Bootstrapping secure communication among sensor nodes deployed in hostile environments is an important and challenging problem. A common approach to solve this problem is to use a key predistribution scheme in which each sensor node is assigned a subset of keys selected from some key pool. The resilience of a key pre-distribution scheme depends on the size of the key pool that the scheme uses for distributing keys among sensor nodes. After deployment, if two sensor nodes are within communication range of one and other, and share at least one common key, then they can establish a secure channel using the common key. We show that, when the key distribution is near-uniform, the maximum size of a key pool that can be used by any key pre-distribution scheme is upper-bounded by s2, where s is the amount of space available on a p sensor node for storing keys and p is the probability that two sensor nodes share a common key. We define the utilization factor ofakey pre-distribution scheme to measure how effective the scheme is in using the largest key pool available at its disposal for fixed values of s and p. We explore the effect of the utilization factor of a scheme on its resilience
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