Verifiable 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 p Z , 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. Our scheme which based on representation integer using the so-called g a d i c  expansion we can see any integer a can build such polynomial so that the polynomial has degree of k, k being the length digits for that integer a . Where the coefficients of that polynomial are taken from the set of {0 ,1, . . . , 1} k g  , 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. Then apply Pederson’s VSS scheme in order to improve our scheme to be Verifiable Secret Sharing Scheme Based on Integer Representation.