With the rapid development of satellite technology and the high transmission efficiency of LEO satellites, LEO satellite communication has received increasing attention. However, the frequent switching of satellite-earth links imposes a great challenge in LEO communication authentication. To tackle this challenge, this paper proposes a Blockchain-based Authentication Protocol Using Cryptocurrency Technology (BAPC), which solves the problem of a long pause time of satellite services caused by user access authentication in a scenario of frequent switching between satellites and ground users. First, we design three stages of the authentication process and introduce the cryptocurrency technology. Using currency transactions as the certificate of authentication improves not only the security of authentication, but also the efficiency of switching authentication. Next, in the network topology, the satellite cluster is divided into multiple regions to improve the efficiency of block consensus. Finally, the protocol is tested through extensive NS2-based simulations, and the results verify that BAPC can greatly shorten the response time of switching authentication and significantly reduce the time of block generation and the network throughput. As the number of users increases, the block generation time and network throughput can be further reduced.