With the prevalence of Internet access, document storage has become a fundamental web service in recent years. One important topic is how to design a secure channel for efficiently sharing documents with another receiver. In this paper, we demonstrate a re‐encryption method that is designed with row complete matrices. With this new method, the document owner can share a ciphertext in the cloud with another receiver by sending a serial number to the server and giving the receiver a corresponding key at the same time. This method ensures that the server cannot obtain the information about key and plaintext and that the receiver cannot obtain the original key of the owner either. Only the owner has the knowledge of all the information. Using this re‐encryption system, the cloud server can provide a secure file‐sharing service without worrying about the shared key management problem. Moreover, the cost of re‐encryption will not increase even when the encryption is strengthened with longer encryption keys.