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Peer-to-peer networks are mainly unstructured, where no specific topology is imposed on the network during its operations. These networks offer a high degree of resilience against network dynamics disrupting the network's operation. Unstructured networks, based on random connections are limited, however, in the performance and node reachability they can offer to applications. In contrast, structured networks impose predetermined connectivity relationships between nodes in order to offer a guarantee on the diameter between requesting nodes and the requested objects. We observe that neither structured nor unstructured networks can simultaneously offer both good performance and resilience in a single algorithm. To address this challenge, we propose Phenix, a peer-to-peer algorithm that can construct low-diameter resilient topologies. Phenix supports low diameter operations by creating a topology of nodes whose degree distribution follows a power-law, while the implementation of the underlying algorithm is fully distributed requiring no central server, thus, eliminating the possibility of a single point of failure in the system. We present the design and evaluation of the algorithm and show through analysis, simulation, and experimental results obtained from an implementation on the PlanetLab testbed that Phenix is robust to network dynamics such as joins/leaves, node failure and large-scale network attacks, while maintaining low overhead when implemented in an experimental network.