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Generation of Boxes and Permutations Using a Bijective Function and the Lorenz Equations: An Application to Color Image Encryption

Author

Listed:
  • Víctor Manuel Silva-García

    (Instituto Politécnico Nacional, IPN-CIDETEC, Ciudad de México 07738, Mexico)

  • Rolando Flores-Carapia

    (Instituto Politécnico Nacional, IPN-CIDETEC, Ciudad de México 07738, Mexico)

  • Manuel Alejandro Cardona-López

    (Instituto Politécnico Nacional, Centro de Investigación en Computación, Ciudad de México 07738, Mexico)

  • Miguel Gabriel Villarreal-Cervantes

    (Instituto Politécnico Nacional, IPN-CIDETEC, Ciudad de México 07738, Mexico)

Abstract

Some images that contain sensitive information and travel through the network require security. Therefore, a symmetric cryptosystem that encrypts images and resists known attacks is developed. Subsequently, in this work, an encryption algorithm known as Image Cipher utilizing Lorenz equation and a Bijective Function—ICLEBF are proposed. In the proposal, the Lorenz equations and the Bijective function are used to generate boxes, the permutation, and schedule keys, considering that all these elements are different in each encryption process. The encryption procedure consists of 14 rounds, where a different box is applied in each round. In this type of algorithm, the impact of quantum computers will be less forceful and can be useful for that epoch. On the other hand, the quality of the encrypted images and the loss of sharpness in decoded images with damage are measured. In addition, an attack from five types of noise (one of which is a developed proposal) is carried out by applying it to encrypted images. Finally, the results of the proposed ICLEBF are compared with other recent image encryption algorithms, including the Advanced Encryption Standard. As a result, this proposal resists known attacks and others that the current standard does not support.

Suggested Citation

  • Víctor Manuel Silva-García & Rolando Flores-Carapia & Manuel Alejandro Cardona-López & Miguel Gabriel Villarreal-Cervantes, 2023. "Generation of Boxes and Permutations Using a Bijective Function and the Lorenz Equations: An Application to Color Image Encryption," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:599-:d:1045635
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    References listed on IDEAS

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    1. Jasra Bhat & Manasha Saqib & Ayaz Hassan Moon, 2022. "Fuzzy extractor and chaos enhanced elliptic curve cryptography for image encryption and authentication," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 697-712, April.
    2. Zhou, Shuang & Zhao, Zhipeng & Wang, Xingyuan, 2022. "Novel chaotic colour image cryptosystem with deep learning," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Zhonghua Liu & Jincheng Shen & Richard Barfield & Joel Schwartz & Andrea A. Baccarelli & Xihong Lin, 2022. "Large-Scale Hypothesis Testing for Causal Mediation Effects with Applications in Genome-wide Epigenetic Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 67-81, January.
    4. Li, Ming & Wang, Mengdie & Fan, Haiju & An, Kang & Liu, Guoqi, 2022. "A novel plaintext-related chaotic image encryption scheme with no additional plaintext information," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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