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Secure group-based communication services are gaining momentum in wireless ad hoc networks (WAHNs). The efficiency and scalability of these services make them suitable for supporting the inherently collaborative computing and communications activities among peer WAHN nodes as well as the growing number of group-based WAHN applications. Key management, which is comprised of dynamic key generation, assignment, and distribution, is at the heart of secure group communications. This work proposes TKGS; an efficient threshold-based key generation scheme for open WAHNs based on collaborative reconstruction of key-generation keys. To mitigate node mal-behavior, a verifiable secret sharing technique is employed, where an (authenticated) dealer node is selected to collect a set number of valid shares and generate new administrative keys. While most existing key management schemes assume reliable and trusted nodes, TKGS provides a distributed solution that is resilient to node failure and mal-behavior. A major advantage of TKGS is its small overhead; collaborative key construction is done in less than two rounds with a very high probability of success.