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In a large scale sensor network, it is infeasible to assign a unique Transport Layer Key (TLK) for each pair of nodes to provide the end-to-end security due to the huge memory cost per node. Thus, conventional key establishment schemes follow a key predistribution approach to establish a Link Layer Key (LLK) infrastructure between neighboring nodes and rely on multihop paths to provide the end-to-end security. Their drawbacks include vulnerability to the node compromise attack, large memory cost, and energy inefficiency in the key establishment between neighboring nodes. In this paper, we propose a novel key establishment scheme, called LAKE, for sensor networks. LAKE uses a t-degree trivariate symmetric polynomial to facilitate the establishment of both TLKs and LLKs between sensor nodes in a two-dimensional space, where each node can calculate direct TLKs and LLKs with some logically neighboring nodes and rely on those nodes to negotiate indirect TLKs and LLKs with other nodes. Any two end nodes can negotiate a TLK on demand directly or with the help of only one intermediate node, which can be determined in advance. As for the LLK establishment, LAKE is more secure under the node compromise attack with much less memory cost than conventional solutions. Due to the location-based deployment, LAKE is also energy efficient in that each node has direct LLKs with most neighbors without spending too much energy on the establishment of indirect LLKs with neighbors through multihop routing.