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Sensor networks pose security and privacy challenges. To maintain confidentiality of sensor communications, it is challenging to bootstrap secure communications among sensors while making sensor networks highly connected when sensors are randomly deployed. Several existing key management schemes either cannot offer strong resilience against node capture attacks or have overly large memory requirement to achieve a high degree of connectivity, which is measured as the fraction of the size of the largest connected component over the size of the entire sensor network. We propose a group-based key pre-distribution scheme using sensor deployment knowledge. In our scheme, we partition a sensor field into a hexagonal grid. Sensor nodes are divided into groups, each of which is deployed into a cell of the grid. Our scheme consists of a series of slightly different methods, depending on how to distribute secret information among neighboring groups and how much information is to be stored in each node. Experimental results show that our scheme achieves a higher degree of connectivity of the sensor network with a lower memory requirement compared to existing schemes. In addition, our scheme offers a stronger resilience against node capture attacks.