i've been looking for correct answers for weeks, but everyone says differently so your the one who to ask, because you're a bitcoin expert here.
Questions:
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?
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Another Question related:
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?
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Last Question.
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)
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if you could answer all this three Question, then i really appreciate it!
Best regards.
-- by the way this is my understanding of bitcoin if i am wrong please correct me i am eager to learn