  A set of mutually distrusting participants that want to agree on a common
opinion must solve an instance of a Byzantine agreement problem. These problems
have been extensively studied in the literature. However, most of the existing
solutions assume that the participants are aware of $n$ -- the total number of
participants in the system -- and $f$ -- an upper bound on the number of
Byzantine participants. In this paper, we show that most of the fundamental
agreement problems can be solved without affecting resiliency even if the
participants do not know the values of (possibly changing) $n$ and $f$.
Specifically, we consider a synchronous system where the participants have
unique but not necessarily consecutive identifiers, and give Byzantine
agreement algorithms for reliable broadcast, approximate agreement,
rotor-coordinator, early terminating consensus and total ordering in static and
dynamic systems, all with the optimal resiliency of $n> 3f$. Moreover, we show
that synchrony is necessary as an agreement with probabilistic termination is
impossible in a semi-synchronous or asynchronous system if the participants are
unaware of $n$ and $f$.
