With the advent of unbounded small-scale dust sensors being deployed in wireless sensor networks, existing authentication protocols for ordinary wireless sensor networks are becoming less efficient for dust sensors. Resource constrained dust nodes must do anything in cooperation with other nodes. Existing key management protocols require large key storage in each node, which cannot be stored in smart dust sensor nodes with strictly limited resources. Given the practical fact that adversaries or non-adversaries cannot retrieve information inside the RAM of minute smart dust sensors, this paper presents a Lightweight Authentication Protocol (LAP) as a key management protocol for smart dust wireless sensor networks with boundless number of nodes. The protocol uses a comparatively fewer number of keys for authentication purposes, and guarantees the security of network in the long run by a rekeying mechanism. Apart from being lightweight, it is quite primitive in the sense that it does not impose any specific requirements on the network, such as on routing and network topology. This allows other security protocols for ordinary sensor networks to use LAP while their initial key distribution setup is in progress. LAP uses a rekeying mechanism in cooperative manner.