Common use of Protocol Unification Clause in Contracts

Protocol Unification. Although described separately in the preceding sections, the four TGDH operations (join, leave, merge and partition) actually represent different strands of a single protocol. We justify this claim with an informal argument below. Obviously, join and leave are special cases of merge and partition, respectively. We observe that merge and partition can be collapsed into a single protocol, since, in either case, the key tree changes and remaining group members lack some number of bkeys. This prevents them from computing the new root key. In a partition, the remaining members (in any surviving group fragment) reconstruct the tree where some bkeys are missing. In case of a merge of two groups, let us suppose that a taller (deeper) tree is merged with a shorter (shallower) tree . Similar to a partition, all members formerly in construct the new tree where some bkeys – those in – are missing. (This view is symmetric since the members in see the same tree but with missing bkeys in the subtree .) We now established that both partition and merge initially result in a new key tree with a number of missing bkeys. In the first round of merge protocol, sponsor in each group broadcasts the key tree after updating its session random. Upon receiving this broadcast message, every member rebuilds a key tree which has some missing bkeys. Filling up this bkeys takes at most rounds. A partition is very similar except the first broadcast message of merge. The apparent similarity between partition and merge allows us to collapse the protocols stemming from all mem- bership events into a single unified protocol. Figure 10 shows the pseudocode. The incentive for doing this is threefold. First, unification allows us to simplify the implementation and minimize its size. Second, the overall security and cor- rectness are easier to demonstrate with a single protocol. Third, we can now claim that (with a slight modification) TGDH is self-stabilizing and fault-tolerant as discussed below. 7 In a join, the new member simply generates its first share.