Secret Sharing Scheme Based On Integer Representation

In Shamir’s scheme that the security based on the numbers of the field of a prime number P which the coefficients' polynomial reduced to modulo P (takes a value from some field , where P is a large prime number). Thus, the adversary must know only the free coefficient of the polynomial in order to break the scheme. From the representation integer using the so-called expansion we can see any integer can build such polynomial so that the polynomial has degree of k, k being the length digits for that integer . Where the coefficients of that polynomial are taken from the set of , we will introduce a small participation improving Shamir’s scheme to share the secret S that will be seen constructed from the whole of the coefficients in the polynomial used, which is based on the representation integer.