If mining hardware was instead dedicated to generating new addresses; how long do you think would it take till someone stumbled on an existing address that had more BTC stored than what the person would have earned by mining?
(
)
Their are 2^160 possible addresses. Lets say 2^32 (4 billion) people use Bitcoin and each generate 2^16 (65 thousand) address. That gives us 2^48 total addresses out of 2^160 possible. The probability of a generated address matching one of these is 1/(2^112).
The probability for two addresses to match is much higher than 1/(2^112) though. It's more complex than doing 2^160/2^48. Check the
Birthday attack.
Also, TiagoTiago mentionned using current mining resources to generate addresses, so I guess it's fair to say that the 2^16 figure is underestimated, that would be more like
2^16
per second. (But there is not 4 billion miners, yet)
While we are on probabilities, and I'm by no means an expert in these, someone mentioned in a previous page of this thread that to find the "1Kahlahan
" vanity address (8 fixed chars) would take roughly
1.28e14 attempts.
I think this is underestimated. (It seems to come from the intuitive 58^8).
My own computation gives me
2.99e+15, which is an order of magnitude higher. (I decode the base58 and do the maths on the hash160).