ajout biblio

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Amaury JOLY
2026-04-08 17:06:53 +02:00
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\subsection{Model extension}
We extend the crash model of Section 1 (same process universe, asynchronous setting, uniquely identifiable messages, and reliable point-to-point channels) with Byzantine faults and Byzantine-resilient dissemination primitives.
\paragraph{Failure threshold.} At most $t$ processes may be Byzantine, and we assume $n > 3t$.
\paragraph{Failure threshold.} At most $t$ processes may be Byzantine, and we assume $n > 3t$, following standard asynchronous Byzantine assumptions~\cite{Bracha87}.
\paragraph{Additional communication primitive.} In addition to reliable point-to-point channels, processes use Reliable Broadcast ($\RB$) with operations $\RBcast(m)$ and $m=\rdeliver()$. We use Bracha's Byzantine RB specification (1987): for a fixed sender and broadcast instance, all correct processes that deliver, deliver the same payload, and Byzantine equivocation on that instance is prevented.
\paragraph{Additional communication primitive.} In addition to reliable point-to-point channels, processes use Reliable Broadcast ($\RB$) with operations $\RBcast(m)$ and $m=\rdeliver()$. We use Bracha's Byzantine RB specification~\cite{Bracha87}: for a fixed sender and broadcast instance, all correct processes that deliver, deliver the same payload, and Byzantine equivocation on that instance is prevented.
\paragraph{Byzantine behaviour}
A Byzantine process may deviate arbitrarily from the algorithm (malformed inputs, selective omission, collusion, inconsistent timing, etc.).
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\subsection{Reliable Broadcast (RB)}
\RB provides the following properties in the model.
\RB provides the following properties in this model (cf.~\cite{Bracha87}).
\begin{itemize}[leftmargin=*]
\item \textbf{Integrity}: Every message received was previously sent. $\forall p_i:\ m = \rbreceived_i() \Rightarrow \exists p_j:\ \RBcast_j(m)$.
\item \textbf{No-duplicates}: No message is received more than once at any process.