"but with the short distances involved that means the fob has to generate and transmit a response within a few nanoseconds."
And the challenge-response pair must be different for every transaction, otherwise the thief can easily grab a SDR with tx capabilities, get to the car and ask for a transmission, record the spectrum, then go near the car owner door, transmit the car challenge and record the key fob response, go back to the car, wait for another challenge transmission and time the response accordingly. Not even need for a second thief.
And the challenge-response pair must be different for every transaction, otherwise the thief can easily grab a SDR with tx capabilities, get to the car and ask for a transmission, record the spectrum, then go near the car owner door, transmit the car challenge and record the key fob response, go back to the car, wait for another challenge transmission and time the response accordingly. Not even need for a second thief.