Deniable ring authentication can be used to facilitate privacy-preserving communication since the receiver accepts authentication while cannot convince a third party that the fact of this authentication occurred. Besides that, the receiver cannot decide the actual sender as the sender identity is hidden among a group of participants. However, the concurrent problem has not been studied well in the interactive deniable ring authentication so far. In this work, we propose a deniable ring authentication protocol to handle concurrent scenario, which achieves full deniability. We construct a CCA2-secure (which is secure against Adaptive Chosen Ciphertext attack) multi-receiver encryption scheme to support this protocol and it requires only 2 communication rounds, which is round-optimal in fully deniable ring authentications. In addition, we observe that efficient fully deniable ring authentication can be applied to location-based service in VANETs to protect vehicle privacy.