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Recently, many multireceiver identity-based encryption schemes have been proposed in the literature. However, none can protect the privacy of message receivers among these schemes. In this paper, we present an anonymous multireceiver identity-based encryption scheme where we adopt Lagrange interpolating polynomial mechanisms to cope with the above problem. Our 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. Furthermore, the proposed scheme is quite receiver efficient since each of the receivers merely needs to perform twice of pairing computation to decrypt the received ciphertext. We prove that our scheme is secure against adaptive chosen plaintext attacks and adaptive chosen ciphertext attacks. Finally, we also formally show that every receiver in the proposed scheme is anonymous to any other receiver.