Cryptanalysis of Wang et al.'s improved anonymous multi-receiver identity-based encryption scheme

Fan et al. proposed an anonymous multi-receiver identity-based encryption scheme in 2010, and showed that the identity of any legal receiver can be kept anonymous to anyone else. In 2012, Wang et al. pointed out that Fan et al.'s scheme cannot achieve the anonymity and that every legal receiver can determine whether the other is one of the legal receivers. At the same time, they proposed an improved scheme based on Fan et al.'s scheme to solve this anonymity problem. Unfortunately, the authors find that Wang et al.'s improved scheme still suffers from the same anonymity problem. Any legal receiver of Wang et al.'s improved scheme can judge whether anyone else is a legal receiver or not. In this study, the authors shall give the detailed anonymity analysis of Wang et al.'s improved scheme.