Quote from: itod on September 30, 2019, 05:23:14 PM

Quote from: MrFreeDragon on September 30, 2019, 12:23:28 AM

Actually this was my question. I'm with you that there are only 2^160 addresses, but almost 2^256 private keys. So there should a collision, because every private key could be converted to the address only in one posible way (if we are talking about the same format, like Legacy, Segwit, bech32)
When we have a private key and the address which was generated from the private key, so the x,y coordinates of the address are in the same group as the basis point. There also should be other private keys which lead to teh same address.

And I also very curious about the ability to sign with different private keys. Imagine that somebody found 2 (or may be more) different private keys to the same address. Is it possible to make outgoing transactions with the both keys or only with that one which was primarirly used? I guess that for Legace addresses it is possible. But for beech32 addresses only one unique private key should be used. Am i right?

Yes you are right, there are about 28 million private keys for every single Bitcoin address. Whichever of these 28 million keys you find, you can take the coins from that address. Problem is you can not find the single one of those private keys by chance, let alone the other ones that lead to the same address, so this is totally unimportant. We humans are very bad with large numbers, so 2^160 looks to us very different to 2^256, while in fact they are both so big that for all practical purposes there is no difference between them, that's why the Bitcoin address scheme is designed this way.

28 million? Oh no, much much more! In average there are 2^96 private key for every bitcoin address. 2^96 is 79.22 * 10^27, so 79 and 27 zeros after it Shocked

It is much much more than you said 28 million!

Problem here for me is not to find the private key, but to find such collission (2 different private keys to the same address). Such finding will help better understand the group of private keys. Examing such collision in details will help to understand the things which are no known now, i beleive. May be we can see something new for this bitcoin transaction chalenge as well.

The collision finding is offtopic here, so some weeks ago I created a separate discussion for it: https://bitcointalk.org/index.php?topic=5185726