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A group theoretic construction of highly nonlinear substitution box and its applications in image encryption

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Abstract

Substitution box is the most significant component of block cipher. The property of nonlinearity is of great importance for the design of secure substitution boxes. Therefore, it is necessary to develop new methods for the production of substitution boxes with a high non-linearity score. In this paper, we have introduced a novel group theoretic method to construct a robust S-box with non-linearity score 113.75 greater than that of AES S-box. The performance of generated S-box is found to be excellent, when examined through various other well-known algebraic criteria such as strict avalanche criterion, bit independence criterion, differential uniformity and linear approximation probability. The suitability of proposed S-box is tested for image encryption applications through different statistical analyses. We got very encouraging outcomes from all these examinations which certify that the generated S-box meets all the criteria needed to be reliable for secure communication and image encryption.

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Authors and Affiliations

  1. Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan

    Abdul Razaq

  2. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

    Awais Yousaf

  3. Department of Mathematics, Government College University Faisalabad, Faisalabad, Pakistan

    Shumaila Akhter & Umer Shuaib

  4. Department of Computer Engineering, Jamia Millia Islamia, New Delhi, 110025, India

    Musheer Ahmad

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  1. Abdul Razaq
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  2. Shumaila Akhter
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  3. Awais Yousaf
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  4. Umer Shuaib
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  5. Musheer Ahmad
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Correspondence to Abdul Razaq.

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Razaq, A., Akhter, S., Yousaf, A. et al. A group theoretic construction of highly nonlinear substitution box and its applications in image encryption. Multimed Tools Appl 81, 4163–4184 (2022). https://doi.org/10.1007/s11042-021-11635-z

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  • DOI: https://doi.org/10.1007/s11042-021-11635-z

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