This paper contributes to the challenging field of security for wireless sensor networks by introducing a keyagreement scheme in which sensor nodes create secure radio connections with their neighbours depending on the aidof third parties. These third parties are responsible only for the pair-wise key establishment among sensor nodes,so they do not observe the physical phenomenon nor route data packets to other nodes. The proposed methodis explained here with respect to four important issues: how secret shares are distributed, how local neighboursare discovered, how legitimate third parties are verified, and how secure channels are established. Moreover, theperformance of the scheme is analyzed with regards to five metrics: local connectivity, resistance to node capture,memory usage, communication overhead, and computational burden.Our scheme not only secures the transmissionchannels of nodes but also guarantees high local connectivity of the sensor network, low usage of memory resources,perfect network resilience against node capture, and complete prevention against impersonation attacks. As it isdemonstrated in this paper, using a number of third parties equals to 10% of the total number of sensor nodes inthe area of interest, the proposed method can achieve at least 99.42% local connectivity with a very low usage ofavailable storage resources (less than 385 bits on each sensor node)