It's not transmitting anything, it works pretty much the same way NFC works. Both the key and the car have their own public/private key pairs(which were obviously set by the manufacturer) and when you touch the handle the car transmits an unlock request to the key, encrypted with the car key's public key(this is going to get confusing lol) - when the key receives the message, it decrypts it using its own private key, if it's correct then it replies with an "ok" message encrypted with the car's public key. When the car receives that it decrypts it using its own private encryption key and opens the doors. Simple, and in theory unbreakable. The issue is that the car doesn't measure how far away from vehicle the key is - it only relies on the fact that the transmitters used by the car and the key are super-low range(like, within 50cm). Which is obviously defeated by using signal boosters.