Presumably the keyfob transmits a generation number, so the car just needs to see that the keyfob code is e.g. 187 ahead of its number, and then do a trial roll

Presumably the keyfob transmits a generation number, so the car just needs to see that the keyfob code is e.g. 187 ahead of its number, and then do a trial roll forward. If it matches, it retains the new generation and secret state, and if not, it retains the old.