Quote from: pawel7777 on January 08, 2017, 01:48:58 PM

Quote from: shorena on January 08, 2017, 12:22:05 PM

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Your source is ~~wrong~~ slightly off as it ignores the birthday paradox. Due to it, on average you have found a collision after checking half of the keyspace with almost certainty. Thus you only need 2^159 key generations. Not that it changes the numbers in any significant way.

Why half? According to the birthday paradox, you'd have near certainty (99.9%) of finding 2 people with matching birthday with as little as 70 people. So wouldn't you need roughly one fifth (366/70) of the key space?

Keep in mind that there will NEVER be more than 2.1 X 10¹⁵ addresses that have any bitcoins in them at all at any given moment in time. (And in reality the number will be MUCH less.)

The birthday paradox assumes that there are 365 possibilities, AND as you add more people (attempts), more of those possibilities are occupied which increases the chance of colliding.

With bitcoin, the number of occupied (bitcoin storing) addresses is fixed at less than 2.1 X 10¹⁵, and doesn't increase beyond that as more addresses are generated. As such, the odds of any randomly generated address colliding with a bitcoin storing address don't increase the way they do with the birthday paradox.

As shorena has pointed out, what does increase is the odds that you will collide with one of the empty addresses that you already generated.