Directed proxy signature in the standard model

A directed signature is a type of signature with restricted verification ability. Directed signatures allow only a designated verifier to check the validity of the signature issued to him, and at the time of trouble or if necessary, any third party can verify the signature with the help of the signer or the designated verifier. Directed signature schemes are widely used in situations where the receiver’s privacy should be protected. Proxy signatures allow an entity to delegate its signing capability to another entity in such a way that the latter can sign message on behalf of the former when the former is not available. Proxy signature schemes have found numerous practical applications such as distributed systems and mobile agent applications. In this paper, we firstly define the notion of the directed proxy signature by combining the proxy signature and directed signature. Then, we formalize its security model and present a concrete scheme in the standard model. Finally, we use the techniques from provable security to show that the proposed scheme is unforgeable under the gap Diffie-Hellman assumption, and invisible under the decisional Diffie-Hellman assumption.