Must the Communication Graph of MPC Protocols be an Expander?

Elette Boyle, Ran Cohen, Deepesh Data, Pavel Hubáček

Research output: Contribution to journalArticlepeer-review


Secure multiparty computation (MPC) on incomplete communication networks has been studied within two primary models: (1) where a partial network is fixed a priori, and thus corruptions can occur dependent on its structure, and (2) where edges in the communication graph are determined dynamically as part of the protocol. Whereas a rich literature has succeeded in mapping out the feasibility and limitations of graph structures supporting secure computation in the fixed-graph model (including strong classical lower bounds), these bounds do not apply in the latter dynamic-graph setting, which has recently seen exciting new results, but remains relatively unexplored. In this work, we initiate a similar foundational study of MPC within the dynamic-graph model. As a first step, we investigate the property of graph expansion. All existing protocols (implicitly or explicitly) yield communication graphs which are expanders, but it is not clear whether this is inherent. Our results consist of two types (for constant fraction of corruptions): Upper bounds: We demonstrate secure protocols whose induced communication graphs are not expander graphs, within a wide range of settings (computational, information theoretic, with low locality, even with low locality and adaptive security), each assuming some form of input-independent setup.Lower bounds: In the plain model (no setup) with adaptive corruptions, we demonstrate that for certain functionalities, no protocol can maintain a non-expanding communication graph against all adversarial strategies. Our lower bound relies only on protocol correctness (not privacy) and requires a surprisingly delicate argument. More generally, we provide a formal framework for analyzing the evolving communication graph of MPC protocols, giving a starting point for studying the relation between secure computation and further, more general graph properties.

Original languageEnglish
Article number20
JournalJournal of Cryptology
Issue number3
StatePublished - Jul 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023, International Association for Cryptologic Research.


Supported by the project 17-09142 S of GA ČR, Charles University project UNCE/SCI/004, and Charles University project PRIMUS/17/SCI/9. This work was done under financial support of the Neuron Fund for the support of science. Supported in part by ISF grant 1861/16, AFOSR Award FA9550-17-1-0069, and ERC Grant no. 307952. Some of the work was done while the author was at MIT and Northeastern University and supported in part by Alfred P. Sloan Foundation Award 996698, ISF grant 1861/16, ERC starting grant 638121, NEU Cybersecurity and Privacy Institute, and NSF TWC-1664445.

FundersFunder number
National Science FoundationTWC-1664445
Air Force Office of Scientific ResearchFA9550-17-1-0069
Alfred P. Sloan Foundation638121, 996698
Massachusetts Institute of Technology
Univerzita Karlova v PrazePRIMUS/17/SCI/9, UNCE/SCI/004
European Research Council307952
Grantová Agentura České Republiky
Israel Science Foundation1861/16
Northeastern University
Neuron Nadační Fond Na Podporu Vědy


    • Communication graph
    • Consensus protocols
    • Expander graph
    • Secure multiparty computation


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