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Synchronous Perfectly Secure Message Transmission with Optimal Asynchronous Fallback Guarantees

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Financial Cryptography and Data Security (FC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13950))

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Abstract

Secure message transmission (SMT) constitutes a fundamental network-layer building block for distributed protocols over incomplete networks. More specifically, a sender \(\textbf{S}\) and a receiver \(\textbf{R}\) are connected via \(\ell \) disjoint paths, a subset of which are controlled by the adversary.

Perfectly-secure SMT protocols in synchronous and asynchronous networks are resilient up to \(\ell /2\) and \(\ell /3\) corruptions respectively. In this work, we ask whether it is possible to achieve a perfect SMT protocol that simultaneously tolerates \(t_s < \ell /2\) corruptions when the network is synchronous, and \(t_a < \ell /3\) when the network is asynchronous.

We completely resolve this question by showing that perfect SMT is possible if and only if \(2t_a + t_s < \ell \). In addition, we provide a concretely round-efficient solution for the (slightly worse) trade-off \(t_a + 2t_s < \ell \).

As a direct application of these results, following the recent work by Appan, Chandramouli, and Choudhury [PODC’22], we obtain an n-party perfectly-secure multi-party computation protocol with asynchronous fallback over any network with connectivity \(\ell \), as long as \(t_a + 3t_s <n\) and \(2t_a + t_s < \ell \).

C.-D. Liu-Zhang—This work was partially carried out while the author was at Carnegie Mellon University, USA. Supported in part 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.

    This trade-off is worse given that \(t_a \le t_s\). Note that any protocol with asynchronous security is also secure when run over a synchronous network.

  2. 2.

    By requiring the distributions \(T_{\mathcal {I}, m}^k\) and \(T_{\mathcal {I}, m'}^k\) to be statistically close or computationally indistinguishable one obtains the notion of statistical security and computational security. In this paper, we are only concerned with perfect security.

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Acknowledgments

The authors would like to thank Martin Hirt for some very insightful discussions related to the material in this work.

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Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Giovanni Deligios

  2. HSLU and Web3 Foundation, Zug, Switzerland

    Chen-Da Liu-Zhang

Authors
  1. Giovanni Deligios
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  2. Chen-Da Liu-Zhang
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Corresponding author

Correspondence to Giovanni Deligios .

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Editors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Foteini Baldimtsi

  2. University of Bern, Bern, Switzerland

    Christian Cachin

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Deligios, G., Liu-Zhang, CD. (2024). Synchronous Perfectly Secure Message Transmission with Optimal Asynchronous Fallback Guarantees. In: Baldimtsi, F., Cachin, C. (eds) Financial Cryptography and Data Security. FC 2023. Lecture Notes in Computer Science, vol 13950. Springer, Cham. https://doi.org/10.1007/978-3-031-47754-6_5

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  • DOI: https://doi.org/10.1007/978-3-031-47754-6_5

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