Communication Lower Bounds for Cryptographic Broadcast Protocols

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publication37th International Symposium on Distributed Computing, DISC 2023
EditorsRotem Oshman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773010
DOIs
StatePublished - Oct 2023
Externally publishedYes
Event37th International Symposium on Distributed Computing, DISC 2023 - L'Aquila, Italy
Duration: 10 Oct 202312 Oct 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume281
ISSN (Print)1868-8969

Conference

Conference37th International Symposium on Distributed Computing, DISC 2023
Country/TerritoryItaly
CityL'Aquila
Period10/10/2312/10/23

Bibliographical note

Publisher Copyright:
© Erica Blum, Elette Boyle, Ran Cohen, and Chen-Da Liu-Zhang; licensed under Creative Commons License CC-BY 4.0.

Keywords

  • broadcast
  • communication complexity
  • dishonest majority
  • lower bounds

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