Threshold signature has important significance. However, the security and impeccable threshold group signature schemes are rarely. In this paper, a multivariate threshold group signature scheme is proposed. After the analysis, a conspiracy attack scheme which could offer forgery attacks to the signature system has been proposed. Then, the paper gives a new matrix multiplication definition and prime matrix concept, so the conspiracy attack immune group signature scheme is achieved. Analysis shows that the scheme not only can fundamentally withstand conspiracy and forgery attacks but the identity of signature members can be traced anonymously as well. Meanwhile, it can realize the unknown ability of group signature secret key by constructing a secure distributed key generation protocol, so the threshold group signature security is greatly enhanced.
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