We propose a broadcast method to establish symmetric keys between wireless sensor nodes and a sink, that achieves a different key for each node. We apply the Elliptic Curve Diffie-Hellman (ECDH) key exchange mechanism in two parts. The first part of the ECDH key exchange is conducted in a secure environment before network deployment to avoid the common man-in-the-middle problem of Diffie-Hellman (DH) schemes. The second part of the key exchange is initiated periodically by the sink using a broadcast message. Thus, the communication overheads in the resource constrained sensor network are reduced.