Enable membership privacy-preserving group signature scheme

Group members can generate an unalterable signature for messages representing the group through group signatures. Conventional group signatures fail to acknowledge that the list of group members is sensitive data by nature. Fully dynamic group signature methods with member privacy have been developed to solve this problem. However, these methods cannot identify instances where the same group member has signed the same message twice since they do not offer message linkability. Signing the same message twice might harm users' interests in specific applications, such as blockchain-based credit and punishment systems. This work introduces a completely flexible group signature system that enhances the privacy of its members while ensuring the traceability of messages alongside a feasible application. Under our method, only the group administrator can recognise if two signatures originate from the same individual within the group, while the list of group members remains completely concealed. Additionally, the group administrator can ascertain the actual identity of the group member. Additionally, any user can confirm whether two distinct signatures for the same communication are from the same signer. Lastly, we show our approach's efficiency and security through several simulation tests and formal security analysis.