Differentially private federated learning has been intensively studied. The current works are mainly based on the \textit{curator model} or \textit{local model} of differential privacy. However, both of them have pros and cons. The curator model allows greater accuracy but requires a trusted analyzer. In the local model where users randomize local data before sending them to the analyzer, a trusted analyzer is not required, but the accuracy is limited. In this work, by leveraging the \textit{privacy amplification} effect in the recently proposed shuffle model of differential privacy, we achieve the best of two worlds, i.e., accuracy in the curator model and strong privacy without relying on any trusted party. We first propose an FL framework in the shuffle model and a simple protocol (SS-Simple) extended from existing work. We find that SS-Simple only provides an insufficient privacy amplification effect in FL since the dimension of the model parameter is quite large. To solve this challenge, we propose an enhanced protocol (SS-Double) to increase the privacy amplification effect by subsampling. Furthermore, for boosting the utility when the model size is greater than the user population, we propose an advanced protocol (SS-Topk) with gradient sparsification techniques. We also provide theoretical analysis and numerical evaluations of the privacy amplification of the proposed protocols. Experiments on real-world datasets validate that SS-Topk improves the testing accuracy by 60.7\% than the local model based FL. We highlight the observation that SS-Topk even can improve by 33.94\% accuracy than the curator model based FL without any trusted party. Compared with non-private FL, our protocol SS-Topk only lose 1.48\% accuracy under $(4.696, 10^{-5})$-DP.

通过隐私放大效应在混洗模型的差分隐私中实现联邦学习的最佳两个世界，提出了SS-Simple，在FL中提供了不足的隐私放大效应，之后通过分层采样提高了隐私放大效应，减少了模型参数维度的数量级，并提出了一种高级方案SS-Topk用于梯度稀疏技术，通过理论分析和实际实验验证了所提出的协议的隐私放大效应。

FLAME：洗牌模型下的差分隐私联邦学习