Shamir Secret Sharing
Computer Science
About Shamir Secret Sharing
Split a secret into finite-field polynomial shares, reconstruct it with a threshold, and show why fewer shares leave every secret possible.
Secret sharing divides information into shares so that a chosen threshold can recover it. In a t-out-of-n Shamir scheme, any t valid shares determine the secret, while fewer than t reveal no information about it under the scheme’s randomness assumptions. Shares are polynomial evaluations in a finite field; the secret sits at x=0. NISTIR 8214, section 2.2 introduces this construction.
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