The key "authenticates" itself to the car when the engine is started. It's kind of like the RFID systems in general use today but more secure because the car and the keys remember each other's secret password. From the service manual:

Connected to the Sentry Key Remote Entry Module (SKREEM) is a Sentry Key Antenna Ring which surrounds the ignition lock cylinder. When the ignition is switched on, the Sentry Key Antenna Ring is supplied with power. A data block is transmitted inductively via the Sentry Key Antenna Ring to the SKREEM and then on to the Powertrain Control Module. If the antenna ring data block content is invalid or if vehicle battery power is too low to build up enough power for the antenna ring, the Powertrain Control Module will not receive the proper signal. This is displayed with the message “Start Error” in the Instrument Cluster.

The SKREEM retains in memory the ID numbers of any ignition key transponder that is programmed into it. For added system security each SKREEM is programmed with a unique secret key code. This code is stored in memory, sent over the CAN (Controller Area Network) data bus to the PCM (Powertrain Control Module), and is encoded to the transponder of every ignition key that is programmed into the SKREEM.