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In this paper, we present a secure multiparty computation (SMC) protocol forsingle-source shortest distances (SSSD) in undirected graphs, where thelocation of edges is public, but their length is private. The protocol works inthe 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 smallseparators (which is the case for e.g. planar graphs); the achievableparallelism is significantly higher than that of classical SSSD algorithmsimplemented on top of an ABB.  We implement our protocol on top of the Sharemind MPC platform, and performextensive benchmarking over different network environments. We compare ouralgorithm against the baseline picked from classical algorithms -privacy-preserving Bellman-Ford algorithm (with public edges).

A Parallel Privacy-Preserving Shortest Path Protocol from a Path Algebra Problem