A novel quantum (t, n) threshold group signature based on d-dimensional quantum system

In this paper, a novel quantum (t, n) threshold group signature scheme is demonstrated on a basis of d-dimensional quantum system. In the scheme, n signatories form a group, and only t or more signatories can generate a valid signature on behalf of this group by means of using the cyclic characteristics of mutually unbiased bases (MUBs). The verifier receives the signature and checks the validation of it by performing the measurements in the specific MUB on the d-dimensional single qudits with the help of a trusted arbitrator. Security analysis shows that our scheme satisfies the requirements of quantum threshold group signature protocol: unforgeability, non-reputation, threshold security, and signatory's privacy. Moreover, our scheme designs a novel method to prevent the known-signature attack that also can be used in other arbitrated quantum signature schemes with the quantum one-time-pad encryption. In terms of efficiency, the proposed scheme uses single qudits instead of common entangled states to restore the initial messages. The difficulty of generating the required single qudits would not grow with the number of signatories involved. Therefore, our scheme has huge advantages in scalability compared to other related schemes and can be realized with current technology.