To protect receiver privacy, researchers constructed anonymous multireceiver encryption by implanting anonymity in multireceiver encryption. It allows a sender to produce the identical ciphertext for multiple designated receivers. Every designated receiver can decrypt the ciphertext, but does not know who the other designated receivers are. Recently, several anonymous multireceiver identity (ID)-based encryption (AMIBE) schemes were proposed without the utilization of certificates. However, these AMIBE schemes are not efficient because their decryption cost of each receiver grows linearly with the number of the designated receivers. Moreover, all the ID-based cryptographic schemes suffer from the key escrow problem, which has been resolved by using certificateless public key settings. Very recently, Islam et al. proposed an anonymous multireceiver certificateless encryption (AMCLE) scheme. However, the encryption cost of a sender is quadric with the number of designated receivers, whereas the decryption cost of each receiver is linear with the number. In this paper, we propose an efficient AMCLE scheme with constant decryption cost, namely, the required decryption cost of each receiver is independent of the number of receivers. When compared with previously proposed AMIBE and AMCLE schemes, our scheme solves the key escrow problem and improves the efficiency of encryption/decryption significantly as well.

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Certificateless public key cryptography is very attractive in solving the key escrow problem which is inherent in identity- (ID-) based public key cryptography. In the past, a large number of certificateless cryptographic schemes and protocols were presented, but a secure certificateless signature in the standard model (without random oracles) is still not accessible until now. To the best of our knowledge, all the previously proposed certificateless signature schemes were insecure under a considerably strong security model in the sense that they suffered from outsiders’ key replacement attacks or the attacks from the key generation center (KGC). In this paper, we propose a certificateless signature scheme without random oracles. Moreover, our scheme is secure under the strong security model and provides a public revocation mechanism, called revocable certificateless signature (RCLS). Under the standard computational Diffie-Hellman assumption, we formally demonstrate that our scheme possesses existential unforgeability against adaptive chosen-message attacks.