The HTRC110 does not have any specific key/authentication commands. However, I recommend that using the read/write commands you interpret the data coming from the HiTag S transponder.
In the HITAG S datasheet in section 5.2.3 you will find the registers that contain the password bytes for authentication mode. And in section 8.1 you will find the general description of the states and how the authentication mode is selected.
Due to the datasheet being under NDA, I am not able to provide the specifics. If you do not have NDA, please let me know so I can provide the instructions.