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Revisiting the Security of DbHtS MACs: Beyond-Birthday-Bound in the Multi-user Setting

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12827))

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Abstract

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs that aim for achieving beyond-birthday-bound security, including SUM-ECBC, PMAC_Plus, 3kf9 and LightMAC_Plus. Recently Datta et al. (FSE’19), and then Kim et al. (Eurocrypt’20) prove that DbHtS constructions are secure beyond the birthday bound in the single-user setting. However, by a generic reduction, their results degrade to (or even worse than) the birthday bound in the multi-user setting.

In this work, we revisit the security of DbHtS MACs in the multi-user setting. We propose a generic framework to prove beyond-birthday-bound security for DbHtS constructions. We demonstrate the usability of this framework with applications to key-reduced variants of DbHtS MACs, including 2k-SUM-ECBC, 2k-PMAC_Plus and 2k-LightMAC_Plus. Our results show that the security of these constructions will not degrade as the number of users grows. On the other hand, our results also indicate that these constructions are secure beyond the birthday bound in both single-user and multi-user setting without additional domain separation, which is used in the prior work to simplify the analysis.

Moreover, we find a critical flaw in 2kf9, which is proved to be secure beyond the birthday bound by Datta et al. (FSE’19). We can successfully forge a tag with probability 1 without making any queries. We go further to show attacks with birthday-bound complexity on several variants of 2kf9.

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Notes

  1. 1.

    This term is mainly due to the usage of Markov inequality and appears in all security bounds of three-key \(\mathsf {DbHtS}\) constructions [24].

  2. 2.

    Here we omit lower-order terms and small constant factors.

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Acknowledgments

Yaobin Shen is more than grateful to Viet Tung Hoang for motivating this work and many helpful discussions. We thank the anonymous reviewers for their useful feedback. Yaobin Shen and Lei Wang were supported partially by National Key Research and Development Program of China (No. 2019YFB2101601). Dawu Gu was supported partially by Natural Science Foundation of China (No. 62072307) and National Key Research and Development Project (No. 2020YFA0712300). Jian Weng was supported by National Natural Science Foundation of China (Grant Nos. 61825203, U1736203, 61732021), Major Program of Guangdong Basic and Applied Research Project (Grant No. 2019B030302008).

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  1. Shanghai Jiao Tong University, Shanghai, China

    Yaobin Shen, Lei Wang & Dawu Gu

  2. Jinan University, Guangzhou, China

    Jian Weng

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  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Shen, Y., Wang, L., Gu, D., Weng, J. (2021). Revisiting the Security of DbHtS MACs: Beyond-Birthday-Bound in the Multi-user Setting. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12827. Springer, Cham. https://doi.org/10.1007/978-3-030-84252-9_11

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