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Thankfully no!
FROST and other MPC Schnorr signing protocols create partial signatures which are signed independently, and then combined to form a final signature.
So your keys can be as separate as you like.
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That is awesome! 👏
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Doesn't this have the same downside as Shamir's secret sharing in that you need to bring all the keys together to construct a "full" bitcoin key. THEN you can sign the transaction.
Using regular multi-sig the keys are actually separate.