New (t, n) threshold directed signature scheme with provable security

Directed signature scheme allows 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 as well. Due to its merits, directed signature scheme is widely used in situations where the receiver's privacy should be protected. Threshold directed signature is an extension of the standard directed signature, in which several signers may be required to cooperatively sign messages for sharing the responsibility and authority. To the best of our knowledge, threshold directed signature has not been well studied till now. Therefore, in this paper, we would like to formalize the threshold directed signature and its security model, then present a new (t, n) threshold directed signature scheme from bilinear pairings and use the techniques from provable security to analyze its security.