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A cluster of 1D quadratic chaotic map and its applications in image encryption

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  • Liu, Lingfeng
  • Wang, Jie

Abstract

Chaotic systems are widely used in designing encryption algorithms for their ideal dynamical performances. One-dimensional (1D) chaotic maps have the highest efficiency in implementation and have achieved great attention. However, 1D chaotic maps have a common security weakness, which is that their key space is relatively small. Therefore, in this paper, a cluster of 1D quadratic chaotic maps is proposed according to the topological conjugate theory. The 1D chaotic map has three tunable parameters which have a significant expansion in parameter space than the traditional 1D chaotic maps. The 1D map is proved to be chaotic theoretically since it is topologically conjugated with a logistic chaotic map. An example of a 1D quadratic chaotic map is provided in this paper, and several numerical simulation results indicate that this 1D quadratic map has ideal chaotic characteristics, which are consistent with the theoretical analysis. To verify the effectiveness of this 1D quadratic map, a novel image encryption algorithm is proposed. The security of this image encryption algorithm is completely dependent on the properties of the 1D quadratic map. Security experimental test results show that this image encryption algorithm has a high-security level, and is quite competitive with other chaos-based image encryption algorithms.

Suggested Citation

  • Liu, Lingfeng & Wang, Jie, 2023. "A cluster of 1D quadratic chaotic map and its applications in image encryption," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 89-114.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:89-114
    DOI: 10.1016/j.matcom.2022.07.030
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    References listed on IDEAS

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    1. Zhu, Hegui & Dai, Lewen & Liu, Yating & Wu, Lijun, 2021. "A three-dimensional bit-level image encryption algorithm with Rubik’s cube method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 754-770.
    2. Zhang, Shijie & Liu, Lingfeng, 2021. "A novel image encryption algorithm based on SPWLCM and DNA coding," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 723-744.
    3. Jie Wang & Lingfeng Liu, 2022. "A Novel Chaos-Based Image Encryption Using Magic Square Scrambling and Octree Diffusing," Mathematics, MDPI, vol. 10(3), pages 1-28, January.
    4. Choi, Jaesung & Kim, Pilwon, 2020. "Reservoir computing based on quenched chaos," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Munir, Noor & Khan, Majid & Jamal, Sajjad Shaukat & Hazzazi, Mohammad Mazyad & Hussain, Iqtadar, 2021. "Cryptanalysis of hybrid secure image encryption based on Julia set fractals and three-dimensional Lorenz chaotic map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 826-836.
    6. Yao Wu & Lingfeng Liu, 2020. "An Iteration-Time Combination Method to Reduce the Dynamic Degradation of Digital Chaotic Maps," Complexity, Hindawi, vol. 2020, pages 1-11, October.
    7. Rania A. Elmanfaloty & Ehab Abou-Bakr, 2020. "An Image Encryption Scheme Using a 1D Chaotic Double Section Skew Tent Map," Complexity, Hindawi, vol. 2020, pages 1-18, October.
    8. Malik, Dania Saleem & Shah, Tariq, 2020. "Color multiple image encryption scheme based on 3D-chaotic maps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 646-666.
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    Cited by:

    1. Achraf Daoui & Mohamed Yamni & Samia Allaoua Chelloug & Mudasir Ahmad Wani & Ahmed A. Abd El-Latif, 2023. "Efficient Image Encryption Scheme Using Novel 1D Multiparametric Dynamical Tent Map and Parallel Computing," Mathematics, MDPI, vol. 11(7), pages 1-29, March.
    2. Shenli Zhu & Xiaoheng Deng & Wendong Zhang & Congxu Zhu, 2023. "Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding," Mathematics, MDPI, vol. 11(1), pages 1-22, January.
    3. Achraf Daoui & Haokun Mao & Mohamed Yamni & Qiong Li & Osama Alfarraj & Ahmed A. Abd El-Latif, 2023. "Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs," Mathematics, MDPI, vol. 11(16), pages 1-28, August.
    4. Erendira Corona-Bermúdez & Juan Carlos Chimal-Eguía & Uriel Corona-Bermúdez & Mario Eduardo Rivero-Ángeles, 2023. "Chaos Meets Cryptography: Developing an S-Box Design with the Rössler Attractor," Mathematics, MDPI, vol. 11(22), pages 1-16, November.

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