> Cryptography is actually difficult for the requirements of a key fob.

No, it's not.

> The next obvious set is along the lines of "device sends an encrypted counter, door enforces that the counter only goes up"

That's already how rolling codes work. Running a strong crypto algorithm (even Ascon/Speck would be fine here) requires negligible power.

The issue is that this system is still susceptible to jam+replay attack. An attacker can jam the transmitter signal, while recording it at the same time. The user assumes that the button press just didn't register and tries again. The attacker also jams this and records the code. But then the attacker replays the _previous_ code that they stored, keeping the latest code for their future use.

This can _also_ be fixed with a simple capacitor-powered timer circuitry, charged during the keypress. The device can stay completely inert at all other times.