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Bitcoin addresses are essentially 160-bit hashes of a 256-bit public key. Huh? How can all possible numbers in 256-bit space be squeezed into 160-bit space? Does that mean any given bitcoin address could be derived from more than just one public key?
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It's really 160 bit hash (RIPEMD160) of an already hashed (SHA256) public secp256k1 elliptic curve key. And yes, on the average, every address has about 2256-160=296 pairs of private/public keys.
There is a possibility that it might be easier for quantum computing to 1st identify any one of the overlapping 2^96 public keys, with an already known companion private key, satisfying the associated P2PKH transaction redemption criteria than trying to factor a 256-bit private key. – skaht – 2018-07-30T20:14:33.310
1I’m not sure I understand your question but if it means what I think it does then it will be beneficial for you to read about hash functions in a general setting. They are by design non injective (since they have a finite codomain and a larger domain) meaning there will be two different inputs that hash to the same output but a good hash function is designed so that the probability of one person being able to find two such inputs is epsilon small – Prince M – 2018-07-28T23:34:32.543