Impossibility of Verifiable Agreement for Dishonest Majorities Sample Clauses

Impossibility of Verifiable Agreement for Dishonest Majorities. We show that if Q2 (which generalizes the notion of honest majority) is not satis- fied, then the Verifiable Agreement problem cannot be solved even in synchronous networks. In contrast, some agreement problems, e.g., Interactive Consistency, can be solved deterministically in this setting for any honesty structure [19]. As the synchronous network is the most strong network model, this result implies non- solvability for all other network classes. Theorem 1. No synchronous deterministic protocol can solve Verifiable Agree- ment if condition Q2 is not satisfied. The error probability of any probabilistic synchronous verifiable agreement pro- tocol in case Q2 is not satisfied is unacceptable large, i.e., at least inversely linear in the number of protocol rounds. Due to space limit, we omit the proofs from this extended abstract.
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