With the rapid advancement of electric power Internet of Things (EPIoT) technology, the development of a secure and efficient energy Internet has become increasingly important. Identification and authentication of electric power terminal devices are fundamental to ensuring the safe and stable operation of the energy Internet. To realize efficient data collection and secure authentication for a large number of terminal devices, this paper proposes an RFID-based authentication scheme for EPIoT. The scheme integrates RFID (radio frequency identification) technology with the national cryptographic algorithms SM3 and SM4, achieving mutual authentication between readers and terminal devices while ensuring secure transmission of power communication data and reducing computational overhead for device tags. Security analysis shows that the proposed scheme satisfies key security requirements, such as untraceability, resistance to replay attacks, de-synchronization attacks, and denial-of-service attacks. Further verification using BAN logic confirms the mutual authentication capability of the scheme, while performance analysis shows advantages in tag computation, storage, communication overhead, and database search efficiency.