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Revisiting iterated attacks in the context of decorrelation theory

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Abstract

Iterated attacks are comprised of iterating adversaries who can make d plaintext queries, in each iteration to compute a bit, and are trying to distinguish between a random cipher C and the perfect cipher C ∗ based on all bits. Vaudenay showed that a 2d-decorrelated cipher resists to iterated attacks of order d when iterations have almost no common queries. Then, he first asked what the necessary conditions are for a cipher to resist a non-adaptive iterated attack of order d. I.e., whether decorrelation of order 2d − 1 could be sufficient. Secondly, he speculated that repeating a plaintext query in different iterations does not provide any advantage to a non-adaptive distinguisher. We close here these two long-standing open problems negatively. For those questions, we provide two counter-intuitive examples.W e also deal with adaptive iterated adversaries who can make both plaintext and ciphertext queries in which the future queries are dependent on the past queries. We show that decorrelation of order 2d protects against these attacks of order d. We also study the generalization of these distinguishers for iterations making non-binary outcomes. Finally, we measure the resistance against two well-known statistical distinguishers, namely, differential-linear and boomerang distinguishers and show that 4-decorrelation degree protects against these attacks.

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Acknowledgments

This work was supported by the European Commission through the ICT program under contract ICT-2007-216646 ECRYPT II and the National Competence Center in Research on Mobile Information and Communication Systems (NCCR-MICS), a center of the SNF under grant number 5005-67322.

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Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne, Route Cantonale, 1015, Lausanne, Switzerland

    Aslı Bay & Serge Vaudenay

  2. Security Engineering, Canadian Imperial Bank of Commerce (CIBC), Toronto, Canada

    Atefeh Mashatan

Authors
  1. Aslı Bay
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  2. Atefeh Mashatan
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  3. Serge Vaudenay
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Correspondence to Aslı Bay.

Additional information

Part of the results in this work were published in [5, 6]. In this paper, the study of generalization of adaptive iterated plaintext-ciphertext distinguishers is added; also the resistance against boomerang and differential-linear distinguishers are analyzed by the techniques in Decorrelation Theory.

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Bay, A., Mashatan, A. & Vaudenay, S. Revisiting iterated attacks in the context of decorrelation theory. Cryptogr. Commun. 6, 279–311 (2014). https://doi.org/10.1007/s12095-014-0101-x

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