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For inter and intra cluster communication, member nodes jointly build a mutual session key called cluster key to allow secure communication. Most existing schemes for cluster key management use messages exchange among the member nodes within a cluster for the new cluster key establishment when a node leaves or joins a cluster. This causes significant communication and computation costs. Furthermore, the secure distribution of cluster keys among member nodes in frequently changing environments is a difficult task without encryption and decryption operations. For secure cluster key management, we utilized polynomial (P) to accomplish effective intra-cluster key management and produced polynomial for making an inter-cluster key distribution. The main contribution is to generate polynomials and broadcast to nodes whenever a change occurs in a network or demanding nodes for secure key management. The presented scheme supports scalability for an increasing number of nodes using polynomials. The proposed scheme increases the lifetime of the network by decreasing the key pool size.