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Communication Lower Bounds for Cryptographic Broadcast Protocols

Authors Erica Blum, Elette Boyle, Ran Cohen, Chen-Da Liu-Zhang

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Author Details

Erica Blum
  • University of Maryland, College Park, MD, USA
Elette Boyle
  • Reichman University, Herzliya, Israel
  • NTT Research, Sunnyvale, CA, USA
Ran Cohen
  • Reichman University, Herzliya, Israel
Chen-Da Liu-Zhang
  • Hochschule Luzern, Switzerland
  • Web3 Foundation, Zug, Switzerland

Funding

  • Blum, Erica: Part of the work was done while the author was an intern at NTT Research.
  • Boyle, Elette: Supported in part by AFOSR Award FA9550-21-1-0046 and ERC Project HSS (852952).
  • Cohen, Ran: Supported in part by NSF grant no. 2055568 and by the Algorand Centres of Excellence programme managed by Algorand Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of Algorand Foundation.
  • Liu-Zhang, Chen-Da: Part of this work was done while the author was at NTT Research.

Cite As Get BibTex

Erica Blum, Elette Boyle, Ran Cohen, and Chen-Da Liu-Zhang. Communication Lower Bounds for Cryptographic Broadcast Protocols. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.DISC.2023.10

Abstract

Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages.

We provide communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound.
 
- Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties.
Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions.
- Weakly adaptive adversary. Our second bound considers n/2 + k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties.
Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality.

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
Keywords
  • broadcast
  • communication complexity
  • lower bounds
  • dishonest majority

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