Earlier quoted context omitted.
Proposal for expensive cars that don't require a button press: The key fob and car contain identical pre-shared random data. (could be gigabytes) Each transaction uses 4 tokens, 2 going in each direction, with each token being 128 bits. Upon a button press, the key fob selects and destroys the next 1-time-use token it contains. It begins to transmit. First the key fob sends a token. The car must respond with the corr…
This is not a bad idea but I can think of two problems in real world execution: a) Car companies won't want to hand out fobs that have any sort of writable memory, takes battery, and risks write memory wearout. Never seen a fob or smartcard that has memory which is written with every individual transaction. Having the fob do a computation on every transaction means it will need a lot more battery (in Wh per year) com…
Actually every SIM card does this. At least when used by a phone to join a mobile network, a SIM writes some timestamp or counter to persistent internal memory. This caused a funny case of SIM cards with very limited lifetime for a German provider (I think it was Congstar), who had a problem in its network that caused frequent authentications of handsets, thereby having them chew through the write cycles of their SIM cards way faster than projected for normal use. The cards became "dead" afterwards.
If I remember correctly, all chip enabled payment cards also have a transaction counter that is updated on every successful transaction.