Data processing on non-trusted infrastructures, such as the public cloud, has become increasingly popular, despite posing risks to data privacy. However, the existing cloud DBMSs either lack sufficient privacy guarantees or underperform. In this paper, we address both challenges (privacy and efficiency) by proposing CrkJoin, a join algorithm that leverages Trusted Execution Environments (TEE). We adapted CrkJoin to the architecture of TEEs to achieve significant improvements in latency of up to three orders of magnitude over baselines in a multi-tenant scenario. Moreover, CrkJoin offers at least 2.9x higher throughput than the state-of-the-art algorithms. Our research is unique in that it focuses on both privacy and efficiency concerns, which has not been adequately addressed in previous studies. Our findings suggest that CrkJoin makes joining in TEEs practical, and it lays a foundation towards a truly private and efficient cloud DBMS.