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Is it possible to brute force bitcoin address creation in order to steal money?

I've tried brainwallet.org and now I wonder, what happens if someone starts to generate a lot of private keys and add them to his wallet (or MtGox account)? That person will eventually get somebody else's private key and be able to use his/her Bitcoins. Am I missing something?

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Tomas
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    Assuming there are 1 million addresses with a non-zero balance, and you can import 1 million keys per second, you will on average get a hit after approximately 3.5 billion billion times the age of the universe. – Pieter Wuille Aug 06 '12 at 15:48
  • Hi Tomas and welcome! See the link now added to the OP. – D.H. Aug 06 '12 at 16:10
  • I get a similar number to Pieter: age_of_universe = 60 * 60 * 24 * 365.25 * 14.6e9; keys_per_second = funded_addresses = 1e6; keys = 2**160; keys / keys_per_second / funded_addresses / age_of_universe -> 3.1720679605540234e+18 I expect he used something other than 14.6 billion years for the age of the universe to get his slightly higher answer. – Chris Moore Aug 06 '12 at 17:36
  • @ChrisMoore Thanks. Really good explanation. I just though that if BTC is the future money, billons of active addresses will be around but that is still really improbable. – Tomas Aug 07 '12 at 03:33
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    Even billions of active addresses is not at all a problem. – Pieter Wuille Aug 08 '12 at 19:22

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