Unmanned Aerial Vehicle (UAV) swarms not only expanded the application areas of UAVs but also brought more complex challenges to security. Both the data collected by UAVs and UAVs themselves are easy targets for hackers. Once a hacker has intercepted communication information or hijacked a UAV, it can cause the disclosure of information and even affect the normal flight of the UAV. In terms of authentication, existing research focuses on building peer-to-peer networks through devices that support blockchain deployments at the edge nodes to form blockchain networks. UAVs cannot run blockchains directly, so fog nodes need to be introduced to assist UAVs in achieving authentication. This paper proposes a UAV authentication solution based on the fog node-assisted blockchain. The solution incorporates smart contracts to ensure trust, along with on-chain registration and authentication for UAVs. In the design of this paper, the main use is made of fog nodes at the edge of each block. The fog nodes serve as agents to register and authenticate the UAVs in their area on the blockchain, thus enabling the authentication of UAVs in different fog node areas. In this paper, the analysis of gas consumption yields a total economic benefit cost of about $$\yen $$¥ 12.77, which is negligible for the safety of the UAVs. Meanwhile, the paper compares the computational overheads, and within 10 UAVs, the computational overhead of this scheme is less than 50 ms, which is significantly lower than the other two schemes.