Privacy-Preserving Minimum Spanning Tree Algorithms in Static Semi-honest Model

Abstract

In 1982, Andrew Yao introduced secure two-party computation (2PC) for the so-called millionaire’sproblem. The problem is about two millionaires Alice and Bob, interested to determine who iswealthier without revealing their actual private property values. Goldreich generalized the securetwo-party computation and formalized the secure multi-party computation. Suppose two telephonecompanies wish to merge to provide better services to end users. Each company has a cost functionfor connecting any pair of houses. They want to connect every house with minimum cost in mergedcompany. Mathematically, given two graphs G1,G2 they want to compute MST(min(G1,G2)). Beforemerging both companies they want to know whether merging will benefit them or not without revelingcost function for any pair of houses. Based on the secure multi-party computation paradigm, wepropose new algorithms for privacy-preserving computation of minimum spanning tree. Our protocolsoffers security against semi-honest adversaries.