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Why don't cars use public key crypto? Is it too expensive to run on a key?

Probably power-wise, yeah. Most keys only have little coin batteries and people want those to last for years.

I have a "smart" BMW car key and it inhales the battery. I don't think it can go more than a couple of weeks without having to be charged.

Could charging in the ignition be good enough to keep it full? Or a secondary dock at home?

I don't really like the idea of short term key batteries, but it sounds like bmw can improve the current system a lot.

There's no ignition in BMWs anymore. Even if you don't go for the full keyless package, the start is still keyless. You just pay extra to have the doors be keyless too.

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