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).

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所有图的拓扑隐藏计算

如果分布式计算中的节点通过部分通信图连接，则称为拓扑隐藏，如果它不显示超出函数输出显示的图信息。先前的结果表明，拓扑隐藏计算协议存在于节点数（Moran–Orlov–Richelson，TCC'15；Hirt 等人，Crypto'16）以及其他图的恒定度和对数直径的图族，例如循环、树和低圆周图（Akavia-Moran，Eurocrypt'17），但一般图的可行性问题是开放的。在这项工作中，我们积极地解决了上述开放性问题：我们证明了拓扑隐藏计算对于决策性 Diffie-Hellman 或二次剩余假设下的所有图都是可行的。我们的技术采用随机或确定性游走来生成覆盖图的路径，我们将 Akavia-Moran 拓扑隐藏广播应用于链图（路径）。为了防止随机游走泄露拓扑信息，我们设计了多个图覆盖序列，这些序列一起在本地等同于在每一轮接收来自每个邻居的消息并从某个邻居发回处理过的消息（以随机排列的顺序） .