The cloud storage services are used to store intermediate and persistent data generated from various resources including servers and IoT based networks. The outcome of such developments is that the data gets duplicated and gets replicated rapidly especially when large number of cloud users are working in a collaborative environment to solve large scale problems in geo-distributed networks. The data gets prone to breach of privacy and high incidence of duplication. When the dynamics of cloud services change over period of time, the ownership and proof of identity operations also need to change and work dynamically for high degree of security. In this work we will study the following concepts, methods and the schemes that can make the cloud services secure and reduce the incidence of data duplication. With the help of cryptography mathematics and to increase potential storage capacity. The proposed scheme works for deduplication of data with arithmetic key validity operations that reduce the overhead and increase the complexity of the keys so that it is hard to break the keys.