Abstract: Many emerging applications arc based upon a group communications model. A new group key management scheme for a secure group communication system based on a geometric approach was proposed. The proposed scheme can be divided into three phases: user registration, group key assignment, and group key computation. In the user registration phase, the group manager computes and gives a secret to the new user based on geometric approaches over a secure channel. In the group key assignment phase, the group manager first constructs a secret circle using the group key.Then it computes a shadow of the group key for each member based on the member's private key. Finally, each member obtains an additional secret point based on his private key. I}he member reconstructs the secret circle by its shadow and the public information,and then obtains the group key in the group key computation phase. Based on simple scheme of group key management, a binary tree of keys is set up to redesign the scheme and demonstrate it hhe computation complexity for rekeying decreases from O(m) to O(log(m)).The public information on the note board keeps the same. No a secure channel is needed when the group key is updated. So this scheme is scalable.

Key words: Group key management, Secure group communication, Geomctric approach, n-dimensional space, Binary tree