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Differential Cryptanalysis in the Fixed-Key Model

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13509))

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Abstract

A systematic approach to the fixed-key analysis of differential probabilities is proposed. It is based on the propagation of ‘quasidifferential trails’, which keep track of probabilistic linear relations on the values satisfying a differential characteristic in a theoretically sound way. It is shown that the fixed-key probability of a differential can be expressed as the sum of the correlations of its quasidifferential trails.

The theoretical foundations of the method are based on an extension of the difference-distribution table, which we call the quasidifferential transition matrix. The role of these matrices is analogous to that of correlation matrices in linear cryptanalysis. This puts the theory of differential and linear cryptanalysis on an equal footing.

The practical applicability of the proposed methodology is demonstrated by analyzing several differentials for RECTANGLE, KNOT, Speck and Simon. The analysis is automated and applicable to other SPN and ARX designs. Several attacks are shown to be invalid, most others turn out to work only for some keys but can be improved for weak-keys.

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Notes

  1. 1.

    All of our source code can be found at https://github.com/TimBeyne/quasidifferential-trails.

  2. 2.

    This is possible due to the way the key-recovery attack works.

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Acknowledgements

We thank Anne Canteaut and Jean-René Reinhard for responding to our questions about their attacks on PRINCE. Tim Beyne is supported by a PhD Fellowship from the Research Foundation – Flanders (FWO). This work was partially supported by the Research Council KU Leuven, grant C16/18/004 on New Block Cipher Structures.

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Authors and Affiliations

  1. imec-COSIC, KU Leuven, Leuven, Belgium

    Tim Beyne & Vincent Rijmen

  2. University of Bergen, Bergen, Norway

    Vincent Rijmen

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  1. Tim Beyne
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  2. Vincent Rijmen
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Correspondence to Tim Beyne .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Beyne, T., Rijmen, V. (2022). Differential Cryptanalysis in the Fixed-Key Model. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13509. Springer, Cham. https://doi.org/10.1007/978-3-031-15982-4_23

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  • DOI: https://doi.org/10.1007/978-3-031-15982-4_23

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