1. (Difficult): I'm not following why in section 12.1 the r's (or s) need to be random and even if they must be random, why can't we choose r's random so that each number is equally likely? I think I need an example or discussion because a worded explanation is confusing to me.
For section 12.2 the Shamir threshold scheme, why do we know p(x) = s(x)? And why is the formula for M so complicated? Why isn't is more like the linear system approach? And why do we need t pairs? I'm not quite getting this but sort of.
2. (Reflection): I like the part at the very end of 12.2 about sharing a secret among two companies A and B such that they need each other to find the secret. I think it's clever and beautiful.
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