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Improved Differential Cryptanalysis on Generalized Feistel Schemes

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Progress in Cryptology – INDOCRYPT 2017 (INDOCRYPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10698))

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Abstract

Nachef et al. used differential cryptanalysis to study four types of Generalized Feistel Scheme (GFS). They gave the lower bound of maximum number of rounds that is indistinguishable from a random permutation. In this paper, we study the security of several types of GFS by exploiting the asymmetric property. We show that better lower bounds can be achieved for the Type-1 GFS, Type-3 GFS and Alternating Feistel Scheme. Furthermore, we give the first general results regarding to the lower bound of the Unbalanced Feistel Scheme.

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Notes

  1. 1.

    We also examine Type-2 Feistel Scheme, but we cannot improve the previous results since it does not have asymmetric property.

  2. 2.

    The full version will be uploaded to Cryptology ePrint archive soon.

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Ivan Tjuawinata, Tao Huang & Hongjun Wu

Authors
  1. Ivan Tjuawinata
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  2. Tao Huang
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  3. Hongjun Wu
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Corresponding author

Correspondence to Ivan Tjuawinata .

Editor information

Editors and Affiliations

  1. Indian Institute of Science (IISc), Bengaluru, India

    Arpita Patra

  2. Department of Computer Science, University of Bristol, Bristol, United Kingdom

    Nigel P. Smart

Appendices

A  Expected Value and Variance of Random Variables Concerning Type-1 Feistel Scheme and UFN(\(k',k\)) When \(k'\) Divides k.

The following table summarises the expected value and variance of the random variables used in the analysis of Type-1 Feistel Schemes.

Table 3. Expected value and variance of random variables concerning Type-1 Feistel Schemes
Full size table

The next table summarises the expected values and variances for random variables used in the analysis of UFN(\(k',k\)) when \(k'\) divides k.

Table 4. Expected value and variance for various cases of UFN(\(k',k\))
Full size table
Table 5. Complexity of Unbalanced Feistel Scheme
Full size table

B  Distinguishability Table for UFN(\(k',k\))

The following tables contain the summary of distinguishability of UFN(\(k',k\)) from a random permutation.

Table 6. Summary of distinguishability of Unbalanced Feistel Scheme
Full size table

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Tjuawinata, I., Huang, T., Wu, H. (2017). Improved Differential Cryptanalysis on Generalized Feistel Schemes. In: Patra, A., Smart, N. (eds) Progress in Cryptology – INDOCRYPT 2017. INDOCRYPT 2017. Lecture Notes in Computer Science(), vol 10698. Springer, Cham. https://doi.org/10.1007/978-3-319-71667-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-71667-1_16

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  • Online ISBN: 978-3-319-71667-1

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