Abstract: A keyless entry system which employs an identification code for each transmitter, a key sequence number, and a rolling code generated by a polynomial equation ensure unauthorized access. The system provides for resynchronization in the event of battery replacement or power failure. The system accommodates activation of a transmitter and incrementation of the rolling code when it is out of range of the receiver. This system further accommodates replacement of lost or stolen keys with a higher priority key, which then prevents access by the lost or stolen transmitter.