Directed proxy signature with fast revocation proven secure in the standard model

As a kind of special proxy signature, directed proxy signature can be used to sign messages, such that only the designated verifier can easily verify the validity of the signature while others cannot. At the same time, if necessary, the proxy signer or designated verifier can prove the validity of the signature to any third party. However, the revocation of delegated rights has never been considered in the existing directed proxy signature schemes. In fact, in these directed proxy signature schemes, even if the period of delegation has expired, the proxy signer still can generate the valid proxy signature, and the original signer can do nothing to prevent it. Therefore, the authors give a solution to the delegation revocation problem and propose a directed proxy signature scheme with fast revocation in this study. The security and the invisibility of the authors’ scheme are proven based on the gap Diffie–Hellman assumption and under the decisional Diffie–Hellman problem in the standard model, respectively.