Impossibility Results. Clearly, the impossibility results of [15] immediately carry over to privacy amplification secure against active op- ponents (where the non-simulatability condition is fulfilled in all non-trivial cases). There exists neither a protocol with perfect synchronization of the accepting states (i.e., both accept or both reject in every case), nor a one-way- transmission protocol satisfying the required properties. D ∞ ≥ − − − Theorem 1: Let α = 2 or α = . Assume that a robust (n, n,α,t, r, ε, δ)-PA-protocol either with perfect synchronization or using only one-way transmission exists. Then either ε r 1, or ε > n t + log(1 2ε−r+1), or δ = 1 holds. − ≤ − −
Impossibility Results. It may seem that accountability can be obtained by always guaranteeing agreement but failing to terminate as soon as 𝑡 ≥ 𝑛/3, by checking evidence before deciding, or by piggybacking a subquadratic number of bits as justifications in classic consensus algorithms. In this section, we show that none of these ideas lead to accountability.
