As an essential tool of secure distributed machine learning, vertical federated learning (VFL) based on homomorphic encryption (HE) suffers from severe efficiency problems due to data inflation and time-consuming operations. To this core, we propose PackVFL, an efficient VFL framework based on packed HE (PackedHE), to accelerate the existing HE-based VFL algorithms. PackVFL packs multiple cleartexts into one ciphertext and supports single-instruction-multiple-data (SIMD)-style parallelism. We focus on designing a high-performant matrix multiplication (MatMult) method since it takes up most of the ciphertext computation time in HE-based VFL. Besides, devising the MatMult method is also challenging for PackedHE because a slight difference in the packing way could predominantly affect its computation and communication costs. Without domain-specific design, directly applying SOTA MatMult methods is hard to achieve optimal. Therefore, we make a three-fold design: 1) we systematically explore the current design space of MatMult and quantify the complexity of existing approaches to provide guidance; 2) we propose a hybrid MatMult method according to the unique characteristics of VFL; 3) we adaptively apply our hybrid method in representative VFL algorithms, leveraging distinctive algorithmic properties to further improve efficiency. As the batch size, feature dimension and model size of VFL scale up to large sizes, PackVFL consistently delivers enhanced performance. Empirically, PackVFL propels existing VFL algorithms to new heights, achieving up to a 51.52X end-to-end speedup. This represents a substantial 34.51X greater speedup compared to the direct application of SOTA MatMult methods.

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