How to Share a Secret

Abstract

We consider the following problem.

• Let S be some secret. A collection of n people E_j share this secret in such a way that

  • each E_j knows some information x_j,

  • for a certain fixed integer k, 2≤k≤n, the knowledge of any k of th x’s enables to find S easily,

  • the knowlegde of less than k of the x’s leaves S undetermined.

This problem was considered first by A. Shamir [79] and he calls such a scheme a (k, n) threshold scheme.