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.
|Title of host publication||Advances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings|
|Editors||Hovav Shacham, Jonathan Katz|
|Number of pages||21|
|State||Published - 2017|
|Event||37th Annual International Cryptology Conference, CRYPTO 2017 - Santa Barbara, United States|
Duration: 20 Aug 2017 → 24 Aug 2017
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||37th Annual International Cryptology Conference, CRYPTO 2017|
|Period||20/08/17 → 24/08/17|
Bibliographical noteFunding 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.
© International Association for Cryptologic Research 2017.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)