So the first section about the idea of secret splitting was pretty straight forward. You want to split up a message between several people. Well you could just give them each a piece and make them put it together.
The next section is a little bit trickier to understand. When all of those people get together do they have to try all of the different combinations of pairs that they have? Even given that the t people will group up and talk together that seems like it would take some doing to recover the message.
Also does having more than t people help your chances? If you have more people does it make it any easier to recover the message?
The Lagrange method seems easier than the linear method as well. And by easier I mean at least more intuitive.
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