Privacy-preserving federated learning (PPFL) enables users to conduct tasks cooperatively without sharing their private datasets. Under the setting of the single key held by all users, the security of PPFL frameworks is guaranteed under the fragile assumption that none would reveal the key without authentication and data verification. To protect the data integrity, participants who fail to pass verification are required to be excluded from the current training round. In addition, the dynamic update of users with heterogeneous resources incurs severe degradation of the training performance in the FL process. Therefore, we propose a federated learning framework, named Solar Federated Learning (SFL). To protect the users’ privacy, we introduce the BCP cryptosystem to provide a multi-key environment and create a data integrity verification and authentication method based on the bilinear aggregation signature and verifiable secret share. To deal with the impact of the dynamical update under the resource heterogeneity, we design a scheme that enables SFL to tolerate participant dropout during the training while still guaranteeing high accuracy. We evaluated the proposed framework based on the MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets. The experimental results indicate the practicality of SFL.