Certificateless message recovery signatures providing girault’s level-3 security

A digital signature with message recovery is a signature that the message itself (or partial of the message) is not required to be transmitted together with the signature. It has the advantage of small data size of communication comparing with the traditional digital signatures. In this paper, combining both advantages of the message recovery signatures and the certificateless cryptography, we propose the first certificatelss signature scheme with message recovery. The remarkable feature of our scheme is that it can achieve Girault’s Level-3 security while the conventional certificateless signature scheme only achieves Level-2 security. The security of the scheme is rigorously proved in the random oracle model based on the hardness of the k bilinear Diffie-Hellman inverse (k-BDHI) problem.