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Tighter Security for Generic Authenticated Key Exchange in the QROM

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14441))

Abstract

We give a tighter security proof for authenticated key exchange (AKE) protocols that are generically constructed from key encapsulation mechanisms (KEMs) in the quantum random oracle model (QROM). Previous works (Hövelmanns et al., PKC 2020) gave reductions for such a KEM-based AKE protocol in the QROM to the underlying primitives with square-root loss and a security loss in the number of users and total sessions. Our proof is much tighter and does not have square-root loss. Namely, it only loses a factor depending on the number of users, not on the number of sessions.

Our main enabler is a new variant of lossy encryption which we call parameter lossy encryption. In this variant, there are not only lossy public keys but also lossy system parameters. This allows us to embed a computational assumption into the system parameters, and the lossy public keys are statistically close to the normal public keys. Combining with the Fujisaki-Okamoto transformation, we obtain the first tightly IND-CCA secure KEM in the QROM in a multi-user (without corruption), multi-challenge setting.

Finally, we show that a multi-user, multi-challenge KEM implies a square-root-tight and session-tight AKE protocol in the QROM. By implementing the parameter lossy encryption tightly from lattices, we obtain the first square-root-tight and session-tight AKE from lattices in the QROM.

Supported by the Research Council of Norway under Project No. 324235.

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Notes

  1. 1.

    For all security bounds in this section, we ignore all additive and negligible statistical terms.

  2. 2.

    This is a relaxed tightness notion from [8] where security loss is at most linear in the security parameter \(\lambda \).

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Authors and Affiliations

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

    Jiaxin Pan & Runzhi Zeng

  2. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Benedikt Wagner

  3. Saarland University, Saarbrücken, Germany

    Benedikt Wagner

  4. University of Kassel, Kassel, Germany

    Jiaxin Pan

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  1. Jiaxin Pan
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Correspondence to Jiaxin Pan .

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  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Pan, J., Wagner, B., Zeng, R. (2023). Tighter Security for Generic Authenticated Key Exchange in the QROM. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14441. Springer, Singapore. https://doi.org/10.1007/978-981-99-8730-6_13

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