Rio LaVigne -- Topology Hiding Computation for All Graphs

Abstract:<br>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&nbsp;<a href="" target="_blank"></a>, 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&nbsp;computation is feasible for all graphs under the Decisional Diffie-Hellman assumption or the Quadratic-Residuosity 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. We can also extend this result to use deterministic walks (exploration sequences), opening up the possibility for a perfectly-complete topology hiding broadcast.<br>Joint work with Adi Akavia and Tal Moran.<br>

Tuesday, February 6, 2018 - 4:15pm to 5:15pm
Gates 463