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Advancing the Meet-in-the-Filter Technique: Applications to CHAM and KATAN

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Selected Areas in Cryptography (SAC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13742))

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Abstract

Recently, Biryukov et al. presented a new technique for key recovery in differential cryptanalysis, called meet-in-the-filter (MiF). In this work, we develop theoretical and practical aspects of the technique, which helps understanding and simplifies application. In particular, we show bounds on MiF complexity and conditions when the MiF-enhanced attack may reach them. We present a method based on trail counting which allows to estimate filtering strength of involved rounds and perform consequent complexity analysis with pen and paper, compared to the computer-aided approach of the original work. Furthermore, we show how MiF can be combined with plaintext structures for linear key schedules, allowing to increase the number of attacked rounds or to reduce the data complexity.

We illustrate our methods on block cipher families Cham and Katan and show best-to-date single-key differential attacks for these ciphers.

The work was supported by the Luxembourg National Research Fund’s (FNR) and the German Research Foundation’s (DFG) joint project APLICA (C19/IS/13641232).

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Notes

  1. 1.

    Here, we consider probability over all intermediate (long) keys. Therefore, the limitation of a fixed-key permutation to have minimum nonzero differential probability \(2^{-|C|+1}\) (over plaintexts/ciphertexts) does not affect this assumption.

  2. 2.

    Codes and other relevant information are available at github.com/cryptolu/MeetInTheFilter_CHAM_KATAN.

  3. 3.

    When extending 8 rounds forward, there are \(2^{64.84}\) possible trails. Since there are only \(2^{64}\) possible ciphertext differences, each ciphertext difference suggests \(2^{0.84}\) trails on average.

  4. 4.

    In a decryption step, due to the register shift, the taps \(x_2,\ldots ,x_5,y_2,\ldots ,y_6\) are increased by 1 in order to match the same bits used in the encryption. This explains why Proposition 3 has an extra step compare to Proposition 4.

  5. 5.

    Experimentally, we obtained an average of \(2^{33.49}\) trails which closely matches the estimates obtained by Proposition 2.

  6. 6.

    Subkey dependency matrices are provided in the supporting code repository.

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Authors and Affiliations

  1. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Alex Biryukov, Je Sen Teh & Aleksei Udovenko

  2. University Sains Malaysia, Gelugor, Malaysia

    Je Sen Teh

Authors
  1. Alex Biryukov
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  2. Je Sen Teh
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  3. Aleksei Udovenko
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Corresponding author

Correspondence to Aleksei Udovenko .

Editor information

Editors and Affiliations

  1. Inria and École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France

    Benjamin Smith

  2. Electrical and Computer Engineering, University of Windsor, Windsor, ON, Canada

    Huapeng Wu

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Biryukov, A., Teh, J.S., Udovenko, A. (2024). Advancing the Meet-in-the-Filter Technique: Applications to CHAM and KATAN. In: Smith, B., Wu, H. (eds) Selected Areas in Cryptography. SAC 2022. Lecture Notes in Computer Science, vol 13742. Springer, Cham. https://doi.org/10.1007/978-3-031-58411-4_16

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  • DOI: https://doi.org/10.1007/978-3-031-58411-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-58410-7

  • Online ISBN: 978-3-031-58411-4

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