Federated learning faces a challenging trade-off between privacy protection and model performance when handling sensitive data, such as in the medical and financial domains. To address this issue, this paper proposes a novel federated learning framework called Random Differential Privacy Federated Adaptive Learning Rate Bound (RDP-FedAB). The framework introduces a new differential privacy mechanism—RandomDP, and integrates the AdaBound optimizer to simultaneously enhance privacy preservation and model performance. RDP-FedAB is particularly suitable for vertical federated learning scenarios, where different clients hold different features of the same set of samples. To protect data privacy and ensure model accuracy during collaborative training, the framework incorporates homomorphic encryption to enable secure computation. Experiments conducted on multiple real-world medical datasets demonstrate that RDP-FedAB achieves excellent classification performance under various privacy budgets, significantly outperforming existing methods, especially under medium and low privacy settings. These results highlight its strong potential in privacy-sensitive applications. Future work will further explore its scalability in large-scale and multi-client environments.