  This paper explores how reliable broadcast can be implemented when facing a
dual adversary that can both corrupt processes and remove messages.More
precisely, we consider an asynchronous $n$-process message-passing systems in
which up to $t_b$ processes are Byzantine and where, at the network level, for
each message broadcast by a correct process, an adversary can prevent up to
$t_m$ processes from receiving it (the integer $t_m$ defines the power of the
message adversary).So, differently from previous works, this work considers
that not only computing entities can be faulty (Byzantine processes), but also
that the network can lose messages.To this end, the paper first introduces a
new basic communication abstraction denoted $k\ell$-cast, and studies its
properties in this new bi-dimensional adversary context.Then, the paper
deconstructs existing Byzantine-tolerant asynchronous broadcast algorithms and,
with the help of the $k\ell$-cast communication abstraction, reconstructs
versions of them that tolerate both Byzantine processes and message
adversaries.Interestingly, these reconstructed algorithms are also more
efficient than the Byzantine-tolerant-only algorithms from which they
originate.The paper also shows that the condition $n>3t_b+2t_m$ is necessary
and sufficient (with signatures) to design such reliable broadcast algorithms.
