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A Novel Group Theoretic and Graphical Approach for Designing Cryptographically Strong Nonlinear Components of Block Ciphers

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Abstract

Substitution box is a significant and only nonlinear constituent of block cipher. S-box plays a central role in converting the intelligible message or plain text, into an enciphered format. Construction of strong S-boxes is an important area of interest for security experts. In this work, we develop a new method to evolve S-boxes with the help of coset graph for the action of \(PSL\left( {2,{\mathbb {Z}}} \right)\) on projective line over the finite field GF (28), a special type of bijective map \(g\) and the symmetric group S256 The capability of the proposed S-boxes to mitigate cryptanalysis is investigated through various performance analyzing parameters. The outcomes of the comparison with the familiar S-boxes indicate that the working abilities of newly designed S-boxes are better than that of many of the well-known S-boxes.

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Author information

Authors and Affiliations

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

    Abdul Razaq

  2. Department of Mathematics, National University of Technology, Islamabad, Pakistan

    Atta Ullah

  3. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Hanan Alolaiyan

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

    Awais Yousaf

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  1. Abdul Razaq
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  2. Atta Ullah
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  3. Hanan Alolaiyan
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  4. Awais Yousaf
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Correspondence to Abdul Razaq.

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Razaq, A., Ullah, A., Alolaiyan, H. et al. A Novel Group Theoretic and Graphical Approach for Designing Cryptographically Strong Nonlinear Components of Block Ciphers. Wireless Pers Commun 116, 3165–3190 (2021). https://doi.org/10.1007/s11277-020-07841-x

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