Key management is a critical issue for wireless sensor networks security. This paper proposes EEHS, a novel Energy Efficient and Highly Survivable dynamic key management scheme for large-scale clustered wireless sensor networks based on Exclusion Basis System (EBS). The major advantages of EEHS are strengthened network security, enhanced energy efficiency, high dynamic performance and good support for network expansion. In EEHS, a novel polynomial-based key—the common polynomial key, is designed and employed as the administration key in the EBS, which can enhance the network survivability under attack. All system keys can be refreshed and revoked according to the compromise of sensor nodes. The function of key assignment and key generation are dispatched to different functional nodes in one cluster and sensor nodes also rotate to act as functional nodes in order to improve the energy efficiency and the network robustness. Simulation and analysis results show that compared with related works, EEHS supports the networks with more energy efficiency, longer lifespan and stronger resilience to node compromise.