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There are many applications of ad hoc sensor networks that have to ensure immunity to adversaries. One challenge is how to bootstrap secure communication among nodes. In this paper we propose a novel key pre-distribution scheme based on polynomials. The properties of our scheme are the same as a scheme presented by Blom, but we propose to use a different technique that can be easily extended if we get rid of a node's computation constrains. By using polynomial-based key pre-distribution, we can reduce the storage requried at receivers down to O(t) where t is a system and security parameter. Moreover using only this information, pairwise keys can be established efficiently for each pair of nodes which enable secure construction of the communication tree.