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More and more orgainizations and institutions make efforts on using externaldata to improve the performance of AI services. To address the data privacy andsecurity concerns, federated learning has attracted increasing attention fromboth academia and industry to securely construct AI models across multipleisolated data providers. In this paper, we studied the efficiency problem ofadapting widely used XGBoost model in real-world applications to verticalfederated learning setting. State-of-the-art vertical federated XGBoostframeworks requires large number of encryption operations and ciphertexttransmissions, which makes the model training much less efficient than trainingXGBoost models locally. To bridge this gap, we proposed a novel batchhomomorphic encryption method to cut the cost of encryption-related computationand transmission in nearly half. This is achieved by encoding the first-orderderivative and the second-order derivative into a single number for encryption,ciphertext transmission, and homomorphic addition operations. The sum ofmultiple first-order derivatives and second-order derivatives can besimultaneously decoded from the sum of encoded values. We are motivated by thebatch idea in the work of BatchCrypt for horizontal federated learning, anddesign a novel batch method to address the limitations of allowing quite fewnumber of negative numbers. The encode procedure of the proposed batch methodconsists of four steps, including shifting, truncating, quantizing andbatching, while the decoding procedure consists of de-quantization and shiftingback. The advantages of our method are demonstrated through theoreticalanalysis and extensive numerical experiments.

Efficient Batch Homomorphic Encryption for Vertically Federated XGBoost