I would like a way to change the private key of a public address, for this you'd of course require the current private key.
Is this at all possible?
I want to prove that it can be done, or prove that it cannot be done.
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The address is mathematically derived from the public key. The public key is mathematically derived from the private key.
Hence, there is a deterministic relationship tying the address to the private key. Every private key has exactly one address it belongs to.
Therefore, changing the private key will also change the address.