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Information-Theoretic Topology-Hiding Broadcast: Wheels, Stars, Friendship, and Beyond

Authors D'or Banoun, Elette Boyle , Ran Cohen

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LIPIcs.ITC.2024.1.pdf
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Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Theory of computation → Cryptographic protocols
Keywords
  • broadcast
  • topology-hiding protocols
  • information-theoretic security

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Abstract

Topology-hiding broadcast (THB) enables parties communicating over an incomplete network to broadcast messages while hiding the network topology from within a given class of graphs. Although broadcast is a privacy-free task, it is known that THB for certain graph classes necessitates computational assumptions, even against "honest but curious" adversaries, and even given a single corrupted party. Recent works have tried to understand when THB can be obtained with information-theoretic (IT) security (without cryptography or setup assumptions) as a function of properties of the corresponding graph class.
We revisit this question through a case study of the class of wheel graphs and their subgraphs. The nth wheel graph is established by connecting n nodes who form a cycle with another "center" node, thus providing a natural extension that captures and enriches previously studied graph classes in the setting of IT-THB.
We present a series of new findings in this line. We fully characterize feasibility of IT-THB for any class of subgraphs of the wheel, each possessing an embedded star (i.e., a well-defined center connected to all other nodes). Our characterization provides evidence that IT-THB feasibility may correlate with a more fine-grained degree structure - as opposed to pure connectivity - of the corresponding graphs. We provide positive results achieving perfect IT-THB for new graph classes, including ones where the number of nodes is unknown. Further, we provide the first feasibility of IT-THB on non-degenerate graph-classes with t > 1 corruptions, for the class of friendship graphs (Erdös, Rényi, Sós '66).

Cite As Get BibTex

D'or Banoun, Elette Boyle, and Ran Cohen. Information-Theoretic Topology-Hiding Broadcast: Wheels, Stars, Friendship, and Beyond. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITC.2024.1

Author Details

D'or Banoun
  • Reichman University, Herzliya, Israel
Elette Boyle
  • Reichman University, Israel
  • NTT Research, Sunnyvale, CA, USA
Ran Cohen
  • Reichman University, Herzliya, Israel

Funding

  • Banoun, D'or: Supported in part by AFOSR Award FA9550-21-1-0046.
  • 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, by ISF grant 1834/23, 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.

References

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