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Wireless sensor networks(WSN) usually consists of a large number of tiny sensors with limited computation capacity, memory space and power resource. WSN's are extremely vulnerable against any kind of internal or external attacks, due to several factors such as resource constrained nodes and lack of tamper-resistant packages. To achieve security in wireless sensor networks, it is important to encrypt messages sent among sensor nodes. In this paper, we propose a scheme called Modified Bloom's Scheme(MBS); it makes use of asymmetric matrices in place of symmetric matrices in order to establish secret keys between node pairs. In this proposed scheme, the network resilience against node capture is substantially improved.