American Journal of Science, Engineering and Technology

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S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm

Received: 20 December 2023    Accepted: 4 January 2024    Published: 18 January 2024
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Abstract

In today's applications of block ciphers, the substitution box (S-box) serves as a critical nonlinear component that is essential for generating complex ciphertext. S-boxes that exhibit lower differential uniformity and increased nonlinearity are more adept at resisting cryptanalytic efforts. The paper proposes that the construction of an 8x8 S-box can be accomplished by selecting non-singular adjacency matrices derived from graph parameters generated by a genetic algorithm. This selection is followed by an affine transformation. This method uses any graph with 8 vertices and its edge count, resulting in a non-singular adjacency matrix. The S-box is then generated by an affine mapping technique using the non-singular adjacency matrix, similar to the approach of the Rijndael algorithm. The effectiveness and reliability of the resulting S-box was rigorously tested against various cryptographic standards. The robustness evaluation included factors such as non-linearity, differential approximation probability, linear approximation probability and strict avalanche criteria. A thorough investigation confirmed that the newly created S-box met the required algebraic properties. Furthermore, a comparative analysis was performed to evaluate the performance of this novel S-box against the most recent counterparts in the literature. In terms of defense against potential malicious exploits, the results indicate a significant advantage. Overall, the results of this study underscore the significant promise and advantages of the proposed S-box-centric cryptographic strategy, positioning it as an attractive alternative to conventional encryption techniques.

DOI 10.11648/j.ajset.20240901.12
Published in American Journal of Science, Engineering and Technology (Volume 9, Issue 1, April 2024)
Page(s) 14-20
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

S-Box, Nonsingular Matrix, Adjacency Matrix, Affine Transformation, Nonlinearity, Strict Avalanche Criterion

References
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  • APA Style

    Abdurazzokov, J. (2024). S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm. American Journal of Science, Engineering and Technology, 9(1), 14-20. https://doi.org/10.11648/j.ajset.20240901.12

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    ACS Style

    Abdurazzokov, J. S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm. Am. J. Sci. Eng. Technol. 2024, 9(1), 14-20. doi: 10.11648/j.ajset.20240901.12

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    AMA Style

    Abdurazzokov J. S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm. Am J Sci Eng Technol. 2024;9(1):14-20. doi: 10.11648/j.ajset.20240901.12

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  • @article{10.11648/j.ajset.20240901.12,
      author = {Javokhir Abdurazzokov},
      title = {S-Box Generation Algorithm by Constructing the Non-Singular Adjacency Matrix Using the Genetic Algorithm},
      journal = {American Journal of Science, Engineering and Technology},
      volume = {9},
      number = {1},
      pages = {14-20},
      doi = {10.11648/j.ajset.20240901.12},
      url = {https://doi.org/10.11648/j.ajset.20240901.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajset.20240901.12},
      abstract = {In today's applications of block ciphers, the substitution box (S-box) serves as a critical nonlinear component that is essential for generating complex ciphertext. S-boxes that exhibit lower differential uniformity and increased nonlinearity are more adept at resisting cryptanalytic efforts. The paper proposes that the construction of an 8x8 S-box can be accomplished by selecting non-singular adjacency matrices derived from graph parameters generated by a genetic algorithm. This selection is followed by an affine transformation. This method uses any graph with 8 vertices and its edge count, resulting in a non-singular adjacency matrix. The S-box is then generated by an affine mapping technique using the non-singular adjacency matrix, similar to the approach of the Rijndael algorithm. The effectiveness and reliability of the resulting S-box was rigorously tested against various cryptographic standards. The robustness evaluation included factors such as non-linearity, differential approximation probability, linear approximation probability and strict avalanche criteria. A thorough investigation confirmed that the newly created S-box met the required algebraic properties. Furthermore, a comparative analysis was performed to evaluate the performance of this novel S-box against the most recent counterparts in the literature. In terms of defense against potential malicious exploits, the results indicate a significant advantage. Overall, the results of this study underscore the significant promise and advantages of the proposed S-box-centric cryptographic strategy, positioning it as an attractive alternative to conventional encryption techniques.
    },
     year = {2024}
    }
    

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    AU  - Javokhir Abdurazzokov
    Y1  - 2024/01/18
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    T2  - American Journal of Science, Engineering and Technology
    JF  - American Journal of Science, Engineering and Technology
    JO  - American Journal of Science, Engineering and Technology
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    AB  - In today's applications of block ciphers, the substitution box (S-box) serves as a critical nonlinear component that is essential for generating complex ciphertext. S-boxes that exhibit lower differential uniformity and increased nonlinearity are more adept at resisting cryptanalytic efforts. The paper proposes that the construction of an 8x8 S-box can be accomplished by selecting non-singular adjacency matrices derived from graph parameters generated by a genetic algorithm. This selection is followed by an affine transformation. This method uses any graph with 8 vertices and its edge count, resulting in a non-singular adjacency matrix. The S-box is then generated by an affine mapping technique using the non-singular adjacency matrix, similar to the approach of the Rijndael algorithm. The effectiveness and reliability of the resulting S-box was rigorously tested against various cryptographic standards. The robustness evaluation included factors such as non-linearity, differential approximation probability, linear approximation probability and strict avalanche criteria. A thorough investigation confirmed that the newly created S-box met the required algebraic properties. Furthermore, a comparative analysis was performed to evaluate the performance of this novel S-box against the most recent counterparts in the literature. In terms of defense against potential malicious exploits, the results indicate a significant advantage. Overall, the results of this study underscore the significant promise and advantages of the proposed S-box-centric cryptographic strategy, positioning it as an attractive alternative to conventional encryption techniques.
    
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Author Information
  • Digital Technologies and Artificial Intelligence Development Research Institute, Tashkent, Uzbekistan

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