HOW TO SHARE A SECRET.

Abstract

The following problem is considered. 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 less than equivalent to k less than equivalent to n , the knowledge of any k of the x's enables to find S easily; the knowledge of less than k of the x's leaves S undetermined. Shamir, who first studied this problem, gives a solution using interpolation of polynomials over a finite field, the secret being some polynomial. A more elementary solution, in which the secret is an integer is given here. These two solutions are particular cases of the use of the Chinese Remainder Theorem.