Sectric: Towards Accurate, Privacy-preserving and Efficient Triangle Counting

Graph data analysis, particularly local triangle counting, plays a pivotal role in deciphering complex relationships within graph data. This method is invaluable across diverse fields such as social networks, transportation, and cybersecurity. However, this process often involves handling sensitive information, necessitating that the relationship between any two nodes is considered private. Differential privacy (DP) is a formal model to address privacy concerns and can be categorized into two types: the central DP (CDP) model, which achieves better result accuracy, and the local DP (LDP) model, which does not assume a trusted server. To bridge the gap between the two models, we propose Sectric, a server-aided crypto-assisted local triangle counting protocol, in this paper. It can achieve the same result accuracy with the same privacy budget as the CDP model without assuming a trusted server. Sectric also explores a new approach in crypto-assisted graph data analysis algorithms that represents a node's neighbors using a set instead of an adjacency vector, and successfully achieves higher efficiency compared to other crypto-assisted solutions. We also conduct theoretical and empirical evaluations to demonstrate that Sectric achieves the design principles.