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Revealed: car industry was warned keyless vehicles vulnerable to theft a decade ago
(www.theguardian.com)
This is a most excellent place for technology news and articles.
Don't know about the article, but most have been doing relay attacks by just forwarding the rolling code sent by the key to unlock and then start the car. It works because keyless entry requires a transaction starting from the car, so you can effectively just stand between the car and wherever the keys are and do easy relay attacks.
Then they usually drive it to a nearby safe location first so they can just reprogram the keys.
I do feel like this could at least be cheaply mitigated by having an immobilizer for the gas pedal that stops throttle input if the key isn't detected after a cooldown after moving a few feet, which would prevent thieves from being able to move the car very far after starting.