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Minimizing Storage space and bandwidth is a challenging task in cloud computing, duplication is the main key term in cloud computing because of large and multiples of digital data stored in single cloud server. Because of rapid usage and expansion of high amount of data, data de-duplication is a challenging task for removing replica related data which has been stored in cloud to reduce storage and space of bandwidth. Secure de-duplication is also a challenging task in cloud storage environment. Convergent encryption based secure de-duplication approach is used traditionally to explore and identify duplicates from multiple users data with de-duplication sharing and uploading data in cloud environment. Because of large volume data, conventional approaches have not meet practical implementation of de-duplication requirements in cloud storage. So we aim that block chain based cloud storage with data de-duplication is the main problem in distributed file storage environment. For predicting dynamic file de-duplication in file sharing of distributed environment, propose a Novel Block chain based Secure De- duplication Authentication scheme (NBSDAS) with high reliability and confidentiality in which the files are distributed to multiple servers and the information of files is recorded on the time-stamped block chain whose central authorities are replaced to automatically decentralize cloud contracts. This proposed approach combined with genetic algorithm to predict and de-duplication with respect to processing dynamic files individually in cloud computing. Security analysis demonstrates that our de-duplication scheme can achieve the proposed security goals while it has limited overhead proved by simulation experiments with comparison to traditional approaches.