In spite of previous widely held belief of the incompatibility of public key cryptography (PKC) schemes for wireless sensor networks (WSNs), some recent works have shown that, PKC based schemes could be implemented for such networks in some ways. The major challenge of employing a PKC scheme in wireless sensor network is posed by the limitations of resources of the tiny sensors. Considering this feature of the sensors, in this paper, we propose an efficient PKC based security architecture with relatively less resource requirements than those of the other previously proposed PKC schemes for WSN. Our security architecture comprises basically of two parts; a key handshaking scheme based on simple linear operations and the derivation of decryption key by a receiver node. Our architecture allows both base-station-to-node or node-to-base-station secure communications, and node-to-node secure communications. Analysis and simulation results show that, our proposed architecture ensures a good level of security for communications in the network and could effectively be implemented using the limited computation, memory and energy budgets of the current generation sensor nodes.