Shamir's Scheme Says It all
Ed Dawson, Diane M. Donovan · Information Security · 1993
Over the past fourteen years many different types of systems for sharing a secret have been proposed. These include t-out-of-n perfect threshold schemes, general secret sharing schemes, democratic schemes, multipart schemes, multilevel schemes and prepositioned schemes. In this paper it is shown that all of these schemes can be implemented by adapting a t-out-of-n perfect threshold scheme originally proposed by Shamir in 1979. This scheme is based on polynomials modulo a large prime. It provides one with an efficient method for generating shares, decoding to recover the secret and changing the access structure when required.