(1) How to abolish group members safely and effectively: Even if a method of abolishing group members is designed, after deleting a group member, the original private key and membership certificate can no longer be used for signature, and the security of his original signature will not be affected. None of the existing group signature schemes can safely and effectively abolish group members.

(2) How to design an efficient algorithm to open the signature, that is, how to make the group administrator open the signature and determine the signer's identity without a lot of calculation.

(3) Looking for some safe and efficient new group signature algorithms: The existing relatively safe and efficient group signature schemes basically rely on RSA signature system, Schnorr signature system and knowledge signature, such as double discrete logarithm, square root of discrete logarithm, representation of elements in finite cyclic group, secret value in a specified interval, etc., and the efficiency is not ideal. Therefore, it is necessary to find a new secure and efficient group signature algorithm.

(4) How to use group signature more widely in e-commerce and other fields. In the existing literature, the application of group signature in e-commerce field is rare. Because group signature can provide good anonymity for signers and enable group managers to open the signature and revoke anonymity when necessary, it can be widely used in many aspects of e-commerce. As long as an efficient group signature algorithm is found, the application of group signature in e-commerce will be feasible.

(5) Research on digital signature related to group signature and its application: The research on digital signature related to group signature and its application is not enough. Hierarchical group signature, group blind signature and multi-group signature all have practical application backgrounds, but the research on them has just started.