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Asymptotically Optimal Message Dissemination with Applications to Blockchains

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Advances in Cryptology – EUROCRYPT 2024 (EUROCRYPT 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14653))

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Abstract

Messages in large-scale networks such as blockchain systems are typically disseminated using flooding protocols, in which parties send the message to a random set of peers until it reaches all parties. Optimizing the communication complexity of such protocols and, in particular, the per-party communication complexity is of primary interest since nodes in a network are often subject to bandwidth constraints. Previous flooding protocols incur a per-party communication complexity of \(\varOmega (l\cdot \gamma ^{-1} \cdot (\log (n) + \kappa ))\) bits to disseminate an l-bit message among n parties with security parameter \(\kappa \) when it is guaranteed that a \(\gamma \) fraction of the parties remain honest. In this work, we present the first flooding protocols with a per-party communication complexity of \(O(l\cdot \gamma ^{-1})\) bits. We further show that this is asymptotically optimal and that our protocols can be instantiated provably securely in the usual setting for proof-of-stake blockchains.

To demonstrate that one of our new protocols is not only asymptotically optimal but also practical, we perform several probabilistic simulations to estimate the concrete complexity for given parameters. Our simulations show that our protocol significantly improves the per-party communication complexity over the state-of-the-art for practical parameters. Hence, for given bandwidth constraints, our results allow to, e.g., increase the block size, improving the overall throughput of a blockchain.

C.-D. Liu-Zhang—The work was partly done while the author was at NTT Research. Partially funded by the Hasler Foundation Project 23090, ETH Zurich Leading House RPG-072023-19 and Protocol Labs Cryptonet RFP-013.

C. Matt—The work was partly done while the author was at Concordium, Zurich, Switzerland.

S.E. Thomsen—The work was partly done while the author was at Aarhus University and afterwards at The Alexandra Institute.

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Notes

  1. 1.

    \(\textsf {ECCast}\) from the use of Erasure-Correcting codes and each party multicasting messages to all parties.

  2. 2.

    \(\textsf {ECFlood}\) from the use of Erasure-Correcting codes in the flooding protocol.

  3. 3.

    For a discussion of why other classical approaches fails in the byzantine setting see Sect. 1.3.

  4. 4.

    Further details on the general setup for our simulations can be found in Sect. 8.

  5. 5.

    For results about the latency see the extended version of this paper [30].

  6. 6.

    To see this for the work of Matt et al., see [33, Corollary 1, Eq (47)]. To make the failure probability negligible in \(\kappa \), each party must forward to any other party with probability \(\varOmega \Big (\frac{\log (n) + \kappa }{n\cdot \gamma }\Big )\) and hence each party will expectedly have \(\varOmega (\gamma ^{-1}\cdot (\log (n) + \kappa ))\) neighbors.

  7. 7.

    One can extend our protocols to handle so-called delayed adaptive adversaries, using techniques presented in [33].

  8. 8.

    The source code, and a description of how to run all benchmarks, can be found at https://github.com/Flooding-Research/optimal-message-dissemination-simulations.

  9. 9.

    The source code is available at https://github.com/Flooding-Research/optimal-message-dissemination-prototype.

  10. 10.

    For a discussion of why other classic approaches fail in the byzantine setting, see Sect. 1.3.

  11. 11.

    For several additional simulations of how the internal parameters influences latency and the redundancy, see the extended version of this paper [30].

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Authors and Affiliations

  1. Lucerne University of Applied Sciences and Arts & Web3 Foundation, Zug, Switzerland

    Chen-Da Liu-Zhang

  2. Primev, Steinhausen, Switzerland

    Christian Matt

  3. Partisia, Aarhus, Denmark

    Søren Eller Thomsen

Authors
  1. Chen-Da Liu-Zhang
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  2. Christian Matt
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  3. Søren Eller Thomsen
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Correspondence to Chen-Da Liu-Zhang , Christian Matt or Søren Eller Thomsen .

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Editors and Affiliations

  1. Zama, Paris, France

    Marc Joye

  2. Ruhr University Bochum, Bochum, Germany

    Gregor Leander

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Liu-Zhang, CD., Matt, C., Thomsen, S.E. (2024). Asymptotically Optimal Message Dissemination with Applications to Blockchains. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14653. Springer, Cham. https://doi.org/10.1007/978-3-031-58734-4_3

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