Dynamic Analysis and Circuit Design of a New 3D Highly Chaotic System and its Application to Pseudo Random Number Generator (PRNG) and Image Encryption
Authors: 
Aceng Sambas, Khaled Benkouider, Sezgin Kaçar, Nurdoğan Ceylan, Sundarapandian Vaidyanathan, Ibrahim Mohammed Sulaiman, Mohamad Afendee Mohamed, Ahmad Faisal Mohamad Ayob, Sishu Shankar MuniAuthors Info & Claims
Abstract
In this paper, a new 3D dynamical system with four quadratic nonlinear terms is presented. It is shown that the proposed chaotic system has two saddle-foci, unstable, equilibrium points. Thus, the proposed chaotic system exhibits self-excited chaotic attractors. Dynamical analysis methods such as Lyapunov exponents spectrum, bifurcation diagrams, and phase portraits are used to explore the complex dynamical behaviors of the proposed chaotic system and analyze its basic qualitative properties. It is shown that the maximal Lyapunov exponent (MLE) of the new chaotic system is 7.196, which is a high value. The proposed highly chaotic system exhibits high complexity and it will be very useful for applications in cryptography, encryption and secure communications. The physical feasibility of the proposed system is verified by implementing its electronic circuit schematic using Multisim software. Additionally, a PRNG has been developed using the derived state variables and analyze with NIST-800–22 test. Lastly, we developed a PRNG-based image encryption and employ it for an encryption. The experimental outcomes obtained prove that the 3D chaotic system-based encryption application presented in this section has a very good performance.
References
[1]
Sambas A, Vaidyanathan S, Zhang X, Koyuncu I, Bonny T, Tuna M, Alcin M, Zhang S, Sulaiman IM, Awwal AM, and Kumam P A novel 3D chaotic system with line equilibrium: Multistability, integral sliding mode control, electronic circuit, FPGA implementation and its image encryption IEEE Access 2022 10 68057-68074
[2]
Guo, S., Fu, Y., Yu, L.: An encrypted multitone modulation method for physical layer security based on chaotic cryptography. Physical Communication 47 (2021). Article ID 101389
[3]
Singh JP and Roy BK A more chaotic and easily hardware implementable new 3-d chaotic system in comparison with 50 reported systems Nonlinear Dyn 2018 93 3 1121-1148
[4]
Yang Q, Qiao X (2019) Constructing a new 3D chaotic system with any num- ber of equilibria. Int J Bifurcation Chaos 29(5). Article ID 1950060
[5]
Signing VRF, kengne J, Kana LK (2018) Dynamic analysis and multista- bility of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity. Chaos, Solitons and Fractals 113, 263–274
[6]
Vaidyanathan S, Benkouider K, and Sambas A A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based syn- chronization design and circuit simulation Arch Control Sci 2022 32 1 123-152
[7]
Chowdhury SN and Ghosh D Hidden attractors: A new chaotic system without equilibria Euro Phys J Spec Topics 2020 229 6 1299-1308
[8]
Ren S, Panahi S, Rajagopal K, Akgul A, Pham V, Jafari S (2018) A new chaotic flow with hidden attractor: The first hyperjerk system with no equilibrium. Zeitschrift fu¨r Naturforschung A 73(3): 239–249
[9]
Dong C (2022) Dynamics, periodic orbit analysis, and circuit implementation of a new chaotic system with hidden attractor. Fractal Fractional 6(4) (2022). Article ID 190
[10]
Sambas A, Mmat M, Vaidyanathan S, Mohamed M, and Sanjaya W A new 4-d chaotic system with hidden attractor and its circuit imple- mentation Int J Eng Technol 2018 7 3 1245-1250
[11]
Yu F, Zhang Z, Shen H, Huang Y, Cai S, Du S (2022) Fpga imple- mentation and image encryption appli-cation of a new prng based on a memristive hopfield neural network with a special activation gradient. Chin Phys B 31(2). Article ID 020505
[12]
AbdElHaleem SH, Abd-El-Hafiz SK, Radwan AG (2022) A generalized framework for elliptic curves based PRNG and its utilization in image encryption. Sci Rep 12(1). Article ID 13278
[13]
Abd El-Latif AA, Abd-El-Atty B, Venegas-Andraca SE (2020) Controlled alternate quantum walk-based pseudo-random number generator and its application to quantum color image encryption. Physica A 547 (2020). Article ID 123869
[14]
Gafsi M, Abbassi N, Hajjaji MA, Malek J, Mtibaa A (2020) Improved chaos-based cryptosystem for medical image encryption and decryption. Scientific Programming 2020. Article ID 6612390
[15]
Mondal B and Mandal T A light weight secure image encryption scheme based on chaos and dna computing J King Saud Univ- Comput Inform Sci 2017 29 4 499-504
[16]
Namasudra S and Deka GC Advances of DNA computing in cryptogra- phy 2018 New York, USA CRC Press
[17]
Zhu H, Zhang X, Xing H, and Feng L Lightweight terminal cross-domain authentication protocol in edge computing environment Chinese J Netw Inform Secur 2023 9 4 74-89
[18]
Kumar ASK and Razak TA A secure crypto-based data outsourcing model for monitoring the smart environment in cloud Int J Sci Technol Res 2020 9 1 124-131
[19]
Das S, Singh MP, Namasudra S (2023) A lightweight authentication and key agreement protocol for Iot-based smart healthcare system. (2023).
[20]
Singh A, Kumar A, Namasudra S (2024) DNACDS: Cloud IoE big data security and accessing scheme based on DNA cryptography. Front Comput Sci 18(1) (2024). Article ID 181801
[21]
Namasudra, S., Nath, S., Majumder, A.: Profile Based Access Control Model in Cloud Computing Environment. (2014).
[22]
Hameed A, Violos J, and Leivadeas A A deep learning approach for IoT traffic multi-classification in a smart-city scenario IEEE Access 2022 10 21193-21210
[23]
Das S, Namasudra S (2022) A lightweight and anonymous mutual authentica- tion scheme for medical big data in distributed smart healthcare systems. IEEE/ACM Trans Comput Biol Bioinform 1–12 (2022).
[24]
Castro, F., Impedovo, D., Pirlo, G.: A medical image encryption scheme for secure fingerprint-based authenticated transmission. Applied Sciences 13(10) (2023). Article ID 6099
[25]
Patel S, Vaish A (2023) Block based visually secure image encryption algorithm using 2d-compressive sensing and nonlinearity. Optik 272. Article ID 170341
[26]
Zhu L, Jiang D, Ni J, Wang X, Rong X, and Ahmad M A visually secure image encryption scheme using adaptive-thresholding sparsification compression sensing model and newly-designed memristive chaotic map Inf Sci 2022 607 1001-1022
[27]
Wolf A, Swift JB, Swinney HL, and Vastano JA Determining lyapunov exponents from a time series Physica D 1985 16 3 285-317
[28]
Grond F, Diebner HH, Sahle S, Mathias A, Fischer S, and Rossler OE A robust, locally interpretable algorithm for lyapunov exponents Chaos, Solitons Fractals 2003 16 5 841-852
[29]
Silva-Juarez A, Tlelo-Cuautle E, de la Fraga LG, Li R Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics. Applied Mathematics and Computation 394 (2021). Article ID 125831
[30]
Chen Z-M A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors Chaos, Solitons Fractals 1993 3 5 575-582
[31]
Dong C (2022) Dynamic analysis of a novel 3d chaotic system with hidden and coexisting attractors: Offset boosting, synchronization, and circuit realization. Fractal Fractional 6(10). Article ID 547
[32]
Qiu H, Xu X, Jiang Z, Sun K, Cao C (2023) Dynamical behaviors, circuit design, and synchronization of a novel symmetric chaotic system with coexisting attractors. Scientific Reports 13(1) (2023). Article ID 1893
[33]
Liu, T., Yan, H., Banerjee, S., Mou, J.: A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation. Chaos, Solitons and Fractals 145 (2021). Article ID 110791
[34]
Zhou W, Wang G, Shen Y, Yuan F, Yu S (2018) Hidden coexisting attrac- tors in a chaotic system without equilibrium point. International Journal of Bifurcation and Chaos 28(10) (2018). Article ID 1830033
[35]
Rahman Z-A, Jasim BH (2022) Hidden dynamics investigation, fast adaptive synchronization, and chaos-based secure communication scheme of a new 3d fractional-order chaotic system. Inventions 7(4) (2022). Article ID 108
[36]
Kacar S A new data-hiding algorithm for multi-channel biomedical signals based on variable-order fractional chaotic neural networks with frequency effect Euro Physical Journal 2022 231 5 929-943
[37]
Kacar S Digital circuit implementation and PRNG-based data secu- rity application of variable-order fractional Hopfield neural network under electromagnetic radiation using Gr´’ unwald-Letnikov method Euro Phys J 2022 231 10 1969-1981
[38]
Aricioglu B and Kacar S Circuit implementation and PRNG applications of time delayed Lorenz system Chaos Theory Appl 2022 4 1 4-9
[39]
Benkouider K, Bouden T, Sambas A, Mohamed MA, Sulaiman IM, Mamat M, and Ibrahim MAH Dynamics, control and secure transmission electronic circuit implementation of a new 3d chaotic system in comparison with 50 reported systems IEEE Access 2021 9 152150-152168
[40]
Zhang X, Wang L, Zhou Z, and Niu Y A chaos-based image encryption technique utilizing Hilbert curves and H-fractals IEEE Access 2019 7 74734-74746
[41]
Li H, Wang Y, and Zuo Z Chaos-based image encryption algorithm with orbit perturbation and dynamic state variable selection mechanisms Opt Lasers Eng 2019 115 197-207
[42]
Wang X, Akgul A, Kacar S, Pham V-T (2017) Multimedia security application of a ten-term chaotic system without equilibrium. Complexity 2017 (2017). Article ID 8412093
[43]
Li Z, Peng C, Tan W, Li L (2021) An effective chaos-based image encryp- tion scheme using imitating jigsaw method. Complexity 2021. Article ID 8824915
[44]
Musanna F and Kumar S A novel fractional order chaos-based image encryption using fisher yates algorithm and 3-D cat map Multimedia Tools and Applications 2019 78 11 14867-14895
[45]
Liu H, Xu Y, Ma C (2020) Chaos-based image hybrid encryption algorithm using key stretching and hash feedback. Optik 216. Article ID 164925
[46]
Kaur G, Agarwal R, and Patidar V Chaos based multiple order optical transform for 2D image encryption Eng Sci Technol Int J 2020 23 5 998-1014
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Publication History
Published: 10 April 2024
Accepted: 02 March 2024
Received: 04 August 2023
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