Data redundancy is a significant issue that wastes plenty of storage space in the cloud-fog storage integrated environments. Most of the current techniques, which mainly center around the static scenes, for example, the backup and archive systems, are not appropriate because of the dynamic nature of data in the cloud or integrated cloud environments. This problem can be effectively reduced and successfully managed by data deduplication techniques, eliminating duplicate data in cloud storage systems. Implementation of data deduplication (DD) over encrypted data is always a significant challenge in an integrated cloud-fog storage and computing environment to optimize the storage efficiently in a highly secured manner. This paper develops a new method using Convergent and Modified Elliptic Curve Cryptography (MECC) algorithms over the cloud and fog environment to construct secure deduplication systems. The proposed method focuses on the two most important goals of such systems. On one side, the redundancy of data needs to be reduced to its minimum, and on the other hand, a robust encryption approach must be developed to ensure the security of the data. The proposed technique is well suited for operations such as uploading new files by a user to the fog or cloud storage. The file is first encrypted using the Convergent Encryption (CE) technique and then re-encrypted using the Modified Elliptic Curve Cryptography (MECC) algorithm. The proposed method can recognize data redundancy at the block level, reducing the redundancy of data more effectively. Testing results show that the proposed approach can outperform a few state-of-the-art methods of computational efficiency and security levels.
