Active distribution network (ADN), as a typically cyber-physical system, develops with the evolution of Internet of Things (IoTs), which makes the network vulnerable to cybersecurity threats. In this paper, the eavesdropping attacks that lead to privacy breaches are addressed for the IoT-enabled ADN. A privacy-preserving energy management system (EMS) is proposed and empowered by secure data exchange protocols based on the homomorphic cryptosystem. During the information transmission among distributed generators and load customers in the EMS, private information including power usage and electricity bidding price can be effectively protected against eavesdropping attacks. The correctness of the final solutions, e.g., optimal market clearing price and unified power utilization ratio, can be deterministically guaranteed. The simulation results demonstrate the effectiveness and the computational efficiency of the proposed homomorphically encrypted EMS.