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The practical deployment of vehicular networks is still a pending issue. In this paper we describe a new self-organized method of authentication for VANETs, which allows their widespread, fast and secure implementation. Our proposal does not involve any central certification authority because the nodes themselves certify the validity of public keys of the other nodes. On the one hand we propose an algorithm that each node must use to choose the public key certificates for its local store. On the other hand, we also describe a new node authentication method based on a cryptographic protocol including a zero-knowledge proof that each node must use to convince another node on the possession of certain secret without revealing anything about it, which allows non-encrypted communication during authentication. Thanks to the combination of the aforementioned tools, the cooperation among vehicles can be used for developing several practical applications of VANETs, such as detection and warning about abnormal traffic conditions. One of the most interesting aspects of our proposal is that it only requires existing devices such as smartphones, because the designed schemes are fully distributed and self-organized. In this work we include an analysis of both an NS-2 simulation and a real device implementation of the proposed algorithms, which enables us to extract promising conclusions and several possible improvements and open questions for further research.