Proxy Re-signature Schemes Without Random Oracles

To construct a suitable and secure proxy re-signature scheme is not an easy job, up to now, there exist only three schemes, one is proposed by Blaze et al. [6] at EUROCRYPT 1998, and the others are proposed by Ateniese and Hohenberger [2] at ACM CCS 2005. However, none of these schemes is proved in the standard model (i.e., do not rely on the random oracle heuristic). In this paper, based on Waters’ approach [19], we first propose a multi-use bidirectional proxy re-signature scheme, denoted as Smb, which is existentially unforgeable in the standard model. And then, we extend Smb to be a multi-use bidirectional ID-based proxy re-signature scheme, denoted by Sid−mb, which is also existentially unforgeable in the standard model. Both of these two proposed schemes are computationally efficient, and their security bases on the Computational Diffie-Hellman (CDH) assumption.