No, you can't 'generate' the key from the encrypted communication.
That's exactly the answer I was looking for. I thought that knowing the data sent to the drive and knowing the encrypted "answer" it returns to the kernel, there would be a way to "elaborate" the key the drive used to encrypt that "answer".
And yes, my idea was to let the TS drive owners have a way to know their key without risking to damage the drive.
Thanks for your help, MacDennis