Sharing encrypted data with different users via public cloud storage is an important research issue. This paper proposes a key-aggregate authentication cryptosystem. The cryptosystem generates a constant-size key that supports flexible delegation of decryption rights for any set of ciphertexts. The key-size is independent of the number of maximum ciphertexts such that the expense of our scheme is stable no matter how frequently users upload files to the cloud server dynamically. In addition, the authentication process in our scheme solves the key-leakage problem of data sharing. Data owner can extract an aggregated key which includes ciphertexts' indices, delegatee's identity and expiration date of the key. The cloud server obtains the identity of download-applicant from the key with public parameter and then controls download right. This paper proves that the authentication key cannot be fudged and the message in this key cannot be denied. In order to achieve efficient and secure data sharing in dynamic cloud storage, the proposed method should be stable in expense, and should be leakage-resilient. Our scheme can satisfy both requirements.