A novel privacy-preserving graph convolutional network via secure matrix multiplication

Graph convolutional network (GCN) is one of the most representative methods in the realm of graph neural networks (GNNs). In the convolution process, GCN combines the structural information of the networks with the features of nodes. In practice, the structure information of the networks and the features of nodes may be controlled by different parties, which can render GCN ineffective when information sharing is constrained by privacy concerns or licensing issues. Therefore, it is of significant importance to design an effective and secure scheme for GCN that can collaboratively merge information from both parties while safeguarding their sensitive data. In this paper, we introduce S-GCN (i.e., Secure GCN Scheme), which employs secure matrix multiplication (SMM) to compute the product of two matrices in a privacy-preserving manner. The S-GCN scheme requires frequent utilization of SMM to merge information from both parties, resulting in high time and space complexity. To address this issue, we introduce SF-GCN (i.e., Secure and Fast GCN Scheme), which minimizes the use of SMM. Additionally, both S-GCN and SF-GCN may be susceptible to privacy breaches when dealing with dense networks. Hence, we further enhance security by introducing differential privacy through the Laplacian mechanism. Experimental results demonstrate that the proposed schemes do not significantly reduce accuracy in downstream tasks, and, more importantly, effectively protect the privacy information of both parties.