Protocol Unification Sample Clauses

Protocol Unification. Although described separately in Section IV, the four STR 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 observed that merge and partition can be collapsed into a single protocol, since, in either case, the key tree changes and the remaining group members lack some number of bkeys that 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, let us suppose that k groups (Tree T1 through Tk) are merging. After the first round of the merge protocol, all members reconstruct the new tree unambiguously and independently where all bkeys from the sponsor node up to the root node are missing similar to the partition protocol. The sponsor in merge is located at the topmost leaf node of the highest key tree. As discussed in Sections IV-D and IV-C, every member reconstructs the key tree after a partition and a merge in one and two rounds, respectively. From these outlines of the merge and partition protocol, we can find some similarities: • Whenever new membership event happens, all current group members first reconstruct the key tree. • The resulting key tree has missing bkeys from the parent node of the sponsor to the root node as well as the sponsor’s blinded session random. • The sponsor generates new session random and computes all keys and bkeys from its parent node up to the node just below the root node. It then broadcasts the whole key tree containing only bkeys and blinded session randoms. • Using the broadcast message, any member can compute the group key. This apparent similarity between partition and merge allows us to combine the protocols stem- ming from all membership events into a single, unified protocol. Fig. 9 shows the pseudocode. 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. 1 receive msg (msg type = membership event) 2 construct new tree 3 while there are missing bkeys 4 if ((I can compute any missing keys and I am the spo...
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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.
Sample 1Sample 2
Protocol Unification. Although described separately in the preceding sections, the four TGDH protocols: 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. It is less clear that merge and partition can be collapsed into a single protocol. To see why this is so we observe that, in either case, the key tree changes and remaining group members lack some number (sometimes none) of blinded keys which prevents them from computing the new root key unilaterally. When a partition occurs, the remaining members (in any surviving fragment) reconstruct the tree where some blinded keys are missing. In case of a merge, let us suppose that a taller (deeper) tree A is merged with a shorter (shallower) tree B. Similar to a partition, all members formerly in A construct the new tree where some blinded keys – those in B – are missing. (This view is symmetric since the members in B see the same tree but with missing blinded keys in the subtree A.) 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 are not concentrated in a new subtree (as in merge) but are, in the most general case, spread all around. As we discuss in section 5.4, every member reconstructs the key tree after a partition in at most h rounds, where h is the tree height. The merge scenario can be viewed as a special case of partition that always completes in two rounds. receive msg (msg type = membership event) construct new tree while there are missing blinded keys if (I can compute any missing keys) /* sponsor? */ compute missing blinded keys /* as many as possible */ broadcast new blinded keys endif receive msg (msg type = broadcast) /* including own broadcast */ update current tree endwhile Figure 10: Unified protocol pseudocode This apparent similarity between partition and merge allows us to lump the protocols stemming from all membership events into a single, unified protocol. (See figure 10 for the pseudocode.) The incentive for this is to simplify...
Sample 1
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 A A B A B 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.
Sample 1
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.
Sample 1

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