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SUMMARY With the popularity of Internet and wireless networks, more and more network architectures are used in multi‐server environment, in which mobile users remotely access servers through open networks. In the past, many schemes have been proposed to solve the issue of user authentication for multi‐server environment and low‐power mobile devices. However, most of these schemes have suffered from many attacks because these schemes did not provide the formal security analysis. In this paper, we first give a security model for multi‐server environment. We then propose an ID‐based mutual authentication and key agreement scheme based on bilinear maps for mobile multi‐server environment. Our scheme can be used for both general users with a long validity period and anonymous users with a short validity period. Under the presented security model, we show that our scheme is secure against all known attacks. We demonstrate that the proposed scheme is well suitable for low‐power mobile devices. Copyright © 2011 John Wiley & Sons, Ltd.

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.