Abstract: This invention publishes a secure group key management approach based upon N-dimensional hypersphere. After initialization, the GC admits the new members and assigns identifiers to them when there are new members joining the group, and deletes the leaving members' private information when there are members leaving the group. If a lot of members join and other members leave the group at the same time, the GC deletes the leaving members' private information, admits the new members, assigns indemnifiers to the new members, and then chooses mapping parameters, mapping each member's and its private information to the points in a multi-dimensional space. The GC calculates the central point of the hypersphere, and publishes the central point, the mapping parameter and the identifiers of leaving members if there are members leave. The group members calculate the mapping points, and then calculate the group keys.