Is it possible to directly encrypt a drive using any card in a smart card reader (even credit card, perhaps?)

As I understand it, a credit card chip or smart card works by sending challenges to the tiny computer on the card, at which point it completes the challenge and replies back with the data. Is it possible to use this to directly encrypt/decrypt data? Conventionally, you just use the card to store a key that is then transferred to the computer, but I think it would be fun to do all decryption/encryption on the tiny computer inside the card so that the host computer never sees the encryption key at all. The problem that I see is that the card itself may only be able to encrypt data which is then verified by the server of the credit card company, and would therefore be unable to decrypt data itself. If it is possible to send both encryption and decryption challenges to the card and get a response, it should be simple to write a program that uses the card to encrypt a folder or a drive (though I imagine it would be very slow) Tldr (or, to clarify): Is it possible to directly send challenges to a credit card or smart card in a smart card reader on linux and get the results back?