That said, Jim Choate writes:
Seems to me the way to do this is to 'dock' the receiver and xmitter prior to leaving (could rationalize it by also doing battery charging at this time) and each time they share a unique one-time pad.
The remote and opener could exchange a list of OTP entry codes. The list could be sufficiently large that docking would be unnecessary for months. With a public key system, the remote could transmit its OTP by radio, eliminating the need for docking hardware.
The problem with this scenario is that in order to keep the security you must keep the door-opener in your possession for the entire time limit the key-list is used. All it would take to circumvent it would be to have somebody gain access to the hardware. Shoot, if you let somebody have access to the opener then it is possible they might put some kind of ghost on the ram and make it possible for them to do all kinds of stuff to circumvent the list. If you dock each time then you don't need that kind of security. For them to get at the opener they would need to gain access to your house in which case they would attack the base-unit. As to the suggestions relating to sync'ed clocks. This would be ok for a day or so but longer than that and the clocks will be far enough out of sync such that they will no longer match keycodes. Clock chips just aren't that accurate.