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Wireless sensor networks are ideal candidates for applications such as target tracking, environment monitoring, military sensing and distributed measurement of seismic activity, etc. Security in wireless sensor networks is critical when there are potential adversaries. Key distribution is one of the most challenging security problems in wireless sensor networks. Nowadays the universal approach is key pre-distribution schemes, such as assigning more than one key to each node. The paper proposed an efficient polynomial-based key predistribution scheme over a finite field for WSN. In this scheme, used with deployment knowledge, sensor nodes are divided into some groups in which nodes are uniformly distributed, and symmetrical polynomials are distributed to nodes. Comparing to the polynomial-based scheme without using deployment strategy shows that not only network connectivity in our scheme has not been declined, but also the resilience against node capture has been greatly improved.