  In this paper, we present a secure multiparty computation (SMC) protocol for
single-source shortest distances (SSSD) in undirected graphs, where the
location of edges is public, but their length is private. The protocol works in
the Arithmetic Black Box (ABB) model on top of the separator tree of the graph,
achieving good time complexity if the subgraphs of the graph have small
separators (which is the case for e.g. planar graphs); the achievable
parallelism is significantly higher than that of classical SSSD algorithms
implemented on top of an ABB.
  We implement our protocol on top of the Sharemind MPC platform, and perform
extensive benchmarking over different network environments. We compare our
algorithm against the baseline picked from classical algorithms -
privacy-preserving Bellman-Ford algorithm (with public edges).
