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A Speech Cryptosystem Using the New Chaotic System with a Capsule-Shaped Equilibrium Curve

Mohamad Afendee Mohamed1, Talal Bonny2, Aceng Sambas3, Sundarapandian Vaidyanathan4, Wafaa Al Nassan2, Sen Zhang5, Khaled Obaideen2, Mustafa Mamat1, Mohd Kamal Mohd Nawawi6,*

1 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Malaysia
2 Department of Computer Engineering, University of Sharjah, Sharjah, 26666, UAE
3 Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia
4 Research and Development Centre, Vel Tech University, Avadi, Chennai, India
5 School of Artificial Intelligence, and Automation, and Key Laboratory of Image Processing, and Intelligent Control of Education Ministry of China, Huazhong University of Science, and Technology, Wuhan, 430074, China
6 Institute of Strategic Industrial Decision Modeling, School of Quantitative Sciences, Universiti Utara Malaysia, 06010, UUM Sintok, Kedah, Malaysia

* Corresponding Author: Mohd Kamal Mohd Nawawi. Email:

Computers, Materials & Continua 2023, 75(3), 5987-6006.


In recent years, there are numerous studies on chaotic systems with special equilibrium curves having various shapes such as circle, butterfly, heart and apple. This paper describes a new 3-D chaotic dynamical system with a capsule-shaped equilibrium curve. The proposed chaotic system has two quadratic, two cubic and two quartic nonlinear terms. It is noted that the proposed chaotic system has a hidden attractor since it has an infinite number of equilibrium points. It is also established that the proposed chaotic system exhibits multi-stability with two coexisting chaotic attractors for the same parameter values but differential initial states. A detailed bifurcation analysis with respect to variations in the system parameters is portrayed for the new chaotic system with capsule equilibrium curve. We have shown MATLAB plots to illustrate the capsule equilibrium curve, phase orbits of the new chaotic system, bifurcation diagrams and multi-stability. As an engineering application, we have proposed a speech cryptosystem with a numerical algorithm, which is based on our novel 3-D chaotic system with a capsule-shaped equilibrium curve. The proposed speech cryptosystem follows its security evolution and implementation on Field Programmable Gate Array (FPGA) platform. Experimental results show that the proposed encryption system utilizes 33% of the FPGA, while the maximum clock frequency is 178.28 MHz.


Cite This Article

M. A. Mohamed, T. Bonny, A. Sambas, S. Vaidyanathan, W. A. Nassan et al., "A speech cryptosystem using the new chaotic system with a capsule-shaped equilibrium curve," Computers, Materials & Continua, vol. 75, no.3, pp. 5987–6006, 2023.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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