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Robustness of Affine and Extended Affine Equivalent Surjective S-Box(es) Against Differential Cryptanalysis

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Foundations and Practice of Security (FPS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13877))

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Abstract

A Feistel Network (FN) based block cipher relies on a Substitution Box (S-Box) for achieving the non-linearity. S-Box is carefully designed to achieve optimal cryptographic security bounds. The research of the last three decades shows that considerable efforts are being made on the mathematical design of an S-Box. To import the exact cryptographic profile of an S-Box, the designer focuses on the Affine Equivalent (AE) or Extended Affine (EA) equivalent S-Box. In this research, we argue that the Robustness of surjective mappings is invariant under AE and not invariant under EA transformation. It is proved that the EA equivalent of a surjective mapping does not necessarily contribute to the Robustness against the Differential Cryptanalysis (DC) in the light of Seberry’s criteria. The generated EA equivalent S-Box(es) of DES and other \(6 \times 4\) mappings do not show a good robustness profile compared to the original mappings. This article concludes that a careful selection of affine permutation parameters is significant during the design phase to achieve high Robustness against DC and Differential Power Analysis (DPA) attacks.

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Notes

  1. 1.

    The S-Box(es), their equivalent mappings and detailed cryptographic profile is available at https://drive.google.com/drive/folders/1-6DNsVdZWT_kkdhJEpZgM-A0Pjtv8wtQ?usp=sharing.

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Authors and Affiliations

  1. National University of Sciences and Technology, Islamabad, 44000, Pakistan

    Shah Fahd, Mehreen Afzal & Waseem Iqbal

  2. Quaid-i-Azam University, Islamabad, Pakistan

    Dawood Shah

  3. University of Surrey, Guildford, UK

    Atiya Hai

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  1. Shah Fahd
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  2. Mehreen Afzal
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  3. Dawood Shah
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  4. Waseem Iqbal
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  5. Atiya Hai
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Correspondence to Shah Fahd .

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  1. University of Ottawa, Ottawa, ON, Canada

    Guy-Vincent Jourdan

  2. Université Grenoble Alpes, Grenoble, France

    Laurent Mounier

  3. University of Ottawa, Ottawa, ON, Canada

    Carlisle Adams

  4. University Toulouse III Paul Sabatier, Toulouse, France

    Florence Sèdes

  5. Telecom SudParis, Palaiseau, France

    Joaquin Garcia-Alfaro

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Fahd, S., Afzal, M., Shah, D., Iqbal, W., Hai, A. (2023). Robustness of Affine and Extended Affine Equivalent Surjective S-Box(es) Against Differential Cryptanalysis. In: Jourdan, GV., Mounier, L., Adams, C., Sèdes, F., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2022. Lecture Notes in Computer Science, vol 13877. Springer, Cham. https://doi.org/10.1007/978-3-031-30122-3_29

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