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We address pairwise and (for the first time) triple key establishment problems in wireless sensor networks (WSN). Several types of combinatorial designs have already been applied in key establishment. A BIBD(v, b, r, k, λ) (or t - (v, b, r, k, λ) design) can be mapped to a sensor network, where v represents the size of the key pool, b represents the maximum number of nodes that the network can support, and k represents the size of the key chain. Any pair (or t-subset) of keys occurs together uniquely in exactly λ nodes; λ = 2 and λ = 3 are used to establish unique pairwise or triple keys. We use several known constructions of designs with λ = 2, to predistribute keys in sensors. We also describe a new construction of a design called strong Steiner trade and use it for pairwise key establishment. To the best of our knowledge, this is the first paper on application of trades to key distribution. Our scheme is highly resilient against node capture attacks (achieved by key refreshing) and is applicable for mobile sensor networks (as key distribution is independent on the connectivity graph), while preserving low storage, computation and communication requirements. We introduce a novel concept of triple key distribution, in which three nodes share common keys, and discuss its application in secure forwarding, detecting malicious nodes and key management in clustered sensor networks. We present a polynomial-based and a combinatorial approach (using trades) for triple key distribution. We also extend our construction to simultaneously provide pairwise and triple key distribution scheme, and apply it to secure data aggregation.