= Adi Shamir
{c}
<Adi Shamir> introduced a polynomial-interpolation construction for <threshold secret sharing> in 1979. In <Shamir's secret sharing>, a secret is the constant term of a random <polynomial> of degree less than $k$ over a <finite field>; shares are its values at distinct nonzero field elements. Any $k$ shares recover the <polynomial> and hence the secret.<How to Share a Secret by Adi Shamir>[pp.612–613]{ref}
Fewer than $k$ shares leave every possible secret equally compatible when the other coefficients are <discrete uniform distribution>[uniformly random]. This is an information-theoretic threshold guarantee, rather than a claim that recovering the secret merely takes a long time. The construction makes distributed authorization and resilience to missing shares compatible. It requires enough field elements for all distinct share positions.
\Image[https://www.weizmann.ac.il/WeizmannCompass/sites/WeizmannCompass/files/uploads/shamir-photo.png]
{title=<Adi Shamir>, portrait published by the Weizmann Institute}
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