  Simplified trusted nodes (STNs) are a form of trusted node for quantum key
distribution (QKD) networks which do not require running a full QKD stack every
instance (i.e., they do not need to run error correction and privacy
amplification each session). Such systems hold the advantage that they may be
implemented with weaker computational abilities, than regular TNs, while still
keeping up with key generation rate demands. The downside is that noise
tolerance is lower. However, to get a better understanding of their suitability
in various scenarios, one requires practical, finite-key security bounds for
STN networks. So far, only theoretical asymptotic bounds are known. In this
work we derive a new proof of security for STN chains in the finite key
setting. We also derive a novel cost function allowing us to evaluate when STNs
would be beneficial from a computational cost perspective, compared with
regular TN networks.
