In the current cross-border electronic commerce (e-commerce) system, various document recording and authorization processes are cumbersome, record sharing efficiency is low, and identity verification is difficult. A method of asymmetric encryption technology combining Blockchain technology and cryptography is proposed. The advantages of asymmetric encrypted communications include high security and ease of multiparties communication collaboration, being applied to a peer-to-peer network formed by Blockchain technology, and making cross-border e-commerce record cross-domain sharing traceable, data immutable, and identity verification simplified. First of all, based on the immutable modification of Blockchain technology and asymmetric encryption technology, file synchronization contracts and authorization contracts are designed. Its distributed storage advantages ensure the privacy of users’ cross-border e-commerce information. Second, the design of the cross-domain acquisition contract can effectively verify the identity and transmission efficiency of both parties to the data sharing, so that illegal users can be safely filtered without a third-party notary institution. The simulation experiment results show that the solution proposed in this paper has obvious advantages in data antitheft, multiparty authentication, and saving system overhead compared with traditional cloud computing methods to solve the problem of sharing medical records. It provides a reference for solving the security problems in the process of data sharing by using the advantages of Blockchain’s decentralization and auditability and provides reference ideas for solving the problems of data sharing and cross-domain authentication.