Anonymous receiver encryption is an important cryptographic primitive. It can protect the privacy of the receiver. In 2010, Fan et al proposed an anonymous multireceiver ID-based encryption by using Lagrange interpolating polynomial. Recently, Wang et al showed that Fan et al's scheme satisfied anonymity of the receivers. Then they provided an improved scheme to fix it and showed that the improved scheme was secure. Unfortunately, we pointed out that Wang et al's improved scheme did't satisfy the receiver's anonymity by analyzing the security of the scheme yet. After analyzing the reason to produce such flaw, we give an improved method to repair it and show that our improved scheme satisfies the receiver's anonymity, and the improved scheme has advantage over Wang et al's scheme in terms of computational cost.

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SUMMARYAs an important component of intelligent transportation systems, vehicular ad hoc networks can provide safer and more comfortable driving circumstance for the drivers. However, communication security and privacy issues present practical concerns to the deployment of vehicular ad hoc networks. Although recent related studies have already addressed most of these issues, most of them have only considered a posteriori countermeasures or a priori countermeasures to prevent the attacks of an adversary. To the best of our knowledge, up to now, only two privacy‐preserving authentication schemes can provide a posteriori countermeasures and a priori countermeasures. But, the computational cost of verifying a signature is relatively high or security proof of the scheme is loose in the two schemes. In this paper, we propose two novel privacy‐preserving authentication schemes. The first one cannot only provide a posteriori and a priori countermeasures, but also has low computational cost in the verification phase and tight security proof. The second one can achieve batch verification on multiple messages. Comparison with Wu et al.'s scheme and Chen et al's scheme, our scheme shows higher efficiency in terms of the computational cost of verifying signature.Copyright © 2013 John Wiley & Sons, Ltd.

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