In this paper, we formalize the notion of distributed sensitive social networks (DSSNs), which encompasses networks like enmity networks, financial transaction networks, supply chain networks and sexual relationship networks. Compared to the well studied traditional social networks, DSSNs are often more challenging to study, given the privacy concerns of the individuals on whom the network is knit. In the current work, we envision the use of secure multiparty tools and techniques for performing privacy preserving social network analysis over DSSNs. As a step towards realizing this, we design efficient data-oblivious algorithms for computing the K-shell decomposition and the PageRank centrality measure for a given DSSN. The designed data-oblivious algorithms can be translated into equivalent secure computation protocols. We also list a string of challenges that are needed to be addressed, for employing secure computation protocols as a practical solution for studying DSSNs.
Classical graph algorithms in the context of MPC were first studied by Brickell and Shmatikov in 2006 @cite_18 . The authors proposed secure two party protocols for computing single source and all pair shortest paths problem. Since then, many graph algorithms have been explored in the MPC setting, including BFS, DFS, Dijkstra, minimum spanning tree and classical flow algorithms @cite_30 @cite_20 @cite_9 . Securely constructing an anonymized version of a network distributedly held by a set of parties has been previously studied for various security models @cite_43 @cite_54 @cite_2 .
@cite_30 @cite_18 @cite_9 @cite_54 @cite_43 @cite_2 @cite_20
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We present oblivious implementations of several data structures for secure multiparty computation (MPC) such as arrays, dictionaries, and priority queues. The resulting oblivious data structures have only polylogarithmic overhead compared with their classical counterparts. To achieve this, we give secure multiparty protocols for the ORAM of (Asiacrypt ‘11) and the Path ORAM scheme of (CCS ‘13), and we compare the resulting implementations. We subsequently use our oblivious priority queue for secure computation of Dijkstra’s shortest path algorithm on general graphs, where the graph structure is secret. To the best of our knowledge, this is the first implementation of a non-trivial graph algorithm in multiparty computation with polylogarithmic overhead. We investigate how to solve several classical network flow problems using secure multi-party computation. We consider the shortest path problem, the Minimum Mean Cycle problem and the Minimum Cost Flow problem. To the best of our knowledge, this is the first time the two last problems have been addressed in a general multi-party computation setting. Furthermore, our study highlights the complexity gaps between traditional and secure implementations of the solutions, to later test its implementation. It also explores various trade-offs between performance and security. Additionally it provides protocols that can be used as building blocks to solve complex problems. Applications of our work can be found in: communication networks, routing data from rival company hubs; benchmarking, comparing several IT appliances configurations of rival companies; distribution problems, retailer supplier selection in multi-level supply chains that want to share routes without disclosing sensible information; amongst others. We investigate the problem of solving traditional combinatorial graph problems using secure multi-party computation techniques, focusing on the shortest path and the maximum flow problems. To the best of our knowledge, this is the first time these problems have been addressed in a general multi-party computation setting. Our study highlights several complexity gaps and suggests the exploration of various trade-offs, while also offering protocols that are efficient enough to solve real-world problems. The single-source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a positively weighted graph G with a source vertex s , find the shortest path from s to all other vertices in the graph. Since 1959, all theoretical developments in SSSP for general directed and undirected graphs have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s . Thus, any implementation of Dijkstra's algorithm sorts the vertices according to their distances from s . However, we do not know how to sort in linear time. Here, a deterministic linear time and linear space algorithm is presented for the undirected single source shortest paths problem with positive integer weights. The algorithm avoids the sorting bottleneck by building a hierarchical bucketing structure, identifying vertex pairs that may be visited in any order.