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Key agreement is a central problem to build up secure infrastructures for networks. Public key technology may not be suitable in many networks of low-end devices, such as ad hoc networks and sensor networks, because of its computation inefficiency and the lack of central authorities in those distributed scenarios. Conventional distributed symmetric key agreement schemes lack scalability due to their large memory cost (O(N), where N is the total number of nodes), and their probabilistic nature cannot ensure key agreement between every pair of nodes. In this paper, we propose a novel symmetric key agreement scheme, which is scalable for large scale networks with very small memory cost per node. A t-degree (k+1)-variate symmetric polynomial is used to achieve key agreement between nodes. The memory cost per node for a network of N nodes is reduced to around k+1radic(k(k+1)!/2) kradicN, where k ges 1. Our scheme is also deterministic in that every pair of nodes can establish a shared key.