I'm not a cryptographer or anything but if I was to design a scheme like this I think I'd have some kind of challenge/response protocol where the fob would send

I'm not a cryptographer or anything but if I was to design a scheme like this I think I'd have some kind of challenge/response protocol where the fob would send a request to unlock, the car responds with a random number it wants signed, the fob signs it and then the car unlocks. The challenge would need to be suitably long and also probably incorporate the current timestamp into it to resist replay attacks. I'm thinking that the fob has a public/private keypair on it, and the car needs to trust the public key of the fob, which would be done by the factory or the owner when buying another fob. I expect if this system were to be correctly implemented with suitably strong key strengths it would be very hard to crack. I guess it's not too cheap to do that but surely schemes like these already exist right? I'm guessing it's on high-end cars only. I've never actually owned or looked at buying a car so I don't know what's on the market.