Shamir's Secret Sharing is a cryptographic algorithm conceived by Adi Shamir in 1979. It is designed to securely distribute a secret among a group of participants, in such a way that only a certain threshold of them can reconstruct the secret. The main idea behind the scheme is to split the secret into pieces, or "shares," using polynomial interpolation.
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Shamir's secret sharing places a secret at the constant term of a random polynomial of degree at most and issues distinct nonzero evaluation pairs . Any shares recover by polynomial interpolation. Given fewer than shares, every candidate constant term has the same number of compatible coefficient tuples, which gives perfect secrecy.