A group key management method based on an n-dimensional sphere is provided. After initialization, when new users join, the group manager accepts and numbers the new users; when users leave, the group manager deletes the confidential information of the leaving users. If there are users joining and leaving at the same time, the group manager deletes the confidential information of the leaving users, accepts the new users joining, numbers the new users and accepts the confidential information of the new users. The group manager then selects the mapping parameters, and snaps the confidential infor...