Cloud computing is an emerging technology that will receive more attention in the future from industry and academia. The cost of this technology is more attractive when it is compared to building the infrastructure. However, there are many security issues coming with this technology as happens when every technology matures. In this research paper data security, data integrity and access control in the public cloud is achieved with significant results. In this process, Third Party Auditor (TPA) and user separation are used successfully. The TPA has a hybrid algorithm for signature generation called MD5withRSA. The access control is used for separate users from data owners and only those users can have access to the owner's data who have granted access by data owners. Data is compressed without affecting the quality of data to reduce the storage cost. The compressed data is then stored in chunks to provide security. The proposed system can be further extended to improve the TPA performance of different types of data on cloud environment.