Cloud computing is an alternative to traditional information technology due to its services. In this paper, a new theory has been introduced three way integrity algorithm.  Here we are checking the accuracy of cloud service provider (CSP) and third party auditor (TPA). It gives an efficient data integrity mechanism between the client and the cloud by using RSA with digital signature on the message digest instead of on the whole data to make computations faster. Our public auditing system can be constructed from the above auditing scheme in two phases, setup and audit phase. The problem of verifying correctness of data storage in the cloud becomes even more challenging. However, this dynamic feature also makes traditional integrity insurance techniques futile and entails new solutions. We propose an extensible and emphatic distributed scheme with explicit dynamic data support to ensure the correctness of users’ data in cloud.