On the Limits of Byzantine-tolerant Spanning Tree Construction in Route-Restricted Overlay Networks
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Route-restricted overlays are peer-to-peer networks where each node can only set up connections to a small subset of nodes determined by the respective user. Popular examples include payment networks such as the Lightning network as well as social overlays such as the Dark Freenet. Routing algorithms are central to such overlays as they enable communication between nodes that are not directly connected. The most promising solution regarding efficiency and scalability are routing protocols based on breadth-first-search (BFS) spanning trees. However, existing approaches fail to address whether and to what extent building such spanning trees is possible in the presence of Byzantine nodes. Our contribution is twofold. We first show that there is no protocol for route-restricted networks that achieves global consensus on a root node and is tolerant to Byzantine nodes at the same time. Second, we design a novel spanning tree construction algorithm based on cryptographic signatures that provably reduces the set of nodes affected by Byzantine attacks. Our simulations substantiate this theoretical result with concrete values based on real-world data sets. For instance, in a social graph of 63392 nodes, the average percentage of nodes affected by an attacker with 200 connections to honest nodes drops from 93
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