Cloud storage can provide flexible and scalable data storage services to users. However, once data is uploaded to the cloud without a copy in local computers,the user loses control of the data physically. So, it is necessary to study a method to ensure users’ data integrity.Avoiding retrieving enormous storage data or checking the data by users, a proof of storage protocol with public auditing was proposed based on the lattice cryptography. The user computed the signatures of the blocks, and outsourced them to cloud servers. Cloud service providers combined the blocks. Third party auditor verified all blocks’ integrity only through the combined message and signature. Based on the Small integer solution assumption, the presented protocol is secure against the lost attack and tamper attack from cloud service providers. Based on the Learning with error assumption, the presented protocol is secure against the curiosity attack from third party auditor. The protocol is quite efficient, requiring just a few matrix-vector multiplications and samplings from discrete Gaussians. However, once data is uploaded to the cloud without a copy in local computers, the user loses control of the data physically. So, it is necessary to study a method to ensure users ’data integrity.Avoiding retrieving enormous storage data or checking the data by users, a proof of storage protocol with public auditing was proposed based on the lattice cryptography. The user computed the signatures of the blocks, and outsourced them to cloud servers. Cloud service providers combined the blocks. Third party auditor verified all blocks’ integrity only through the combined message and signature. Based on the Small integer solution assumption, the presented protocol is secure against the lost attack and tamper attack from cloud service providers. Based on the Learning with error assumption, the presented protocol is secure against the curiosity attack from third party auditor. The protocol is quite efficient, requi ring just a few matrix-vector multiplications and samplings from discrete Gaussians.