Securely computing graph convolutional networks (GCNs) is critical for applying their analytical capabilities to privacy-sensitive data like social/credit networks. Multiplying a sparse yet large adjacency matrix of a graph in GCN--a core operation in training/inference--poses a performance bottleneck in secure GCNs. Consider a GCN with $|V|$ nodes and $|E|$ edges; it incurs a large $O(|V|^2)$ communication overhead. Modeling bipartite graphs and leveraging the monotonicity of non-zero entry locations, we propose a co-design harmonizing secure multi-party computation (MPC) with matrix sparsity. Our sparse matrix decomposition transforms an arbitrary sparse matrix into a product of structured matrices. Specialized MPC protocols for oblivious permutation and selection multiplication are then tailored, enabling our secure sparse matrix multiplication ($(SM)^2$) protocol, optimized for secure multiplication of these structured matrices. Together, these techniques take $O(|E|)$ communication in constant rounds. Supported by $(SM)^2$, we present Virgos, a secure 2-party framework that is communication-efficient and memory-friendly on standard vertically-partitioned graph datasets. Performance of Virgos has been empirically validated across diverse network conditions.

翻译：安全计算图卷积网络（GCNs）对于将其分析能力应用于社交/信用网络等隐私敏感数据至关重要。在GCN中乘以图的稀疏但庞大的邻接矩阵——训练/推理中的核心操作——构成了安全GCN的性能瓶颈。考虑一个具有$|V|$个节点和$|E|$条边的GCN；它会产生巨大的$O(|V|^2)$通信开销。通过建模二分图并利用非零元位置的单调性，我们提出了一种将安全多方计算（MPC）与矩阵稀疏性相协调的协同设计。我们的稀疏矩阵分解将任意稀疏矩阵转换为结构化矩阵的乘积。随后定制了用于不经意置换和选择乘法的专用MPC协议，从而实现了我们的安全稀疏矩阵乘法（$(SM)^2$）协议，该协议针对这些结构化矩阵的安全乘法进行了优化。这些技术共同在恒定轮次内实现了$O(|E|)$的通信量。在$(SM)^2$的支持下，我们提出了Virgos——一个安全的双方框架，在标准的垂直切分图数据集上具有通信高效和内存友好的特点。Virgos的性能已在不同网络条件下得到实证验证。