Sensor networks are ad-hoc mobile networks that include sensor nodes with limited computational and communication capabilities. They have become an economically viable monitoring solution for a wide variety of applications. Obviously, it is important to ensure security and, taking into account limited resources available in wireless sensor networks, the use of symmetric cryptography is strongly recommended. In this paper we present a light-weight authentication model for wireless sensor networks composed of a key management and an authentication protocol. It is based on simple symmetric cryptographic primitives with very low computational requirements, and it achieves better results than other similar proposals in the literature. Compared to SPINS and BROSK protocols, our system can reduce energy consumption by up to 98% and 67% respectively. It also scales well with the size of the network, due to it only requiring one interchanged message, regardless of the total number of nodes in the network.