Abstract: The mutual authentication between the Mobile Station(MS) and Switching and Management Infrastructure(SwMI) for TETRA is analyzed in this paper and theoretical analysis shows that some drawbacks exist when using the shared secrets in the challenge-response protocol: (1) Open attack for known text might occur once the communication security between visiting location register and home location register can not be guaranteed; (2) It is difficult to store and maintain large amount of authentication keys when the network is large. An authentication protocol for TETRA using identity-based public keys for the SwMI authenticate the MSs and an authentication protocol based on hash chain for the MSs authenticate the SwMI are presented based on the theoretical analysis, which can effectively compensate the above-mentioned drawbacks.