Common use of Communication Complexity Clause in Contracts

Communication Complexity. The most expensive steps in the protocol are the run of BA(κ) in Step 1 (which itself consists of κ parallel runs of BA(1)) and the distribution of the long blocks in Step 2. The costs for Step 1 are bounded as O(κ6 · n) since every run of BA(1) costs O(κ5 · n). The costs for Step 2 are bounded by O(l · n). Overall, we obtain a complexity of O(n · l + κ6 · n).

Communication Complexity. The most expensive steps in the protocol are the run of BA(κ) in Step 1 (which itself consists of κ parallel runs of BA(1)) and the distribution of the long blocks in Step 2. The costs for Step 1 are bounded as O(κ6 O(κ3 · n) since every run of BA(1) costs O(κ5 O(κ2 · n). The costs for Step 2 are bounded by O(l · nn + κ2n), given that each of O(κ) parties send a message of length ℓ/κ + κ to all parties. Overall, we obtain a complexity of O(n · l + κ6 κ3 · n).