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As data privacy is gradually valued by people, federated learning(FL) has emerged because of its potential to protect data. FL uses homomorphic encryption and differential privacy encryption on the promise of ensuring data security to realize distributed machine learning by exchanging encrypted information between different data providers. However, there are still many problems in FL, such as the communication efficiency between the client and the server and the data is non-iid. In order to solve the two problems mentioned above, we propose a novel vertical federated learning framework based on the DFP and the BFGS(denoted as BDFL), then apply it to logistic regression. Finally, we perform experiments using real datasets to test efficiency of BDFL framework.