Mass Leave. If the no. of leaving members are very large then it is better to reinitialize the tree with other than the leaving members. So if be the total no. of members in initial group and is the no. of leaving members from current group then The message cost of the mass leave operation is: Total no. of point multiplication is: Note that after numerous group operations like join, leave, mass join etc. the resultant key tree becomes quit unbalanced. So as suggested in [27] when the key tree reaches a certain imbalance point, we should rebalance the tree and treat the rebalance operation as the group operation required. The imbalance point can vary depending on network and efficiency requirement. The proposed paper does not provide any new rebalancing scheme however protocol can use any scheme discussed in [27]. Also sometimes it is more suitable to reinitialize the tree instead of rebalancing. 5. AUTHENTICATION Although the proposed protocol is based on elliptic curve Diffie Xxxxxxx which is secure and not easy to break, the entire system is vulnerable if the keys are not securely distributed. Therefore, we should implement an authentication algorithm in the protocol. There are several ways to authenticate a group key exchange, such as centralized authentication, implicit authentication, and pairwise authentication [3, 4, 9, 11, 16]. In all operations of the protocol any of the above authentication schemes can be used. The advantages and limitations of different authentication schemes are discussed in CCEGK [27].
