Topology hiding computation on all graphs
Author(s)LaVigne, Rio (Kristen Rio)
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
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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 the Decisional Diffie-Hellman 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).
Thesis: S.M., Massachusetts Institute of Technology, Department of Department of Electrical Engineering and Computer Science, 2017.Cataloged from PDF version of thesis.Includes bibliographical references (pages 63-65).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.