Quantum threshold group signature

In most situations, the signer is generally a single person. However, when the message is written on behalf of an organization, a valid message may require the approval or consent of several persons. Threshold signature is a solution to this problem. Generally speaking, as an authority which can be trusted by all members does not exist, a threshold signature scheme without a trusted party appears more attractive. Following some ideas of the classical Shamir’s threshold signature scheme, a quantum threshold group signature one is proposed. In the proposed scheme, only t or more of n persons in the group can generate the group signature and any t − 1 or fewer ones cannot do that. In the verification phase, any t or more of n signature receivers can verify the message and any t − 1 or fewer receivers cannot verify the validity of the signature. Supported by the National Basic Research Program of China (973 Program)(Grant No. 2007CB311100), the National High-Technology Research and Development Program of China (Grant Nos. 2006AA01Z419 and 2006AA01Z440), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 90604023), the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No. KM200810005004), the Scientific Research Foundation for the Youth of Beijing University of Technology (Grant No. 97007016200701), the Doctoral Scientific Research Activation Foundation of Beijing University of Technology (Grant No. 52007016200702), the ISN Open Foundation, and the National Laboratory for Modern Communications Science Foundation of China (Grant No. 9140C1101010601)