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A key pre-distribution scheme is a method by which initially an off-line trusted authority T A distributes pieces of information among a set of users. Later, each member of a group of users can compute a common key for secure communication. In this paper we present a Keying Material Based Key Pre-distribution Scheme, i.e., a group of users, using secret information preloaded in their memory and some public information retrieved from a keying material server, can compute a common key. We first formally define the keying material based key pre-distribution scheme in terms of the entropy, and give lower bounds on the amount of information each user has to keep secret. Then, we describe its applications for sensor networks.