This paper proposes a secret sharing based fast node authentication technique applicable to Flying Ad-Hoc Network (FANET) that can be used to construct self-organized communication network in multi drones and drone squadrons operations. Before deployment, each node stores an exponential share, exponential secret and a portion of PUF CRP table. After being deployed in the field, in the early-stage of network formation, each node broadcasts its ID, exponential share and a hash value of PUF Response and pseudo-random number. Then each node performs a reconstruction of the exponential secret using the exponential shares transmitted from neighboring nodes. When the exponential secret is reconstructed, simultaneous authentication is completed for all nodes that have transmitted the exponential share used in the reconstruction. A node that transmits an incorrect exponential share to disturb the reconstruction of the exponential secret during the authentication process can be detected before performing the reconstruction through the verification of the hash value, and will be excluded from the reconstruction.