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In vehicular ad hoc networks (VANETs), the security and privacy of vehicle data are core issues. In order to analyze vehicle data, they need to be computed. Encryption is a common method to guarantee the security of vehicle data in the process of data dissemination and computation. However, encrypted vehicle data cannot be analyzed easily and flexibly. Because homomorphic encryption supports computations of the ciphertext, it can completely solve this problem. In this paper, we provide a comprehensive survey of secure computation based on homomorphic encryption in VANETs. We first describe the related definitions and the current state of homomorphic encryption. Next, we present the framework, communication domains, wireless access technologies and cyber-security issues of VANETs. Then, we describe the state of the art of secure basic operations, data aggregation, data query and other data computation in VANETs. Finally, several challenges and open issues are discussed for future research.

Based on the learning with errors over rings (RLWE) assumption, a leveled fully homomorphic encryption (FHE) by the approximate eigenvector method under the same public key is proposed, which security can be reduced to the shortest vector problem on ideal lattices in the worst case. And the leveled FHE under different public keys is realized by the secret key switching without dimension reduction. Combine the public key of leveled FHE with the identity, we bring forward an efficient identity‐based leveled FHE scheme from the RLWE assumption. The security analysis shows that our identity‐based leveled FHE scheme is selective‐ID secure against chosen‐plaintext attacks in the random oracle model. And the efficiency analysis and simulation results show that the proposed identity‐based leveled FHE scheme is much more efficient than Gentry's and Wang's identity‐based cryptosystems based on the learning with errors assumption. Copyright © 2016 John Wiley & Sons, Ltd.