Wireless sensor networks consist of numerous small-sized nodes equipped with limited computing power and storage as well as energy-limited disposable batteries. In this networks, nodes are deployed in a large given area and communicate with each other in short distances via wireless links. For energy efficient networks, dynamic clustering protocol is an effective technique to achieve prolonged network lifetime, scalability, and load balancing which are known as important requirements. this technique has a characteristic that sensing data which gathered by many nodes are aggregated by cluster head node. In the case of cluster head node is exposed by attacker, there is no guarantee of safe and stable network. Therefore, for secure communications in such a sensor network, it is important to be able to encrypt the messages transmitted by sensor nodes. Especially, cluster based sensor networks that are designed for energy efficient, strongly recommended suitable key management and authentication methods to guarantee optimal stability. To achieve secured network, we propose a key management scheme which is appropriate for hierarchical sensor networks. Proposed scheme is based on polynomial key pool pre-distribution scheme, and sustain a stable network through key authentication process.