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In mobile peer-to-peer networks, proposed service discovery protocols disregard the exposure of the participating peers' privacy details (privileged information). In these methods, the participating peers must provide their identities during the service discovery process to be authorized to utilize services. However, a peer may not be willing to reveal its privileged information until it identifies the service providing peer. So these peers face a problem, should the service requesting or the service providing peer reveal the identity first. The protocol presented in solves this problem to some extent and discover the services available in the service requester's vicinity in a single-hop time sync peers only. In this paper, we propose a privacy-preserving model based on challenged/response idea to discover the services available in the mobile peer-to-peer network even when the moving service requester and the service provider are at a multi-hop distance away. The performance studies shows that our protocol does preserve the privacy in a communication efficient way with reduced false positives in comparison to one other recently proposed protocol.