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On the Double Differential Uniformity of Vectorial Boolean Functions

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Progress in Cryptology - AFRICACRYPT 2024 (AFRICACRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14861))

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Abstract

We introduce the double differential distribution table (DDDT) and the double differential uniformity of a vectorial Boolean function to study the security of an S-box to differential attacks. We study several properties of the DDDT and the double differential uniformity and present their explicit values for three of the most practical vectorial Boolean functions: the inverse function, the Gold function, and the Bracken-Leander function. The double differential uniformity is an extension of the differential uniformity and the Feistel boomerang uniformity. It can be used as a distinguisher, and a new criterion for the security of an S-box derived from a vectorial Boolean function against differential attacks.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris VIII, LAGA, University Sorbonne Paris Nord, CNRS, UMR 7539, 93430, Paris, France

    Said Eddahmani & Sihem Mesnager

  2. Telecom Paris, 91120, Palaiseau, France

    Sihem Mesnager

Authors
  1. Said Eddahmani
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  2. Sihem Mesnager
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Correspondence to Said Eddahmani .

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Editors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Serge Vaudenay

  2. University of Birmingham, Birmingham, UK

    Christophe Petit

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Eddahmani, S., Mesnager, S. (2024). On the Double Differential Uniformity of Vectorial Boolean Functions. In: Vaudenay, S., Petit, C. (eds) Progress in Cryptology - AFRICACRYPT 2024. AFRICACRYPT 2024. Lecture Notes in Computer Science, vol 14861. Springer, Cham. https://doi.org/10.1007/978-3-031-64381-1_1

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  • DOI: https://doi.org/10.1007/978-3-031-64381-1_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-64380-4

  • Online ISBN: 978-3-031-64381-1

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