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Construction of highly non linear component of block cipher based on mclaurin series and mellin transformation with application in image encryption

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Abstract

A substitution box (S-box) in data encryption is a non-linear tool that conducts substitution to assure the overall security of the system. S-box is the most important part of the block cipher. The non-linearity trait is critical for the construction of more reliable substitution boxes in data encryption. As a result, new approaches for generating high no n-linear S-boxes are required. Using the Mellin transformation and the McLaurin series, this work suggests an approach for creating Substitution boxes with a high non-linearity value of 112.5. S-box construction consists of three phases. In step 1, we build a sequence from a function's McLaurin series and then apply Mellin transformation to the sequence's terms without substituting limits. In the second phase, we solved all of the coefficients under mod 257, and in the third step, we improved the unpredictability of the initial S-box by using a particular permutation of Symmetric group \({S}_{256}\). Furthermore, the algebraic characteristics of S-box are evaluated using various tests, including non-linearity (NL), Bit Independent Criterion (BIC), Strict Avalanche Criterion (SAC), Linear Approximation Probability (LAP), and Differential Uniformity (DU), all of which certify the algebraic properties of the S-box.

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Authors and Affiliations

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

    Abid Mahboob

  2. Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan

    Imran Siddique

  3. Department of Mathematics, University of Management and Technology, Sialkot Campus, Pakistan

    Muhammad Asif

  4. Department of Mathematics, University of Education, Vehari Campus, Pakistan

    Muhammad Nadeem & Aysha Saleem

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  1. Abid Mahboob
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  2. Imran Siddique
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Correspondence to Imran Siddique.

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Mahboob, A., Siddique, I., Asif, M. et al. Construction of highly non linear component of block cipher based on mclaurin series and mellin transformation with application in image encryption. Multimed Tools Appl 83, 7159–7177 (2024). https://doi.org/10.1007/s11042-023-15965-y

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