1. I had a hard time following the Vandermonde matrix, and struggled to understand how a subset of the people can find the secret. Also, is there some kind of theorem which says the minimum number of people who need to get together in order to find the secret for each of these methods? If the matrix is not invertible, it won't work right?
2. Although I did understand the theory behind these concepts, I think it's really interesting that they exist. It seems counterintuitive that any subset of t people can find the message. Are there instances where threshold schemes are used other than military and business? I know these two areas practically run the world, but it would be cool to hear about more situations where this is used.
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