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We introduce the prefix routing over set elements (PROSE) protocol for scalable routing in MANETs based on the combined use of prefix labels and distributed hashing. In PROSE, nodes use neighbor-to-neighbor signaling to label themselves with prefix labels that provide implicit routing from any node to any network destination. Nodes implement a distributed hash table to store the mappings between node identifiers (e.g., a MAC or IP address) and their prefix labels. Destinations publish their existence and sources subscribe to their intended destinations. We show that PROSE provides correct routing based on prefix labels and that its signaling overhead grows sub-linearly with the network size. We present simulation and testbed results that illustrate the benefits of PROSE compared to traditional MANET routing protocols.