Key generation is an important challenge among the issues related to security in wireless sensor network. Each node has a set of keys called key-chain rather than a single shared key. The key-chains are generated at the base station and stored in the ROMs of sensor nodes prior to deployment. This paper brings in the idea of deterministic approach to key generation. There is no need to assume a probability that any two nodes are neighbors. We use combinatorics based approach using a block design technique called symmetric Balanced Incomplete Block Design (BIBD). We construct multiple key-spaces out of a key pool from which the key-chains are formed. The main contribution to this work is the use of multiple key spaces to decrease memory utilization at each sensor node, retain connectivity and still not hamper the resilience of the network. It decreases the redundancy in key generation. It eliminates the dependency between the number of keys in the key-chain and number of nodes in the network.
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