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I understand that the situation I am describing is unlikely (because we have 1.46 Quindecillion possible Bitcoin addresses), but let's imagine that someone generated the same address as mine.

Is there any protection against a duplication of private and public keys if someone's new address matches the existing address where bitcoins are already stored?

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The mitigation is the absolutely massive address space. Other than that, there is no way to 'protect' or otherwise 'claim' a keypair/address as yours and yours alone. If someone (by some unfathomable coincidence) manages to generate the same address that your wallet did, then you will both be able to spend any funds locked to that address.

Thankfully, the chances of this happening are super duper incredibly small. You would expend far more energy (money) looking for an already-used address than you could ever be expected to make by taking the bitcoin you are hunting for.

Perhaps worth mentioning: the above holds true iff the private keys for the address in question are generated in a suitably random (high entropy) way. If you use a poor source of entropy, then it become much, much easier for someone to brute force search for your keys.

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If you are worried of this extremely unlike event you could use a multisig address where multiple keys need to be known to spend the funds

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  • Hi @MikeD, Does multisig guarantee that the second owner of address cannot spend bitcoins without my knowledge?
    – user125245
    Aug 21, 2021 at 21:28
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    If for example it is a 2-of-2 multisig the second owner would need to find both of the keys to spend the coins
    – Mike D
    Aug 21, 2021 at 21:44
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    This does not help. Yes, it means that someone through the same script would indeed to find both keys, but that's overkill. All they need is to randomly stumble upon another script which hash matches your multisig, and the odds for that happening are either equal (for P2WSH or P2TR) or significantly larger (for P2SH) than randomly hitting the same keys! If you're worried about events which have such near-impossibly small probabilities, suddenly all security assumptions break down.
    – Pieter Wuille
    Aug 21, 2021 at 23:56
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    @PieterWuille the odds of finding another script with the same hash is the same but the odds of this random script being executable is pretty close to 0
    – Mike D
    Aug 22, 2021 at 6:31
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    @MikeD Well, no, because people only (deliberately) create scripts they themselves can spend from. If you're worried about people randomly creating keys that match your keys, you should be equally (if not more) be afraid of people randomly creating scripts that match your script - it's exactly the same.
    – Pieter Wuille
    Aug 22, 2021 at 12:44

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