Cross-user deduplication is an emerging technique to ease the burden of cloud storage in big data era by storing only one copy of duplicate data. Efficiency reflects the feasibility and is a basic consideration when applying the deduplication scheme. However, in order to achieve certain level of security, existing works suffer from heavy overhead of computation as well as communication, which is a big obstacle for the actual deployment. In this paper, we propose an efficient cross-user deduplication scheme for encrypted data, which takes the lead to consider the efficiency during deduplication and makes it a reality to achieve secure deduplication in a lightweight way. To ensure the efficiency, we utilize the proposed re-encryption technique together with a non-interactive convergent key generation scheme to eliminate the cost of users and support batch verification of recovered data. The simulation results show that, with the same level of security guaranteed, the proposed scheme is more efficient comparing with the state of the art.