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Wallet Derivation Path Question

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I have a really basic cryptography question that I can't seem to find a straight answer for on Google.

Let's say I create another wallet on my hardware device by changing the derivation path. Is there a way for someone to figure out that the NEW wallet comes from the same private key? I am not asking whether they can figure out the private key. I know that answer to that is no. I am asking whether the relationship between two wallet addresses from the same private key is also a secret.

submitted by /u/peeping_somnambulist
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