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A key pre-distribution scheme is a method by which initially an off-line trusted authority 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 an asymmetric key pre-distribution scheme. Instead of assuming that the network is comprised entirely of identical users in conventional key pre-distribution schemes, the network now consists of a mix of users with different missions, i.e., ordinary users and keying material servers. A group of users, using secret keys preloaded in their memory and public keying material retrieved from one keying material server, can compute a session key. The properties of this method are that, the compromise of keying material servers does not reveal any information about users' secret keys and the session keys of privileged subset of users; if computational assumptions are considered, each user has very low storage requirement. These properties make it attractive for sensor networks. We first formally define the asymmetric key pre-distribution scheme in terms of the entropy and give lower bounds on user's storage requirement and the public keying material size. Then, we present its constructions and applications for sensor networks.