Cloud computing is recognized as one of the most promising solutions to information technology, e.g., for storing and sharing data in the web service which is sustained by a company or third party instead of storing data in a hard drive or other devices. It is essentially a physical storage system which provides large storage of data and faster computing to users over the Internet. In this cloud system, the third party allows to preserve data of clients or users only for business purpose and also for a limited period of time. The users are used to share data confidentially among themselves and to store data virtually to save the cost of physical devices as well as the time. In this paper, we propose a discrete dynamical system for cloud computing and data management of the storage service between a third party and users. A framework, comprised of different techniques and procedures for distribution of storage and their implementation with users and the third party is given. For illustration purpose, the model is considered for two users and a third party, and its dynamical properties are briefly analyzed and discussed. It is shown that the discrete system exhibits periodic, quasiperiodic and chaotic states. The latter discerns that the cloud computing system with distribution of data and storage between users and the third party may be secured. Some issues of data security are discussed and a random replication scheme is proposed to ensure that the data loss can be highly reduced compared to the existing schemes in the literature.