As an important branch of federated learning, vertical federated learning (VFL) enables multiple institutions to train on the same user samples, bringing considerable industry benefits. However, VFL needs to exchange user features among multiple institutions, which raises concerns about privacy leakage. Moreover, existing multi-party VFL privacy-preserving schemes suffer from issues such as poor reliability and high communication overhead. To address these issues, we propose a privacy protection scheme for four institutional VFLs, named FVFL. A hierarchical framework is first introduced to support federated training among four institutions. We also design a verifiable replicated secret sharing (RSS) protocol
-sharing and combine it with homomorphic encryption to ensure the reliability of FVFL while ensuring the privacy of features and intermediate results of the four institutions. Our theoretical analysis proves the reliability and security of the proposed FVFL. Extended experiments verify that the proposed scheme achieves excellent performance with a low communication overhead.