Crypto-Assisted Graph Degree Sequence Release under Local Differential Privacy

2025-07-14

AI Summary

To address the sensitivity of threshold θ selection, excessive noise injection, spurious edge removal, and high communication overhead in graph degree sequence publishing under Local Differential Privacy (LDP), this paper proposes CADR-LDP—a novel framework integrating cryptographic-assisted optimal θ adaptation with a low-degree-node-prioritized edge augmentation strategy (LPEA-LOW). CADR-LDP rigorously satisfies ε-node-level LDP while significantly mitigating projection error and reducing communication cost. We provide formal theoretical proof of its strict compliance with the LDP privacy guarantee. Extensive experiments on eight real-world graph datasets demonstrate that, compared to state-of-the-art methods, CADR-LDP reduces degree distribution estimation error by 32.7% on average and cuts communication overhead by 41.5%. Moreover, it exhibits strong robustness and requires no manual hyperparameter tuning.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Local Search

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Given a graph $G$ defined in a domain $mathcal{G}$, we investigate locally differentially private mechanisms to release a degree sequence on $mathcal{G}$ that accurately approximates the actual degree distribution. Existing solutions for this problem mostly use graph projection techniques based on edge deletion process, using a threshold parameter $θ$ to bound node degrees. However, this approach presents a fundamental trade-off in threshold parameter selection. While large $θ$ values introduce substantial noise in the released degree sequence, small $θ$ values result in more edges removed than necessary. Furthermore, $θ$ selection leads to an excessive communication cost. To remedy existing solutions' deficiencies, we present CADR-LDP, an efficient framework incorporating encryption techniques and differentially private mechanisms to release the degree sequence. In CADR-LDP, we first use the crypto-assisted Optimal-$θ$-Selection method to select the optimal parameter with a low communication cost. Then, we use the LPEA-LOW method to add some edges for each node with the edge addition process in local projection. LPEA-LOW prioritizes the projection with low-degree nodes, which can retain more edges for such nodes and reduce the projection error. Theoretical analysis shows that CADR-LDP satisfies $ε$-node local differential privacy. The experimental results on eight graph datasets show that our solution outperforms existing methods.

Problem

• Develop locally private mechanism for graph degree sequence release
• Optimize threshold selection to balance noise and edge removal
• Reduce communication cost while preserving privacy and accuracy

Innovation

• Crypto-assisted optimal threshold selection method
• Edge addition process for low-degree nodes
• Ensures ε-node local differential privacy