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SoK: Game-Based Security Models for Group Key Exchange

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Topics in Cryptology – CT-RSA 2021 (CT-RSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12704))

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Abstract

Group key exchange (GKE) protocols let a group of users jointly establish fresh and secure key material. Many flavors of GKE have been proposed, differentiated by, among others, whether group membership is static or dynamic, whether a single key or a continuous stream of keys is established, and whether security is provided in the presence of state corruptions (forward and post-compromise security). In all cases, an indispensable ingredient to the rigorous analysis of a candidate solution is a corresponding formal security model. We observe, however, that most GKE-related publications are more focused on building new constructions that have more functionality or are more efficient than prior proposals, while leaving the job of identifying and working out the details of adequate security models a subordinate task.

In this systematization of knowledge we bring the formal modeling of GKE security to the fore by revisiting the intuitive goals of GKE, critically evaluating how these goals are reflected (or not) in the established models, and how they would be best considered in new models. We classify and compare characteristics of a large selection of game-based GKE models that appear in the academic literature, including those proposed for GKE with post-compromise security. We observe a range of shortcomings in some of the studied models, such as dependencies on overly restrictive syntactical constrains, unrealistic adversarial capabilities, or simply incomplete definitions. Our systematization enables us to identify a coherent suite of desirable characteristics that we believe should be represented in all general purpose GKE models. To demonstrate the feasibility of covering all these desirable characteristics simultaneously in one concise definition, we conclude with proposing a new generic reference model for GKE.

The full version [PRSS21] of this article is available as entry 2021/305 in the IACR eprint archive.

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Notes

  1. 1.

    CRYPTO, Eurocrypt, Asiacrypt, CCS, S&P, Usenix Security, and the Journal of Cryptology.

  2. 2.

    TCC, PKC, CT-RSA, ACNS, ESORICS, CANS, ARES, ProvSec, FC.

  3. 3.

    We appreciate that many more publications introduce other GKE constructions (e.g., [BC04, ABCP06, JKT07, JL07, Man09, NS11, XHZ15, BDR20]). However, we did not identify that they contribute new insights to the modeling of GKE.

  4. 4.

    Since our analysis started before [ACDT20] was submitted to CRYPTO 2020, we consider a fixed preprint version [ACDT19] here. Note that the two follow-up works [ACJM20, AJM20] use simulation-based security models.

  5. 5.

    We further clarify on the relation between local instances and parties and their participation in sessions in the full version [PRSS21].

  6. 6.

    Surprisingly, this holds even for models that appeared in close succession in publications of the same authors.

  7. 7.

    The case of [ACC+19] is somewhat special: While their syntax in principle allows that parties operate multiple instances, their security definition reduces this to strictly one instance per party. For their application (secure instant messaging) this is not a limitation as parties are short-lived and created ad-hoc to participate in only a single session.

  8. 8.

    In continuation of Footnote 7: The case of [ACC+19] is special in that the requirement is an ephemeral asymmetric key, that is, a public key that is ad-hoc generated and used only once.

  9. 9.

    Consider, for instance, that situations stemming from participants concurrently performing conflicting operations might have to be resolved, as have to be cases where participants become temporarily unavailable without notice.

  10. 10.

    In some cases, however, it seems feasible to reverse-engineer some information about an assumed syntax from the security reductions also contained in the corresponding works.

  11. 11.

    Although \(\mathrm {exec}\) and \(\mathrm {proc}\) could implicitly initialize the state internally, we treat the state initialization explicitly for reasons of clarity.

  12. 12.

    \(\mathcal {P}(\mathcal {X})\) denotes the powerset of \(\mathcal {X}\).

  13. 13.

    During the research for this article, we found two recent papers’ security definitions for two-party authenticated key exchange that, due to reusing the partnering definition for multiple purposes, cannot be fulfilled: Li and Schäge [LS17] and Cohn-Gordon et al. [CCG+19] both require in their papers’ proceedings version for authentication that an instance only computes a key if there exists a partner instance that also computed the key (which is impossible as not all/both participants compute the key simultaneously). Still, the underlying partnering concept suffices for detecting reveals and challenges of the same key (between partnered instances).

  14. 14.

    Note that every manipulated bit in the transcript (including signatures or MAC tags themselves) dissolves partnering.

  15. 15.

    Moreover, in [BCP02b, ACC+19], party secrets cannot be derived via state exposures. Although [ACC+19] allow the exposure of instance states, their syntax, strictly speaking, does not have a method for using party secrets in the protocol execution, even though their construction makes use of them (violating the syntax definition).

  16. 16.

    Note, for example, that post-compromise security is rather irrelevant for short-lived static GKE protocols.

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Acknowledgments

We thank the reviewers of CT-RSA 2021 for their detailed and helpful comments. B.P. was supported by the European Union’s Horizon 2020 Research and Innovation Programme under Grant Agreement No. 786725 – OLYMPUS. P.R. was supported by the research training group “Human Centered Systems Security” (NERD.NRW) sponsored by the state of North-Rhine Westphalia. D.S. was supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant RGPIN-2016-05146 and NSERC Discovery Accelerator Supplement grant RGPIN-2016-05146.

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Authors and Affiliations

  1. IBM Research – Zurich, Rüschlikon, Switzerland

    Bertram Poettering

  2. TU Darmstadt, Darmstadt, Germany

    Paul Rösler

  3. Ruhr University Bochum, Bochum, Germany

    Jörg Schwenk

  4. University of Waterloo, Waterloo, Canada

    Douglas Stebila

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  1. Bertram Poettering
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  2. Paul Rösler
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Correspondence to Paul Rösler .

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  1. ETH Zürich, Zürich, Switzerland

    Kenneth G. Paterson

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Poettering, B., Rösler, P., Schwenk, J., Stebila, D. (2021). SoK: Game-Based Security Models for Group Key Exchange. In: Paterson, K.G. (eds) Topics in Cryptology – CT-RSA 2021. CT-RSA 2021. Lecture Notes in Computer Science(), vol 12704. Springer, Cham. https://doi.org/10.1007/978-3-030-75539-3_7

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