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An ad hoc wireless network permits wireless mobile nodes to communicate without prior infrastructure. Due to the limited range of each wireless node, communication sessions between two nodes are usually established through a number of intermediate nodes. Unfortunately, some of these intermediate nodes might be malicious, forming a threat to the security or confidentiality of exchanged data. While data encryption can protect the content exchanged between nodes, analysis of communication patterns may reveal valuable information about end users and their relationships. Using anonymous paths for communication provides security and privacy against traffic analysis. To establish these anonymous paths, all nodes build a global view of the network by exchanging routing information. In dynamic ad hoc networks, building this global view is not an option. In this paper, we propose and analyze a distributed route construction algorithm for use in the establishment of anonymous routing paths in ad hoc wireless networks.