Secure distributed data storage can shift the burden of maintaining a large number of files from the owner to proxy servers. Proxy servers can convert encrypted files for the owner to encrypted files for the receiver without the necessity of knowing the content of the original files. In practice, the original files will be removed by the owner for the sake of space efficiency. Hence, the issues on confidentiality and integrity of the outsourced data must be addressed carefully. In this paper, we propose two identity-based secure distributed data storage (IBSDDS) schemes. Our schemes can capture the following properties: (1) The file owner can decide the access permission independently without the help of the private key generator (PKG); (2) For one query, a receiver can only access one file, instead of all files of the owner; (3) Our schemes are secure against the collusion attacks. Although the first scheme is only secure against the chosen plaintext attacks (CPA), the second scheme is secure against the chosen ciphertext attacks (CCA). To the best of our knowledge, it is the first IBSDDS schemes where an access permissions is made by the owner for an exact file and collusion attacks can be protected in the standard model.