  The multicast key-dissemination problem over noiseless networks, introduced
by Langberg and Effros [ITW 2022], here called the ``key-cast'' problem,
captures the task of disseminating a shared secret random key to a set of
terminals over a given network. Unlike traditional communication, where
messages must be delivered from source to destination(s) unchanged, key-cast is
more flexible since key-cast need not require source reconstruction at
destination nodes. For example, the distributed keys can be mixtures of sources
from which the sources themselves may be unrecoverable.
  The work at hand considers key dissemination in the single-source,
multiple-multicast network coding setting, i.e., the ``multiple key-cast''
problem. Here, distinct keys are to be simultaneously transmitted from a single
source node to multiple terminal sets, one shared random key per multicast set.
Scenarios include the secure setting, in which only the source and intended
destinations gain information about a given key; and the non-secure setting in
which the only requirement is that the knowledge of one key does not reveal
information about another. In both settings, we present combinatorial
conditions for key dissemination and design corresponding multiple key-cast
schemes. In addition, we compare the multiple key-cast rate with and without
the restriction of source reconstruction, the former corresponding to
traditional forms of communication; key-cast achieves a strict advantage in
rate when source reconstruction is relaxed.
