BASIC TREEOPERATION Sample Clauses

BASIC TREEOPERATION. In this section we introduce the four basic operation: join, leave, merge, and partition. All proto share a common framework with the following notable features: A group key can be computed from any member’s secret share (i.e., any leaf value) and all bkeys on the co- path to the root. It is easy to see that knowledge of its own secret share and all sibling bkeys on the path to the root enables a member to compute all intermediate keys on its key- path, including the root group key. This is similar to other tree based schemes where each member is required to know all keys on the path from itself (leaf) to the root. Although not strictly necessary for computing group key, our protocol also requires each member to know all bkeys in the entire key tree. As will be seen below, this makes the handling of future membership changes more efficient and robust. As part of the protocol, a group member can take on a special sponsor role which involves computing intermediate keys and broadcasting to the group. Each broadcasted message contains the sender’s view of the key tree which contains each bkey known to the sender. Any member in the group can unilaterally take on this responsibility, depending on the type of membership event. In some cases, such as a partition event, multiple sponsors might be involved. In case of an additive change (join or merge), all group members identify a unique sponsor. This sponsor is responsible for updating its secret key share, computing affected (S(l,v),Bk(l,v)) pairs and broadcasting all bkeys of the new tree to the rest of the group. The common criteria for sponsor selection is determined by the tree maintenance strategy. We emphasize, from the outset, that sponsor is not a privileged entity: its only task is the updating and broadcasting of tree information to the group. In response to a subtractive membership change (leave or partition), all members update the tree in the same manner. Since the case of partition subsumes the case of a single leave, we discuss it in more detail. Group partition results in a smaller tree since some leaf nodesdisappear. As a result, some sub trees acquire new siblings; therefore, new intermediate keys and bkeys must be computed through a ▇▇▇▇▇▇-▇▇▇▇▇▇▇ exchange between the new siblings sub-trees. The computation proceeds in a bottom-up fashion with each member computing keys and bkeys until either: it blocks due to a dependency on a new sibling bkey that it does not yet know, or it computes the new ...