The tremendous growth of digital data in cloud storage systems is a critical issue, as many duplicate data in storage systems cause extra load. Cloud Service Providers (CSPs) often employ Data Deduplication techniques to eliminate redundant data and store only one copy of data to save storage space and reduce transmission costs. Data Deduplication is mostly effective when multiple clients outsource the same data to cloud storage, but it raises security and ownership issues. This paper proposes a secure, Proof of Ownership (PoW)-based Data Deduplication scheme that has a low communication overhead and ensures that only valid cloud clients can download and decrypt ciphertext from cloud storage. The Advanced Encryption Standard (AES) is used as the encryption algorithm in the proposed scheme. It utilizes two modes of AES encryption, namely, Cipher Block Chaining (CBC) and Galois Counter Mode (GCM), with single-threading and multi-threading to upload and download ciphertext between the client and the server to measure the effect of upload and download times. We present a new approach for PoW to reduce communication overhead. PoW enables owners of the same data to prove to the cloud server that they own the data in a robust way. The comparison between CBC and GCM is implemented in a Java environment with two scenarios: single-threading and multi-threading. The simulation results show that AES-GCM with multi-threading is better during the uploading and downloading times