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In 2010, Fan et al. presented an anonymous multi-receiver identity-based encryption scheme where they adopt Lagrange interpolating polynomial mechanism. They showed that their scheme makes it impossible for an attacker or any other message receiver to derive the identity of a message receiver such that the privacy of every receiver can be guaranteed. They also formally showed that every receiver in the proposed scheme is anonymous to any other receiver. In this work, the authors study the security of Fan et al.'s anonymous multi-receiver identity-based encryption scheme. It is regretful that they found their scheme is insecure. Every receiver in Fan et al.'s scheme is not anonymous to any other receiver. The authors showed that simple protocol changes can fix these weaknesses and render Fan et al.'s scheme. The improved scheme is proved to satisfy the confidentiality and receiver anonymity in the random oracle.