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Q: Is there supposed to be a unique polynomial when given t shares for (t,n) Shamir Secret Sharing scheme?

GordonI always thought that part of the idea behind SSS was that there is only a single $t-1$ degree polynomial through $t$ unique points; that this holds when the polynomial coefficients are over the reals and also in particular for SSS when the elements are chosen from a finite field. However I'm run...


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