following 5 steps verify the integrity of the dealer to the Share holders: Dealer chooses polynomial P, distributes shares (as per Shamir's secret sharing scheme). Dealer constructs a very large number (k) of random polynomials of degree t, and distributes shares. Share-holder chooses a random subset of polynomials. Dealer reveals shares of the m chosen polynomials and sums of remaining sums then shares the result as well. Each share-holder or verifier ascertains that all revealed polynomials are degree-t, and corresponds to its own known share. The secret s remains safe and unexposed. These 5 steps will be done in small number of iterations to achieve high probability result about the dealer integrity. Diagnosis 1: Because the degree of polynomial is less than or equal to t and because the Dealer reveals the other polynomials (step 4), the degree of the polynomial P must be less than or equal to t (second observation case 1, with height probability when these steps are repeated in different iterations). Diagnosis 2: One of the parameters for the problem was to avoid exposing the secret which we are attempting to verify. This property is kept through the use of Algebra homomorphism to perform validation. (A set of random polynomials of degree at most t together with a set of sums of P and other polynomials of degree at most t gives no useful information about P.) Secret ballot elections Verifiable secret sharing can be used to build end-to-end auditable voting systems. Using the technique of verifiable secret sharing one can satisfy the election problem that will be described here. In the election problem each voter can vote either 0 (to oppose) or 1 (for support), and the sum of all votes will determine election's result. For the election to execute, it is necessary to make sure that the following conditions are fulfilled: The voters' privacy should not be compromised. The election administrator must verify that no voter committed fraud. If using verifiable secret sharing, n tellers will replace the single election administrator. Each voter will distribute one share of its secret vote to every one of the n tellers. This way the privacy of the voter is preserved and the first condition is satisfied. Reconstruction of the election's result is easy, if there exist enough tellers to discover polynomial P. The interactive proof can be generalized slightly to allow verification of the vote shares. Each