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A Modular Approach to the Security Analysis of Two-Permutation Constructions

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

Abstract

Constructions based on two public permutation calls are very common in today’s cryptographic community. However, each time a new construction is introduced, a dedicated proof must be carried out to study the security of the construction. In this work, we propose a new tool to analyze the security of these constructions in a modular way. This tool is built on the idea of the classical mirror theory for block cipher based constructions, such that it can be used for security proofs in the ideal permutation model. We present different variants of this public permutation mirror theory such that it is suitable for different security notions.

We also present a framework to use the new techniques, which provides the bad events that need to be excluded in order to apply the public permutation mirror theory. Furthermore, we showcase the new technique on three examples: the Tweakable Even-Mansour cipher by Cogliati et al. (CRYPTO ’15), the two permutation variant of the pEDM PRF by Dutta et al. (ToSC ’21(2)), and the two permutation variant of the nEHtM\(_p\) MAC algorithm by Dutta and Nandi (AFRICACRYPT ’20). With this new tool we prove the multi-user security of these constructions in a considerably simplified way.

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Acknowledgments

This work was supported in part by the Research Council KU Leuven: GOA TENSE (C16/15/058). The author was supported by a Ph.D. Fellowship from the Research Foundation - Flanders (FWO). I want to thank Tim Beyne and the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

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

    Yu Long Chen

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  1. Yu Long Chen
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Correspondence to Yu Long Chen .

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  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Chen, Y.L. (2022). A Modular Approach to the Security Analysis of Two-Permutation Constructions. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_13

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  • DOI: https://doi.org/10.1007/978-3-031-22963-3_13

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