Does the order of Lagrange interpolation have any role in reconstructing the secret key in Shamir's secret share?
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What do you mean by order in this context? – Daniel S Apr 30 '23 at 12:40
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Hint: in Shamir secret sharing so that $k$ shares our of $n$ allow to reconstruct the secret, what's the degree of the polynomial used? It's going to be the Lagrange interpolation polynomial fitting the $k$ shares. – fgrieu Apr 30 '23 at 14:04