ANN-based chaotic PRNG in the novel jerk chaotic system and its application for the image encryption via 2-D Hilbert curve

Aceng Sambas; Xuncai Zhang; Issam A R Moghrabi; Sundarapandian Vaidyanathan; Khaled Benkouider; Murat Alçın; İsmail Koyuncu; Murat Tuna; Ibrahim M Sulaiman; Mohamad Afendee Mohamed; Muhamad Deni Johansyah

doi:10.1038/s41598-024-80969-z

ANN-based chaotic PRNG in the novel jerk chaotic system and its application for the image encryption via 2-D Hilbert curve

Sci Rep. 2024 Nov 28;14(1):29602. doi: 10.1038/s41598-024-80969-z.

Authors

Aceng Sambas^{1

2}, Xuncai Zhang³, Issam A R Moghrabi^{4

5}, Sundarapandian Vaidyanathan^{6

7}, Khaled Benkouider⁸, Murat Alçın⁹, İsmail Koyuncu¹⁰, Murat Tuna¹¹, Ibrahim M Sulaiman^{12

13}, Mohamad Afendee Mohamed¹, Muhamad Deni Johansyah¹⁴

Affiliations

¹ Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kampung Gong Badak, 21300, Kuala Terengganu, Malaysia.
² Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya, 46196, Indonesia.
³ College of Electric Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450001, China.
⁴ Computer Science Department, School of Arts and Sciences, University of Central Asia, Naryn, Kyrgyz Republic. issam.moughrabi@ucentralasia.org.
⁵ Department of Information Systems and Technology, Kuwait Technical College, Kuwait, Kuwait. issam.moughrabi@ucentralasia.org.
⁶ Centre for Control Systems, Vel Tech University, Avadi, Chennai, Tamil Nadu, 600 062, India.
⁷ Centre of Excellence for Research, Value Innovation & Entrepreneurship (CERVIE), UCSI University, Kuala Lumpur, Malaysia.
⁸ Laboratory of Automatic and Signals of Annaba (LASA), Badji-Mokhtar University, B.P. 12, 23000, Sidi Ammar, Annaba, Algeria.
⁹ Department of Mechatronics Engineering, Faculty of Technology, Afyon Kocatepe University, Afyon, Turkey.
¹⁰ Department of Electrical and Electronics Engineering, Faculty of Technology, Afyon Kocatepe University, Afyon, Turkey.
¹¹ Department of Electrical and Energy, Technical Sciences Vocational School, Kırklareli University, Kırklareli, Turkey.
¹² School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah, Malaysia.
¹³ Faculty of Education and Arts, Sohar University, Sohar, 311, Oman.
¹⁴ Department of Mathematics, Universitas Padjadjaran, Jatinangor Sumedang, 45363, Indonesia.

Abstract

In this paper, we introduce a category of Novel Jerk Chaotic (NJC) oscillators featuring symmetrical attractors. The proposed jerk chaotic system has three equilibrium points. We show that these equilibrium points are saddle-foci points and unstable. We have used traditional methods such as bifurcation diagrams, phase portraits, and Lyapunov exponents to analyze the dynamic properties of the proposed novel jerk chaotic system. Moreover, simulation results using Multisim, based on an appropriate electronic implementation, align with the theoretical investigations. Additionally, the NJC system is solved numerically using the Dormand Prince algorithm. Subsequently, the Jerk Chaotic System is modeled using a multilayer Feed-Forward Neural Network (FFNN), leveraging its nonlinear mapping capability. This involved utilizing 20,000 values of x₁, x₂, and x₃ for training (70%), validation (15%), and testing (15%) processes, with the target values being their iterative values. Various network structures were experimented with, and the most suitable structure was identified. Lastly, a chaos-based image encryption algorithm is introduced, incorporating scrambling technique derived from a dynamic DNA coding and an improved Hilbert curve. Experimental simulations confirm the algorithm's efficacy in enduring numerous attacks, guaranteeing strong resiliency and robustness.

Keywords: ANN; Chaos; Circuit design; FPGA; Hilbert curve; Image encryption; PRNG.