Penguin: Parallel-Packed Homomorphic Encryption for Fast Graph Convolutional Network Inference

The marriage of Graph Convolutional Network (GCN) and Homomorphic Encryption (HE) enables the inference of graph data on the cloud with significantly enhanced client data privacy. However, the tremendous computation and memory overhead associated with HE operations challenges the practicality of HE-based GCN inference. GCN inference involves a sequence of expensive matrix-matrix multiplications, and we observe that directly applying the state-of-the-art HE-based secure matrix-matrix multiplication solutions to accelerate HE-GCN inference is far less efficient as it does not exploit the unique aggregation mechanism of two-dimension graph node-features in GCN layer computation. As a result, in this paper, we propose a novel HE-based ciphertext packing technique, i.e., Penguin, that can take advantage of the unique computation pattern during the HE-GCN inference to significantly reduce the computation and memory overhead associated with HE operations.Specifically, Penguin employs (i) an effective two-dimension parallel packing technique for feature ciphertext with optimal graph node partitioning and graph feature interleaving, and (ii) an interleaved assembly technique that can effectively make use of the blank slots to merge ciphertexts after feature reduction and significantly reduce the costly rotation operation.We provide theoretical analysis and experimental validation to demonstrate the speedup achieved by Penguin in accelerating GCN inference using popular GCN models and datasets. Our results show that Penguin can achieve up to $\sim10\times$ speedup and around $\sim79$% reduction in computational memory overhead, significantly outperforming state-of-the-art solutions. To the best of our knowledge, this is the first work that can ensure the protection of both graph structure and features when accelerating HE-GCN inference on encrypted data. Our code is publicly available at https://github.com/ranran0523/Penguin.