A designated verifier signature scheme with undeniable property in the random oracle

In designated verifier signature, only the designated verifier can confirm the validity of a signature and it is applied widely in many environments such as electronic voting. However, most of designated verifier signature schemes cannot distinguish the real signer when the signer and the designated verifier arises a dispute on a signature. In other words, most of existing designated verifier signature schemes have not the undeniable property, namely the signer can deny a generated signature or the designated verifier can deny a simulating signature. In this paper, two designated verifier signature schemes with undeniable property are proposed. The first designated verifier signature scheme with undeniable property is called DVSSWUP-1 and another is called DVSSWUP-2. The both schemes satisfy the unforgeability and non-transferability. What's more, when the signer or the designated verifier denies the signature, a third party can distinguish the signature. Therefore, the proposed two designated verifier signature schemes not only protect the privacy of the signer but also keep the undeniable property of the traditional digital signature schemes.