Differentially Private Triangle Counting Assisted by $k$-Anonymity in Two-Party Models

Triangle counting is essential for analyzing network structures and optimizing recommendation systems, yet it can lead to privacy breaches if individual data is not adequately protected during the analysis. Differential privacy has become a widely adopted standard to safeguard personal privacy. Current research mainly focuses on central and local models, which differ in applicability and performance. The central model cannot be applied when graph data is distributed among multiple parties without a trusted central server, while the local model provides unsatisfactory performance. In this paper, we explore a two-party scenario where each party holds private information about a group of users and is not allowed to disclose this information to the other party. We have proposed a scheme called HTTC-DPk, which ensures both differential privacy and k-anonymity, and is better suited to the constraints of the two-party setting compared to both central and local models. Our method integrates the noisy maximum degree computation for both intra-party and inter-party edges, along with the differentially private inter-party triangle counting based on two-party interactions. Additionally, we introduce an enhanced scheme HTTC-DPk* that strikes a balance between accuracy and communication costs, particularly suitable for large-scale graphs. We have provided comprehensive theoretical proof of our scheme's privacy and demonstrated through extensive experiments that our approach performs well under various cases.