Shamir’s Secret Sharing is an algorithm in cryptography created by Adi Shamir. It is a form of secret sharing, where a secret is divided into parts, giving each participant its own unique part, where some of the parts or all of them are needed in order to reconstruct the secret.
More formally, in a secret sharing scheme there is one dealer and n players. The dealer gives a secret to the players, but only when specific conditions are fulfilled. The dealer accomplishes this by giving each player a share in such a way that any group of t (for threshold) or more players can together reconstruct the secret but no group of less than t players can. Such a system is called a (t,n)-threshold scheme.
A popular technique to implement threshold schemes uses polynomial interpolation (“Lagrange interpolation”). This method was invented by Adi Shamir in 1979. You can play around with such a scheme on the demo page.
Note that Shamir’s scheme is provable secure, that means: in a (t,n) scheme one can prove that it makes no difference whether an attacker has t-1 valid shares at his disposal or none at all; as long as he has less than t shares, there is no better option than guessing to find out the secret.