Third party cloud storage and access permissions play a vital role in security analysis and user access control. User access control and data verification are the important revolutionary technologies to provide security and control unauthorized users. Third party cloud servers are built without proper security measures and user control mechanisms. User can access the data such as documents, media or other type of files using third party generated authentication key and secret information. Traditional cloud security mechanisms are independent of data integrity verification to the authorized data users. Third party cloud servers are vulnerable to different type of message integrity attacks. Traditional message integrity algorithms are depend on the file size, hash size and security parameters. In order to overcome the security related issues in commercial cloud servers, an improved hash based message integrity verification process was proposed in this paper. Proposed message integrity algorithm was tested on attributed based encryption process. Proposed cloud based hash algorithm generates 512 bit size hash value to each file in the third party cloud servers. Only authorized users can access the required files using his/her identity along with the message integrity value. Experimental results show that proposed cloud based hash algorithm outperformed well compare to existing models in terms of file size, time and attacks are concern.