In order to solve the problem of digital signatures leaking identity information from both parties during the identity authentication process,a bidirectional identity authentication scheme with designated verifier based on SM9 is proposed.This scheme is based on a responsive bidirectional i-dentity authentication model,which incorporates random group elements generated by the other par-ty into the process of generating digital signatures during the identity authentication stage.At the same time,adding a timestamp to the greeting message during the key agreement phase,to make the session key timeliness.Theoretical analysis results indicate that this scheme can effectively prevents attackers from performing replay attacks on session keys while protecting the privacy of identity in-formation of both authentication parties.Compared with other schemes,this scheme has good effi-ciency while providing higher security.