 47, 3, 365-378 (2019) · doi:10.1002/cta.2581
[42] Tlelo-Cuautle, E.; De la Fraga, L. G.; Pham, V.-T.; Volos, C.; Jafari, S.; Quintas-Valles, A. D. J., Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points, Nonlinear Dynamics, 89, 2, 1129-1139 (2017) · doi:10.1007/s11071-017-3505-2
[43] Li, P.; Zhang, W.; Li, Z.; Liu, W.; Halang, W. A., FPGA implementation of a coupled-map-lattice-based cryptosystem, International Journal of Circuit Theory and Applications, 38, 1, 85-98 (2010) · Zbl 1191.94094 · doi:10.1002/cta.553
[44] Yu, F.; Liu, L.; He, B., Analysis and FPGA realization of a novel 5D hyperchaotic four-wing memristive system, active control synchronization, and secure communication application, Complexity, 2019 (2019) · doi:10.1155/2019/4047957
[45] Azzaz, M. S.; Tanougast, C.; Maali, A.; Benssalah, M., An efficient and lightweight multi‐scroll chaos‐based hardware solution for protecting fingerprint biometric templates, International Journal of Communication Systems, 33, 10, e4211 (2020) · doi:10.1002/dac.4211
[46] Hagras, E. A. A.; Saber, M., Low power and high-speed FPGA implementation for 4D memristor chaotic system for image encryption, Multimedia Tools and Applications, 79, 8, 23203-23222 (2020) · doi:10.1007/s11042-019-08517-w
[47] Guillén-Fernández, O.; Meléndez-Cano, A.; Tlelo-Cuautle, E.; Núñez-Pérez, J. C.; Rangel-Magdaleno, J. J., On the synchronization techniques of chaotic oscillators and their FPGA-based implementation for secure image transmission, PLoS One, 14, 2, e0209618 (2019) · doi:10.1371/journal.pone.0209618
[48] Tlelo-Cuautle, E.; Díaz-Muñoz, J. D.; González-Zapata, A. M., Chaotic image encryption using hopfield and hindmarsh-rose neurons implemented on FPGA, Sensors, 20, 5, 1326 (2020) · doi:10.3390/s20051326
[49] Tlelo-Cuautle, E.; Pano-Azucena, A. D.; Guillén-Fernández, O.; Silva-Juárez, A., Synchronization and applications of fractional-order chaotic systems, Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications (2019), Cham, Switzerland: Springer, Cham, Switzerland
[50] Sivaraman, R.; Rajagopalan, S.; Amirtharajan, R., FPGA based generic RO TRNG architecture for image confusion, Multimedia Tools and Applications, 79, 2, 13841-13868 (2020) · doi:10.1007/s11042-019-08592-z
[51] Wang, Z.; Sun, Y.; Cang, S., A 3-D spherical chaotic attractor, Acta Physica Polonica B, 42, 2, 235-247 (2011) · doi:10.5506/aphyspolb.42.235
[52] Núñez Pérez, J. C.; Adeyemi, V. A.; Gutierrez Osuna, S. E.; Sandoval Ibarra, Y.; Tlelo Cuautle, E., Secure communication system based on synchronized 3D spherical chaotic systems, Proceedings of the IEEE International Conference on Engineering Veracruz (ICEV) · doi:10.1109/ICEV50249.2020.9289654
[53] Zhou, T.; Chen, G., A simple smooth chaotic system with a 3-layer attractor, International Journal of Bifurcation and Chaos, 14, 5, 1795-1799 (2004) · Zbl 1129.37325 · doi:10.1142/s0218127404010175
[54] Shilnikov, L. P., A case of the existence of a countable number of periodic motions, Soviet Mathematics - Doklady, 6, 163-166 (1965) · Zbl 0136.08202
[55] Shilnikov, L. P., A contribution to the problem of the structure of an extended neighbourhood of a rough equilibrium state of saddle-focus type, Mathematics of the USSR-Sbornik, 10, 1, 91-102 (1970) · Zbl 0216.11201
[56] Sira-ramírez, H.; Cruz-hernández, C., Synchronization of chaotic systems: a generalized Hamiltonian systems approach, International Journal of Bifurcation and Chaos, 11, 5, 1381-1395 (2001) · Zbl 1206.37053 · doi:10.1142/s0218127401002778
[57] Pei, L. J.; Liu, S. H., Application of generalized Hamiltonian systems to chaotic synchronization, Nonlinear Dynamics and Systems Theory, 9, 4, 415-432 (2009) · Zbl 1206.37052
[58] Sadoudi, S.; Tanougast, C.; Azzaz, M. S.; Dandache, A., Design and FPGA implementation of a wireless hyperchaotic communication system for secure real-time image transmission, EURASIP Journal on Image and Video Processing, 2013, 43 (2013) · doi:10.1186/1687-5281-2013-43
[59] Sayed, W. S.; Radwan, A. G.; Elnawawy, M., Two-dimensional rotation of chaotic attractors: demonstrative examples and FPGA realization, Circuits, Systems, and Signal Processing, 38, 10, 4890-4903 (2019) · doi:10.1007/s00034-019-01096-z
[60] Tuna, M.; Fidan, C. B., Electronic circuit design, implementation and FPGA-based realization of a new 3D chaotic system with single equilibrium point, Optik, 127, 24, 11786-11799 (2016) · doi:10.1016/j.ijleo.2016.09.087
[61] Gribunin, V. G.; Okov, I. N.; Turincev, I. V., Cifrovaya Steganografiya. [Digital Steganography], 262 (2017), Berlin, Germany: M: SOLON-Press, Berlin, Germany
[62] Koppu, S.; Viswanatham, V. M., A fast enhanced secure image chaotic cryptosystem based on hybrid chaotic magic transform, Modelling and Simulation in Engineering, 2017 (2017) · doi:10.1155/2017/7470204
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