In VANETs, owing to the openness of wireless communication, it is necessary to change pseudonyms frequently to realize the unlinkability of vehicle identity. Moreover, identity authentication is needed, which is usually completed by digital certificates or a trusted third party. The storage and the communication overhead are high. This paper proposes a triple pseudonym authentication scheme for VANETs based on the Cuckoo Filter and Paillier homomorphic encryption (called TriNymAuth). TriNymAuth applies Paillier homomorphic encryption, a Cuckoo Filter combining filter-level and bucket-level, and a triple pseudonym (homomorphic pseudonym, local pseudonym, and virtual pseudonym) authentication to the vehicle identity authentication scheme. It reduces the dependence on a trusted third party and ensures the privacy and security of vehicle identity while improving authentication efficiency. Experimental results show that the insert overhead of the Cuckoo Filter is about 10 μs, and the query overhead reaches the ns level. Furthermore, TriNymAuth has significant cost advantages, with an OBU enrollment cost of only 0.884 ms. When the data rate in VANETs dr≤ 180 kbps, TriNymAuth has the smallest total transmission delay cost and is suitable for shopping malls and other places with dense traffic.