Designing secure authentication mechanisms in wireless sensor networks in order to associate a node to a secure network is not an easy task due to the limitations of this type of networks. In this paper, we propose different multi-hop node authentication protocols for wireless sensor networks. For each protocol, we provide a formal proof to verify the security of our proposals using Scyther, which is an automatic cryptographic protocols verification tool. We also provide implementation results in terms of execution time consumption obtained by real measurements on TelosB motes. These protocols offer different security mechanisms depending on the design of the protocol itself. Moreover, we evaluate the overhead of protection of each solution by studying the effect on execution time overhead of each protocol. Finally, we propose a mechanism to detect possible attack based on our evaluation results.