Asymptotic Performance Analysis Sample Clauses

Asymptotic Performance Analysis. In general, causal broadcast requires additional metadata in every message to establish the causal order- ing. The size of this metadata is proportional to the number of concurrently sent messages by different group members, O(n) in the worst case [10]. However, we are able to reduce this overhead to zero because our DCGKA protocol does not require full causally ordered delivery. Instead, DCGKA only requires that: • each group member’s messages are delivered in order; • acknowledgment messages are delivered after the message they acknowledge. The acknowledgment messages and the sequence numbers that are already contained in DCGKA mes- sages in plaintext are sufficient to ensure this. Additionally, Authenticated Causal Broadcast requires a PCS signature to authenticate the sender of each message (Section 5.2), adding a constant-size over- head to each message. The encryption that is applied to application messages (Section 7.6) and direct messages (2SM) also adds a constant overhead. Each direct message also requires a constant number of public-key operations on both the sender and the recipient side. Each create, update, or remove DCGKA operation broadcasts one constant-size control message and sends O(n) constant-size direct messages. Each other group member replies by broadcasting a constant- size acknowledgment, resulting in O(n) network traffic overall. The operation requires O(n) public key operations at the sender, and O(1) public key operations for each other group member. Add operations send one constant-size control message and one direct message (the welcome mes- sage to the new user), and require O(1) public key operations at the sender. Each other group member broadcasts a constant-size acknowledgment and sends one constant-size direct message to the new mem- ber, resulting in O(n) network traffic overall. The acknowledgments require in total O(n) public key operations by the added user and O(1) public key operations by each other group member. The welcome message contains the history of group membership operations; in principle, its size is proportional to the number of previous membership operations and their acknowledgments—typically O(n2). In prac- xxxx, the welcome message only needs to include enough data to be able to evaluate the DGM function. Techniques from Conflict-free Replicated Data Types (CRDTs) [39, 41] can be used to design efficient representations of group membership history. As an optimization, a group member can choose to d...
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