Abstract: Multivariate public key encryption scheme which can resist attacks by quantum computer is believed to be an alternative security cryptography scheme in the post-quantum age. A multivariate group signature scheme was proposed. After an analysis of the scheme, a conspiracy attack scheme which could offer forgery attacks to the signature system was proposed. Then, a new matrix multiplication definition and prime matrix concept were given, and a conspiracy attack immune group signature scheme was proposed. Analysis shows that the scheme can not only fundamentally withstand conspiracy and forgery attacks, but trace the identity of signature members anonymously. Meanwhile, it can realize the unknown ability of group signature secret keys by constructing a secure distributed key generation protocol, thus greatly enhancing group signature security.

Key words: multivariate, group signature, conspiracy attack, forgery attack