Strong Designated Verifier Signature Scheme Resisting Replay Attack

Strong designated verifier signature shows that only designated user can verify the validity of the signature, others who have not signer's private key or verifier's private key cannot judge the signature's originator. Lee et al. presented a designated verifier signature scheme to realize signature's verification in the limited time. We demonstrate that Lee et al.'s scheme is insecure. Other legal users can forge valid signatures which convince designated verifier. In this paper, we show a concrete forgery attack of Lee et al.'s scheme and propose a new strong designated verifier signature scheme with time limit. In our new scheme, message and time stamp don't need transmit in public, which are embedded in signature via the method of signcryption. Only signer and designated verifier can recover those secrete values. Based on the Bilinear Diffie-Hellman problem and Pre-Image Resistance assumption, it is proved that new strong designated verifier signature scheme can resist the ordinary forgery attack and replay attack, and enforce signature verification with time limit.