Common use of Corollaries Clause in Contracts

Corollaries. Now that we have proven Theorem 1, we can instantiate BAAuth and ▇▇▇▇▇ with concrete protocols in order to obtain concrete crypto-agnostic protocols. Before we state those corollaries, one point needs to be addressed. Bit complexity in the sabotaged setting. In order to maximize the generality of our results, the only assumption we made about BAAuth, ▇▇▇▇▇, as explained in Definition 4, is that we are provided with round complexity bounds for these protocols. In particular, we are given no such guarantee for bit complexity. As such, in the sabotaged setting, when the parties run BAAuth, which is an authenticated ts-secure BA protocol, we have no a-priori upper bound for the amount of bits sent by honest parties during the execution, hence why we define the bit complexity of a protocol w.r.t. a particular adversary. When considering concrete protocols, however, each party can infer a bound from the description of the protocol on the number of messages it has to send, and if is exceeded, an honest party can simply halt BAAuth and move onto Sync with input . The corollaries we state assume that such a modification was made to the final protocol.