Common use of Partition Protocol Clause in Contracts

Partition Protocol. Assume that a network fault causes a partition of the -member group. From the viewpoint of each remaining member, this event appears as a concurrent leave of multiple members. The partition protocol is involves multiple rounds; it runs until all members compute the new group key. In the first round, each remaining member updates its tree by deleting all partitioned members as well as their respective parent nodes and “compacting” the tree. The procedure is as follows: All leaving nodes are sorted by depth order. Starting at the deepest level, each pair of leaving siblings is collapsed into its parent which is then marked as leaving. This node is re-inserted into the leaving nodes list. The above is repeated until all leaving nodes are processed, i.e., there are no more leaving nodes that can be collapsed. The resulting tree has a number of leaving (leaf) nodes but every such node has a remaining sibling node. Now, for each leaving node we identify a sponsor using the same criteria as described in Section 5.3. Each sponsor now computes keys and bkeys on the key-path as far up the tree as possible. Then, each sponsor broadcasts the set of new bkeys. Upon receiving a broadcast, each member checks whether the message contains new bkeys. This procedure iterates until all members obtain the group key. (Recall that a member can compute the group key if it has all the bkeys on its co-path.) 5 Hereafter, we count number of mudular exponentiations that need to be computed in serial. Step 1: Every member updates key tree by by removing the leaving member node and relevant parent node, removes all keys and bkeys from the leaf node related to the sponsor to the root node. Sponsor additionally generates new share and computes all [ ] pairs on the key-path, broadcasts updated tree including only bkeys. Step 2: Every member computes the group key using .

Partition Protocol. Assume that a network fault causes a partition of the -member n-member group. From the viewpoint of each remaining member, this event appears as a concurrent leave of multiple members. The partition protocol is involves multiple rounds; it runs until all members compute the new group key. In the first round, each remaining member updates its tree by deleting all partitioned members as well as their respective parent nodes and “compacting” the tree. The procedure is as follows: All leaving nodes are sorted by depth order. Starting at the deepest level, each pair of leaving siblings is collapsed into its parent which is then marked as leaving. This node is re-inserted into the leaving nodes list. The above is repeated until all leaving nodes are processed, i.e., there are no more leaving nodes that can be collapsed. The resulting tree has a number of leaving (leaf) nodes but every such node has a remaining sibling node. Now, for each leaving node we identify a sponsor using the same criteria as described in Section 5.3. Each sponsor now computes keys and bkeys on the key-path as far up the tree as possible. Then, each sponsor broadcasts the set of new bkeys. Upon receiving a broadcast, each member checks whether the message contains new bkeys. This procedure iterates until all members obtain the group key. (Recall that a member can compute the group key if it has all the bkeys on its co-path.) 5 Hereafter, we count number of mudular exponentiations that need to be computed in serial.) Step 1: Every member • updates key tree by by removing all the leaving member node nodes and relevant their parent node, • removes all keys and bkeys from the leaf node related to the sponsor to the root node. Sponsor additionally , – Each sponsor Mst • If Mst is the shallowest rightmost sponsor, generates new share and share, • broadcasts updated tree T^st including only bkeys. • computes all [ [key, bkey] pairs on the key path until it can proceed, Mst Ts (BK∗ ) ^ st t Step 2 to h (Until a sponsor Msj computes the group key-path, ) – Each sponsor Mst • broadcasts updated tree T^st including only bkeys. • computes all [key, bkey] pairs on the key path until it can proceed, Mst Ts (BK∗ ) ^ st t Step 2h + 1: Every member computes the group key using .T^st