In view of the existing ciphertext sharing scheme, there is too large calculation of user clients, and each user manages too many secret keys. Moreover, it does not support personal sharing and other issues. Thus the Public Cloud is introduced into the ciphertext sharing scheme, and a security file-sharing framework of the Public Cloud is proposed. And based on this framework, a new ciphertext sharing scheme is designed. In this scheme, the vast majority of computation and storage are outsourced to the Public Cloud. The user simply saves two private key components occupying small space. The client only needs a little computation to complete encryption and decryption of the shared file. The security analysis shows that the scheme can deal with not only the conspiracy attack from malicious users, but also the plaintext-chosen attack in the generic group model and the random oracle model.