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That is if you want to amplify the signal. But if it's an adversary, they need to do a sort-of MITM to take the car's signal, amplify it, and then turn around and take the key's response and forward it to the car.

I don't think the problem is that people in possession of the vehicle's key can open it from too far away. The problem is that people who don't have possession of the key can open the car and drive off with it.

Is there a source for that? I find it hard to believe.

Some googling yields this discussion:

http://physics.stackexchange.com/questions/101913/why-does-a...

See this video by Sixty Symbols: https://www.youtube.com/watch?v=0Uqf71muwWc

I did too, but I saw this video (which is part of the very entertaining Sixty Symbols series, btw) which had a demonstration.

https://www.youtube.com/watch?v=0Uqf71muwWc

EDIT: i_cannot_hack got the link in before me. Kudos ;)

Top Gear did this experiment and it worked.