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An efficient anonymous communication protocol, called MANET anonymous peer-to-peer communication protocol (MAPCP), for P2P applications over mobile ad-hoc networks (MANETs) is proposed in this work. MAPCP employs broadcasts with probabilistic flooding control to establish multiple anonymous paths between communication peers. It requires no hop-by-hop encryption/decryption along anonymous paths and, hence, demands lower complexity of computation and power consumption than other anonymous routing protocols for MANETs. Since MAPCP builds multiple paths to multiple peers within a single query phase without using an extra route discovery process, it is more efficient in P2P applications. Through analysis and extensive simulations, we demonstrate that MAPCP always maintains a higher degree of anonymity than a MANET anonymous single-path routing protocol in a hostile environment. Simulation results also show that MAPCP is resilient to passive attacks in data forwarding for both one-to-one and one-to-many communications.