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Dynamic analysis of a novel chaotic system with no linear terms and use for DNA-based image encryption

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Abstract

The present paper proposes the design of a new image encryption scheme based jointly on DNA coding and the chaotic sequence generated by a new 3D chaotic system without linear terms. The mathematical model of the proposed system is built from Sprott B system by introducing a quadratic nonlinearity in each linear term of the system except the constant term. This modification is done with the aim to build a very simple chaotic system without linear terms and with stylish mathematical expression. The system is analyzed in-depth to show its complex dynamics. This contribution also shows the possibility of the sequences of such types of oscillators without linear term to efficiently encrypt images. Thus, based jointly on the special randomness generated by this system with no linear terms and DNA encoding, a robust cryptosystem is proposed. The feasibility and robustness of the proposed image encryption scheme are evaluated by several security tests such as statistical and differential analysis, occlusion, and data loss attack as well as brute force attack. Thus, the technique achieved correlations close to zero, entropy values greater than 7.99, and key space greater than 2100. Besides, differential analysis shows that NPCR and UACI are greater than 99.60% and 33%, respectively. Furthermore, the quantitative analyzes of occlusion and data loss attacks as well as the results of comparison with some benchmark algorithms prove the efficiency and security of the proposed cryptosystem. To the best of author’s knowledge, none of the chaotic systems above mentioned without linear terms has been applied in the field of image encryption. Therefore, this contribution promotes the evolution of nonlinear science and its applications in image encryption using DNA coding.

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Funding

Zeric Tabekoueng Njitacke has been supported by the Polish National Science Centre under the Grant OPUS 14 No.2017/27/B/ST8/01330.

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Authors and Affiliations

  1. Department of Electrical Engineering and Industrial Computing, University Institute of Technology, P.O. Box 8698, Douala, Cameroon

    Nkapkop Jean De Dieu

  2. Research Centre for Nuclear Science and Technology, Institute of Geological and Mining Research, P.O. Box 4110, Yaounde, Cameroon

    Folifack Signing Vitrice Ruben

  3. Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Tsafack Nestor

  4. Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon

    Njitacke Tabekoueng Zeric

  5. Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon

    Kengne Jacques

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  1. Nkapkop Jean De Dieu
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  2. Folifack Signing Vitrice Ruben
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  4. Njitacke Tabekoueng Zeric
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Correspondence to Folifack Signing Vitrice Ruben.

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Nkapkop Jean De Dieu, Folifack Signing Vitrice Ruben, Tsafack Nestor, Njitacke Tabekoueng Zeric and Kengne Jacques declare that they have no conflict of interest.

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De Dieu, N., Ruben, F.S.V., Nestor, T. et al. Dynamic analysis of a novel chaotic system with no linear terms and use for DNA-based image encryption. Multimed Tools Appl 81, 10907–10934 (2022). https://doi.org/10.1007/s11042-022-12044-6

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