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Peer-to-peer paradigm is increasingly employed for organizing distributed resources for various applications, e.g. content distribution, open storage grid etc. In open environments, even when proper access control mechanisms supervise the access to the resources, privacy issues may arise depending on the application. In this paper, we introduce, PANACEA, a system that offers high and tunable privacy based on an innovative resource indexing approach. In our case, privacy has two aspects: the deducibility of a resource's existence/non-existence and the discovery of the provider of the resource. We systematically study the privacy that can be provided by the proposed system and compare its effectiveness as related to conventional P2P systems. Employing both probabilistic and information-theoretic approaches, we analytically derive that PANACEA can offer high privacy, while preserving high search efficiency for authorized users. Our analysis and the effectiveness of the approach have been experimentally verified. Moreover, the privacy offered by the proposed system can be tuned according to the specific application needs, which is illustrated with a detailed simulation study.