Efficient Certificateless Signature and Group Signature Schemes

Group signatures are studied in newly proposed certificateless public key setting. The security model for the certificateless group signature scheme is put forward. Using bilinear pairings, a certificateless signature scheme is presented, which is formally proven in the random oracle. At the same time, a group signature scheme, based on the certificateless signature scheme given in this paper, is constructed. The former is computationally efficient in that it just needs one pairing operation in its signing and verification phases, the latter just needs two pairing operations. So they have advantage in performance. The security of these schemes is based on the fact that the computational Diffie-Hellman problem is hard. This group signature scheme not only enjoys all the security requirements of a group signature, but also is a dynamic group signature scheme that allows users to join or leave the group freely without updating the group public key and other group members private signing key. Besides, the length of the signature is independent of the numbers of the group members. Due to its security, high efficiency and freedom from certificate management, the group signature scheme may have practical applications in electronic commerce and electronic voting, etc.