Universally composable secure proxy re-signature scheme with effective calculation

In proxy re-signature scheme, the semi-trust proxy is given special information to convert user A's signature into another user B's signature on the same message m. This has numerous application, such as simplifying the certificate management by constructing a secure channel between two authentication centers, simplifying group signature management by making each signature transformed to the group's signature, helping relieve some common key management headaches by resigning without the authentication center, and constructing digital right management (DRM) interoperable system by sharing the certification. In this paper, we proposed a novel proxy re-signature scheme with universally composable security. The proposed scheme is unidirectional, single-use, key optimal, non-transitive and non-temporary. Its security is based on Computational Diffie-Hellman assumption in the random oracle model. Furthermore, we present the universal composable based security definition of proxy re-signature, as well as the equivalent game based definition. If a scheme is proved to be safe in our game, it will have the universally composable property, which will simplify the future security analysis. Finally, we support the proposed scheme with detailed security and performance analysis.