A Crypto-Assisted Approach for Publishing Graph Statistics with Node Local Differential Privacy

Publishing graph statistics under node differential privacy has attracted much attention since it provides a stronger privacy guarantee than edge differential privacy. Existing works related to node differential privacy assume a trusted data curator who holds the whole graph. However, in many applications, a trusted curator is usually not available due to privacy and security issues. In this paper, for the first time, we investigate the problem of publishing graph statistics under Node Local Differential privacy (Node-LDP), which does not rely on a trusted server. We propose an algorithm to publish the degree distribution with Node-LDP by exploring how to select the graph projection parameter in the local setting and how to execute the graph projection locally. Specifically, we propose a crypto-assisted local projection method based on cryptographic primitives, achieving the higher accuracy than our baseline pureLDP local projection method. Furthermore, we improve our baseline graph projection method from node-level to edge-level that preserves more neighboring information, owning better utility. Finally, extensive experiments on real-world graphs show that crypto-assisted parameter selection owns better utility than pureLDP parameter selection, and edge-level local projection provides higher accuracy than node-level local projection, improving by up to 57.2% and 79.8%, respectively.