1) I guess I don't fully understand how if each person has a different part of the secret, that if only a few members of the group collaborate, they can somehow guess or deduce the other part of the secret? Also how can we have more than one solution? The book talks about how if the determinant is not zero, then we have a unique solution, and that happens when we have distinct xk's. But why would they not be distinct? Sorry these are probably silly questions.
2) This secret sharing is an idea that I had never really considered before and I think it is really interesting. Especially when they talked about how they used this same idea to control nuclear weapons in Russia because two out of the three people were needed to actually launch the missiles. It would be scary to think that one person could have the control to release something like that.
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