Common use of Merge Protocol Clause in Contracts

Merge Protocol. In this instant assume that m merging group needs to merge with c current group. The existing merging group director detects to achieve maximum signal strength what is measured as the closest member between itself and current group members. The current group director is the member what has maximum signal strength with merging group director. After the merging process, the leftest leaf of shorter tree becomes the right child of a new intermediate node. The root of the longer tree is left child of the new intermediate node. After the current group director received the MERGE_MESSAGE message, it refreshes session random key, computes keys and blinded keys, and sends the current group’s key tree containing the all blinded keys to merging group director. Later, the merging group director updates key tree by combining the merging group’s key tree and current group’s key tree at the new root node, the director chooses session random key, computes keys and blinded keys up to the root node, and broadcasts new key tree containing the all blinded keys to all members in new group. Finally, the group key is calculated independently by each member. Figure 3.8 shows the initial situation before current group merges with other group. After that Figure 3.9 shows the example of merge operation. The member that has maximum signal strength of merging group director, M5, is M1, and then M1 is current group director. The conclusion of merge protocol is shown as follows: Step 1: The director of current group what selects new session random key, computes blinded keys and sends updated key tree to the merging group director. Step 2: The merging group director selects its new session random key, combines key tree, computes the all blinded keys, and broadcasts the new key tree containing the only all blinded keys. Step 3: Each member computes the secret group key. 1 3 3 1 BK = s β β[1,0] = β1β3 [1,0] [1,1] [1,1] 4 [0,0] 4 K[1,1] = s4 director BK[2,1] = s β[1,0] s-1 [2,0] M1 BK ∗ [2,1] M3

Merge Protocol. In Like the TBG in previous protocol, this instant assume protocol assumes that m merging group needs to merge with c current group. The existing merging group director detects to achieve maximum signal strength what is measured as the closest member between itself and current group members. The current group director is the member what that has maximum signal strength with merging group director. After the merging process, the leftest smaller group is merged onto the larger one, i.e. to place a smaller key tree directly on top of the larger one. If group sizes are equal, it can order them according to some other criteria. A new intermediate node with two children is created. The root of the larger tree becomes the left child of new intermediate node, while the deepest leaf of shorter the smaller tree becomes the right child of a new intermediate node. The root of smaller tree becomes the longer tree is left child root of the new intermediate nodetree. After the current group director received receives the MERGE_MESSAGE message, it refreshes session random key, computes keys and blinded keys, and sends the current group’s key tree containing the all authenticated blinded keys to merging group director. Later, the merging group director computes blinded key of current group’s key tree, updates key tree by combining the merging group’s key tree and current group’s key tree at the new root node, the director chooses session random key, computes keys and blinded keys up to the root node, and broadcasts unicasts new key tree containing the all authenticated blinded keys to all members in new group. Finally, the group key is calculated independently by each membermember after computed blinded key. Figure 3.8 4.7 shows the initial situation before current group merges with other group. After that Figure 3.9 shows the example of merge operation. The member that has maximum signal strength of merging group director, M5M6, is M1M4, and then M1 M4 is current group director. After that Figure 4.8 shows the authenticated key tree that merging director, M6, received from current group director, M4. Figure 4.9 shows the authenticated key tree that M3 received from merging group director, M6, after merging group director merges the key tree. Figure 4.10 shows the key tree after M2 computes keys and blinded keys. The conclusion of merge protocol is shown as follows: Step 1: The director of current group what director that selects new session random key, computes compute blinded keys and sends updated update key tree with authenticated blinded key to the merging group director. Step 2: The merging group director computes the current group blinded Step 3: The merging group director selects its new session random key, combines key tree, computes the all blinded keys, keys and broadcasts the new key tree containing the only all blinded keys. Step 3: Each member computes the secret group key. 1 3 3 1 BK = s β β[1,0] = β1β3 [1,0] [1,1] [1,1] 4 [0,0] 4 K[1,1] = s4 director BK[2,1] = s β[1,0] s-1 [2,0] M1 BK ∗ [2,1] M3