So total possible public keys are 2^256 and are mapped to a set of 2^160 (160 bits) addresses. Since there are more public keys and private keys than addresses, but every public key can be mapped to an 160 bits address, there must be then in average 2^256 / 2^160 = 2^96 keys to each address. so if there are 2^96 addresses for each bitcoin address, so does all that 2^96 addresses that one Address have, share ALL the same public key? because that's what you need in order to have the same RIPEMD-160 hash. so only private key which changes, not public key with the 2^96 key possible keys per Address right?
In theory there are 2^96
privatekeys for each bitcoin address. Yes! that is correct. And
each one of those 2^96 private keys will generate a
different publickey but all those 2^96 publickeys will generate the same rmd160 hash.
Also one address can be generated from compressed or uncompressed publickey
But actually no one has ever found one example.
So if all my thoughts are right, then from what i understood, All addresses of bitcoin exists only 1 TIME from the range ( 160 bits ) 0 - ( FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ), and the rest 2^96 addresses per address start to exists after the range of 2^160, so starting from 2^161. Is that also correct?
All addresses of bitcoin exists only 1 TIME from the range... there are no proof of that "ONLY ONE TIME..." maybe yes but repeat there is no proof of that.
There are the possibility that one address have 1 or more private keys under the range of 2^0 to 2^160
If my previous sentence is correct then that means that there are ranges of 160 bits that can haven't a specific address for example the "1111111111111111111114oLvT2" hash rmd160: 0000000000000000000000000000000000000000
We haven't enough computer power to prove or disprove that, proof of that is that the puzzle 64 is still there.
Then if bitcoin addresses have 160 bits, can't we just try to Bruteforce that 160 bits from ( 0 - FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ) Hex-Range with high number of Random peta/keys checks - - using BSGS, won't we have a 1 of 2^160 chance of unlocking any addresses that have the public key? can that work using BSGS right, or with BSGS that method doesn't work? (even with low chance, i still believe in luck)
Not really because there are 2^256 publickeys different for each other so unless that publickey was under that 2^160 range, only in that case it will be found.
But we still can't solve the publickey for the puzzle 120
Times to solve the puzzle 160 at specific speeds:
Puzzle 160 @ 1 Megakeys/s (10^6): 23171956451847141650870193314248525 years
Puzzle 160 @ 1 Gigakeys/s (10^9): 23171956451847141650870193314248 years
Puzzle 160 @ 1 Terakeys/s (10^12): 23171956451847141650870193314 years
Puzzle 160 @ 1 Petakeys/s (10^15): 23171956451847141650870193 years
Puzzle 160 @ 1 Exakeys/s (10^18): 23171956451847141650870 years
Puzzle 160 @ 1 Zettakeys/s (10^21): 23171956451847141650 years
Puzzle 160 @ 1 Yottakeys/s (10^24): 23171956451847141 years