Efficient key establishment is an important problem for secure group communications. The communication and storage complexity of group key establishment problem has been studied extensively. In this paper, we propose a new group key establishment protocol whose computation complexity is significantly reduced. Instead of using classic secret sharing, the protocol only employs a linear secret sharing scheme, using Vandermonde Matrix, to distribute group key efficiently. This protocol drastically reduces the computation load of each group member and maintains at least the same security degree com...