Atomic Broadcast

An atomic broadcast protocol must satisfy the following properties, all of which should hold with high probability (as a function $1- negl(\lambda)$ of a security parameter $\lambda$) in an asynchronous network and in spite of an arbitrary adversary:
\begin{enumerate}
  \item (Agreement) If any correct node outputs a transaction $tx$, then every correct node outputs $tx$.
  \item (Total Order) If one correct node has output the sequence of transactions $\langle tx_{0}, tx_{1},\ldots, tx_{j} \rangle$ and another has output $\langle tx'_{0}, tx'_{1}\ldots,tx'_{j'}\rangle$, then $tx_{i}=tx'_{i}$ for $i\le \min(j,j')$.
  \item (Censorship Resilience) If a transaction $tx$ is input to $N-f$ correct nodes, then it is eventually output by every correct node.
\end{enumerate}