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With the rapid development of unmanned aerial vehicles (UAVs), often referred to as drones, their security issues are attracting more and more attention. Due to open-access communication environments, UAVs may raise security concerns, including authentication threats as well as the leakage of location and other sensitive data to unauthorized entities. Elliptic curve cryptography (ECC) is widely favored in authentication protocol design due to its security and performance. However, we found it still has the following two problems: inflexibility and a lack of backward security. This paper proposes an ECC-based identity authentication protocol LAPEC for UAVs. LAPEC can guarantee the backward secrecy of session keys and is more flexible to use. The time cost of LAPEC was analyzed, and its overhead did not increase too much when compared with other authentication methods.