This study is to investigate new schemes for distributing cryptographic keys in sensor networks. Sharing a key is the very first step to realize secure communication over an untrusted network infrastructure, but commonly used cryptographic techniques cannot be employed for sensor networks due to the restriction of computational resources of sensor nodes. A practical solution to this issue is to predistribute cryptographic keys in sensor nodes before they are deployed. A focal point in this solution is the choice of keys that are assigned to a sensor node. Eschenauer et al. considered to choose keys randomly, and Chan et al. also followed the random choice approach. We consider in this paper a new approach in which keys are assigned according to a basic algebraic geometry. The performance of the proposed scheme is investigated analytically.