  The increasing sophistication of available quantum networks has seen a
corresponding growth in the pursuit of multi-partite cryptographic protocols.
Whilst the use of multi-partite entanglement is known to offer an advantage in
certain abstractly motivated contexts, the quest to find practical advantage
scenarios is ongoing and substantial difficulties in generalising some
bi-partite security proofs still remain. We present rigorous results that
address both these challenges at the same time. First, we prove the security of
a variant of the GHZ state based secret sharing protocol against general
attacks, including participant attacks which break the security of the original
GHZ state scheme. We then identify parameters for a performance advantage over
realistic bottleneck networks. We show that whilst channel losses limit the
advantage region to short distances over direct transmission networks, the
addition of quantum repeaters unlocks the performance advantage of
multi-partite entanglement over point-to-point approaches for long distance
quantum cryptography.
