Over the last few years, identity (ID)-based encryption (IBE) without requiring certificate management offers a practical alternative to public key encryption. However, how to revoke misbehaving/compromised identities in ID-based public key setting becomes a new and critical issue. In the past, there was little work on studying this revocation problem. In 2008, Boldyreva et al. proposed a revocable IBE (RIBE) and its associated revocation solution that used a binary tree structure to reduce the authority's periodic workload in Boneh and Franklin's IBE. However, Boldyreva et al.'s RIBE raised enormous computation costs for encryption and decryption procedures. Both IBEs require a secure channel between each user and the authority to transmit user's periodic private keys, thus the authority and each user need to encrypt and decrypt the private keys for each period. In this article, we present an efficient RIBE with a public channel, which provides a practical alternative to the previously proposed revocation solutions, while it remains efficient for encryption and decryption. Under the bilinear Diffie–Hellman assumption, we demonstrate that our RIBE with a public channel is semantically secure against adaptive chosen plaintext attacks and adaptive chosen ciphertext attacks.

The identity (ID)-based public-key system using bilinear pairings defined on elliptic curves offers a flexible approach to simplify the certificate management. In 2006, the IEEE P1363.3 committee has defined the ID-based public-key system with bilinear pairings as one of public-key cryptography standards. In this, an authenticated key agreement (AKA) protocol is one important issue that provides mutual authentication and key exchange between two parties. Owing to the fast growth of mobile networks, the computational cost on the client side with low-power computing devices is a critical factor in designing an AKA protocol suited for mobile networks. In this paper, we present an efficient and secure ID-based mutual authentication and key exchange protocol using bilinear pairings. Performance analysis and experimental data are given to demonstrate that our proposed protocol is well suited for a client–server environment with low-power mobile devices. In comparison with the recently proposed ID-based protocols, our protocol has the best performance on the client side.

With rapid growth of mobile wireless networks, handheld devices are popularly used by people and many mobile applications have been rapidly developed. Considering the limited computing capability of smart cards or mobile devices, the security scheme design suitable for these mobile devices is a nontrivial challenge. A user authentication scheme is a mechanism to authenticate a remote user over an open network. In 2006, Das et al. proposed an identity (ID)-based remote user authentication scheme with smart cards using bilinear pairings. Unfortunately, their scheme is insecure against forgery attack. Recently, Giri and Srivastava proposed an improved scheme to overcome the forgery attack. The computational cost required by the Giri–Srivastava scheme is expensive, especially for smart cards with limited computing capability. In addition, the Giri–Srivastava scheme is unable to be used for a multi-server environment. This paper presents an efficient and secure ID-based remote user authentication scheme using bilinear pairings. Based on the computational Diffie–Hellman assumption, we show that the proposed scheme is secure against existential forgery on adaptively chosen-message and ID attack in the random oracle model. As compared with the recently proposed pairing-based authentication schemes, our scheme has better performance in term of the computational cost and it is suitable for a multi-server environment in distributed networks. Performance analysis and experimental data of related pairing operations on smartcards are given to demonstrate that our scheme is well suited for mobile devices with limited computing capability.