Currently, it is rapidly increasing convergence services based on various mobile devices with sensors like Smart Home. Specifically the mobility of the sensors in Smart Home merged with wireless sensor networks (WSN) brings security issues such as re-authentication and tracing the node movement. We extend our novel and efficient node authentication and key exchange protocol that support Irregular distribution. Compared with previous protocols, our protocol has only a third of communication and computational overhead. We expect our protocol to be the efficient solution that increases the lifetime of sensor network(1).