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A new group key management scheme against the unreliable wireless communication channel and unsafe environment was proposed for wireless sensor network (WSN). In the proposed scheme, broadcast polynomial, generated over finite field Fq based on the secret sharing, was employed to revoke compromised sensor nodes. In order to tolerate key-update message loss, group session keys were generated as one-way hash chain sequence and distributed in advance. The analysis showes that the scheme has better performance in terms of the computation and communication overhead.