Logistics companies are increasingly adopting private blockchains for enhanced data management because of the trends in cooperation. Nevertheless, this practice poses new challenges concerning the security and sharing of data. The real-time nature and diversity of logistics data increase the difficulty of protecting the data. Additionally, when transportation information changes, downstream enterprises must promptly adjust their production plans to accommodate these alterations. The strict access controls of private blockchains can obstruct downstream enterprises from obtaining data, posing a challenge to the overall operational efficiency. In this paper, we propose an innovative logistics data protection scheme that employs private set intersection (PSI) and blockchain cross-chain technology to achieve data security. In our scheme, logistics companies within the logistics consortium are added as trusted agents to the public blockchain, enabling downstream enterprises to acquire logistics data integration from the public blockchain. Utilizing an RSA-based PSI protocol, our approach enhances exchange efficiency while protecting private data without transmitting additional information. We evaluate the performance of the proposed solution through a series of experiments, and the results demonstrate that our solution can achieve secure and efficient logistics data exchange.