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Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant

Author

Listed:
  • Ernesto Moya-Albor

    (Facultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, Mexico
    These authors contributed equally to this work.)

  • Andrés Romero-Arellano

    (Facultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, Mexico
    These authors contributed equally to this work.)

  • Jorge Brieva

    (Facultad de Ingeniería, Universidad Panamericana, Augusto Rodin 498, Ciudad de México 03920, Mexico
    These authors contributed equally to this work.)

  • Sandra L. Gomez-Coronel

    (Instituto Politecnico Nacional, UPIITA, Av. IPN No. 2580, Col. La Laguna Ticoman, Ciudad de México 07340, Mexico
    These authors contributed equally to this work.)

Abstract

In this work, a color image encryption and decryption algorithm for digital images is presented. It is based on the modular discrete derivative (MDD), a novel technique to encrypt images and efficiently hide visual information. In addition, Langton’s ant, which is a two-dimensional universal Turing machine with a high key space, is used. Moreover, a deterministic noise technique that adds security to the MDD is utilized. The proposed hybrid scheme exploits the advantages of MDD and Langton’s ant, generating a very secure and reliable encryption algorithm. In this proposal, if the key is known, the original image is recovered without loss. The method has demonstrated high performance through various tests, including statistical analysis (histograms and correlation distributions), entropy, texture analysis, encryption quality, key space assessment, key sensitivity analysis, and robustness to differential attack. The proposed method highlights obtaining chi-square values between 233.951 and 281.687 , entropy values between 7.9999225223 and 7.9999355791 , PSNR values (in the original and encrypted images) between 8.134 and 9.957 , the number of pixel change rate (NPCR) values between 99.60851796 % and 99.61054611 % , unified average changing intensity (UACI) values between 33.44672377 % and 33.47430379 % , and a vast range of possible keys > 5.8459 × 10 72 . On the other hand, an analysis of the sensitivity of the key shows that slight changes to the key do not generate any additional information to decrypt the image. In addition, the proposed method shows a competitive performance against recent works found in the literature.

Suggested Citation

  • Ernesto Moya-Albor & Andrés Romero-Arellano & Jorge Brieva & Sandra L. Gomez-Coronel, 2023. "Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant," Mathematics, MDPI, vol. 11(10), pages 1-35, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2396-:d:1152585
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    References listed on IDEAS

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    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Zhu, Shenli & Deng, Xiaoheng & Zhang, Wendong & Zhu, Congxu, 2023. "Secure image encryption scheme based on a new robust chaotic map and strong S-box," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 322-346.
    3. 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.
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