Data deduplication is an effective mechanism that reduces the required storage space of cloud storage servers by avoiding storing several copies of the same data. In contrast with server-side deduplication, client-side deduplication can not only save storage space but also reduce network bandwidth. Clientside deduplication schemes, however, might suffer from serious security threats. For instance, an adversary can spoof the server and gain access to a file he/she does not possess by claiming that she/he owns it. In order to thwart such a threat, the concept of proof-of-ownership (PoW) has been introduced. The security of the existing PoW scheme cannot be assured without affecting the computational complexity of the client-side deduplication. This paper proposes a secure and efficient PoW scheme for client-side deduplication in cloud environments with minimal computational overhead. The proposed scheme utilizes convergent encryption to encrypt a sufficiently large block specified by the server to challenge the client that claims possession of the file requested to be uploaded. To ensure that the client owns the entire file contents, and hence resist collusion attacks, the server challenges the client by requesting him to split the file he asks to upload into fixed-sized blocks and then encrypting a randomly chosen block using a key formed from extracting one bit at a specified location in all other blocks. This ensures a significant reduction in the communication overhead between the server and client. Computational complexity analysis and experimental results demonstrate that the proposed PoW scheme outperforms state-of-the-art PoW techniques.