 Shamir's secret sharing

Shamir's secret sharing places a secret $N$ at the constant term of a random polynomial $f\in {\mathbb{F}}_p[X]$ of degree at most $r-1$ and issues distinct nonzero evaluation pairs $(x_i,f(x_i))$. Any $r$ shares recover $f$ by polynomial interpolation. Given fewer than $r$ shares, every candidate constant term has the same number of compatible coefficient tuples, which gives perfect secrecy.

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.