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order of Lagrange interpolation in reconstruction of secret key

lt flag

Does the order of Lagrange interpolation have any role in reconstructing the secret key in Shamir's secret share?

Daniel S avatar
ru flag
What do you mean by order in this context?
fgrieu avatar
ng flag
Hint: in [Shamir secret sharing](https://en.wikipedia.org/wiki/Shamir%27s_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.
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