Structured encryption for triangle counting on graph data

Triangle counting is an important metric on graph analysis for graph data such as social networks. To protect the privacy of graph data, researchers have proposed differential privacy-based triangle counting methods, but the counting results are flawed by estimation errors. A recent study proposes approximate triangle counting on encrypted graph data to achieve triangle counting of the entire graph, but cannot calculate the number of triangles formed between each individual node and its neighbors. In addition, triangle counting on graph is not fully investigated based on other privacy-preserving techniques, such as structured encryption for triangle counting on graph data. To improve the accuracy of triangle counting on graph data, we proposed two types of structured encryption for triangle counting on graph data (STE-TC) with various efficiency-security tradeoffs and combined it with homomorphic encryption to achieve triangle counting between each individual node and its neighbors that can evaluate the importance of this node. We proposed two triangle counting methods in both asymmetric key and symmetric key settings to satisfy different sharing requirements in the cloud. The security analysis and experimental results show that the proposed methods are feasible and practical.(c) 2023 Elsevier B.V. All rights reserved.