Centralized vs. Decentralized Group Key Management. In this subsection, we compare the performance of our interval-based algorithms and a centralized key management approach. We consider the centralized logical key tree (LKT) ap- proach [14] upon which our Batch algorithm is developed (see Section III-B). Similar to the interval-based algorithms, we assume that the key tree in the LKT approach is a binary tree and that the keys of the tree nodes are computed based on the TGDH protocol [11]. Among the group members, we select a group controller that centrally renews the group key at periodic rekeying intervals. We assume that the group controller knows the keys of all the nodes in the key tree and that a newly joining member sends its individual secret key to the group controller via a secure channel. At the beginning of a rekeying interval, the group controller first rekeys all (non-leaf) renewed nodes using the TGDH protocol. It then encrypts the updated secret key of each renewed node with the respective secret keys of the two child nodes via any symmetric encryption algorithm. Afterward, it broadcasts the encrypted keys to the group. Every member, upon receiving the encrypted keys, decrypts the keys along its key path with the secret keys it holds.
