Privacy-Preserving Graph Algorithms in the Semi-honest Model

We consider scenarios in which two parties, each in possession of a graph, wish to compute some algorithm on their joint graph in a privacy-preserving manner, that is, without leaking any information about their inputs except that revealed by the algorithm’s output. Working in the standard secure multi-party computation paradigm, we present new algorithms for privacy-preserving computation of APSD (all pairs shortest distance) and SSSD (single source shortest distance), as well as two new algorithms for privacy-preserving set union. Our algorithms are significantly more efficient than generic constructions. As in previous work on privacy-preserving data mining, we prove that our algorithms are secure provided the participants are “honest, but curious.”