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Improvements of Attacks on Various Feistel Schemes

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Paradigms in Cryptology – Mycrypt 2016. Malicious and Exploratory Cryptology (Mycrypt 2016)

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Abstract

In this paper, we use a tool that computes exact values for expectations and standard deviations of random variables involved in generic attacks on various Feistel-type schemes in order to get a better study of these attacks. This leads to the improvement of previous attacks complexities: either we need less messages than expected or we can attack more rounds. These improvements are given for different sizes of the inputs. We also show that for rectangle attacks, there are more differential paths than presented in previous attacks and this strengthens the attacks.

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Notes

  1. 1.

    \(\varphi =2\) most of the time, but there are some rectangle attacks with \(\varphi =4\). There can be many values for \(\varphi \) even odd ones [14, 17].

  2. 2.

    The project is at this link: https://github.com/CryptoCergy/project.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cergy-Pontoise, CNRS UMR 8088, 2 Avenue Adolphe Chauvin, 95011, Cergy-Pontoise Cedex, France

    Emmanuel Volte, Valérie Nachef & Nicolas Marrière

Authors
  1. Emmanuel Volte
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  2. Valérie Nachef
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  3. Nicolas Marrière
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Corresponding author

Correspondence to Valérie Nachef .

Editor information

Editors and Affiliations

  1. Multimedia University, MMU, Cyberjaya, Malaysia

    Raphaël C.-W. Phan

  2. Snapchat and Columbia University, New York, New York, USA

    Moti Yung

Appendices

A Proof of Proposition 4

Proof

We have:

figure a

So, \(\displaystyle \sum _{f\in \mathcal {B}_{kn}} \sum _{M\in J_m}\sum _\mathbf{i ,\mathbf j } n_{\mathbf{i},f,M}n_{\mathbf{j},f,M}=\)

So,

Thus

as claimed    \(\square \)

B Simulation of Some KPA Attacks

We have made simulations of several attacks for small values of n in order to confirm our main results (Table 16). The results of these simulations are consistent with the theoretical study. The process of the simulations is as follow: we choose a random instance of the studied scheme (a Feistel type scheme) and a random permutation (generated by a classical Feisel scheme with 20 rounds). Then we start the attack for m messages and we count the number of plaintext/ciphertext pairs that verify the relations involved for the studied scheme and for the permutation. Finally, we repeat these steps 50 times in order to compute the mean value for the studied Feistel scheme and for the permutation and the standard deviation for the permutation.

Table 16. Simulation 50 times.
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Volte, E., Nachef, V., Marrière, N. (2017). Improvements of Attacks on Various Feistel Schemes. In: Phan, RW., Yung, M. (eds) Paradigms in Cryptology – Mycrypt 2016. Malicious and Exploratory Cryptology. Mycrypt 2016. Lecture Notes in Computer Science(), vol 10311. Springer, Cham. https://doi.org/10.1007/978-3-319-61273-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-61273-7_16

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