Transformer models have gained significant attention due to their power in machine learning tasks. Their extensive deployment has raised concerns about the potential leakage of sensitive information during inference. However, when being applied to Transformers, existing approaches based on secure two-party computation (2PC) bring about efficiency limitations in two folds: (1) resource-intensive matrix multiplications in linear layers, and (2) complex non-linear activation functions like $\mathsf{GELU}$ and $\mathsf{Softmax}$. This work presents a new two-party inference framework $\mathsf{Nimbus}$ for Transformer models. Specifically, we propose a new 2PC paradigm to securely compute matrix multiplications based on an outer-product insight, which achieves $2.9\times \sim 12.5\times$ performance improvements compared to the state-of-the-art (SOTA) protocol. Furthermore, through a new observation of utilizing the input distribution, we propose an approach of low-degree polynomial approximation for $\mathsf{GELU}$ and $\mathsf{Softmax}$, which improves the performance of the SOTA polynomial approximation by $2.9\times \sim 4.0\times$, where the average accuracy loss of our approach is 0.08\% compared to the non-2PC inference without privacy. Compared with the SOTA two-party inference, $\mathsf{Nimbus}$ improves the end-to-end performance of $BERT_{base}$ inference by $2.7\times \sim 4.7\times$ across different network settings.

Privacy-preserving machine learning has drawn increasingly attention recently, especially with kinds of privacy regulations come into force. Under such situation, Federated Learning (FL) appears to facilitate privacy-preserving joint modeling among multiple parties. Although many federated algorithms have been extensively studied, there is still a lack of secure and practical gradient tree boosting models (e.g., XGB) in literature. In this paper, we aim to build large-scale secure XGB under vertically federated learning setting. We guarantee data privacy from three aspects. Specifically, (1) we employ secure multi-party computation techniques to avoid leaking intermediate information during training, (2) we store the output model in a distributed manner in order to minimize information release, and (3) we provide a novel algorithm for secure XGB predict with the distributed model. Furthermore, by proposing secure permutation protocols, we can improve the training efficiency and make the framework scale to large dataset. We conduct extensive experiments on both public datasets and real-world datasets, and the results demonstrate that our proposed XGB models provide not only competitive accuracy but also practical performance.