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I'm not really well versed in the necessary terminology to get the answer I need from searching. As I understand, there are 2^160 possible addresses, and 2^256 possible private keys, so each address corresponds to roughly 2^(256-160)=2^96 private keys.

Let's say I generate a key pair and the corresponding address, how would one go about finding other key pairs that correspond to the same address if you already have at least 1 set of keys that generated that address? Is it possible?

Apologies if this has been answered already, I couldn't find the answer I am looking for.

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It's not possible, practically speaking.

A P2PKH Bitcoin address is computed as RIPEMD160(SHA256(publickey)). Since public keys are unique, to find another keypair that results in the same address, you're essentially trying to find a hash collision on SHA256 or RIPEMD160, which is extremely difficult.

The most "efficient" way to find such a collision would be to iterate over the entire private key space.

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    Searching for another input that has the same hash as a given input is technically called a "2nd preimage", and it is indeed intractable (needs ~2^160 trials). A collision is something else: namely looking for two inputs that hash to the same thing, without one of the two being given already. – Pieter Wuille May 29 at 18:39
  • Thank you for the clarification. – Rein Ernst May 31 at 8:32

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