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Authenticated Key Exchange and Signatures with Tight Security in the Standard Model

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Book cover Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12828))

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Abstract

We construct the first authenticated key exchange protocols that achieve tight security in the standard model. Previous works either relied on techniques that seem to inherently require a random oracle, or achieved only “Multi-Bit-Guess” security, which is not known to compose tightly, for instance, to build a secure channel.

Our constructions are generic, based on digital signatures and key encapsulation mechanisms (KEMs). The main technical challenges we resolve is to determine suitable KEM security notions which on the one hand are strong enough to yield tight security, but at the same time weak enough to be efficiently instantiable in the standard model, based on standard techniques such as universal hash proof systems.

Digital signature schemes with tight multi-user security in presence of adaptive corruptions are a central building block, which is used in all known constructions of tightly-secure AKE with full forward security. We identify a subtle gap in the security proof of the only previously known efficient standard model scheme by Bader et al. (TCC 2015). We develop a new variant, which yields the currently most efficient signature scheme that achieves this strong security notion without random oracles and based on standard hardness assumptions.

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Notes

  1. 1.

    Our signatures are only re-randomizable over all strings output by the signing algorithm. The impossibility result from [3] requires uniform re-randomizability over all strings accepted by the verification algorithm, which does not hold for our scheme.

  2. 2.

    We are aware of the generic constructions of bounded-CCA secure KEMs from CPA-secure KEMs [8], but they do not seem to offer tight security in a multi-challenge setting.

  3. 3.

    For instance, openssl speed aes shows that AES-256 is only about 1.5 times slower than AES-128 on a standard laptop computer. Given that the cost of symmetric key operations is already small in comparison to the public key operations, we consider this as negligible.

  4. 4.

    The arrow notion \(\pi _i^s \leftarrow \pi _j^t\) means \(\pi _i^s\) (not necessarily \(\pi _j^t\)) has computed and accepted the original key.

  5. 5.

    It is also possible to define the trivial attack regardless of \(FirstAcc\), but our definition of \(\mathbf{TA6} \) and \(\mathbf{TA7} \) is minimal and makes our security model stronger.

  6. 6.

    Given \((1) \wedge (2)\), (3.1) indicates a successful impersonation of \(P_j\), (3.2) suggests one instance of \(P_i\) has multiple partners, and (3.3) corresponds to a successful replay attack.

  7. 7.

    This is different to the BKP IBE where \([\mathbf {{B}}^\top \mathbf {x}_{i,j}]_1\) and \([x'_{n}]_1\) are not available to an adversary.

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Acknowledgments

We would like to thank the reviewers for their helpful comments. Shuai Han and Shengli Liu were partially supported by National Natural Science Foundation of China (Grant Nos. 61925207, 62002223), Guangdong Major Project of Basic and Applied Basic Research (2019B030302008), Shanghai Sailing Program (20YF1421100), Young Elite Scientists Sponsorship Program by China Association for Science and Technology, and the National Key Research and Development Project 2020YFA0712300. Tibor Jager was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement 802823. Eike Kiltz was supported by the BMBF iBlockchain project, the EU H2020 PROMETHEUS project 780701, DFG SPP 1736 Big Data, and the DFG Cluster of Excellence 2092 CASA. Doreen Riepel was supported by the Deutsche Forschungsgemeinschaft (DFG) Cluster of Excellence 2092 CASA. Sven Schäge was supported by the German Federal Ministry of Education and Research (BMBF), Project DigiSeal (16KIS0695) and Huawei Technologies Düsseldorf, Project vHSM.

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Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shuai Han & Shengli Liu

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Shuai Han & Shengli Liu

  3. Bergische Universität Wuppertal, Wuppertal, Germany

    Tibor Jager

  4. Ruhr-Universität Bochum, Bochum, Germany

    Eike Kiltz, Doreen Riepel & Sven Schäge

  5. Westone Cryptologic Research Center, Beijing, 100070, China

    Shengli Liu

  6. Department of Mathematical Sciences, NTNU – Norwegian University of Science and Technology, Trondheim, Norway

    Jiaxin Pan

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  1. Shuai Han
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Correspondence to Shengli Liu .

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Editors and Affiliations

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

    Tal Malkin

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

    Chris Peikert

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Han, S. et al. (2021). Authenticated Key Exchange and Signatures with Tight Security in the Standard Model. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12828. Springer, Cham. https://doi.org/10.1007/978-3-030-84259-8_23

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  • DOI: https://doi.org/10.1007/978-3-030-84259-8_23

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