Protocol Unification Sample Clauses

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.

Protocol Unification. Although described separately in the preceding sections, the four STR oper- ations: join, leave, merge and partition, actually represent different expression of a single protocol. We justify this claim with an informal argument below. Obviously, join and leave are special cases of merge and partition, respec- tively. It is less clear that merge and partition can be collapsed into a single protocol, because in either case, the key tree changes and the remaining group members lack some number (sometimes none) of blinded keys or blinded ses- sion randoms which prevents them from computing the new root key. When a partition occurs, the remaining members reconstruct the tree where some blinded keys are missing. In case of a merge, a shorter tree A is merged into a taller tree B. Any member in B now can compute the group key since it knows blinded session random of any member in A. The deepest member in A also can compute the group key since it knows the blinded session random of any other member in A and blinded group key of B. Using the broadcast message any member now can compute the new group key. We established that both partition and merge initially result in a new key tree with a number of missing blinded keys. In case of merge, the missing blinded keys can be distributed in two rounds. This is because a sponsor in both of A and B broadcasts its own subtree including all blinded keys. Any member in a given subtree can compute the new root key after receiving both broadcasts. The case of partition is very similar except that the missing blinded keys and the new group key can be distributed in one round. This apparent similarity between partition and merge allows us to lump the protocols stemming from all membership events into a single, unified protocol. The following figure shows the pseudocode. receive msg (msg type = membership event) construct new tree while there are missing blinded keys if (I can compute any missing keys and I am the sponsor) compute missing blinded keys broadcast new blinded keys endif receive msg (msg type = broadcast) update current tree endwhile The incentive for this is threefold. First, unification allows us to simplify the implementation and minimize its size. Second, the overall security and correctness are easier to demonstrate with a single protocol. Third, we can now claim that (with a slight modification) the STR protocol is self-stabilizing and fault-tolerant as discussed below.

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. B A A B A B 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 log2k rounds. A partition is very similar except the first broadcast message of merge. Recall that every member reconstructs the key tree after a partition in at most min(log2 p, h) rounds, where h is the tree height and p is the number of leaving members.

Protocol Unification. Although described separately in the preceding sections, the four STR operations: join, leave, merge and partition, actually represent different expression of a single protocol. We justify this claim with an informal argument below. Obviously, join and leave are special cases of merge and partition, re- spectively. It is less clear that merge and partition can be collapsed into a single protocol, because in either case, the key tree changes and the re- maining group members lack some number (sometimes none) of blinded keys or blinded session randoms which prevents them from computing the new root key. When a partition occurs, the remaining members re- construct the tree where some blinded keys are missing. In case of a merge, a shorter tree is merged into a taller tree . Any member in now can compute the group key since it knows blinded session ran- dom of any member in . The deepest member in also can compute the group key since it knows the blinded session random of any other member in and blinded group key of . Using the broadcast message any member now can compute the new group key.