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Wireless sensor networks comprise individual sensor nodes with limited storage and computational power. These restrictions can cause difficulty when establishing secure communication links between nodes. Expensive encryption schemes, such as Diffie-Hellman key exchange, simply cannot be effectively implemented. As a consequence, alternative methods are necessary to provide adequate security. One such technique involves randomly distributing several encryption keys and then requiring nodes to discover neighbors that share a subset of these assigned keys. Once compatible neighbors are located, communication is secured through the use of symmetric encryption. Though the requirements for this scheme are less than complex asymmetrical algorithms, each sensor node is still required to store several keys and node-to-key associations. In this paper, we advocate a simplistic approach that reduces key storage while limiting a network's susceptibility to being compromised. The approach is based on assigning a single randomly-selected key to each node. The paper presents a detailed analysis of the resilience of the proposed scheme to the collusion attacks and studies the implications on the network connectivity.