Computation-efficient key establishment in wireless group communications

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 compared to existing schemes employing traditional secret sharing. The security strength of this scheme is evaluated in detail. Such a protocol is desirable for many wireless applications where portable devices or sensors need to reduce their computation as much as possible due to battery power limitations. This protocol provides much lower computation complexity while maintaining low and balanced communication complexity and storage complexity for secure group key establishment.