Breaking into a modern KESSY system in a VW without a key nearby is a bit harder than that. The key length (that's the bits-and-bytes encryption key) is too long to brute force attack (test each possible key in sequence), and KESSY includes measures that will slow down responses to rapid key requests to prevent this kind of attack. I doubt a pure electronic attack without a physical key would be a fruitful exercise against most rolling code systems.
A good locksmith would more likely compromise the physical door lock to gain access to the cabin, at which point your options increase rapidly. In some VWs at this point the easiest way to drive off with the car is to bring a dash cluster (which is where the immobiliser is housed) and a key coded to that cluster. Swap the dash cluster (30 second job), use your own key to start the car.
With a key nearby it's much easier. You can use a signal booster to bridge the physical gap between car and key, so if the key is within the range of your antennas you can start the car as if it was in your pocket. Useful if stealing a car when the owner is home.
Another more recent innovation is a key storer. Essentially it's a device with 3 radios and some shaped antennas that captures digital keys and plays them back at a future time.
It works like this - as the car thief you hide the device near the car. It sends out a signal on one radio that provides background noise on the frequency the car key uses to communicate with KESSY to prevent the real key talking to the car.
When the real key comes close and the owner goes to unlock their car, a second radio captures the encryption key. The car doesn't unlock though as the noisy radio has blocked the signal.
The owner tries again, and again a new encryption key is captured by the device, but this time it plays back the first key on the 3rd radio. The car recognises the valid key and unlocks.
Sometime in the future the owner goes away, taking their keys and leaving the car. Your device has one valid encryption key stored, so you play that back, the car unlocks and off you drive.
All scary stuff, though unless you're a professional targeting high-end cars you'd probably just as easily break into the house, grab the actual car keys and go from there.
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