Wireless sensor networks and Internet of Things (IoT) are part of dynamic networks as new nodes can join while existing members can leave the system at any time. These networks mainly suffer from severe resource constraints like energy, storage and computation, which makes securing communications between nodes a real challenge. Several key establishment protocols have been proposed in the literature. Some of them are based on symmetric polynomials. However, the latter solutions have some limitations, such as the resilience to node capture attacks as well as the storage and computation overheads that are high for constrained nodes. In this paper, we propose a lightweight polynomial-based key management scheme for dynamic networks. The proposed scheme allows nodes to be able to establish secure communications between them, and ensures dynamism by supporting node addition and deletion after the setup phase. It also resists to node capture attack. The performance evaluation shows that our scheme reduces both the storage and computation overheads when compared to other related polynomial-based protocols.