Topology-Hiding Computation on All Graphs
Name
145_2019_9318_ReferencePDF.pdf
Size
527.11 KB
Format
Adobe PDF
Checksum (MD5)
fdd4d9f653a1c7a960a812255bb3ac29
Author(s)
Akavia, Adi
LaVigne, Rio
Moran, Tal
Date Issued
March 15, 2019
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
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 computation is feasible for all graphs under either the decisional Diffie–Hellman or quadratic residuosity assumption. Our techniques employ random or deterministic 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 graph-covering sequences that, together, are locally identical to receiving at each round a message from each neighbor and sending back a processed message from some neighbor (in a randomly permuted order).
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00145-019-09318-y
