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Finding an optimal key assignment (subject to given constraints) for a keypredistribution scheme in wireless sensor networks is a difficult task. Hence,most of the practical schemes are based on probabilistic key assignment, whichleads to sub-optimal schemes requiring key storage linear in the total numberof nodes. A graph theoretic framework is introduced to study the fundamentaltradeoffs between key storage, average key path length (directly related to thebattery consumption) and resilience (to compromised nodes) of keypredistribution schemes for wireless sensor networks. Based on the proposedframework, a lower bound on key storage is derived for a given average key pathlength. An upper bound on the compromising probability is also given. Thisframework also leads to the design of key assignment schemes with a storagecomplexity of the same order as the lower bound.

A Graph Theoretic Approach for Optimizing Key Pre-distribution in Wireless SensorNetworks