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The increasing popularity of distributed and collaborative applications prompts the need for secure communication in collaborative groups. Some distributed collaborative key management protocols have been proposed to provide group communication privacy and data confidentiality for collaborative groups. However, most of them rekey on each member change, and the costs of group rekeying can be quite substantial for large groups with frequent membership changes. In this paper, we propose a efficient distributed key agreement scheme using a distributed one-way function tree named EDKAS which can significantly reduce the computation and communication costs of maintaining the group key especially in a highly dynamical environment based upon period-based group rekeying. Performance of the period-based group rekeying algorithm is analyzed and evaluated under different settings. A comparison with previous work has shown that EDKAS provides high rekeying efficiency while preserving both distributed and collaborative properties.