In this paper, we propose SeGrid, a secure framework for establishing grid keys in low duty cycle sensor networks, for which establishing a common key for each pair of neighboring sensors is unnecessary since most sensors remain in sleep mode at any instant of time. SeGrid intends to compute a shared key for two grids that may be multihop away. This design explores the fact that for most applications, closer grids have higher probability and desire for secure message exchange. SeGrid relies on the availability of a low-cost public cryptosystem. The query and update of the corresponding public shares are controlled by a novel management protocol such that the closer the two grids, the shorter the distance to obtain each other's public share. We instantiate SeGrid based on Blom's key establishment to illustrate the computation of a grid key.