µTGDH Sample Clauses

µTGDH. Each node ⟨l, v⟩ is associated with a secret key k(l,v⟩ and a public key K(l,v⟩ = k(l,v⟩G. Secret keys of leaf nodes are chosen and kept secret by associated members. Every k(l,v⟩, 0 ≤ v ≤ 2l − 1, 0 ≤ l ≤ h where h is the height of the tree, is computed using Xxxxxx-Xxxxxxx key exchange between nodes ⟨l + 1, 2v⟩ and ⟨l + 1, 2v + 1⟩ either as k(l,v⟩ = map(k(l+1,2v⟩K(l+1,2v+1⟩) or k(l,v⟩ = map(k(l+1,2v+1⟩K(l+1,2v⟩). The secret group key K = k(0,0⟩ can be computed by any member Mi if it knows all public keys K(l,v⟩ in the tree. Although original descrip- tion of TGDH does not specify the setup procedure, we de- rive the protocol in Figure 6 with respect to the group key structure and techniques of other protocols of the suite. In the setup protocol the sponsor of the (sub)tree is always the rightmost member. In additive events new member (or the sponsor of the merged group) sends own (group’s) public key(s). Members determine the insertion node of the new member (or merged group’s tree) that is the rightmost node that does not increase the height of the tree. Sponsor Ms of the event that is the rightmost member of the updated tree, changes own contribution k(ls,vs⟩, computes all new secret keys and public keys in its path up to the root, and broadcasts the updated tree with all public keys so that other members can update the tree and the group key upon the sponsor’s message. In subtractive events leaf nodes of leav- ing members are deleted from the tree. In case of leave the sponsor Ms is the rightmost member of the subtree rooted at the leaving member’s sibling node. Computations of Ms are equal to those in additive events. In case of partition the leave protocol is performed for every partitioned member in parallel. Thus, there may exist multiple sponsors that com-