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>Is that true for every single Bitcoin transaction

I think so, for outgoing transaction (aka to remove from the address), it's kind of needed to verify the signature.

The 2^66 is only for this game where only 66 bits were left unknown. In the general case obtaining the private key from the public key is much longer.



Ah gotcha, that's what I missed. Thanks for your explanation. For a regular address, even with the public key, if there are 256 unknown bits it'd be 2^128, which is statistically unlikely to be solvable.




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