Quote from: HeRetiK on November 07, 2019, 08:33:48 PM

Quote from: naska21 on November 07, 2019, 08:02:53 PM

That means that each single key may correspond roughly to 2²⁵⁶ / 2¹⁶⁰ = 2⁹⁶ addresses, right?

No, it's straight up 2^160 addresses, no need to divide. RIPEMD-160 is used to hash the SHA-256 hash of the corresponding public key [1], reducing the P2PKH address space from a potential 2^256* to 2^160.

*slightly smaller, ECDA's private key space does not cover the full 2^256 [2]

Quote from: naska21 on November 07, 2019, 08:02:53 PM

So in fact addresses are not unique in their nature cuz bunches of them have the same private keys.

There's also P2SH and Bech32 Bitcoin addresses, so any private key corresponds to at least 3 valid Bitcoin addresses.

[1] https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
[2] https://en.bitcoin.it/wiki/Private_key

Then you didn't get what I have intended to say, There are 2²⁵⁶ private keys. There are 2¹⁶⁰ legacy addresses calculated from those keys by applying RIPEMD-160 to SHA-256 hash of those keys. It means at the end we have collision as only 2¹⁶⁰ legacy addresses will correspond to the whole set of 2²⁵⁶ private keys. Roughly each address can be accessible through the set of 2⁹⁶ keys.