Leave Protocol

 

Assume that we have $n$ members and a member $M$_d leaves the group. In this case, the sponsoris the right-most leaf node of the subtree rooted at the leaving member's sibling node. In the leave protocol every member updates its key tree by deleting the leaf node corresponding to $M$_d. The former sibling of $M$_d is promoted to replace $M$_d's parent node. The sponsorpicks a new secret share, computes all keys on its key path up to the root, and broadcasts the new set of blinded keys to the group. This information allows all members to recompute the new group key.

Assuming the setting of figure 3, if member $M$₃ leaves the group, every member deletes nodes $1,1$ and $2,2$. After updating the tree, the sponsor$M$₅ picks a new key $K$_2,3 , recomputes $K$_1,1 , K_0,0 , BK_2,3 and $BK$_1,1 , and broadcasts the updated tree $T$₅ with $BK$₅. Upon receiving the broadcast message, all members compute the group key. Note that $M$₃ cannot compute the group key, though it knows all the blinded keys, because its share is no longer part of the group key.

  
Figure 3: Tree updating in leave operation