Leave Protocol. Once again, we start with members and assume that member leaves the group. The sponsor in this case is the rightmost leaf node of the subtree rooted at the leaving member’s sibling node. First off, as shown in Figure 4, each member updates its key tree by deleting the leaf node corresponding to . The former sibling of is promoted to replace ’s parent node. The sponsor generates a new key share, computes all pairs on the key-path up to the root, and broadcasts the new set of bkeys. This allows all members to compute the new group key. , and broadcasts the updated tree with . Upon receiving the broadcast message, all members compute the group key. Note that cannot compute the group key, though it knows all the bkeys, because its share is no longer part of the group key. One round and one message are required to complete a leave protocol. The number of modular exponentiation depends on the location of the leaving member and tree structure. Its upper bound is if all pairs on the key-path of the deepest node need to be recomputed. When either left or right subtree has single node and it is the sponsor (i.e. for example, its sibling leaves the group), 3 modular exponentiations are required (two by the sponsor and one by all other members).
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Sources: Group Key Agreement, Group Key Agreement