> Regarding storing parts of the secret here and there: it's basically and "m out of n" scheme AFAICT. There are many variations of this but the overall idea is

> Regarding storing parts of the secret here and there: it's basically and "m out of n" scheme AFAICT. There are many variations of this but the overall idea is that you can afford to lose (n - m) parts and yet you'll be able to recover the secret. And if a thief were to steal parts, he'd need m parts to be able to recover the secret. The difference between a Shamir scheme and a true multi-signature scheme is that the former requires combining the m-of-n pieces to reveal the single private key to sign a transaction, which is a huge vulnerability and single point of failure. Bitcoin script allows the m-of-n signatures to remain geographically dispersed, each signing the transaction with only their own key, so no single party ever needs to possess the full private key.