Privacy-Preserving Subgraph Matching Protocol for Two Parties

Abstract

Graph data structure has been widely used across many application areas, such as web data, social network, and cheminformatics. The main benefit of storing data as graphs is there exists a rich set of graph algorithms and operations that can be used to solve various computing problems, including pattern matching, data mining, and image processing. Among these graph algorithms, the subgraph isomorphism problem is one of the most fundamental algorithms that can be utilized by many higher level applications. The subgraph isomorphism problem is defined as, given two graphs [Formula: see text] and [Formula: see text], whether [Formula: see text] contains a subgraph that is isomorphic to [Formula: see text]. In this paper, we consider a special case of the subgraph isomorphism problem called the subgraph matching problem, which tests whether [Formula: see text] is a subgraph of [Formula: see text]. We propose a protocol that solve the subgraph matching problem in a privacy-preserving manner. The protocol allows two parties to jointly compute whether one graph is a subgraph of the other, while protecting the private information about the input graphs. The protocol is secure under the semi-honest setting, where each party performs the protocol faithfully.