Topology-hiding computation on all graphs

Adi Akavia, Rio LaVigne, Tal Moran

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


A distributed computation in which nodes are connected by a partial communication graph is called topology-hiding if it does not reveal information about the graph beyond what is revealed by the output of the function. Previous results have shown that topology-hiding computation protocols exist for graphs of constant degree and logarithmic diameter in the number of nodes [Moran-Orlov-Richelson, TCC’15; Hirt et al., Crypto’16] as well as for other graph families, such as cycles, trees, and low circumference graphs [Akavia-Moran, Eurocrypt’17], but the feasibility question for general graphs was open. In this work we positively resolve the above open problem: we prove that topology-hiding MPC is feasible for all graphs under the Decisional Diffie-Hellman assumption. Our techniques employ random-walks to generate paths covering the graph, upon which we apply the Akavia-Moran topology-hiding broadcast for chain-graphs (paths). To prevent topology information revealed by the random-walk, we design multiple random-walks that, together, are locally identical to receiving at each round a message from each neighbors and sending back processed messages in a randomly permuted order.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings
EditorsHovav Shacham, Jonathan Katz
PublisherSpringer Verlag
Number of pages21
ISBN (Print)9783319636870
StatePublished - 2017
Externally publishedYes
Event37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States
Duration: 20 Aug 201724 Aug 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10401 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference37th Annual International Cryptology Conference, CRYPTO 2017
Country/TerritoryUnited States
CitySanta Barbara

Bibliographical note

Funding Information:
A. Akavia—Work partly supported by the ERC under the EU’s Seventh Framework Programme (FP/2007–2013) ERC Grant Agreement no. 307952. R. LaVigne—This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. Research also supported in part by NSF Grants CNS-1350619 and CNS-1414119, and by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236. T. Moran—Supported by ISF grant no. 1790/13.

Publisher Copyright:
© International Association for Cryptologic Research 2017.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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