Shamir's Secret Sharing [SEP] named after
Shamir's Secret Sharing
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.
To reconstruct the original secret, a minimum number of parts is required. In the threshold scheme this number is less than the total number of parts. Otherwise all participants are needed to reconstruct the original secret.
High-level explanation.
Shamir's Secret Sharing is used to secure a
form" of that unique polynomial.
Although named after Joseph Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring It is also an easy consequence of a formula published in 1783 by Leonhard Euler.
Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration and Shamir's secret sharing scheme in cryptography.
Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. As changing the points formula_2 requires recalculating the entire interpolant, it is often easier to use