The problem is for the unit in the car to emit a signal that is received by the unit in the garage. The signal is to cause the door to open. Eavesdroppers may capture signals and replay them. The garage unit must ignore these. Accumulated transmissions from the car unit must not provide clues sufficient to produce a signal that will open the door. Provision must be made for legitimate but garbled transmissions. There is no receiver in the car and no transmitter in the garage.
This protocol serves also for electronic car keys that unlock car doors and open trunks.
Here is my solution.
Eric Hughes’ Solution; (Like mine. Crossed mine in the mail; interesting comments)
Matt Blaze’s Protocol and general comments.(Note that a hash function may replace the block cipher.)
Keying the two units merely puts the same random 100 bit counter value in each. This is conceptually simpler but may be marginally more complex to actually implement.