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Network-Agnostic Security Comes (Almost) for Free in DKG and MPC

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Advances in Cryptology – CRYPTO 2023 (CRYPTO 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14081))

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Abstract

Distributed key generation (DKG) protocols are an essential building block for threshold cryptosystems. Many DKG protocols tolerate up to \(t_s<n/2\) corruptions assuming a well-behaved synchronous network, but become insecure as soon as the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions, but only tolerate \(t_a<n/3\) corruptions, even when the network is well-behaved.

In this work, we ask whether one can design a protocol that achieves security guarantees in either scenario. We show a complete characterization of network-agnostic DKG protocols, showing that the tight bound is \(t_a+2t_s <n\). As a second contribution, we provide an optimized version of the network-agnostic multi-party computation (MPC) protocol by Blum, Liu-Zhang and Loss [CRYPTO’20] which improves over the communication complexity of their protocol by a linear factor. Moreover, using our DKG protocol, we can instantiate our MPC protocol in the plain PKI model, i.e., without the need to assume an expensive trusted setup.

Our protocols incur comparable communication complexity as state-of-the-art DKG and MPC protocols with optimal resilience in their respective purely synchronous and asynchronous settings, thereby showing that network-agnostic security comes (almost) for free.

R. Bacho—The author was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 507237585.

D. Collins—This work was partially carried out while the author was visiting CISPA.

C.-D. Liu-Zhang—CMU and NTT Research and supported by the NSF award 1916939, DARPA SIEVE program, a gift from Ripple, a DoE NETL award, a JP Morgan Faculty Fellowship, a PNC center for financial services innovation award, and a Cylab seed funding award.

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Notes

  1. 1.

    In this model, the public keys of corrupted parties can be generated arbitrarily.

  2. 2.

    Note that a possibly biased secret can still be sufficient for applications like threshold signatures, as highlighted in [GJKR07, BL22].

  3. 3.

    This discussion omits a minor technical detail: the adversary must not be able to broadcast incorrect messages on behalf of honest parties, even in asynchrony. Ensuring this, however, is easy using digital signatures.

  4. 4.

    The simplified description tolerates only fail-stop corruptions. To achieve security against active adversaries, one needs NIZKs at appropriate steps of the protocol. See Sect. 6 for details.

  5. 5.

    We emphasise that t-security does not imply t-intrusion tolerance.

  6. 6.

    For rounds \(r\ge t+1\) we only require \(t+1\) signatures including the sender’s.

  7. 7.

    We conjecture that the protocol without these extra messages also satisfies consistency, but the protocol as written has the same asymptotic complexity and therefore we leave it as future work to prove it.

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Authors and Affiliations

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

    Renas Bacho & Julian Loss

  2. Saarland University, Saarbrücken, Germany

    Renas Bacho

  3. EPFL, Lausanne, Switzerland

    Daniel Collins

  4. Luzern University of Applied Sciences and Arts, Lucerne, Switzerland

    Chen-Da Liu-Zhang

  5. Web3 Foundation, Houston, USA

    Chen-Da Liu-Zhang

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    Helena Handschuh

  2. Brown University, Providence, RI, USA

    Anna Lysyanskaya

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Bacho, R., Collins, D., Liu-Zhang, CD., Loss, J. (2023). Network-Agnostic Security Comes (Almost) for Free in DKG and MPC. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_3

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  • DOI: https://doi.org/10.1007/978-3-031-38557-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38556-8

  • Online ISBN: 978-3-031-38557-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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