Although statistically impossible, imagine that two different private keys share the same public key. Would that addresses be able to create new Bitcoins? Let's say that private keys A1 and A2 have the same public key A. I use wallet B to send 1 Bitcoin to A. Both A1's and A2's wallets would show a 1 Bitcoin balance. Now both A1 and A2 send 1 Bitcoin to B at approximately the same time. Will B now have 2 Bitcoins, or would one of the transactions fail?
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To be exact, in ECC it is completely impossible for two distinct privatekeys to produce the same publickey. However nearly all Bitcoins (i.e. TXOs) are locked either to a script or to an address which is a 160-bit hash of a publickey (represented either in compressed or uncompressed form), not the actual publickey, so collision on an address is theoretically possible, albeit much less likely than your brain spontaneously exploding.– dave_thompson_085Aug 22, 2021 at 2:57
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2 Answers
There can only be a single spend of a transaction output, it doesn't matter if there's multiple private keys which correspond to a script. It is functionally the same as one private key signing two transactions, they can't co-exist due to the consensus rules of Bitcoin.
Since A1 and A2 have the same public key, it means that the network will treat them as one person.
